Dynamics of reactive and non-reactive capacitively coupled radio-frequency driven plasma discharges in response to nanoparticle formation

Transcription

1 Dynamics of reactive and non-reactive capacitively coupled radio-frequency driven plasma discharges in response to nanoparticle formation DISSERTATION zur Erlangung des Grades Doktor der Naturwissenschaften an der Fakultät für Physik und Astronomie der Ruhr-Universität Bochum von Brankica Sikimić aus Novi Sad, Serbien Bochum 213

2 1. Gutachter: Prof. Dr. Jörg Winter 2. Gutachter: Prof. Dr. Henning Soltwisch Datum der Disputation:

3 Contents 1 Introduction Plasmas in nature and technology Capacitively coupled radio frequency plasmas Reactive and dusty plasmas Research focus and structure of the thesis Dusty plasmas Fundamental properties of dusty plasmas Dust charging Orbital motion limited theory Forces on dust particles Confinement of nanoparticles in RF discharges Formation of dust particles in plasmas Plasma polymerization Control of the plasma polymerization process by plasma pulsing Plasma-dust interaction: effects of dust presence on plasma parameters Experimental system Reactor design RF power supply: CW and pulsing mode Impedance matching Diagnostic techniques Determination of electron density Microwave interferometry Langmuir probe Optical diagnostic techniques Laser absorption spectroscopy Basic principles Experimental setup Laser-induced fluorescence Basic principles

4 6 Contents Experimental setup Ultraviolet spectroscopy Experimental setup Laser light scattering Experimental setup Time resolved electron density in pulsed reactive and dusty plasmas Electron density and electron temperature in capacitively coupled RF discharges Time evolution of electron density during one pulsing period Electron density in pulsed plasmas with various gas mixtures Power dependence of electron density Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms Argon metastable states Time-resolved density of argon metastable atoms in pulsed non-reactive and reactive plasmas Time evolution of argon metastable densities during one pulsing period Argon metastable density in pulsed plasmas with various gas mixtures Power dependence of argon metastable densities Space resolved densities of argon metastable atoms during the process of dust particle growth A global model for plasma afterglow Model description Experimental conditions Model assumptions Balance equations Pure argon plasma afterglow Dusty plasma afterglow Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas Introduction DC-bias voltage The non-invasive diagnostics for measurement of DC-bias voltages Determination of ion fluxes and ion densities from the DC-bias voltage Time evolution of the electrode voltage during one pulsing period Calculation of ion fluxes Estimation of ion densities

5 Contents Results and discussion Dependence of electrode DC-bias voltage on gas mixture and applied RF power Dependence of ion flux on gas mixture and applied RF power Estimated ion densities under various discharge conditions Dynamics of the pulsed reactive discharge in response to thin film deposition Introduction Effect of deposited thin film on various plasma parameters: Experimental results Experimental conditions Deposition rate of a-c:h films The effects of deposited thin films on electron densities, electron temperatures and plasma potentials The effects of deposited thin films on argon metastable densities The effects of deposited thin films on average electrode voltages, ion fluxes, and ion densities Discussion Electron density and electron temperature Argon metastable density Electrode voltage Dust density distribution in symmetrically driven RF discharges Introduction Dust distribution during a cycle of the dust particle growth Dust distribution in pulsed plasmas Interaction of ultraviolet radiation with plasma-suspended nanoparticles Introduction Results and discussion UV extinction on dust particles suspended in reactive and non-reactive gas mixtures UV extinction on dust particles during one cycle of dust growth Summary 169 Bibliography 173

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7 1 Introduction 1.1 Plasmas in nature and technology Physics of plasmas has become an objective of research in science and technology over the last century. A need to study processes in plasma has emerged in the last decades, since they can be used in a great number of industrial applications. Material processing is one of the areas in which the plasma has found a broad application. For instance, plasma-assisted processing is an important step in the microelectronic industry, providing surface modification by thin film deposition, etching, ion implantation and other processes for fabrication of integrated circuits [1, 2, 3]. New materials with special properties (e.g. amorphous silicon, diamond-like carbon) can be also designed with the help of plasma. A great attention is focused on the application of plasma in energy conversion, using fusion reactors to induce a controlled thermonuclear fusion, or using magnetohydrodynamic (MHD) power generators to convert thermal and kinetic energy to electricity [4, 5]. Furthermore, plasma processing has a great potential in emerging research fields, such as plasma medicine (for sterilization, wound healing), nanoscience and nanotechnology (nanoparticle materials for photovoltaics, light-emitting devices) or environmental applications (air sterilization, control of air pollutants) [6]. Beside the artificial production of plasmas in industrial conditions, plasmas can occur naturally. Stars, interstellar, interplanetary, and intergalactic media are some examples of plasmas in space. Although more rare than in the space, plasmas can be also found in terrestrial conditions, in form of lightnings, polar auroras, and in the Earth s ionosphere. Thus, plasma is an important field of study in astrophysics and space physics, which allows to explore and to comprehend the processes occurring in these environments. In order to understand better the phenomena in both natural and artificial plasmas, an effort has been made to produce analogues of these plasmas in laboratory conditions. The laboratory plasmas provide an insight into the plasma characteristics and mechanisms which are, so far, more or less understood. Beside this, a knowledge on different plasma processes enables to understand their mutual relations, as well as their control, which is one of the most important benefits of laboratory investigations. Plasma is defined as an ionized gas, often referred to as a "fourth state of matter". It is distinguished from a neutral gas by an increased energy, which leads to the decomposition of 9

8 1 1 Introduction atoms or molecules of the neutral gas into electrically charged ions and electrons. The neutrals can be fully or partially ionized, depending on the energy input into such system. The energy delivered to the plasma determines the temperatures of its constituents (electrons T e, ions T i, and neutrals T g ), but also the degree of ionization, defined as a ratio of ion to neutral densities in the discharge χ i = n i /n g. Fully ionized plasmas (e.g. stars) are characterized by high temperatures of the species inducing χ i 1, as well as the thermal equilibrium (T e = T i = T g ). The weakly-ionized plasmas, with χ i 1, consist mostly of neutrals with a small fraction of charged particles, ions and electrons. In either case, the presence of charged particles induces the formation of a microscopic electromagnetic field, with Lorentz force affecting the motion of these particles. The mutual interaction of the charged particles due to Coulomb force is responsible for a collective behavior of the particles. The collective interaction has, as a consequence, several important features of plasmas, such as plasma oscillations, Debye screening, or plasma quasineutrality [4]. 1.2 Capacitively coupled radio frequency plasmas Low-temperature plasmas are often referred to as gas discharges, in which the plasma is generated electrically after supplying a gas with a sufficiently high voltage. A great variety of gas discharges originates from the possibility to vary their parameters: chemical composition, pressure, electromagnetic field structure, reactor configuration, or temporal behavior [7]. Consequently, gas discharges are employed for different industrial applications, such as surface modification, production of lamps, gas lasers, plasma displays, or for environmental or biomedical purposes. In this work, a focus is set on low-pressure, capacitively coupled (CC) radio frequency (RF) discharges. In this type of gas discharges, plasma is maintained by applying a time-varying voltage across two electrodes immersed in a processing gas and enclosed in a reactor (figure 1.1). The frequency of the voltage alternation can be found in the range of radio frequencies, extending between 1 MHz and 1 MHz. The typical frequency used for industrial purposes is MHz with its harmonics. The electric field across the two electrodes, forming a capacitor, is responsible for ignition and maintenance of the discharge [1]. The electrodes in a capacitively coupled RF discharge may be insulated by a dielectric material, unlike in direct current (DC) glow discharges. This arises from the fact that the RF discharge is not sustained by a secondary electron emission from the cathode, as in DC glow discharges, but by an oscillation of the electron cloud with an applied time-varying electric field [7]. The powered electrode in the system is commonly connected to the RF power supply through a blocking capacitor C b, as presented in figure 1.1. The role of the blocking capacitor is to provide the equality of electron and ion currents flowing from the discharge over a single RF period, resulting in the zero net current [1, 8].

9 11 Sheath Bulk Sheath Figure 1.1: A scheme of a capacitively coupled RF discharge. The RF voltage V RF is supplied to the electrodes through a blocking capacitor C b. Two regions can be distinguished within the plasma (bulk and sheath), with significant differences in light emissions. C b V RF The pressure range at which the plasma operates determines the number of collisions between the charged species and the surrounding neutral gas atoms. In the low pressure range (p < 1 2 Pa), plasmas are characterized by a low collision rate, resulting in a weak ionization degree. Moreover, due to the inefficient transfer of energy to the charged species, differences in magnitudes and gradients of species temperatures appear in low pressure RF plasmas. Thus, the plasma is not in a local thermal equilibrium (LTE), having T e T i, T g [1]. A consequence of the application of time-varying voltage across the electrodes is the oscillation of electron cloud instantaneously following the electric fields in the discharge [1, 4]. The instantaneous response of electrons is possible due to the high electron plasma frequency: n e e ω e = 2, (1.1) m e ε where n e and m e are the density and the mass of electrons in the discharge, respectively, e is the elementary charge, and ε is the vacuum permittivity. The electron plasma frequency ω e is typically in GHz range for low-pressure RF plasmas, therefore it is much higher than the frequency of the applied voltage ω RF = 2π f RF, so the electrons can easily follow it. In contrast to this, heavy ions can usually respond only to time-averaged electric fields, since ω RF > ω i = n i e 2 /(m i ε ) (n i is the ion density and m i is the ion mass). The difference in masses of ions and electrons, hence in their mobilities, results also in the formation of boundary layers in the vicinity of the electrodes, so called sheaths [1, 4, 8]. The role of electrode sheaths is to confine the electrons in the discharge, as well as to accelerate the positive ions to the electrodes. Over a single RF cycle, a net positive charge is aggregated within the sheath, making it a positive space charge region, with the increased density of

10 12 1 Introduction ions over electrons n i > n e. In contrast to it, an approximate equality of the electron and ion densities n = n i n e is valid in the plasma bulk region, where n denotes the plasma density. A significant difference in the light emission is observed in the plasma bulk and the plasma sheath regions, with an example shown in figure 1.1. The sheath is designated as a "dark space" with a low light emission. This characteristic originates from the reduced electron density in the sheath, which is the cause of a lower rate of electron-neutral collisions, thus a reduced relaxation of the excited states of neutrals produced in these collisions [9]. In the central, bulk region, the electron densities are much higher, thereby the light emission from this region is more intensive. The charge separation causes the formation of an electric field within the sheath, directed from the plasma to the electrodes. The electric field distribution E(r) at point r is related to the charge densities through Gauss s law [9]: E(r) = e ε (n i n e ). (1.2) In the ideal case of quasineutrality n i = n e in the plasma bulk, the electric field is equal to zero in this region, according to (1.2). However, a small electric field penetration can be observed in the plasma bulk, i.e. in the pre-sheath areas [1]. In the sheath region, the electric field, formed due to the charge separation, is responsible for the acceleration of positive ions from the plasma bulk, further inducing the ion bombardment of electrode or wafer positioned on the electrode. Since the electric field is correlated to the electric potential by E(r) = ϕ(r), the distribution of the electric potential can be also found from the space charge distribution: 2 ϕ(r) = e ε (n i n e ). (1.3) As a consequence of the net positive discharge in the sheath, the electric potential differs in the bulk and in the sheath. In the plasma bulk, the plasma obtains a positive potential with respect to other surfaces surrounding the plasma, designated as the plasma potential [2, 8]. Due to the positive plasma potential, the electrons stay confined in the discharge, as they cannot overcome the potential barrier. In RF discharges, the plasma potential can fluctuate following the RF excitation [9]. Only during a small fraction of time within the RF cycle, the plasma potential becomes equal to the potential developed on the electrode, enabling the electrons to escape the discharge in order to balance with previously escaped ions [1, 1]. However, during the most of the RF cycle, the plasma potential is larger than the electrode potential, retaining the electrons which tend to leave the plasma, by reflecting them back into the plasma bulk [1, 4]. Furthermore, the positive plasma potential with respect to the walls/electrodes enhances the escape of the ions at approximately the same rate as the electrons. Consequently, the overall quasineutrality of the plasma is sustained. Here it has to be noted that the plasma potential keeps the positive value also in the presence of any electrically isolated object, such

11 13 as a dust particle or a probe in the discharge. In the sheath region, the variation of the potential becomes very rapid. The sheath potential drop is adjusting itself in such manner, that the fluxes of ions and electrons leaving the plasma stay approximately equal, in order to sustain the plasma [1]. Depending on the driving voltage applied to the discharge, the sheath voltage can obtain different values. In a case of an electrically isolated electrode touching the plasma, the sheath voltage V s acquires the value of the floating potential ϕ f of the electrode, arising from the equality of the electron and ion fluxes to the electrode [1]: V s = ϕ f = T ( ) e 2 ln mi. (1.4) 2πm e In RF discharges, the high driving voltages lead to the formation of high-voltage capacitive sheaths between the plasma and the electrodes, having V RF T e. The RF excitation applied to the electrodes induces changes in the potential developed on the electrode as a response of ion and electron fluxes flowing from the plasma bulk. The electrode obtains also a negative potential dependant on the electron temperature, however shifted more negatively with respect to the floating voltage [8, 1]. This voltage, known as the electrode self-bias voltage, is responsible for the higher ion bombarding energies delivered to the targets (electrodes or wafers) in RF discharges. It has to be noted, that almost all of the RF voltage applied to the discharge is dropped across the sheath regions of the RF discharge [1]. Thus, the behavior of the sheath region is of a crucial significance in order to follow the processes in the RF discharge. Energy exchange plays an important role in sustaining the discharge. Thereby, the energy of electrons gives a major contribution, since electrons predominantly respond to the electric fields in the discharge [1, 9]. In order to sustain the discharge, the energy absorbed by the electrons has to be in a balance with the electron energy lost in different processes occurring in the discharge. The energy transfer from the source to the discharge itself takes place mostly due to the different mechanisms of electron heating in the discharge, such as stochastic heating, ohmic heating, or secondary-electron heating [1]. In low-pressure RF discharges, the electron heating is governed mainly by a stochastic heating, which arises from the electrons impinging on the oscillating sheath and the energy transfer in these collisions. Ohmic heating, caused by the acceleration of electrons by electric fields and an energy exchange in electron-neutral collisions, is a dominant electron heating mechanism at higher pressures. The losses of electron energy occur in different processes, either in interaction with other species (ionization, excitation, neutral gas heating), or in collisions with the walls. The total balance of absorbed and lost energy in the discharge determines also the density of electrons in the discharge [1]. The RF power can be delivered to the discharge in a sequence of pulses with typical lengths ranging between microseconds and milliseconds, i.e. by pulsing the plasma [1, 7]. The pulsing signal is determined by a pulsing frequency and a duty cycle, defined as the length of

12 14 1 Introduction the power-on phase. The signal from the RF generator is usually mixed with the pulsing signal before being transferred to the discharge. The alternation of the power-on and power-off phases results in the temporal evolutions of the plasma parameters, resembling to the charging and discharging of a capacitor. Thus, plasma pulsing introduces significant changes in the dynamics of the plasma species, their densities, energy distributions and fluxes, as well as in the sheath formation. Eventually, the temporal behavior of the plasma parameters enables the possibility to distinguish and to investigate the mechanisms responsible for various plasma processes. The method of plasma pulsing has shown some advantages over the continuous power transfer. It provides significantly higher peak voltages and peak currents at the same average power as in continuous discharges, which leads to higher plasma densities during the RF-on phase [11, 12]. Consequently, higher rates of different processes, such as sputtering, excitation and ionization, can be achieved. In addition to this, variations of the pulsing frequency and duty cycle have been found as a method for optimization and control of the processing plasmas [11]. Plasma pulsing has been proved as a helpful tool in surface etching processes, providing a high etching rates, selectivity and anisotropy [12, 13, 14]. Due to this, the reduction of wafer damage or etch profile distortion has been enabled, contributing to the significantly higher efficiencies of the production processes. Finally, the density of negative ions can be diminished by pulsing the plasma [15, 16]. This feature has a mayor influence on the control of dust particles formation, which is one of the topics of this thesis. 1.3 Reactive and dusty plasmas Discharges containing chemically reactive gases are widely applied in the plasma processing industry, especially for surface modification processes, thin film deposition, or in etching and sputtering systems [1, 3]. The chemical processes induced by the presence of reactive gases in the discharge is of a great importance for the variety of processes occurring in plasmas. Beside positive ions and electrons, negative ions can appear in the reactive plasmas as a consequence of the electron attachment to atoms or molecules with high electron affinity. A further interaction between the plasma constituents may lead to their agglomeration and to the formation of dust particles in the plasma. The dust particles acquire a large electric charge by collecting electrons and ions from the plasma, thus becoming a significant component in the discharge and a research objective of several different scientific disciplines and industrial applications. In industry, dust particles are considered as an unwanted, but sometimes unavoidable consequence of the application of reactive gases, since they can contaminate or destroy a processed target (wafer, integrated circuit). Consequently, the performance and the efficiency of the conducted industrial process may be significantly reduced. Furthermore, the appearance of the dust in the plasma processing related to the surface modification may lead to the con-

13 15 tamination of the deposited films and alternation of its properties [17, 18]. However, in some industrial applications, the presence of the dust in plasmas can be an advantage. A research focus is presently shifted to the development of new materials with special, tailored characteristics, produced by the implementation of nano-sized dust particles into certain materials in order to improve their mechanical, chemical or optical characteristics (e.g. [6, 19]). The presence of dust particles has been also observed in plasmas applied in controlled fusion devices [2, 21, 22]. Their appearance is related to the plasma-surface interaction processes, such as evaporation and sublimation of the wall material, as well as the flaking of the redeposited thin film layers [2]. The presence of dust particles in fusion reactors has several consequences. The most important one is a safety problem, including the health issues, arising from the radioactivity and chemical reactivity of the dust created in fusion reactors. Other problems regard the pollution of the plasma by particles, causing the reduced performance, or its deposition on diagnostic equipment. It is believed that dust particles presence will have to be carefully treated in the future fusion devices, such as ITER [23]. Dust is a large research objective in astrophysics and space science, because of their presence in various domains in the space or on the Earth [23]. Under terrestrial conditions, the occurrence of dust is more seldom, due to the reduced ionization rates or lack of energies high enough to enhance the production of dusty systems with collective behavior. The dust appears at higher altitudes of the Earth s atmosphere, beginning with the ionosphere (about 9-12 km above Earth) and extending through the magnetosphere. In many regions of space, numerous solid dust particles can be found, ranging in their sizes from sub-nanometer to several hundreds of micrometers. The dust particles are constituents of the large number of systems in space, such as interstellar media, planetary rings (e.g. Saturn rings), planetary atmospheres (e.g. Titan) or comet tails. The dust condensation has been also observed in shocks after supernova explosions. Moreover, the formation of stars or planets might be impacted by the presence of dust clouds in their vicinity. The chemical and the physical processes induced by the dust presence might play a decisive role in the formation and behavior of all of these systems. The appearance of dust in various technological processes, as well as numerous discoveries of particles in astrophysical conditions have been a great motivation to study dusty plasmas. Although a large number of mechanisms induced by the dust presence in plasmas have been studied in last decades [23, 24, 25], a lack of knowledge about specific processes occurring in dusty plasmas is still present. The complexity of dusty plasmas arises from the interwoven physical and chemical processes between the dust particles and other plasma species. Dust particles act as small probes inserted into the discharge, since they can be significantly larger than the other plasma species (electrons, positive and negative ions). Not only the chemistry, but also the physical properties of the discharge can be strongly modified after the appearance of dust. The impact of dust particles on some plasma parameters, such as electron density and

14 16 1 Introduction electron temperature, has been already well investigated (e.g. [26]). In spite of an extensive research, there is a relatively limited knowledge on the mechanisms in dusty plasmas which are responsible for various processes, starting from the initial dust formation, growth, or the particle charging. Beside the chemical structure, it is important to study the dynamics of dust particles, once they appear in the discharge. This may help to discard the particles as a contamination material in surface modification technologies, but to use them for more efficient control of the production processes, or in emerging research fields, such as production of new materials with tailored properties. The laboratory dusty plasmas can also be a useful tool in the research of astrophysical phenomena, trying to simulate and study dust widespread in the space. 1.4 Research focus and structure of the thesis In this thesis, the dynamics of capacitively coupled RF discharges at low pressures is investigated. The research focus is set on the reactive and non-reactive plasmas and their response to the formation of nano-sized dust particles from the precursor molecules in the process of plasma polymerization. As a precursor gas, highly reactive acetylene is used. In order to distinguish the dust influence, plasma pulsing is applied as a method which enables the control of the dust formation. As the presence of dust particles changes the discharge conditions, it is of an essential importance to determine their influence on different plasma parameters. Various diagnostic approaches have been applied in order to examine plasma parameters, such as densities and temperatures of plasma species, fluxes, currents, and voltages at different surfaces in the discharge. The aim of the simultaneous measurements is to observe the behavior and to determine the mutual relations between the key plasma parameters under various discharge conditions (energy input and energy losses, gas composition, electrode surface conditions). The measurements can furthermore provide the knowledge about the effects which become significant in the discharges with the large density of dust particles. Thus, the behavior of various plasma parameters can give an insight into the mechanisms which are relevant for the dust-related processes: formation, growth or charging. This thesis is structured as follows: Chapter 2 reviews the physics of complex plasmas, primarily regarding the aspects which are relevant for this work, such as electron densities and temperature, process of plasma polymerization, plasma pulsing, dust-free (void) region, or forces acting on particles. Chapters 3 and 4 describe the experimental system applied for the investigation of the reactive and dusty plasmas. The configuration of the experimental system is given in chapter 3. Chapter 4 gives an overview of the applied diagnostic techniques, describing

15 17 their basic principles and the implementation to the current experimental setup. Chapter 5 reports on the time evolutions of electron densities in pulsed RF plasmas. An accent is on the behavior of electron densities in reactive and non-reactive plasmas under various discharge conditions, particularly in the presence of the dust particles in the discharge volume. Chapter 6 regards the temporal evolutions of argon metastable atom density under various discharge conditions, including their response to the formation of dust particles. In addition to this, a spatial distribution of the argon metastable atoms between the electrodes is found in dust-free and dusty plasmas. Chapter 7 relates the densities of electrons and argon metastable atoms, presented in chapters 5 and 6, through a global, space-averaged model. The global model is developed to provide an insight into production and loss mechanisms in the afterglow phase of the pure argon plasma and argon plasma containing large densities of nanoparticles. Chapter 8 presents a non-invasive technique to determine ion fluxes and ion densities from a change of the DC component of electrode voltage in pulsed plasmas. The estimated ion densities are compared to the simultaneously and independently measured electron densities. This chapter describes the diagnostic method and discusses the necessary conditions for the proper determination of ion fluxes and ion densities. Chapter 9 describes the influence of the deposition of hydrocarbon coatings on electrodes on various plasma parameters, such as electron density, argon metastable density, plasma potential and electron temperature. It is believed that the conditions on electrodes have an impact on the initiation of the dust production process in the discharge. Chapter 1 investigates the distribution of dust particles during a cycle of dust growth in continuously and pulsed driven discharges. The observation of the spatial distribution of dust density may provide an explanation of non-uniformities of other plasma parameters (electron and metastable densities, electron temperature and others). Another interest arises from the observation of the dust-free, void region developed within the dust cloud, which may also influence on the dynamics in the dust-containing plasmas. Chapter 11 deals with ultraviolet (UV) spectroscopy in complex plasmas. The aim is to explore the absorption of high-energetic UV radiation by hydro-carbonaceous dust particles. This is a point of interest in astrophysics, amongst others to explain the UV bump at nm. Chapter 12 gives a summary of the investigated results.

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17 2 Dusty plasmas This chapter introduces some characteristics of plasmas containing dust particles and describes previous theoretical and experimental findings which are important for this work. The section 2.1 gives an overview of the fundamental processes relevant for the dynamics of dust particles in a plasma volume, such as dust charging and forces acting on dust particles in a discharge. A description of the dust formation and growth follows in section 2.2, with an emphasis on the plasma polymerization process and its control by pulsing the plasma. A response of the plasma to the formation of dust particles is described in section 2.3, particularly regarding to the effect of dust on electron density and electron temperature. 2.1 Fundamental properties of dusty plasmas Dusty plasmas studied in the laboratory conditions are also referred to as complex plasmas. This name emerges from the mutual interaction between the plasma and the dust particles suspended in the plasma. The presence of dust particles affects the plasma properties, but also the plasma modifies the properties of dust particles. Consequently, the plasma and the dust particles form a new, complex system, with new phenomena emerging from the coupling effect. The basic process in complex plasma is the charging of dust particles, which is responsible for the variety of effects occurring in these plasmas Dust charging The impact of dust on the plasma originates from the charge of the dust particles, acquired by collecting the electrons and ions from the surrounding plasmas. In laboratory plasmas, the dust particles are usually negatively charged, as a consequence of higher mobilities of electrons in comparison to ions. The dust particles found in the space can be either positively or negatively charged, depending on the external radiation sources, such as ultraviolet radiation. The dust charging can occur also due to the other mechanisms: secondary, thermoionic, or photoelectric emission of electrons from the particle surface [24]. The large charge acquired by the dust particle is responsible for the strong interactions between the particles themselves, with other plasma components or with electromagnetic fields. A remarkable consequence of the charge-related interactions in plasmas is a possibility of self-organization, i.e. the formation of ordered structures of dust particles, called plasma crystals [27]. Plasma crystals are 19

18 2 2 Dusty plasmas formed when the Coulomb interactions between the dust particles exceed their thermal energies, leading to the crystal-like positioning of the particles [27, 28]. However, these conditions are not always fulfilled in the plasma, so the dynamics of plasma particles in the discharge may pass through different phases, such as gaseous-like and liquid-like phase. Thus, the investigation of phase transitions, the individual phases, waves, or other kinetics of particles are significant research subjects regarding the complex plasmas. The charge of a dust particle found in plasma is a complex parameter, depending on the conditions in the plasma, as well as the size of the particles. The changes of the plasma conditions provoke the fluctuations of the dust charge, developed mostly due to the currents of electrons and ions to the particle. Due to the complexity of these processes, several numerical models have been developed to describe the dust charging. One of the first models was the Orbital Motion Limited (OML) theory, developed in 192s by Mott-Smith and Langmuir [29] to describe the charging of an electrostatic probe immersed in plasma. However, some limitations of the OML model have urged the development of the charging models which offer a more precise treatment of dust in plasma (e.g. [3]). A brief overview of the dust potential and the dust charge obtained by the OML method follows. Orbital motion limited theory The orbital motion limited theory observes the trajectories of electrons and ions surrounding a solid, spherical dust particle with radius r d immersed in plasma. Several assumptions have to be accounted for the dust charge estimation: a) dust is isolated (no influence of other surrounding dust particles), b) plasma is collisionless (no losses of electrons and ions on their path to the dust), and c) there are no barriers in the effective potential [24]. Moreover, the criterion of the small dust radius in comparison to the Debye (screening) length λ D = ε k b T e /(e 2 n ) is usually satisfied in laboratory plasmas, i.e. r d λ D. The collision theory is applied to determine the trajectories of electrons and ions approaching a single dust particle, taking into account their collection by the dust. The laws of conservation of energy and angular momentum allow the calculation of a maximum impact parameter b coll, which represents an effective dust radius [25]: ( b coll = r d 1 eϕ(r ) 1/2 d). (2.1) Here, ϕ(r d ) is the potential at the particle surface, and E = 1 2 m e,iv 2 e,i is the energy of the plasma component (m e,i masses, and v e,i velocities of electrons or ions, respectively). The ion or electron approaching to the dust particle at a distance smaller than the impact parameter r < b coll is collected by the dust particle, hence contributing to the overall dust charge. The cross sections for the collection of plasma components by the dust particle is given by σ coll = E

19 21 πb 2 coll [25]. For ions, the cross section can be calculated by [28]: σ i = πr 2 d ( 1 2eϕ(r d) m i v 2 i ), (2.2) whereas the cross section for the electron collection takes a form: { ( ) πr 2 σ e = d 1 + 2eϕ(r d) eϕ(r m i v 2 d ) < 1 e 2 m ev 2 e eϕ(r d ) 1 2 m ev 2 e (2.3) Assuming the Maxwellian velocity distribution and integrating over the total velocity range, the currents of ions I i and electrons I e to the dust particle obtain the following forms [28]: ( I i = πrd 2 en iv Ti 1 eϕ(r ) d) k B T i ( ) I e = πrd 2 en eϕ(rd ) ev Te exp. k B T e In (2.4), v Ti and v Te are the thermal velocities of ions and electrons, respectively, given by: v Ti,e = (2.4) 8k B T i,e πm i,e. (2.5) The collection of positive or negative charge by the dust particle continues according to: dq d dt = k I i,e. (2.6) However, by acquiring the charge, the potential on the dust surface ϕ(r d ) changes, further provoking the repulsion of electrons and the attraction of ions. The equilibrium state occurs when the electron and ion currents to the particle equate: I i = I e. (2.7) A numerical solution of the currents equilibrium gives a floating potential on the dust surface ϕ f and a steady-state dust charge Q d. In laboratory conditions, the floating potential of the dust particle obtains a negative value, due to m e m i, and it is proportional to the electron temperature [31]: ϕ f T e /Z d. (2.8) The obtained floating dust potential ϕ f can be used to estimate the steady-state dust charge Q d : Q d = Z d e = C d ϕ f. (2.9)

20 22 2 Dusty plasmas In (2.8) and (2.9), Z d is a number of elementary charges collected by the dust particle, whereas the dust capacitance C d is obtained considering the dust particle as a spherical capacitor with radius r d λ D [25]: ( C d = 4πε o r d 1 + r ) d 4πε o r λ d. (2.1) D According to (2.7) - (2.1), a dust particle with a radius r d = 5 nm in argon plasma, an electron temperature k B T e = 2 ev and an ion temperature k B T i =.26 ev, obtains a floating potential of ϕ f = 5 V and Z d = 175 elementary charges per particle. The plasma quasineutrality is valid also if the dust particles are present in the discharge. However, in complex plasmas, the condition of equality between positively and negatively charged particles has an altered form, which takes into account the number of elementary charges per dust particle Z d and the dust density n d : n i n e + Z d n d. (2.11) The application of plasma pulsing can also contribute to the fluctuation of the charge on the dust particle. Depending on the pulsing frequency and the duty cycle, dust particles can be totally or partially discharged over the plasma afterglow phase, whereas they can charge again during the power-on phase. The discharging of the dust particles induces a release of ions and electrons into the plasma volume, thus affecting their densities. One of the effects of charge fluctuation is an anomalous behavior of electron density in pulsed plasmas containing hydro-carbonaceous nanoparticles [32], which is reviewed in section 2.3. The effects of various production and loss processes on the dust charging in pulsed complex plasmas are implemented in the global model described in chapter Forces on dust particles Various forces act on dust particles immersed in the plasma, confining them in the plasma volume or dragging them out of it to the walls or to the pumps [25, 28]. Hence, forces on particles determine their distribution and transport in the plasma volume. However, due to the impact of dust particles on plasma parameters (e.g. electron and ion densities and temperatures, metastable densities), the dust distribution within the plasma volume also may affect the distribution of these parameters in axial and radial directions. Two types of forces can be differentiated in dusty plasmas: forces due to the charge effects (electrostatic force, ion and electron drag force) and charge-independent forces (gravity, neutral drag force and thermophoresis). A schematics of the forces acting on negatively charged dust particles in the discharge is presented in figure 2.1. A brief overview of these forces follows further in this section.

21 23 T 1 Electrode Plasma F thermophoretic T > T 1 2 F neutral drag F electrostatic Figure 2.1: Forces acting on the negatively charged dust particles in the plasma. Electric field T 2 Electrode F ion drag F gravity Electrostatic force The electrostatic force is a force which confines the dust particles in the plasma volume [25]. The escape of electrons to the walls is prevented due to the high plasma potential compared to the potentials of electrodes and reactor walls. It is the force of an external field E acting on a dust particle with radius r d and charge Q d. In the plasma with uniform plasma density and assuming r d λ D, the electrostatic force can be approximated by [28]: F el = Q d E 4πε r d ϕ f E. (2.12) The electrostatic force is proportional to the dust radius r d, emerging from the r d -dependence of the dust charge Q d. Ion drag force The ion drag force appears due to the interactions between negatively charged dust particles and ions flowing in the discharge. The motion of ions in the field of the dust particle can result in the momentum transfer between the ion and the dust particle. The momentum transfer exchange occurs through two mechanisms: a) direct collisions of ions and dust particles, and b) Coulomb scattering of ions in the electric field of dust particle [25, 33]. Hence, the ion drag force F id consists of two components, the collection force and the orbit force [33]: F id = F id,coll + F id,or. (2.13) The collection force F id,coll results from the collection of ions by dust particles and it can be expressed by: F id,coll = πbcoll 2 n im i v s v i, (2.14) where b coll is the maximal impact parameters calculated by (2.1), n i and m i are the density

22 24 2 Dusty plasmas and mass of the ions in the discharge, respectively, v s = (v 2 i + v 2 T i ) 1/2 is the geometric mean of the ion drift velocity v i and the thermal ion velocity v Ti [25]. The orbit force F id,or is a force arising from the deflection of the ion in the local field of the dust particle, instead of its collection [28]. In this case, b coll determined by (2.1) is the minimum impact parameter. The orbit force is obtained according to [33]: with σ Coul as the cross section for Coulomb scattering: F id,or = n i m i σ Coul v s v i, (2.15) σ Coul = 2πb 2 π/2 ln ( λ 2 D + b 2 π/2 b 2 coll + b2 π/2 and b π/2 as the impact parameter for 9 scattering: ), b π/2 = Q d e 4πε m i v 2. s The ion drag force becomes significant when the ion flux becomes large. The large ion flux can be found near the electrode sheath region, pushing the dust particles towards the electrodes [34]. Furthermore, the large ion flux at higher applied powers may also expel the dust particles from the central region of the plasma bulk. The presence of the negative ions induces the appearance of the negative-ion drag force, which may become of significance in electronegative plasmas widely used in the plasma processing technologies [35]. Similar to the ion drag force, an electron drag force arises due to the momentum transfer between electrons and dust particles. However, the small mass of electrons makes the electron drag force practically negligible compared to the other forces in the discharge [24]. Gravity A gravitational force F g pushes the dust particles in the discharge downwards, following the gravitational acceleration g [25]: F g = m d g = 4 3 πr3 d ρ dg. (2.16) In (2.16), the mass of a spherical dust particle m d is proportional to its volume and the mass density ρ d. Thus, the gravitational force scales with the cube of the dust radius F g r 3 d. Neutral drag force The neutral drag force arises from the friction of a dust particle moving through the neutral gas, inducing an exchange of the momentum transfer due to the mutual collisions between

23 25 neutrals and dust particles [25]. This force is responsible for the dust particle ejection from the plasma bulk region [34]. Two regimes can be distinguished, depending on the relation between the neutral mean free path λ n and the dust radius r d, defined as the Knudsen number = λ n /r d. In the high pressure regime, the Knudsen number has a low value and the K n neutral drag force is obtained from the fluid dynamics using the Stoke s law: F nd = 6πηr d v s, (2.17) with η representing the dynamic viscosity and v s the relative velocity between the dust and the gas. At lower pressures typically used in the plasma processing, the neutral mean free path is larger than the dust radius λ n r d, i.e. Knudsen number is high K n 1. In this kinetic regime, the neutral drag force can be estimated according to [36]: F nd = δ 4 3 πr2 d m nn n v Tn (v d v n ). (2.18) Here, m n, n n, and v Tn are the mass, the density, and the thermal velocity of neutral gas, respectively, while (v d v n ) is the relative velocity between dust particles and neutral atoms or molecules. The parameter δ can take different values depending on the collision mechanisms between gas and dust particles [28]. According to (2.18), F nd rd 2 in the kinetic regime. Thermophoretic force The thermophoretic force is pronounced if a gradient of neutral gas temperature exists in the discharge, appearing usually by heating or cooling the electrode [25, 28]. The higher temperatures induce the higher velocities of the neutral gas atoms with respect to their velocities in the cold regions. As the consequence of different momentum transfers from the gas to the dust particles in hot and cold regions, a thermophoretic force is induced, pushing the particles toward the colder regions. The thermophoretic force can be expressed by [25]: F th = r 2 d v Tn ( 1 + 5π 32 ) (1 α) κ T T n, (2.19) with κ T as a translational thermal conductivity and T n temperature gradient of the neutral gas. The coefficient α 1 for dust surface temperatures and neutral gas temperatures below 5 K. The thermophoretic force is proportional to the square of the dust particle radius and it is independent of the gas pressure.

24 26 2 Dusty plasmas Figure 2.2: Laser light scattering on hydro-carbonaceous nanoparticles in a capacitively coupled argon/acetylene RF discharge Confinement of nanoparticles in RF discharges The forces acting on dust particles influence several aspects of their dynamics in a discharge: particle confinement, levitation and ejection from the discharge. The size of a dust particle and its charge are the most important parameters which affect the forces acting on these particles and the particle distribution in the discharge. Directions of forces acting on negatively charged dust particles are presented in figure 2.1. The electrostatic force is directed to the discharge center, enabling the particle trapping inside the plasma bulk. In opposition to it, other forces tend to expel the particles out of the plasma. The gravity pulls the particles towards the lower electrode. The ion drag force drags the particles out from the bulk region towards the electrodes. The neutral drag force is leading the dust particles out from the bulk in the direction of the neutral atoms or molecules flow, i.e. to the pump exhaust. If present, the thermophoretic force is pushing the dust particles to the regions with colder neutral temperatures. The balance between all these forces determines the positions of particles within the plasma volume. In the plasmas containing dust particles with radii in µm range, the gravitational and electrostatic force are dominating [25]. The µm-sized particles often levitate in the sheath region of the lower electrode or near the sheath edge, as a consequence of the balance of gravity and electrostatic force. In contrast to it, the role of gravity is smaller or almost negligible in the case of nanometer-sized dust particles, enabling their distribution throughout the whole plasma volume. However, initially nm-sized dust particles can grow up to the critical sizes during the process of dust growth in reactive plasmas, when gravity may cause the dust ejection from the discharge. In RF plasmas with nanoparticles, the distribution of dust particles in the plasma bulk region is often nonhomogeneous and subjected to various influences, such as waves, instabilities or other phenomena [37]. One of the consequences of the dust growth and the balance of the forces acting on particles, a dust-free region, void, can be formed inside the dust cloud [37, 38, 39]. Goree et al. [39] proposed a decisive impact of electrostatic force and ion drag force on the void development. The formation of a void has been observed even in the microgravity condition (e.g. [4]). Figure 2.2 shows an example of a void formed during the growth of hydro-carbonaceous nanoparticles in a capacitively coupled argon/acetylene RF

25 27 discharge used in this thesis. Laser light scattering experiments reveal a bright dust cloud occupying almost the whole plasma bulk, separated from the electrodes by the dark, dust-free sheaths. A dark area inside the plasma bulk, a void, appears due to the lack of dust particles on which the laser light can be scattered. The appearance of a void and the other phenomena characteristic for the distribution of the dust particles during one cycle of the dust growth in RF discharges are described in chapter Formation of dust particles in plasmas In laboratory plasmas applied for the scientific research, the dust particle can appear in the plasma as a consequence of different mechanisms. As one method, the particles can be externally injected into the discharge chamber via dust dispensers. Such complex plasmas with injected particles (with typical radii in the micrometer range) provide suitable conditions for research of the particle charging mechanisms, mutual interactions of particles or with other plasma components, self-organizational structures (plasma crystals), collective behavior in form of dust waves, phase transitions and many other effects occurring in such plasmas (e.g. [24, 41]). The dust particles can also appear in a discharge due to the erosion of the material found in the discharge reactor or by sputtering from a target [42]. The formation of nano- to micrometer-sized dust particles is a common characteristics of discharges containing reactive gases, as previously mentioned in section 1.3. This process has been observed under a variety of discharge conditions and gas mixtures (silane, fluorocarbons, hydrocarbons), which makes them suitable for a wide range of applications. The admixtures of rare gases with silane (SiH 4 ) are used for the production of silicon-based devices, such as solar cells (e.g. [25]). Due to their commercial use, the dusty plasmas with silane have been thoroughly investigated and the dust formation and growth mechanisms are well known. In etching processes, fluorocarbon plasmas (CF 4 or C 2 F 2 ) have been widely applied [43]. The plasmas containing hydrocarbon gases, such as methane (CH 4 ) and acetylene (C 2 H 2 ), are important for the study of astrophysical dust analogues, but also in the technological processes for the deposition of diamond-like films, which provide improved mechanical and optical characteristics [44, 45]. This work focuses on the plasmas containing acetylene as a dust precursor gas. The presence of acetylene in a discharge is characterized by the spontaneous formation of dust particles, which is related to the more rapid polymerization in comparison to other hydrocarbon molecules (e.g. methane) [46, 47]. Moreover, acetylene may be created in a discharge as a product of polymerization of other hydrocarbon molecules [47]. Furthermore, acetylene can be also applied for the investigation of astrophysical dust. Previous investigations have shown that the nm-sized hydro-carbonaceous particles, formed by plasma polymerization from acetylene monomers under certain discharge condition, represents a good laboratory simulation of interstellar dust, so called astroanalogue [48].

26 28 2 Dusty plasmas Plasma polymerization Due to the complexity of physical and chemical processes, the plasma polymerization process in hydrocarbon plasmas is not completely understood. However, a general scheme of the dust particle formation and growth mechanisms is recognized [25]. The formation of dust particles in plasmas can occur in a homogenous nucleation process, in which the precursor gas molecules are dissociated and ionized in a series of chemical reactions. The homogeneous nucleation process is characterized by the spherical shape of the formed dust particles, in contrast to the asymmetric dust particles formed in the flaking processes (heterogeneous nucleation). The dust formation and growth in the reactive plasmas can be described as a four-step process [25]: I The process begins by the dissociation of the precursor molecules (monomers). The polymer molecules, resulting from the dissociation, participate in the formation of the primary clusters. These primary clusters are mainly neutral or singly-negatively charged. The positively charged clusters produced in this phase are accelerated to the walls by the electric fields in the sheaths, whereas the negatively charged ones stay in the plasma bulk. II The second phase is nucleation and cluster growth phase. The nucleation phase takes place after the primary clusters had reached the critical sizes. The small clusters with radius up to several nanometers, the "protoparticles", are formed, retaining the neutral and single (positive or negative) charge. III The coagulation or agglomeration phase begins when the density of protoparticles reaches its critical value. The protoparticles agglomerate into the macroscopic nanoparticles with radii up to several tens of nanometers. Beside its growth, the particle becomes multiply negatively charged due to the enhanced electron attachment. IV The last phase concerns the growth of particles up to µm sizes. Due to the negative charge, the particle growth does not occur via agglomeration processes, but rather by condensation (sticking) of neutral species (radicals) and positive ions to larger particles. This phase is relatively slow compared to other phases. As previously mentioned, the presence of acetylene in plasma can lead to a very rapid formation of dust particles. However, there is no unique scheme for the initiation of the dust formation processes. The formation of the primary clusters (phase I) can be conducted via different chemical pathways: negative ions, positive ions and neutral radicals [49]. The negative ions can play a significant role due to their long residence times in the discharges [5]. The primary clusters may be negative ions C 2 H formed in a process of dissociative attachment of C 2 H 2 [51]: C 2 H 2 + e C 2 H + H. (2.2)

27 29 The anion C 2 H can further enter into chemical reactions with surrounding acetylene molecules forming the larger polymer chains: C 2 H + C 2 H 2 C 4 H + H 2 (2.21). C 2n H + C 2 H 2 C 2n+2 H + H 2 (n = 2, 3, 4...). Another possible pathway for negative ion production and further polymerization is proposed in [52]: C 2 H 2 + e H 2 CC (2.22). C 2n H 2 + C 2H 2 C 2n+2 H 2 + H 2 (n = 2, 3, 4...). The positive acetylene ions C 2 H + 2 are created in ionization processes. These positive ions can also react with acetylene molecules in the discharge, participating in the formation of positively-charged hydrocarbon polymers which can represent the primary clusters. The following reaction pathway is proposed [49]: C 2 H + 2 +C 2 H 2 C4 H + 2 +C 2 H 2 C6 H + 2 +C 2 H 2 C8 H + 2 etc. (2.23) Highly reactive radicals C 2 H can be produced via electron impact dissociation of acetylene [5]: C 2 H 2 + e C 2 H + H + e. These radicals can easily enter into subsequent reactions with acetylene, contributing to the initiation of the neutral primary cluster production: C 2 H + C 2 H 2 C 4 H 2 + H Control of the plasma polymerization process by plasma pulsing In rare gas discharges supplied with reactive gases, a spontaneous formation of nanometersized dust particles in continuously driven (CW) discharges is a well known phenomenon. However, due to the contamination issues, this is an undesired characteristic of reactive plasmas used for deposition or etching. One of the efficient techniques to control dust appearance is the modulation of RF power by pulsing the plasma with an appropriate frequency and pulse length [15, 16, 32, 5, 53]. The proper selection of the pulsing frequency can influence the initial phase of dust formation, i.e. the formation of primary clusters. Howling et al. [53] suggest that the polymerization

28 3 2 Dusty plasmas in RF silane plasmas propagates via negative ion chemistry. Their study shows the strong reduction of high mass polymer molecules, necessary for the formation of primary clusters, after pulsing the RF plasma with frequencies of about 1 khz. This effect is contributed to the decay of elementary anions in the power-off (afterglow) phase, which prevents further polymerization to higher mass molecules. The formation of dust particles in reactive plasmas containing hydrocarbons has been investigated by Berndt et al. [32, 5]. By pulsing the RF signal with a frequency less than 7 Hz, the formation of hydro-carbonaceous dust particles can be suppressed. This may be attributed to the decay of density of elementary anions, e.g. C 2 H in (2.2) (assuming the polymerization goes via anions). Higher pulsing frequencies above 7 Hz provide the critical concentration of precursors and radicals to be kept in the plasma, thus enhancing the process of dust formation. In plasmas pulsed at higher frequencies, the dust particle formation resembles the spontaneous dust formation in CW-driven discharges. 2.3 Plasma-dust interaction: effects of dust presence on plasma parameters After the formation or injection of dust particles into a discharge, significant changes of various plasma parameters may occur. These changes concern the chemical composition in the discharge, as well as the physical properties of plasma components (densities, temperatures, profiles, heating mechanisms, etc.) [25, 26, 54]. Even without sensitive diagnostic techniques, the appearance of dust particles in discharge can be recognized due to the striking changes in the light emission from the plasma [26]. The dust particles collect ions and electrons, thus representing additional loss channels for these plasma components. A remarkable consequence of the dust particle presence in the plasma is the strong reduction of free electron density, arising from the negative charging of dust particles (e.g. [26, 32]). In order to sustain the discharge, the enhanced losses of electrons have to be compensated by an appropriate mechanism of electron production. This can be achieved by an increase of the mean electron energy, i.e. the electron temperature, thereby enabling more effective production of electrons and ions by electron impact ionization [26]. Bouchoule and Boufendi [55] attribute the strong increase of the electron temperature to the penetration of electric field in the plasma after the appearance of the dust. Indeed, the electric field distribution in the discharge is changed when the dust particles are present, in comparison to dust-free plasmas [25]. This is characterized by the smaller electric field in the plasma sheath and much larger electric field in the plasma bulk. Consequently, the heating mechanisms in the dusty plasmas are significantly different to the heating in dust-free plasmas, with the dominating power dissipation in the plasma bulk [25]. Another consequence of the dust presence is the change of the plasma impedance from capacitive to resistive, so called α γ transition, which is reflected to the current-voltage characteristics and current-voltage

29 31 phase shifts in dusty plasmas [25]. In pulsed RF plasmas with large concentration of hydro-carbonaceous dust particles, the electron density exhibits an unusual, anomalous behavior after switching the RF power off [32]. This is manifested by an increase of electron density in the first moments of the plasma afterglow phase. The peak of electron density in the plasma afterglow phase is reached in several hundreds of µs, after which the electron density starts to decay in an expected manner. In [32], Berndt et al. contribute this effect to the periodical charging and discharging of the particles during the plasma pulsing, which occurs as a consequence of the ion/electron recombination on the dust surface, collection of positive ions or release of free electrons due to various possible mechanisms (secondary electron emission due to the impact of electrons, ions, UV photons, metastable atoms, fast electrons etc.). Moreover, Berndt et al. [32] suggest that this anomalous effect is gas-related, as it has not been observed in silane plasmas. However, the exact mechanisms which participate in the release or production of free electrons have not been understood in detail. A possible mechanisms which may be responsible for the anomalous electron density in the plasma afterglow have been investigated in chapter 7 of this work.

30

31 3 Experimental system The investigation of reactive and nonreactive plasmas has been performed in a capacitively coupled discharge reactor, applying the various diagnostic techniques. In this chapter, the design of the reactor and the operational discharge parameters are introduced. 3.1 Reactor design A side view of the low pressure, capacitively coupled discharge system used for the present investigations is shown in figure 3.1. The discharge reactor is a cylindrical vessel made of stainless steel with diameter D r = 5 cm and height H = 3 cm. The walls of the reactor are grounded. The discharge is produced between two parallel-plate stainless steel electrodes with equal diameters D e = 3 cm. Each electrode is additionally connected to a grounded stainless steel plate of the same area. The size of electrodes is larger than in the conventionally used Gaseous Electronics Conference (GEC) reference cell, nevertheless it is corresponding to the reactors used for the industrial purposes (e.g. circuit fabrication or surface processing). The distance between the electrodes can be regulated by two stepper motors, which enable the vertical positioning of each electrode without opening the reactor and disturbing the vacuum by surrounding impurities. The electrode distance used in the present work is L = 7 cm. A radio frequency generator (Adret electronique - Frequency Synthesizer Type: 61A) with the working RF frequency f = MHz is connected to the electrodes through a specially designed impedance matching circuit. Both electrodes are symmetrically driven by the RF signal. A directional power meter (Rohde & Schwarz R NAS) is used to monitor the forward and the reflected power of the applied RF signal at the place of the RF generator output. As a consequence of the power losses in the transmission lines (cables, contacts etc.) or the impedance matching, the RF power coupled into the discharge is strongly decreased compared to the power nominally supplied by the RF generator. In the scope of this work, the input RF power, ranging between 1 and 8 W, actually corresponds to the forward power measured by the directional power meter. The reflected power is maintained below 5 % of the input RF power by impedance matching performed prior to the measurement. To achieve a high vacuum, a pumping system consisting of two oil-sealed rotary pumps 1 and a turbo-molecular pump is installed. In the first stage, the oil-sealed rotary pump is used to evacuate the reactor to the pressures below 1 mbar. With the help of the second rotary 1 Leybold Trivac 33

32 34 3 Experimental system 1 11 M RF power supply 8 2 M Figure 3.1: The reactor design - 1. plasma and electrodes; 2. stepper motors to regulate electrode distance; 3. RF power supply; 4. rotary pumps; 5. turbo-molecular pump; 6. gas bottles with pressure reducers; 7. mass flow controllers and the pressure control system; 8. mechanical valve; 9. non-reactive gas inlet; 1. reactive gas inlet; 11. window for laser; 12. FTIR spectrometer. pump and the turbo-molecular pump (nominal pumping speed of 15 l/s), the background pressures in the range of 1 6 mbar are achieved. The measurement of the background pressure in the reactor is performed by a vacuum gauge based on the Bayard-Alpert principle from Leybold-Heraeus (Model Ionivac IM21). Higher pressures in the pumping lines can be followed by a Pirani manometer from Leybold-Heraeus (Model Thermovac TM22). The discharge has been supplied with argon as a carrier gas, or in admixture with reactive acetylene. The carrier gases enter the reactor via two laterally positioned gas inlets, while the reactive gases are injected through an inlet on the top of the reactor. The gas flow, typically in the range.5-1 sccm 2, is controlled by mass flow controllers (MKS Instruments Type 1B). 2 sccm = standard cubic centimeter; 1 sccm = 1/55.18 mbar l/s

33 35 The absolute pressure of the feed gas in the reactor during the experiments is measured by a Baratron capacitive manometer (MKS Type 627). The gas pressure can be varied by changing the pumping speed through a mechanical valve placed between the discharge reactor and the turbo-molecular pump. A total gas pressure of p = 1 Pa is used for the measurements performed in this work. The consequence of the use of reactive gases in experiments is the deposition of thin polymer films on the reactor s surfaces. The thin film can contaminate the electrodes, walls, windows, or measuring equipment inserted in the reactor (e.g. probes, mirrors), thus influencing the discharge properties or the applied diagnostic technique. In the present investigations, the deposited film is removed from the reactor by sputtering with an oxygen (O 2 ) plasma prior to the measurements. The plasma-activated atomic oxygen reacts with the thin film components (hydrogen or carbon), forming the products such as CO, CO 2, OH, or others, which are pumped out of the chamber. Typical discharge parameters used for the cleaning process are: O 2 flow Q = 1 sccm, total pressure p = 1 Pa, and input RF power P = 8 1 W. The time of the film removal by the oxygen plasma depends on the degree of the electrode contamination in previous experiments. The film residues are removed most efficiently from the electrodes, while the other surfaces, which stay contaminated, have to be cleaned manually. The gas inlets, positioned laterally in front of two golden mirrors of the Fourier Transform Infrared (FTIR) spectrometer, significantly reduce the contamination of these mirrors, thus providing the accuracy of this diagnostic technique. The reactor is supplied with 8 paired windows and several ports. The large number of ports and windows allows the simultaneous application of various diagnostic techniques necessary to investigate the complex plasmas. An overview of the applied diagnostic techniques and their implementation to the experiments are given in chapter RF power supply: CW and pulsing mode The RF generator supplies both electrodes symmetrically with the sinusoidal RF signal passing through the RF power supply system. The RF signals delivered to the separate electrodes are shifted in phase by ϕ = 18. This configuration is known as a "push-pull" configuration. Its advantage is a reduction of the harmonic content of the system, resulting in the linear dynamic current/voltage (I/V) characteristic over an RF period [56]. This allows to consider the discharge as a linear device with the equivalent resistance and capacitance depending only on the fundamental driving frequency. Moreover, the total sheath capacitance of the symmetrically driven discharge is linear (time-independent), although it is a combination of the capacitances of two non-linear sheaths, which depend on the time evolutions of the individual sheath voltages [1, 57]. Another advantage of the symmetrically driven discharges is a strong decrease of the plasma potential (with respect to the ground), resulting in a strong decrease of the RF current in radial direction [56]. Therefore, the discharge can be treated as

34 36 3 Experimental system CW mode Electrode 1 RF Amp RF generator Wideband RF amplifier Directional power meter Impedance matching Electrode 2 Pulsing mode Function generator Figure 3.2: Frequency mixer Mini-Circuits ZAY-1 RF power supply: Continuous-wave (CW) and Pulsing mode. "one-dimensional" with a dominant current flow in the axial direction. This characteristic can become important when considering the electron and ion currents to the electrodes presented in chapter 8. The RF power supply system is presented in figure 3.2. On its path to electrodes, the RF signal from the RF generator is first amplified by a wide-band RF amplifier. Afterwards, the RF signal passes through the impedance matching circuit, which enables the push-pull configuration and the signal delivery to both electrodes. In this manner, the sinusoidal signal is continuously delivered to the electrodes, which is designated as "CW mode" in figure 3.2. Beside continuously, the RF signal can be delivered to the electrodes as a series of pulses with a chosen frequency and pulse length, i.e. by pulsing the plasma. The schematics of the experimental setup used for pulsing the plasma is presented in figure 3.2, denoted as "Pulsing mode". A frequency mixer (Mini-Circuits ZAY-1) is used to mix the RF signal from the RF generator with a rectangular signal from a pulse generator (Hewlett Packard 8111A 2 MHz Pulse/Function Generator). The frequency and the pulse length (duty cycle) of the modulated RF signal correspond to the same parameters of the rectangular signal. In the present work, the frequency is varied between.1 and 1 khz, while the duty cycle is set to 5%. After the modulation, the signal is delivered to the electrodes following the same electrical path as in the CW mode. Several problems concerning the experimental equipment can occur due to the plasma pulsing. For instance, the range of the applicable frequencies and duty cycles can be limited by the RF generator, which has been improved by using the pulse generator in combination with the RF amplifier (figure 3.2). The measuring equipment, such as Langmuir probes, can also be affected by the altering power-on and power-off phases. Therefore, a proper synchronization of the measuring equipment with the pulsing cycle is necessary. Another problem may occur due to the poor impedance matching of the pulsing plasma, which will be discussed in the following section.

35 37 5 C 2 C 4 C 6 Electrode 1 V RF C 1 C 5 Electrode 2 C 3 Figure 3.3: The electrical circuit of the impedance matching network. The variable capacitors have nominal capacitances: C 1 = 27 pf, C 2 = C 3 = 6 pf, C 4 = C 5 = 155 pf, and C 6 = 1 pf. 3.3 Impedance matching In order to provide an efficient transfer of the RF power from the source to the discharge, an impedance matching is necessary. The impedance matching enables a maximal power to be transferred to the discharge, at the same time minimizing the losses in the transmission lines (cables, contacts) and preventing the reflection of the power back to the source. The impedance matching is achieved by a specially designed network placed between the source and the discharge, which has the role to adjust the impedance of the RF discharge to the internal impedance of the RF source (typically 5 Ω). The schematics of the electrical circuit used for the impedance matching of the applied symmetrically driven discharge is shown in figure 3.3. The network consists of an transformer and variable capacitors. The push-pull function is provided by the transformer, which splits the input RF signal into two equal, but phase-shifted signals, that are forwarded to electrodes. The variable elements of the matching network (inductances and capacitances) can be tuned, until the standing wave ratio in the directional power meter has a unity value. This indicates that the discharge impedance corresponds to the internal resistance of RF generator. However, due to the power losses in the contacts or the transmission lines, the ideal unity standing wave ratio is not easy to achieve. In the experiments, the standing wave ratio is kept below 2. The equivalent capacitance of the matching box has a role of the blocking capacitor, thus coupling the discharge capacitively to the RF generator. Due to the presence of the blocking capacitor in the external circuit, the net DC current is equal to zero. It has to be noted that the insulation of electrodes by a thin film can also provide the capacitive coupling of the discharge, thus having the same effect as the blocking capacitor [58]. Plasma pulsing can also disrupt the ideal conditions of impedance matching. This is a consequence of the significant differences of the plasma impedances in the power-on and power-off phases. The alternating plasma impedance causes the poor impedance matching especially if the automatic matching circuits are used. The power delivered to the discharge

36 38 3 Experimental system in the power-on phase might also deposit in the matching circuit during the power-off phase. In the present work, the impedance matching is performed using the pure argon plasma. Thereby, the impedance matching circuit is tuned to achieve the lowest reflected power and the largest steady-state electron density during the power-on phase of the pulsed plasma. The impedance matching adjusted in the pure argon plasma is further applied for other gas mixtures.

37 4 Diagnostic techniques In this chapter, an overview of the applied diagnostic techniques and their implementations in the experimental setup are presented. The chapter is divided into 2 sections. The first section 4.1 deals with the diagnostic methods used for the measurements of electron densities. The second section 4.2 gives an overview of different optical diagnostics applied throughout this work. The laser absorption spectroscopy and laser induced fluorescence are employed to investigate the dynamics of argon metastable atoms. The ultraviolet spectroscopy is applied to follow the absorption and extinction spectra in the ultraviolet spectral region. The laser light scattering technique is used to investigate the dynamics of dust particles and the void region in dusty plasmas. 4.1 Determination of electron density The electron density is one of the key parameters necessary for a plasma characterization. The temporal and spatial behavior of the electron density and its relation to the other discharge parameters (discharge size, gas, pressure, temperature, applied power, etc.) are necessary to understand the discharge processes and to be able to control them. Various diagnostic tools have been developed to investigate the electron densities. Depending on their impact on the discharge, the plasma diagnostics can be passive or active. Active tools, such as probes, can disturb the discharge characteristics only because of their presence in the discharge. On the other hand, the passive diagnostics do not influence the discharge conditions, nevertheless, they often provide only space-averaged values (e.g. microwave interferometry) or they are model-dependent (e.g. optical emission spectroscopy). In the scope of this work, two different diagnostic methods have been employed to determine the electron density and the related parameters under various discharge conditions. A non-invasive technique of microwave interferometry is applied to measure the average electron densities in the central region of the discharge. The microwave interferometry has been compared to an invasive Langmuir probe method, which measures local electron densities. The following sections describe the basic principles of these methods and their applications to the experimental setup Microwave interferometry Microwave interferometry is a non-invasive diagnostic technique for the measurement of electron densities suitable for plasma processes which contain reactive gases. Standard techniques for the measurement of electron density, such as Langmuir probes, can be inaccurate 39

38 4 4 Diagnostic techniques due to the film deposition or etching processes on the probe surface. An additional problem is the physical presence of the probe in the plasma, which can cause a perturbation of the plasma and disturbances in the accurate measurements of electron densities. Microwave interferometers have the advantage to measure the electron density without disturbing the plasma. They yield a spatially averaged electron density in the line of sight, in contrast to the Langmuir probes, which provide local densities at the point of measurement. The method of microwave interferometry is based on the dependence of the refractive index of the plasma on the electron density. The refractive index is correlated to the wavelength and propagation constant of the microwave beam traveling through the plasma. The average electron density in the plasma can be determined from the difference in the phase shift measured across the regions with and without plasma. The relation between angular frequency ω of the electromagnetic wave traversing the plasma and its propagation constant k is expressed by the dispersion relation [1]: k = ± κ P k, (4.1) where κ P is the relative dielectric constant of the plasma and k = ω/c is the propagation constant in vacuum (c is the speed of light). For high microwave frequencies, the collisions between electrons and neutrals can be neglected, therefore the relative plasma dielectric constant κ P can be reduced to [1]: κ P = 1 ω2 pe ω 2. (4.2) Here, ω pe = e 2 n e /(ε m e ) is the electron plasma frequency, depending on the electron density n e in the plasma. The refractive index of the plasma n P is related to the electron density through the relative dielectric constant κ P, thus the plasma frequency ω pe : n 2 P = κ P = 1 ω2 pe ω 2. (4.3) The space and time variation of the electromagnetic wave (microwave) propagating through a medium (plasma) can be described by a geometric-optics approximation: Ψ = Ψ exp j(ωt k r). On its way through the plasma (plasma length l), a change in the spatial phase shift of the microwave occurs. In the x direction, the phase shift can be found according to: ϕ(x) = l k(x)dx. (4.4) The difference in phase shifts of the waves crossing the plasma ϕ P and vacuum ϕ can be

39 41 Transmitter with dielectric rod antenna Receiver with dielectric rod antenna Plasma path Microwave beam 26.5 GHz Reference path 3 E 9 Electronic unit Oscilloscope / Data acquisition Figure 4.1: Microwave interferometer MWI a principle scheme calculated by: l ϕ = ϕ P ϕ = k(x)dx k l (4.5) ( ) 1/2 l = k 1 ω2 pe ω 2 dx k l. The common frequencies of microwave interferometers are usually higher than the plasma frequency ω ω pe, allowing a Taylor series expansion for small numbers 3 in (4.5): ϕ k e 2 l 2ω 2 n e (x)dx. (4.6) ε m e Hence, according to (4.6), the averaged electron density is directly proportional to the difference in the phase shifts along the wave propagation line (i.e. plasma length) and it can be measured directly by: n e = 2ω2 ε m e k e 2 ϕ. (4.7) l In this work, absolute electron densities are measured by a super-heterodyne microwave interferometer MWI 265 developed by JE PlasmaConsult GmbH 4. The microwave interferometer is operating at frequency of 26.5 GHz, with an output power of 4 mw and a temporal resolution of 1 µs. High frequency stability is achieved by using a dielectric resonator oscillator, while a super-heterodyne frequency conversion scheme is used for the registration of the phase shift by the plasma. The principle scheme of the MWI 265 is presented in figure 4.1. The microwave interferometer consists of two microwave units with 2 dielectric rod antennae 3 (1 x 2 ) 1/ x2 4

40 42 4 Diagnostic techniques positioned on the opposite windows of the discharge reactor. The first unit is a transmitter of a microwave beam at 26.5 GHz, while the second unit serves as a receiver. The transmitting unit splits the microwave beam into two parts: the first signal passes through a flexible coaxial cable, representing a reference path, while the second signal crosses the plasma path. The two signals are adjusted to have the same amplitude and a phase shift by 18, which provides the zero electron density in the absence of the plasma. The phase-shifted signal passing through the plasma is compared to the unaffected signal in the reference path within the electronic unit. The measured phase shift is further used to obtain the absolute electron density averaged in the line of sight between the transmitting and the receiving antennae. The electronic unit display shows the instantaneous absolute value of electron density in cm 3. A BNC-type 5 Ω outlet socket allows the connection of an oscilloscope to the electronic unit in order to observe the time resolved electron densities in pulsed plasmas. In this case, one channel of the oscilloscope displays a voltage proportional to the electron density, with the output signal calibrated to 1 9 cm 3 /mv. The effects of the refraction in the metallic discharge chamber are reduced by installing 2 dielectric lenses on the windows in front of the rod antennae. The lenses provide focusing of the majority of the microwave signal into the center of the reactor between 2 electrodes, enabling the sufficient level of the received signal. Because of this, the obtained output signal is the average electron density in the central part of the reactor, cm around the central axis radial to the electrodes. The electron density in the area outside plates is considered to be negligible, due to the large size of electrodes compared to the total path between the microwave antennae and a steep decrease in the electron density profile in this area Langmuir probe The Langmuir probe is a well-established diagnostic technique, proposed first by Langmuir and Mott-Smith in 1926 [29]. The method was developed over the years, becoming one of the most often used diagnostics for the determination of plasma parameters in low-temperature plasmas. Similarly to other probe diagnostics, the Langmuir probe is an invasive technique, since the probe is physically inserted into the discharge. The presence of the probe in the discharge often causes disturbances and perturbations due to inhomogeneities or probe contamination. Therefore, the application of the Langmuir probe in reactive and dusty plasmas can lead to misinterpretations of the collected information. However, this technique is easyto-implement and can provide the time and space distributions of various plasma parameters, which makes it a common method used for plasma characterization. The Langmuir probe consists of a wire inserted into the discharge and biased externally by a ramp voltage. The electric field, formed due to the potential difference between the plasma and the applied ramp voltage, induces currents of the charged particles (electrons and posi-

41 43 Current (ma) Ion saturation current Electron current Electron saturation current Floating potential Plasma potential Ramp voltage (V) Figure 4.2: Typical Langmuir probe I/V characteristic measured in this work. Figure 4.3: The APS3 Langmuir probe measuring system (Source [59]). tive ions) to the probe. The probe current response to the increasing ramp voltage represents the Langmuir probe I/V characteristic. The basic plasma parameters, such as electron density, positive ion density, electron temperature, electron energy distribution function (EEDF) and plasma potential can be derived from the I/V probe characteristic. A typical probe characteristic, measured in the present experiments, is shown in figure 4.2. Three zones can be distinguished in the I/V characteristic, depending on the relation between the ramp potential V r to the plasma potential V P [1]: 1. For sufficiently negative ramp voltages compared to the plasma potential V r V P, the probe collects only positive ions, while the negatively charged electrons are strongly repelled. The probe current corresponds then to the ion saturation current I p = I is. 2. The gradual increase of the ramp voltage (V r < V P ) enables the electrons with higher energies to reach the probe, beside the positive ions. Thus, the increasing electron current is now a significant part of the total probe current I p = I i I e. At the floating potential V f, the electron and ion currents to the probe become equal, therefore the probe draws zero current from the plasma I p =. 3. At the ramp voltages higher than the plasma potential V r > V P, the probe becomes positively charged with respect to the plasma. Electrons with smaller energies can now reach the probe, whereas the positive ions are repelled. The probe current is determined by the electron saturation current I p = I es, which is independent of the further increase of the ramp voltage. In the case of cylindrical probes, the plateau of the electron saturation is usually not reached, but the current continues to increase (figure 4.2). Due to the higher mobility of the electrons compared to ions, the electron saturation current is significantly higher than the ion saturation current I es I is.

42 44 4 Diagnostic techniques The probe biased with the same potential as the surrounding plasma V r = V P collects all the electrons and ions without restrictions, causing the positive net current to the probe. The discharge parameters can be derived from the I/V characteristic applying the orbital motion limited theory for the cylindrical and spherical Langmuir probes [6]. In the present work, the following principles have been applied to find the plasma parameters. The floating voltage V f is read directly from the I/V characteristics, as shown in figure 4.2. The plasma potential V P represents the inflection point of the probe characteristic, hence it can be found from the second derivative of the measured I/V curve. The electron energy distribution function F(E) is related to the second derivative of the I/V characteristic, calculated according to the Druyvesteyn method [59, 61] by: F(E) = 1 ( ) 8me E 1/2 d 2 I e A p e 3 dvr 2, with E = e(v P V r ). (4.8) Here, E is the energy of electrons necessary to overcome the potential barrier and to be able to reach the probe with a cross section A p, determined as a difference of the plasma potential V P and the applied ramp voltage V r. In (4.8), the current I e corresponds only to the electron current to the probe, obtained by subtracting the ion saturation current I is from the measured total probe current I e = I p I is. The local electron density at the position of the probe is found by an integration of EEDF over the range of the applied ramp voltages: n e = F(E)dE. (4.9) The mean electron energy T e (in electron volts) is then calculated according to: T e = 2 E F(E)dE. (4.1) 3n e The plasma parameters have been numerically calculated from the I/V characteristics using a program written in MATLAB. For the investigation of the various plasma parameters in the pulsed argon discharge, the Langmuir probe system APS3 [59], presented in figure 4.3, is applied. It consists of a Langmuir probe, a stepper motor, and a APS3 electronic system. The implementation of the probe to the current experimental setup is shown in figure 4.4. As the probe antenna, a cylindrical wolfram wire with the length l p = 1 mm and diameter d p = 5 µm is used. The probe tip is supplied with an MHz filter. The probe is attached to the discharge chamber by an adapter. Additionally, a stepper motor is used to drive the probe in and out of the reactor. The position of the probe can be previously set by the APS3 electronic system. In order to avoid deposition of a thin film on the probe during the work with reactive and dusty plasmas, the

43 45 RF Plasma 1 cm 1 2 Langmuir probe 15 cm RF Trigger Output t d APS3 Electronic system RF generator f mixer Delay generator Function generator Legend: 1 - Shutter valve 2 - Stepper motor and adapter Figure 4.4: The application of the Langmuir probe measuring system to the experiment. probe is retreated from the reactor and isolated from the influence of the reactive gases by a shutter valve, installed between the adapter and the reactor window. Due to the lengths of the adapter and the shutter valve, the furthest possible position of the probe within the discharge is at r = 1 cm from the discharge center (figure 4.4). The APS3 electronic system allowed a control of the measurement and the data acquisition by setting various parameters: the range, resolution and averaging number of the ramp voltage, the current range, the probe position, and the triggering system. Typical settings for the measurements by the Langmuir probe applied in the present work are given in table 4.1. A single I/V characteristic is acquired each 2 µs, with the acquisition time of 6 µs. The time resolution of the measurement can be adjusted by setting the number of measurements per step (table 4.1). Signal-to-noise ratio is approved by increasing the number of data acquisition for each point. An important issue in the pulsed discharges is a synchronization of the Langmuir probe measurements with the pulsing cycle. In the present work, the rectangular signal from the pulse generator, used for the plasma pulsing, is applied as an external trigger for the acquisition of I/V characteristics (figure 4.4). The triggering signal can be additionally shifted within the pulsing cycle with the help of a delay generator. In this work, the Langmuir probe is used to investigate the time evolution of various plasma parameters in pulsed argon plasma, in order to observe the influence of the electrode surface conditions on these parameters. These results are presented in chapter 9.

44 46 4 Diagnostic techniques Ramp voltage settings Range -1 V : 4 V Increment.2 V Cycles per mean value 5 Ramps per mean value 5 Current range ± 1 ma Trigger settings External trigger Yes Measurements per step 2 Probe position r = 1 cm Table 4.1: Typical settings for the measurements by the Langmuir probe applied in the present work. 4.2 Optical diagnostic techniques Optical diagnostic techniques are established as non-invasive in-situ methods widely used for the investigation of plasma processes, which provide high spatial and temporal resolutions of the observed parameters. Passive and active optical methods can be distinguished, depending on the applied radiation source. Passive methods, such as optical emission spectroscopy or actinometry, rely on the investigation of optical emission generated by the plasma itself and provide semi-quantitative information on the excitation phenomena in plasmas. However, these techniques are highly model-related, since they require a previous knowledge on the kinetic processes in the plasma. Active optical methods use external light sources to induce excitation of the species from the ground into a higher energetic state. In contrast to optical emission spectroscopy, which can evaluate only the densities of excited states, absorption techniques enable the detection of absolute densities of the species in their ground state. Two active techniques, laser absorption spectroscopy (LAS) and laser induced fluorescence (LIF), have been used in this work to investigate the dynamics of long-living metastable states of argon atoms in reactive and non-reactive plasmas containing nano-sized particles. Besides, in the following sections are also described the experimental setups for the ultraviolet spectroscopy and the laser light scattering Laser absorption spectroscopy Absorption spectroscopy is an optical diagnostic technique employed for the direct measurements of the absolute densities of species in the ground state and the determination of neutral gas temperature inside the plasma. This technique is enhanced by the introduction of lasers with tunable frequencies as external light sources [62, 63]. The application of lasers provides the high spatial resolutions because of the directionality of the laser beam. The selectivity of the investigated species is improved by the high spectral resolution, provided by the fine tuning of the laser frequency. Additional methods, such as lock-in technique or multi-pass

45 47 arrangement, can also compensate the small absorption volume in case of some discharge configurations (e.g. microjets). Due to its non-invasiveness, high resolution and sensitivity, the LAS technique can be applied to investigate the reactive and dusty plasmas, thus enriching the knowledge about the dynamics and mutual dependence of different species in these plasmas. Basic principles Absorption spectroscopy is based on the excitation of atoms or molecules in a medium by absorbing the energy coming from the incident electromagnetic radiation, i.e. laser light [62, 64]. The absorption of incident light induces an electronic transition from the ground level to the excited state, thereby decreasing the intensity of the transmitted light. The absorption is proportional to the amount of absorbing species which are found in the laser light path. Therefore, by measuring the intensity of the transmitted light, it is possible to determine the density of the absorbing species. The spectral intensities of the incident I (ν) and transmitted I(ν) radiations are related through the Beer-Lambert law: I(ν) = I (ν) exp ( α(ν)l), (4.11) where l is the path length through the absorbing medium and α(ν) the spectral absorption coefficient (figure 4.5a). The spectral absorption coefficient α(ν) at frequency ν describes the electronic transition between the ground-state (denoted as "1") and the excited level (denoted as "2") by [62]: α(ν) = ( n 1 g ) 1 n 2 σ 12 (ν). (4.12) g 2 Here, E 1 and E 2 are energies, g 1 and g 2 statistical weights, and n 1 and n 2 population densities of the respective levels (figure 4.5b). The electron transition between two levels will take place if their energy difference corresponds to the energy of the incident photon E = E 2 E 1 = hν. The probability for the absorption process at a resonant frequency ν is described by the absorption cross section σ 12 (ν): σ 12 (ν) = σ ϕ(ν). (4.13) In (4.13), the coefficient σ is the frequency-integrated absorption cross section which is related to the absorption B 12 and emission A 21 transition probabilities (Einstein coefficients), the oscillator strength of the line f 12, or the transition dipole momentum µ by [65]: σ = + σ 12 (ν)dν (4.14) = hν c B 12 = g 2 g 1 λ 2 8π A 21 =

46 48 4 Diagnostic techniques (a) - I I e l ( n) ( ) (b) n 2 l E g 2, 2 n 1 E g 1, 1 n = n 1 - (g 1/g 2)n2 /2 Figure 4.5: Absorption of the incident light passing through an absorbing medium is described by the Beer Lambert law (a), where the spectral absorption coefficient depends on the population densities of the energetic levels involved in the transition (b) (after [64]). 1 2 Line profile and linewidth of a spec- Figure 4.6: tral line. = 1 πe 2 4πε m e c f 12 = g 2 2π 2 g 1 3ε hλ µ 2. The quantities in (4.14) have their usual meanings: Plank s constant h, the speed of light in vacuum c, the permittivity of free space ε, the elementary charge e, the mass of an electron m e, and the wavelength λ = c/ν. Although the integration extends over the total frequency range, only a small interval ν ± ν actually contributes to the absorption [64]. In (4.13), ϕ(ν) is a spectral line profile, which describes the spectral distribution of the absorbed light intensity around the central frequency ν = (E 2 E 1 )/h. The spectral lines obtained in the experiments are always broadened, not only due to the limitations of the measuring equipment, but also as a consequence of intrinsic physical effects, such as the lifetime of the energetic states involved in the electron transition, the velocity distribution of the species in the gas, and the gas pressure. As a consequence, the absorption of light radiation extends over a range of frequencies around the central frequency ν. Besides, the absorption can be shifted relative to ν. Figure 4.6 shows a typical spectral line profile ϕ(ν). A characteristic quantity is a full width at half maximum (FWHM) δν, called a "linewidth". The FWHM is defined as a frequency interval (ν 1 < ν < ν 2 ), where the intensity of the line profile has decreased to the half value of its maximum at ν : ϕ(ν 1 ) = ϕ(ν 2 ) = 1 2 ϕ(ν ). (4.15) The main mechanisms of spectral line broadening are the Doppler broadening and the pressure broadening. Besides, the natural linewidth plays a role at very low pressures and temperatures. The principles of these broadening mechanisms are summarized below.

47 49 Natural linewidth The natural linewidth arises from the quantum-mechanical uncertainty of the energy of the states involved in the transition [62]. Due to the limited lifetime τ of an excited electronic state, the energy of this state has an uncertainty E = h/τ, according to the Heisenberg uncertainty principle. Upon the emission from the excited into the ground state, an emitted photon will have a range of possible frequencies: ν = E h = 1 2πτ ν = δν n (4.16) which corresponds to the natural linewidth δν n. The natural broadening mechanism gives the normalized line profile in the form of Lorentzian function: ϕ n (ν ν ) = 1 π δν n /2 (ν ν ) 2 + (δν n /2) 2 ( ) ϕ(ν n )dν = 1 (4.17) with respect to the central frequency ν. The natural linewidth usually cannot be directly observed because it is concealed by other broadening mechanisms, such as Doppler or pressure broadening. Doppler broadening The Doppler broadening is a dominant linewidth broadening mechanism at low pressures. It arises from the thermal motion of gas atoms or molecules relative to an observer. The motion of atoms and molecules with a velocity v, having a component along the propagation of the light beam, causes a Doppler shift of their absorption or emission frequency: ω = ω + k v, (4.18) hence, leading to the broadening of the spectral line profile. The velocity of the species in gas, depending on the gas temperature T g and the mass of the species M a, follows a Maxwell- Boltzmann distribution. The normalized line profile function around the central frequency ν takes the form of a Gaussian function [62]: ϕ D (ν ν ) = 2 ln (2)/π δν D exp ( 4 ln (2) (ν ν ) 2 ) ( δν 2 D The Doppler linewidth δν D is related to the gas temperature T g by: δν D = 2ν c ) ϕ(ν D )dν = 1. (4.19) 2 ln (2) k BT g M a (4.2) where k B is the Boltzmann constant. The gas temperature T g can be determined from the experimentally measured Doppler width according to (4.2), assuming that the lifetime of the

48 5 4 Diagnostic techniques atoms in excited state is short enough to preserve their velocity distribution, thus the velocity distribution of the atoms in ground state [66, 67]. Pressure broadening The broadening of the spectral line profile can arise also due to the interaction with neighboring atoms or molecules in the gas [62]. At elevated gas pressures, the collisional rate of the species in the gas increases. Collisions reduce the effective lifetime of the electronic states involved in the transitions and lead to the broadening of the spectral linewidths, according to the Heisenberg s uncertainty principle. Therefore, similarly to the natural linewidth, the spectral line profile is described by the Lorentzian function (4.17). Additionally to the linewidth broadening, the collisions between the atoms or molecules in the gas can induce a spectral shift of the line center. Taking into account the spectral absorption cross section σ and the spectral line profile ϕ(ν), the population density of the species in the initial state n 1 can be determined from the spectral absorption coefficient α(ν) [65]. It follows from (4.12) - (4.14): α(ν) = σ n 1 ϕ(ν). (4.21) For the electronic transitions where the energy difference between the levels is much higher than the gas temperature E 2 E 1 k B T g, the population density of the upper state n 2 can be neglected. Hence, the LAS technique provides the direct determination of absolute densities of the long-living absorbing species n 1. The spectral absorption coefficient α(ν) is determined experimentally from the transmittance of the laser light across the plasma path I(ν)/I (ν), accounting for 4 different signals: 1. PL(ν) - total signal (discharge on and laser on), 2. PE(ν) - plasma emission (discharge on and laser off), 3. L(ν) - initial laser radiation (discharge off and laser on), and 4. B(ν) - background signal (discharge off and laser off). The intensity of the laser radiation prior to the absorption process I (ν) is obtained by subtracting the background signal from the initial laser radiation without the absorbing species I (ν) = L(ν) B(ν). The intensity of the laser radiation after the absorption by the absorbing species in plasma is I(ν) = PL(ν) PE(ν). By subtracting the plasma emission PE(ν), the effects of the reflections in the discharge reactor and the emission coming from the discharge itself are accounted for. The obtained transmittance I(ν)/I (ν) is related to the spectral ab-

49 51 sorption coefficient α(ν) and the absorption length l according to the Beer-Lambert law (4.11): I(ν) PL(ν) PE(ν) = = exp ( α(ν)l). (4.22) I (ν) L(ν) B(ν) Integrating (4.22) over the whole range of frequencies, a surface of the absorption line S in frequency units can be calculated: S abs = ln ( ) I (ν) dν = σ l n I(ν) 1. (4.23) Taking into account the broadening mechanisms and the spectral line profile, the absolute density of the absorbing species can be calculated from (4.23): n 1 = 1 σ l S abs. (4.24) The absolute density of the absorbing species n 1 can be determined by (4.24), assuming the homogeneous density distribution along the absorption path. Experimental setup In the present work, the laser absorbtion spectroscopy is applied to examine the time evolution of the absolute density of argon metastable atoms in 3 P 2 state (1s 5 in the Paschen s notation) in reactive and dusty plasmas. A schematic diagram of the experimental system used for LAS is presented in figure 4.7. An external cavity diode laser (ECDL) in a Littman configuration (Sacher Lasertechnik, Marburg, Germany 5 ) is employed as a light source. The width of the laser line of about 1 MHz is much smaller than the typical Doppler width of the absorption line (δν D.8 GHz). This allows to record the profile of the absorption line with a high spectral resolution by scanning the laser frequency across the absorption line. Fine and accurate scan of the laser frequency is achieved by changing the voltage on a piezoelectric element that moves one of the cavity mirrors. In order to follow the radiative transition between argon s levels 1s 5 2p 7 in the Paschen s notation, the central laser frequency is set to an argon line at λ = nm. On its path to the discharge, the laser beam from the ECDL passes first through an optical isolator 6 (OI in figure 4.7), an optical component which prevents unwanted feedback into the ECDL and allows the light transmission only in one direction. After the optical isolator, two beam-splitters (BS) divide the laser light into 3 beams, one of them crossing the discharge and the other two serving for the precise frequency calibration

50 52 4 Diagnostic techniques ECDL OI BS BS PD3 Plasma Legend: ECDL - Diode laser OI - Optical isolator BS - Beam splitter FPI - Fabri-Perot interferometer RC - Reference cell PD - Photo diode DO - Digital oscilloscope FPI PD1 RC PD2 DO Figure 4.7: Experimental setup for laser absorption spectroscopy. The first laser beam is guided through a confocal Fabry-Pérot interferometer (FPI in figure 4.7) to perform an in situ frequency calibration. The Fabry-Pérot interferometer employs the multiple-beam interference, through which the high spectral resolving power used for the linewidth of the laser is achieved. The confocal interferometer consists of two spherical mirrors facing one another, with radii equal to their mutual distance R = d. The laser rays entering the interferometer parallel to its axis are multiply reflected within the interferometer gap. After leaving the interferometer, the transmitted rays mutually interfere, forming the interference pattern of alternating dark and light concentric rings. The photodiode PD1 detects peaks of the transmission intensity each time the laser frequency is tuned to a transmission maximum. The frequency separation between two successive interference maxima, known as the free spectral range (FSR), depends on the distance d between two mirrors. For the confocal type of FPI, the free spectral range is approximated by ν c/(4d) [62]. The knowledge about the frequency distance between two intensity peaks allows the relative calibration of the frequency axis and the measured absorption spectra. The mirror separation of the Fabry- Pérot interferometer used in the scope of this work is d = 2 cm, with the free spectral range ν = 375 MHz. At argon line λ = nm, the wavelength separation corresponding to the FSR of ν = 375 MHz is λ = νλ 2 /c = nm. For the absolute calibration of the frequency scale, an argon low-pressure reference cell (RC in figure 4.7) is employed. The electronic transitions and the radiation absorption after the laser beam crosses the reference cell occur at well known frequencies. Hence, if the observed spectral range covers the electronic transition in the RC, the signal detected by the photodiode PD2 has an absorption dip. Due to the long absorption length through the reference cell and its low pressure, the spectral profile of the absorption line is determined by the Doppler broadening mechanism. The comparison of the signal from the reference cell (with known frequency range) and the signal passing through the discharge path allows the precise absolute calibration of the frequency scale. The third part of the laser light entered the discharge chamber, after being attenuated down

51 53 to 1 µw by a set of neutral density filters in order to avoid optical saturation [65]. The signal passes through the discharge reactor parallel to the electrodes and it is detected by a photodiode PD3. The position of the beam entrance and the photodiode could be varied, enabling the measurement at different positions in the axial direction (parallel to the electrodes). The signals detected by the photodiodes are simultaneously recorded by a digital oscilloscope (DO in figure 4.7). The signal-to-noise ratio is improved by averaging the acquired signal. In the pulsed plasmas, the signal crossing the discharge, detected by the photodiode PD3, is externally triggered by the rectangular pulse from the function generator (see figure 3.2) in order to synchronize it with the pulsed RF discharge. The final determination of the argon metastable atom Ar m ( 3 P 2 ) density is obtained from the Beer-Lambert law (4.22), considering the Gaussian line profile caused by Doppler broadening: ln I (ν) I(ν) = g 2 λ 2 g 1 8π A 21 l n m 2 (ln 2)/π exp δν D ( 4 ln 2 (ν ν ) 2 δν 2 D ), (4.25) where A 21 = s 1 is the emission Einstein coefficient of the argon line λ = nm, g 2 = 3 and g 1 = 5 are statistical weights for the upper and lower energy levels, n m is the density of absorbing species, l =.3 m is the absorption length (equal to the diameter of electrodes), and δν D is the Doppler line width (4.2). Setting the laser frequency at the center of the absorption line ν, the absolute density of the argon metastable atoms can be deduced: n m = 4πg 1 δν D ln I g 2 lλ 2 (ln 2)/π I. (4.26) The gas temperature T g is assumed to be known from the previous measurements by Stefanović et al. [67], performed for the similar experimental conditions Laser-induced fluorescence Laser-induced fluorescence (LIF) is an in-situ non-invasive active optical technique which can provide information on the nature of the species in the discharge by following their excited and lower energy states. Moreover, LIF spectroscopy can be employed to measure relative or absolute densities of the investigated species, temperature, kinetic energies or other parameters. High sensitivity, spatial and temporal resolutions, and selectivity of the observed species are important features, which make LIF widely used experimental technique in the plasma physics (e.g. [63, 68]). In this work, the LIF method is applied to investigate the dynamics of argon metastable atoms Ar m ( 3 P 2 ) during a cycle of a dust particle growth. While the laser absorption spectroscopy informs about the absolute values of the observed states assuming the homogeneous distribution along the laser beam, the laser-induced fluorescence provides their spatial distri-

52 54 4 Diagnostic techniques bution along the laser beam. In this section, a basic principles of the LIF are described, as well as the experimental setup used in the current work. Basic principles The laser-induced fluorescence is based on the selective excitation of an atom or molecule in a ground or a long-living excited state into an upper electronic state by absorption of laser radiation [68]. The absorption is followed by the spontaneous relaxation (fluorescence) of the excited states back to the lower energetic states by photon emission. A simple scheme of the LIF mechanism is shown in figure 4.8. The laser frequency is tuned to match the absorption line of the observed atom or molecule. The species in the ground state or long-living (metastable) state 1 with energy E 1 is excited to a higher energetic state 2 with energy E 2 by the laser photon with the frequency ν laser = (E 2 E 1 )/h. After the excitation, the spontaneous emission of the fluorescent radiation to another exited state 3 with lower energy takes place, where the wavelength of the emitted photon corresponds to the energy difference of the involved levels ν LIF = (E 3 E 2 )/h. The fluorescence signal is focused into a detector through a wavelength filter, which may be at a particular wavelength (e.g. interference filter) or scannable (e.g. monochromator). The intensity of the observed LIF signal I LIF is proportional to the population density n 2 of the excited level 2 (figure 4.8): I LIF = KA 23 n 2, (4.27) where K is a coefficient depending on the geometry and the spectral response of the detector, and A 23 is the transition probability for the spontaneous emission 2 3 [68]. For the determination of the population density, it is necessary to know the rates of the processes involved in the transitions caused by the laser radiation and to solve the appropriate set of rate equations. The rate equation for the level 2 is determined by the production and loss processes [68]: dn 2 dt = B 12 ρ l (ν)n 1 (B 21 ρ l (ν) + A 2 + R 2 )n 2 + C 2. (4.28) The dominant population process of the energetic level 2 is the induced excitation of the ground-state energetic level 1 by the laser, described by the term B 12 ρ l (ν)n 1 in (4.28). The excitation rate depends on the population density n 1 of the state 1, the Einstein transition probability B 12 for absorption process, and the spectral energy density ρ l (ν) = I laser /(hν laser ), which represents the number of photons with energies equal to hν laser per unit volume involved in the excitation process. Furthermore, the population of the state 2 can be increased through other processes, such as diffusion, electron-impact excitation, radiative cascades or collisional transfers from other excited states. These processes, described by the term C 2 in (4.28), are usually negligible compared to the excitation. The dominating loss process influencing the depopulation of the level 2 is the sponta-

53 55 Figure 4.8: Energy diagrams of the levels involved in one-photon laser-induced fluorescence, with corresponding population densities n i, energies E i and statistical weights g i. n, 2 E, g 2 2 n, 3 E, g 3 3 n, 1 E, g 1 1 h laser = E 2 - E 1 h LIF = E 2 - E 3 neous de-excitation with the rate A 2 in (4.28). The rate coefficient A 2 is determined by the spontaneous emission from the level 2 towards all the levels i with lower energies by A 2 = i A 2i. Thus, the resultant spontaneous emission probability corresponds to the sum of inverse of the natural lifetimes between levels 2 and i : A 2 = i 1/τ 2i. The depopulation of the level 2 can occur through the induced de-excitation with the rate coefficient B 21 ρ l (ν), where B 21 is the Einstein coefficient for stimulated emission. The stimulated emission and absorption are correlated through B 21 /B 12 = g 1 /g 2, where g 1 and g 2 are the statistical weights for levels 1 and 2, respectively. The depopulation of the level 2 may be also accomplished by non-radiative transitions from the level 2. This is achieved mostly through the collisional de-excitation. The rate coefficient R 2 is equal to the sum of the rates of all collision-induced transitions: R 2 = q k 2q n q, where n q is the density of the species q participating in the collision. The population density n 2 can be determined from the stationary state dn 2 /dt =, when the production and loss processes in (4.28) become balanced. Depending on the intensity of the applied laser radiation, two regimes can be distinguished [63, 68]. For low laser intensities (B 21 ρ l A 2 + R 2 ), the fluorescence signal I LIF is proportional to the ground state population n 1 and the laser intensity ρ l : I LIF = K A 23B 12 A 2 + R 2 n 1 ρ l. (4.29) The high laser intensities may lead to the saturation of the absorption transition 1 2, hence the fluorescence signal I LIF becomes independent on the laser intensity ρ l : I LIF = Kn 1 g 2 g 1 A 23 A 2 + R 2. (4.3) Hence, following (4.29) and (4.3), the relation of the applied laser intensity to the production and loss processes has to be accounted for in order to properly calculate the absolute density of the investigated species. Nevertheless, regardless of the laser intensities, the measured fluorescence signal I LIF can qualitatively serve to follow the relative changes of the population density of the absorbing species. In reactive and dusty plasmas, the change of the fluorescence intensity can help to identify the processes occurring in the plasma volume under the differ-

54 56 4 Diagnostic techniques ECDL = nm PE PL 1 cm IF ICCD Plasma 15 cm LIF image Figure 4.9: A sideview of the experimental setup for laser-induced fluorescence, with an example of the recorded LIF image. Legend: EDCL - external cavity diode laser, IF - interference filter, ICCD - camera. ent conditions. In particular, a high spatial resolution of the population density may enable a better understanding of production and loss processes in different regions of the discharge. Experimental setup In the scope of this work, the laser-induced fluorescence technique is employed to follow the dynamics of argon metastable atoms in 3 P 2 state during one cycle of the dust particles growth. The time and space resolved measurements of the LIF signal may give an insight into the behavior of the metastable atoms under different discharge conditions. The experimental setup used for the LIF is the same as for the laser absorption spectroscopy (figure 4.7 in section 4.2.1). In contrast to LAS setup, the third laser beam is sent perpendicular to the electrodes, as presented in figure 4.9. The laser beam, previously directed by the set of the mirrors to the top of the reactor, enters the reactor through a window installed at its top. In order to avoid the reflections of the laser beam, 2 mm holes are perforated in all electrode plates. The LIF signal is observed perpendicular to the electrodes, but shifted to r = 1 cm from center of the reactor (figure 4.9). The laser beam, supplied by the external cavity diode laser (ECDL) at a central wavelength of λ = nm, is used for excitation of argon metastable atoms Ar m ( 3 P 2 ). The signal from the argon reference cell is applied to keep the laser frequency at the center of the argon line λ = nm. The induced fluorescence is observed at the wavelength λ = nm, corresponding to the transition 2s 7 1s 4 in the Paschen s notation. The LIF signal from the whole plasma region is imaged onto an ICCD camera (Princeton Instruments Type PI- MAX 124 RB-SG with ST133A controller). The resolution of the camera is 124 x 256 pixels, although only images with 1 x 256 pixels around the laser beam are recorded during the experiment, in order to achieve a faster data acquisition. In order to isolate the LIF signal at nm and to reject the plasma emission on other wavelengths, a dielectric interference

55 57 filter 7 is positioned in front of the ICCD camera. An example of the recorded LIF image is given in figure 4.9. The recorded LIF image contains not only the information about the distribution of Ar m ( 3 P 2 ) atoms, but also about the emission coming from the plasma and the background. These signals have to be accounted for the proper determination of the argon metastable distribution. The final LIF signal I LIF is obtained by: I LIF = PL PE n dist. (4.31) Here, PL is the total acquired signal, i.e. the LIF signal containing the emission from the surrounding plasma. The PL signal is found as a value of the recorded signal at the position of the laser along the axial direction, denoted as PL in the LIF image in figure (4.9). The emission signal coming from the plasma PE is obtained from the LIF image at the place without laser beam (PE in the LIF image in figure 4.9). Assuming a constant gas temperature, the intensity distribution of the calculated LIF signal provides the relative variation of argon metastable atom density along the laser beam [66]. Another possibility to obtain the argon metastable atom density distribution is to subtract the LIF image recorded with the blocked laser from the LIF image recorded in the presence of the laser. This approach may be questionable when investigating complex plasmas, due to the fast changes which may happen between the recording of two subsequent images. The results of the laser induced fluorescence experiments are reported in section Ultraviolet spectroscopy A study of the absorption spectra of atomic and molecular gases in the ultraviolet (UV) spectral region, extending between the visible wavelengths of 4 nm and the X-ray wavelengths of 1 nm, can be performed using the UV spectroscopy as a diagnostic technique. The UV spectral region can be divided into the near UV region with wavelengths λ > 2 nm and the vacuum-ultraviolet (VUV) region, having λ < 2 nm [69]. The corresponding photon energies in the UV spectral region range between 3 and 12 ev. The absorption of highly energetic UV photons by atoms or molecules induces photochemical reactions, which may affect the chemical properties of the investigated material. The UV spectroscopy can be, particularly, employed for the investigation of astrophysical (e.g. chemical composition of interstellar media, molecular clouds etc.), atmospheric (e.g. in interaction with solar atmosphere) or environmental phenomena (e.g. combustion) [69]. In the course of this thesis, the UV spectroscopy is applied to investigate the interaction of UV radiation with plasma-suspended nanoparticles grown in the process of plasma polymerization from acetylene monomers. The analysis of the absorption spectrum in the UV region is complementary to the previous analysis of infrared (IR) spectra of dust particles with the 7 central wavelength λ = nm, transmittance T = 93.6 %

56 58 4 Diagnostic techniques same chemical composition [7], which proved to be a suitable astroanalogue [48]. Due to the small wavelengths in the UV spectral region, the scattering of incident UV light on dust particles (I s λ 4 ) should be large compared to the IR spectra. Furthermore, the examination of dust interaction with UV radiation may provide information on some prominent absorption and extinction characteristics, such as the UV bump at nm [71, 72, 73]. For this purpose, an experimental system for the in situ absorption measurements in the near UV and VUV region has been installed and tested. The following section describes in detail the installed experimental setup for UV spectroscopy. Experimental setup The UV spectroscopy is based on the measurement of the intensity of the transmitted radiation I(ν) after passing through a dust cloud and its comparison to the incident radiation intensity I (ν). Thus, the Beer-Lambert s law (4.11) is also used to describe the absorption by the dust could [69]. In typical experimental configurations used for UV and VUV spectroscopy, the incident light radiation from a VUV light source passes through the absorption region and is transferred to a VUV spectrometer for the detection of wavelength and line profile. The dispersed light is detected by a photodetector, such as photographic plate or CCD array. Due to the strong absorption of VUV radiation by air (mostly oxygen), the VUV spectrometry is performed in an evacuated system or in nitrogen atmosphere. Furthermore, the focusing elements (lenses, mirrors) for the VUV spectroscopy have to be carefully chosen, because of the absorption of VUV radiation by most of materials [64]. The VUV spectrometers are usually designed in the Rowland arrangement using a concave diffraction grating as a dispersing element. In this configuration, very good focusing properties are achieved if the elements of the spectrometer are placed on the Rowland circle, with a diameter equal to the curvature radius of the diffraction grating. At its central point, the diffraction grating is positioned tangentially to the Rowland circle, whereas the entrance and exit slit (or detector) of the spectrometer also lie on the Rowland circle [69, 74]. Application of the concave diffraction grating introduces astigmatism as a major abberation of the system. Astigmatism appears as a consequence of the focusing only in horizontal plane, projecting a point into a vertical line. These abberations may be corrected by using specially designed gratings, such as holographic gratings or variable line spacing gratings [75]. A comprehensive study of the vacuum-ultraviolet spectroscopy, with a detailed review of VUV instrumentation (light sources, spectrometers, detectors etc.), is edited by Samson and Ederer [76, 77]. A simplified scheme of the experimental setup applied for the UV spectroscopy in this work is shown in figure 4.1. The system consists of a deuterium lamp used as a light source, a VUV spectrometer with the concave diffraction grating and system for wavelength scan-

57 59 VUV Spectrometer 2 Deuterium Lamp Plasma Cathodeon Deuterium Lamp Power supply C CCD camera Data acquisition Figure 4.1: A scheme of the experimental setup for the ultraviolet spectroscopy, consisting of a deuterium lamp as a light source and a CCD camera as a detector, and the following elements: 1. O- ring; 2. cooling fan on the lamp protective housing; 3. plan-convex lenses; 4. MgF 2 windows; 5. shutter; 6. entrance slit of VUV spectrometer; 7. holographic grating; 8. stepper motor to change wavelength; 9. exit slit of VUV spectrometer; 1. CCD camera adapter wedge; 11. shutter control unit; 12. turbomolecular pump; 13. rotary pump. ning, and a VUV sensitive CCD camera. The VUV light path, from the lamp to the detector, is enclosed and evacuated by a pumping system consisting of a turbo-molecular pump (Pffeifer, Model TMU71P) and a membrane vacuum forepump. The vacuum pressure maintained in the system is about mbar. As a VUV radiation source, a 3-watt Heraeus analytical deuterium VUV lamp (Model J59) is used. The lamp emits a UV continuum spectrum ranging between 112 and 37 nm, with a high intensity between 112 and 16 nm, which can be seen in the spectral response shown in figure The low wavelength of 112 nm is enabled due to the lamp sealed by a magnesiumfluoride (MgF 2 ) window. A Cathodeon deuterium lamp power supply (Model C713) is used for the lamp operation. The deuterium lamp is attached to the vacuum system using an O- ring sealing 8 around the lamp nose. The part of the lamp outside of the vacuum system is enclosed in a metallic housing to protect from the UV radiation emitted into the surrounding atmosphere. The lamp housing is also supplied by a cooling fan, mounted in order to prevent the lamp from overheating. The optical alignment of the deuterium lamp with the entrance slit of the VUV spectrometer is of a great importance for the proper application of the UV and VUV spectroscopy. For this purpose, a deuterium lamp nose is mounted on one end of a metallic tube, having its other end attached to the reactor chamber. The deuterium lamp is positioned at the focal distance 8 Schott Flange 2 (GL 45).

58 6 4 Diagnostic techniques Figure 4.11: The spectral response of the VUV deuterium lamp J59 in the range 1-2 nm. Source: Heraeus Noblelight Analytics Ltd. of a MgF 2 VUV plano-convex lens 9, thus enabling the VUV light collimation. The length of the metallic tube is several times longer than the focal length, providing enough length for the parallel beams of VUV radiation to enter into the discharge chamber. Furthermore, the parallel beams of VUV radiation enter into and leave the discharge chamber through MgF 2 windows, thus transmitting the VUV light of smaller wavelengths. After leaving the discharge reactor, the parallel VUV light beams pass through a second, optically aligned metallic pipe with length of about 1 meter. The VUV radiation is focused onto the entrance slit of the VUV spectrometer by the second MgF 2 VUV plano-convex lens. An additional vacuum compatible shutter 1 is positioned between the metallic pipe and the VUV spectrometer, which has to role to regulate the light transferred to the VUV spectrometer. The shutter is controlled by a shutter driver controller 11, which is connected to the CCD camera. The VUV spectrometer used in the current work is a McPherson Model 234/32 vacuum monochromator with a focal length.2 meter 12. The monochromator is configured to work as a spectrometer by using a CCD array as a detector on the place of the exit slit. The entrance slit is mounted on the entrance of the VUV spectrometer and its opening is regulated by a precision micrometer. In the current configuration, the entrance and exit slit are additionally reversed to enable the proper mounting of camera to the spectrometer. The optical design of the spectrometer is similar to the Seya-Namioka design, however with a deviation angle of θ = 64 degrees, instead of 7 [78]. A good focusing in a large spectral range is achieved by rotating the diffraction grating about the vertical axis through the center of the grating [77]. The diffraction grating used in the VUV spectrometer is a 12 grooves/mm type IV aber- 9 Korth Kristalle GmbH, Model W; f (15nm) = 152 nm, 25±.2 nm ø, R = 73 ± 5 %. 1 Company Uniblitz by Vincent Associates, Model VS14mm shutter, 14 mm aperture. 11 Company Uniblitz by Vincent Associates, Model VCM-D1 single channel shutter driver controller. 12

59 61 ration corrected, master holographic concave grating. The grating is coated by Al/MgF 2, thus suitable for the application in the VUV spectral range. It is positioned in a grating holder with three grating adjustments which enable the grating rotation and its proper optical alignment [78]. The reflection and diffraction of the incident light beam of the wavelength λ on the concave diffraction grating is governed by the grating equation: ± mλ = d(sin α + sin β), (4.32) where α and β are incidence and diffraction angles of the light beam, respectively, measured with respect to the grating normal [75]. The width of a single groove is denoted as d in (4.32). According to the sign convention for incident and reflection angles, the angles α and β have opposite signs if they lie on opposite sides of the grating normal. Following these arguments, the diffraction equation (4.32) may be observed as a function of the constant deviation angle θ = α β(= 64 ) and wavelength-dependent scan angle ϕ(λ) = α + β: ± mλ = 2d cos θ 2 sin ϕ 2. (4.33) From (4.33), it can be seen that the incidence and the diffraction angles depend on the wavelength of the incident light: α(λ) = mλ arcsin 2d cos (θ/2) + θ 2 (4.34) β(λ) = mλ arcsin 2d cos (θ/2) θ 2. (4.35) The rotation of the stepper motor, i.e. the sine driving scanning system provides the change of the angles ϕ, thus the wavelength of the incident light beam. The angular dispersion dβ/dλ and the linear dispersion dl/dλ provide an information on the separation between the diffracted light of different wavelengths [75]: dβ dλ = m d cos β (4.36) dl dλ = Lm d cos β, (4.37) where l is the corresponding arc length of the angle β at radius L. Besides, the reciprocal linear dispersion dλ/dl is often used to describe the dispersion of the spectrometer. For the current experimental conditions, the angular dispersion is dβ/dλ /nm, the linear dispersion is dl/dλ.283 mm/nm, and the reciprocal linear dispersion is dλ/dl 3.5 nm/mm, assuming m = 1, β = 32 and L = 2 mm equal to the nominal focal length of the VUV spectrometer. Taking into account the width of the CCD array placed on the exit slit position in the spectrometer configuration, the portion of the spectrum observable on the chip

60 62 4 Diagnostic techniques can be estimated. For the CCD array with width l CCD = µm= 26.8 mm, a spectrum of = 94.7 nm can be seen. The camera system PIXIS-XO:4B from Princeton Instruments 13 is mounted at the place of the exit slit of the VUV spectrometer and applied as a detecting system. The camera system contains the camera and the power supply. The camera is supplied by a windowless, back illuminated CCD chip without anti-reflection coating, which enables to detect the radiation in X-ray and VUV range with higher sensitivity and higher resolution [79]. The size of the CCD array is pixels, with a pixel size 2 µm, hence with a total image area of mm. The camera is designed for the applications in ultra-high vacuum environment, having the ConFlat Flange and all-metal seals. Furthermore, the application of the vacuum environment allows the thermoelectric air cooling of CCD arrays up to 75 C, which causes a significant reduction of the dark current. The camera control and the image acquisition occurs through a USB 2. interface connection to a computer, which provides the fast readout speeds. The PI Winspec software 14 (V 2.7.2) is used for the control of the image acquisition as well as for the control of the external shutter. In the current experimental setup, the shutter is connected to the camera through a LOGIC OUT connector of the camera. Image focusing on the whole width of the CCD array is improved by using a custom-made adapter wedge between the camera and the exit slit of the spectrometer. The adapter wedge sets the proper angle to match the exit focal plane, leaving.643". As a result, the image on the CCD chip is properly focused on the whole chip length. The experimental results of the UV spectroscopy on nanometer-sized dust particles are reported in chapter Laser light scattering The laser light scattering is a well established imaging technique applied for the investigation of dusty plasmas to observe the dust particle motion. This non-invasive in situ technique is based on the alternation of the laser beam direction and intensity when it strikes a particle. The changes occur due to the combination of reflection, refraction or diffraction of the laser beam, whereas the absorbtion is excluded. Depending on the relation between the size of dust particle and the wavelength of the incident light, three scattering regimes may be distinguished [8]: Rayleigh scattering: the size of the particles is much smaller than the incident beam wavelength r d λ. The scattered irradiance is proportional to I s r 6 p/λ 4. Mie scattering: the size of particles is comparable to the wavelength r d λ. In particular, the Mie scattering is referred to scattering of electromagnetic radiation on the

61 63 Laser Micro Line generator 5 LM (682 nm) Schäfter + Kirchoff GmbH PCO.edge scmos camera (256 x 216 px) PC / Data acquisition CamWare V3.8 AFG Function generator TDS224B Oscilloscope / Synchronization Figure 4.12: Light scattering experimental setup. spherically shaped particles. Due r d λ, the light is actually scattered separately on the smaller, outer parts of the particle. The resulting scattering is a sum of scattering on separate parts of the particle. Fraunhofer diffraction: the size of the particle becomes much larger than the wavelength r d λ. The particle acts as an obstacle, causing light scattering around the object and formation of dark and bright bands, i.e. diffraction pattern. In the present work, the laser light scattering is employed to observe the dynamics of the dust particles during one cycle of their growth and in the pulsed plasmas. The performed measurements provide an insight into the distribution of dust particles in different phases of the dust growth cycle. The maximal radius of the dust particles is estimated to about 7 nm, thus the scattering occurs in the Rayleigh and in the Mie scattering regime. The experimental setup applied for the laser light scattering on dust particles is presented in the following section. Experimental setup Figure 4.12 presents a simplified scheme of the experimental setup employed for the laser light scattering experiments. The particles are illuminated by a solid state laser 15. The laser has a wavelength of 682 nm and an output power of P < 4 mw. The in-built beam shaping optics is used to form the laser sheet with desired fan angle and line width, which illuminates the central region of the discharge perpendicular to the electrodes. The focal length is adjusted manually. 15 Schäfter+Kirchhoff Laser Microline Generator, Model 25CM-66-4-M26-A8-S-2, and Lens Model 5LM8-S325.

62 64 4 Diagnostic techniques The scattered laser light is detected by a CCD camera system at a scattering angle of 9. The camera system consists of a PCO.edge camera with scientific CMOS imaging sensor 16 and the lens system Nikon AF Nikkor 5 mm, f/1.4d. The camera is supplied by a high resolution chip of pixels (pixel size µm). The high resolution, low noise and fast frame rates enable to observe the dust particle dynamics on the sub-micrometer scale. Both camera and laser are synchronized with a trigger signal provided by a function generator 17 and monitored on a digital oscilloscope 18. In the case of continuously driven plasma, the laser is chopped by a trigger signal with a frequency of 1 Hz, whereas the camera is recording with a frame rate of 2 frames per second (2 Hz). Hence, two images are recorded each second: 1. with laser scattering on dust particles, and 2. without laser scattering i.e. only plasma emission. The subtraction of the recorded signals provides the information on the dust distribution without the emission of the surrounding plasma. In the case of the pulsed plasmas at frequency f = 1 Hz and duty cycle 5 %, the laser is pulsed at 5 Hz and the camera at 1 Hz. Such synchronization and triggering of the observed signals provides the dust density distribution in the pulsed plasma. The exact time of the image recording can be set up by delaying the camera signal for an chosen delay time within one pulsing cycle Tektronix AFG Tektronix TDS224B.

63 5 Time resolved electron density in pulsed reactive and dusty plasmas In this chapter, the experimental results on electron densities in low-pressure pulsed capacitively coupled RF discharges are reported. In the introductory section 5.1, the role of electrons and the relation to electron temperature in capacitively coupled RF discharges is described. The following section 5.2 presents a typical time evolution of the electron density during one pulsing cycle. The behavior of electron density in the various gas mixtures, including in the presence of dust particles, is investigated in section 5.3. The final section 5.4 refers to the RF power dependence and the gas mixture dependence of the measured electron densities, observing separately the power-on and the afterglow phase of the pulsed discharge. 5.1 Electron density and electron temperature in capacitively coupled RF discharges Electron density is one of the most important plasma parameters, which can be used to indicate the significant processes in the plasma and to control them. Electrons play an essential role in the discharge, providing a transfer of energy from the external electric field (supplied by a generator and a matching box) to the processing gas [1]. Being the lightest species in the discharge, the electrons absorb energy from the external electric field, get accelerated, and collide with other plasma constituents. Due to the non-elastic collisions of high-energy electrons with atoms or molecules of the processing gas, many processes in plasmas occur, such as ionization, dissociation, or fragmentation of gas neutrals. On one hand, the collisions lead to the efficient maintenance of the discharge (e.g. electron-impact ionization), thus increasing the electron density. On the other hand, the collisions can enhance the formation of reactive species (positive and negative ions, metastable states, radicals), which play an important role in the chemical processes occurring in the discharge. Beside the electron density, the electron temperature has a significant role in the discharge, since it determines the efficiency of different processes in the discharge through the reaction rates. The temperatures of different species in the discharge are determined by the gain of energy from the applied electric field, as well as the energy transfer to the plasma species through elastic and non-elastic collisions, or to the surrounding (radiation, heat transfer to 65

64 66 5 Time resolved electron density in pulsed reactive and dusty plasmas the walls), as previously described in chapter 1. The energy distribution of the electron population in a discharge is described by the electron energy distribution function (EEDF). A majority of electrons in the discharge have energies below the threshold energies for dissociation E diss and ionization E ion of the processing gas, experiencing only elastic collisions with neutral gas. The processes of dissociation or ionization occur due to the electrons with energies belonging to the high-energy tail of the distribution function. The EEDF can be considered Maxwellian, with average electron energy E e related to the effective electron temperature T 19 e by: E e = 3 2 k BT e. (5.1) A better approximation of EEDF in typical non-lte plasmas is obtained from a Druyvesteyn distribution [81]. In this case, a depletion of high-energy tail due to non-elastic collisions is included, which results in more electrons at low energies and smaller number of electrons at high-energy end of EEDF. Both electron density and electron temperature in an RF discharge depend on many different parameters: dimensions of the discharge (electrode size, distance between electrodes), applied RF power and its losses, gas composition, applied pressure, conditions on the chamber walls or wafer surface, instabilities in the plasma and many others. A large number of experimental and theoretical studies have been performed to study the dependence of electron density and electron temperature on the variety of discharge conditions. In a capacitively coupled RF discharge, the dynamics of electrons cannot be separated from the dynamics of the RF sheaths (see chapter 1.2). In the past, several theoretical models (e.g. [1, 57, 82, 83]) have been developed in order to describe the behavior of a CC RF discharge and to determine different plasma parameters. In global, volume-averaged models developed by Lieberman [82, 83], the parameters of a symmetrically driven CC RF discharge are estimated for a set of control parameters (gas pressure, power, frequency, geometry). The control parameters determine the processes which prevail in the plasma (transport of the species in the discharge and their profile). The electron temperature is obtained from the particle balance in a steady-state, i.e. by balancing the number of particles produced in the plasma volume by ionization with the number of particles lost to the walls. It has to be noted that the electron temperature is independent of the particle density, but it depends only on the control parameters. Once the electron temperature is known, the particle (plasma) density can be calculated from the power balance under the steady state conditions: the energy absorbed from the RF excitation has to be in balance with the energy lost in different processes (electron and ion production, collisions and losses to the walls). Knowing the electron temperature and the electron density, the other parameters of the discharge can be estimated, such as ion 19 In the following text, the electron temperature is expressed in electron-volts T e (ev), associated to the electron temperature in Kelvins T e (K) by: k B T e = et e [1].

65 67 bombarding energy, sheath thickness, DC potentials, currents and fluxes. The pulsed RF discharges have been also studied in the past both experimentally (e.g. [84, 85, 86]) and theoretically (e.g. [11, 12, 87]). These investigations show that the efficiency of the production and loss processes in the discharge depend strongly on the pulsing frequency and the pulse length. A global model for pulsed argon discharges, developed by Ashida and Lieberman [11], shows that the choice of the pulsing frequency and the duty cycle can significantly influence the time evolution of electron density and electron temperature. According to this model, the electron density and the electron temperature respond only weakly to the plasma pulsing if the pulsing period is very short. For the longer pulsing periods, the electron density and the electron temperature can reach the steady state conditions during the power-on phase, however, the electron densities may have significantly higher values than in the CW plasmas at the same RF power. The pulsing frequencies and duty cycles applied in this thesis correspond to the latter case. Beside the power modulation, the change in the electron production and loss processes can occur due to the application of the reactive gases and the appearance of dust particles. Many experimental (e.g. [32, 88, 89, 9, 91]) and theoretical (e.g. [54, 88, 9, 92, 93]) investigations have been conducted in order to analyze the behavior of electron density in different kinds of dusty plasmas. Some of these studies are devoted to the explanation of the effects in the dusty plasma afterglow phase, observing different parameters: electron density [32], secondary electron emission [9], residual dust charge [91], dust de-charging [93]. The following sections describe the systematically measured electron densities in pulsed RF plasmas under various discharge conditions. In order to understand better the appearance of the dust particles in the discharge and the corresponding response of the plasma, it is necessary to know and understand the behavior of electron density in non-reactive (argon) plasmas, as well as in the reactive (acetylene-containing) plasmas in which the particles still have not been formed. Beside in various gas mixtures, dependencies of electron densities on applied RF power and change of surface conditions have been observed. The response of the electron density to different conditions at electrode surfaces, caused by the thin film deposition, is described in details in chapter 9. The behavior of electron density at these discharge conditions may provide an insight into the dynamics of pulsed discharges and the processes which are relevant at individual stages of the pulsing cycle. Especially, the afterglow phase of the discharge is important to monitor the loss processes in the plasma, which are otherwise masked by the large production during the power-on phase.

66 68 5 Time resolved electron density in pulsed reactive and dusty plasmas 5.2 Time evolution of electron density during one pulsing period The experimental results in this chapter refer to the electron densities measured in the capacitively - coupled RF plasma pulsed by a frequency of f = 1 Hz and a duty cycle 5%. The corresponding pulsing period T P = 1 ms is divided into two equally long phases: power-on and afterglow phase. The applied pulsing frequency and the duty cycle enable the electron density to reach the steady-state conditions during the power-on phase and to decay to zero density during the plasma afterglow [11]. However, due to the power modulation, short transient turn-on and turn-off periods occur at the beginning of both power-on and afterglow phase [84]. A typical time evolution of the electron density measured by the microwave interferometer in pure argon pulsed plasma is reported in figure 5.1. The argon plasma offers a relatively simple discharge chemistry, providing information about the characteristic phases in the discharge. The measured electron densities correspond to the line-of-sight averaged densities in the central region of the discharge (see section 4.1.1). The electron density n e is determined by the various electron production P e and electron loss L e, which can be summarized by an electron balance equation: dn e dt = P e L e, (5.2) which is valid during the whole pulsing cycle. However, due to different energy input into the discharge during the power-on and the afterglow, the production and loss processes of electrons significantly differ in these two phases. In the power-on, the discharge initially passes through a short, turn-on phase, during which a breakdown occurs [85]. The breakdown is characterized by an exponential growth of electron density and the formation of electrode sheaths. However, during the turn-on phase, the electron density is still small, whereas the electron temperature is characterized by a high "overshoot" value. The "overshoot" of electron temperature is attributed to the absorbtion of the delivered RF power by relatively low number of electrons present in this phase in the discharge [11]. The plasma potential often also experiences an initial overshoot, following the electron temperature. The currents of electrons and ions from the plasma to the powered surfaces initiate the charging of the blocking capacitance in the matching network, i.e. the formation of the DC-bias voltage. During the turn-on phase, the impedance is usually mismatched and the plasma impedance varies until the steady-state condition are reached. The steady-state condition in the power-on phase of the pulsed plasmas is achieved when the rates of electron production an losses balance P e = L e. The behavior of plasma parameters in this phase resembles to their behavior in the continuously driven discharges. The steady-state electron density, denoted as n e in this work, stays approximately constant until the end of the power-on, whereas the electron temperature decreases to a medium steady-

67 69 Argon (P = 2 W) Turn-on Steady-state Turn-off Late afterglow POWER-ON AFTERGLOW Figure 5.1: The characteristic phases in the time evolution of electron density in pure argon plasma pulsed by pulsing frequency f = 1 Hz and 5 % duty cycle. The measurement is performed applying the microwave interferometry. state value [11]. A medium plasma potential is sufficient to prevent the escape of electrons from the plasma [84]. Furthermore, the plasma impedance, predominantly capacitive in its nature (due to the presence of sheaths), is optimally matched with the impedance of the RF generator. The plasma afterglow phase proceeds after the RF power is switched off. The turn-off period begins with a rapid depletion of the high-energy tail of the electron energy distribution function, which occurs at time scales less than 1 µs [94]. The mean electron (and ion) energies decrease in a time scale up to several tens of µs [94]. Consequently, the plasma potential rapidly decreases, following the electron temperature decrease. The decay of electron density happens on longer time scales (several 1 µs). The decrease of electron density is followed by the disappearance of electrode sheaths. The impedance matching is also disrupted during the turn-off phase. It has to be emphasized that in the early phase of the plasma afterglow, the energies of electrons and ions may still be high enough to enable the charge separation and the ambipolar diffusion of electrons and ions. Due to the higher mobility of electrons compared to ions µ e µ i, the ambipolar diffusion coefficient D a is determined by the diffusion coefficient of ions D i and the ratio of electron and ion temperatures [1]: ( D a D i 1 + T ) e. (5.3) T i When the electron density and the electron temperature decrease, the diffusion of electrons

68 7 5 Time resolved electron density in pulsed reactive and dusty plasmas and ions separate and their escape from the discharge enters into a free diffusion regime [91]. After the transient turn-off phase in the plasma afterglow, the discharge enters into a late afterglow phase. The electron temperature has decreased to nearly thermal values (T e T g ), whereas the plasma potential drops, enabling the escape of electrons from the discharge. Thus, only a small electron density can be found in the discharge in the late afterglow. For the appropriate frequencies and duty cycles, the electron density drops to zero. In the scope of this work, it is assumed that the electron temperature T e (t) decays exponentially during the turn-off phase in the plasma afterglow according to: ) T e (t) = T e exp ( tτε. (5.4) Here, T e is the steady-state electron temperature at the end of the power-on phase and τ ε is a corresponding decay time constant in the plasma afterglow. The estimation of electron temperature decay time τ ε is done previously in a Monte-Carlo simulation, applied for the conditions similar to those in these experiments (p = 5 mtorr, f = MHz, initial energy distribution is Maxwellian with 2.15 ev of mean energy in pure argon plasma) [9]. For the electrons with energies larger than 3 ev, τ ε is found to be less than 1 µs, which occurs largely due to the high cross section for elastic scattering, hence the efficient electron energy losses [2]. The time interval [, τ ε ] is denoted as the turn-off phase. During the late afterglow phase (t > τ ε ), it is assumed that electron temperature stays approximately constant with a value T aft. In argon plasma, this value usually lies between the gas temperature T g and.1 ev [95, 96], which has been also used in this work. The decay of electron density in the plasma afterglow can be also approximated by an exponential function with a single decay time constant τ e : ) n e (t) = n e exp ( tτe. (5.5)

69 Electron density in pulsed plasmas with various gas mixtures The electron density is investigated in the pulsed plasmas using various mixtures of argon (gas flow Q = 8 sccm) and acetylene (Q =.5 sccm), while keeping the total gas pressure constant at p = 1 Pa. The density of argon neutral atoms is estimated to: n g = p k B T g m 3, (5.6) where T g = 294 K [67]. The density of acetylene is estimated to n C2 H 2 = m 3. These conditions have been proved as suitable for the production of hydro-carbonaceous dust particles from the acetylene monomers (see section 2.2). The production of dust particles is enhanced by pulsing the plasma at frequencies above 7 Hz for about 3 minutes, in order to obtain the particles with radii up to r d = 5 7 nm. The production of dust particles in argon/acetylene plasma is prevented by applying the pulsing frequency of 1 Hz. Hence, the electron density is measured in 4 mixtures: 1. pure argon plasma, 2. argon/acetylene plasma before the formation of dust particles, 3. argon/acetylene plasma after the formation of dust particles, 4. argon plasma with formed dust particles after evacuating acetylene from the discharge chamber. In the following text, the electron densities in each of the gas mixture will be described and discussed. Pure argon plasma The overall behavior of electron density in the pure argon plasma is described in the previous section 5.2. The balance between electron production and loss processes, described by the balance equation (5.2), determines the electron density in both power-on and afterglow phase. In the pure argon plasma, electrons can be produced in several processes, such the ionization from the ground-state of argon atom, the ionization from excited states of argon atoms, or in the processes of collisions between two argon metastable atoms (metastable pooling). The electrons are lost predominantly through the diffusion to the reactor surfaces (electrodes or walls). The time evolutions of electron densities in the pure argon plasma are presented in figures 5.2 (curves "Argon"). After the plasma ignition, the electron density rapidly increases (rise time in order of 3 µs at P = 2 W), until it reaches a steady-state value (n e = m 3 at P = 2 W). During the plasma afterglow phase, the electron density decays exponentially according to (5.5). The decay time of electron density in pure argon plasma is found to be in

70 72 5 Time resolved electron density in pulsed reactive and dusty plasmas Electron density (1 15 m -3 ) Electron density (1 15 m -3 ) P = 2 W power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust afterglow Time (ms) (a) Electron densities in various mixtures at P = 2 W P = 6 W power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust afterglow Time (ms) (c) Electron densities in various mixtures at P = 6 W. Electron density (1 15 m -3 ) Electron density (1 15 m -3 ) P = 4 W power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust afterglow Time (ms) (b) Electron densities in various mixtures at P = 4 W P = 8 W power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust afterglow Time (ms) (d) Electron densities in various mixtures at P = 8 W. Figure 5.2: Time evolution of electron density in pulsed plasmas ( f = 1 Hz, duty cycle = 5 %) in various gas mixtures: pure argon ( ), argon/c 2 H 2 ( ), argon/c 2 H 2 /dust ( ), and argon/dust ( ). order τ e.5 ms at P = 2 W. The behavior of electron density in the plasma afterglow is treated in more details by the global model presented in chapter 7. It has to be noted, that the electron density in the pure argon plasma may also vary depending on the conditions on the electrode surfaces and the concentration of impurities in the plasma volume. In the case of electrodes covered by a thin film, the electron density keeps its general behavior (figure 5.1). However, the values of steady-state electron density n e in the power-on phase and the electron decay time τ e in the plasma afterglow phase may change depending on the amount of insulating film on electrodes. The effect of the thin film deposition on electron density is in details described and discussed in chapter 9.

71 73 Argon/acetylene plasma An addition of acetylene into the reactor introduces new chemical reactions which can affect the plasma parameters and their dynamics in the discharge. Many numerical models have been previously developed in order to study the plasma chemistry in acetylene containing discharges (e.g. [49, 52, 97]). These models refer primarily to the pathways of the precursor formation in acetylene plasmas and show a great variety of possible reactions between acetylene and high mass molecules created in the polymerization process. Different mechanisms can be responsible for the production and losses of electrons in argon/acetylene plasmas. Beside the production in processes characteristic for pure argon plasmas, electrons can be produced in acetylene-related processes, some of which are listed in table 5.1. Furthermore, the electrons can be lost in processes such as electron attachment by acetylene or other polymer molecules, which can also impact the density of electrons in the discharge. The competition between all these processes, accompanied by the evolution of electron temperature in the discharge, determines the time evolution of electron density in pulsed argon/acetylene plasmas. The experimental results for electron densities in pulsed argon/acetylene plasmas are shown in figures 5.2 (curves "Ar/C 2 H 2 "). It can be noticed that the electron density in the argon/acetylene plasma follows the same behavior as in the pulsed pure argon plasma, although certain changes are observed in both power-on and afterglow phase. In the turn-on phase, increase of electron densities to steady-state values n e occurs in the time scale of 2 µs (at P = 2 W), which is slightly faster than in the pure argon plasmas. Moreover, a small elevation of electron density can be observed in the initial phase before reaching the steady-state values. A similar increase can be noticed in the time evolution of argon metastable densities in argon/acetylene plasmas (figure 6.2). The following mechanism may be responsible for this characteristic. The elevations of both electron and argon metastable densities are probably related to the increased ionization and excitation frequencies, arising from the overshoot of electron temperature in the turn-on phase of the argon/acetylene plasma. The same increase of densities lacks in the pure argon plasmas, in spite of the presence of T e overshoot. The differences between pure argon and argon/acetylene plasmas may lie in the strongly reduced densities of argon metastable atoms in argon/acetylene mixture, encountering due to their quenching with acetylene atoms. In the pure argon plasma, the initial T e overshoot is compensated by both excitation and ionization processes and production of electrons and argon metastable atoms. In contrast to this, due to the strong reduction of Ar m atoms in argon/acetylene plasmas, the T e overshoot is probably more slowly compensated, which is manifested by the slight increase of both electron and Ar m densities before reaching their steady-state values.

72 74 5 Time resolved electron density in pulsed reactive and dusty plasmas Reaction type Reaction Threshold energy (ev) Excitation Ar + e Ar m + e Ionization Ar + e Ar + + 2e C 2 H 2 + e C 2 H e 11.4 C 4 H 2 + e C 4 H e 1.19 C 6 H 2 + e C 6 H e 9.55 Dissociative ionization C 2 H 2 + e C 2 H + + H + 2e 16.5 C 2 H 2 + e C H 2 + 2e 17.5 Dissociative attachment C 2 H 2 + e C 2 H + H 2.75 C 2 H 2 + e H 2 CC 2.74 Quenching Ar m + C 2 H 2 C 2 H + H + Ar - Table 5.1: Examples of collisions in argon/acetylene RF discharges and their corresponding threshold energies [52]. The steady-state electron density in the argon/acetylene plasma is achieved after the balance of electron production and loss processes. The experimental results show an increase of steady-state electron density in argon/acetylene plasma over n e in a pure argon plasma (figure 5.2). However, the ratio between n e in the pure argon and in the argon/acetylene plasma may vary depending on the electrode surface conditions. For instance, for the electrodes covered with a thin film, the steady-state electron density in the pure argon plasma increases (see chapter 9), thus approaching the value of n e in the argon/acetylene plasma. Similar values of the steady-state electron densities in pure argon and argon/acetylene plasma suggest there is a compensation between the processes which involve argon (ionization or metastable pooling) and acetylene. For instance, the production of electrons in metastable pooling reactions is probably strongly reduced due to the decrease of argon metastable densities in argon/c 2 H 2 plasmas. Instead of in these processes, electrons may be produced in the C 2 H 2 -related reactions, some of which require slightly smaller threshold energies than the electron-impact collisions of argon atoms (see table 5.1). However, the electron densities in argon/acetylene plasma are determined also by the rate coefficients of the corresponding reactions and by the densities of other reactants or plasma components. For the accurate determination of electron density, a proper model has to be developed, which would include all the relevant reactions. In the plasma afterglow phase, the electron production processes become smaller due to the rapid decay of electron temperature in the afterglow. Therefore, the loss processes predominantly affect the electron dynamics in the discharge. The experimental results (figure 5.2) show an exponential decay of electron density in the argon/acetylene plasma afterglow according to (5.5). The electron decay time constant τ e in argon/acetylene plasma afterglow exhibits a decrease compared to τ e in pure argon plasma. The faster decay of electron density may be related to the additional electron loss channel due to the presence of acetylene. How-

73 75 ever, the threshold energies necessary for the electron attachment by C 2 H 2 or its products exceed the electron energies available in the plasma afterglow phase [49, 52]. Therefore, the fast decrease of electron density in the plasma afterglow is probably only indirectly related to the presence of C 2 H 2. The reduced electron decay times in the afterglow of argon/acetylene plasmas may be connected to the decreased electron production in the processes related to argon metastable atoms, which are quenched by acetylene (figure 6.2). Argon/acetylene/dust plasma The next investigated mixture is argon/acetylene plasma with nanoparticles formed by plasma polymerization of C 2 H 2 monomers. Although the dust particles represent primarily an electron loss channel, they can be also involved in the electron production through a release of electrons in collisions with ions or metastable atoms. Such electron release may become important in pulsed plasmas, to explain the observed increase of electron density during the dusty plasma afterglow. The experimental results of electron density in argon/ acetylene/dust mixture and the relation to the other gas mixtures are presented in figures 5.2 (curves "Argon/C 2 H 2 /Dust"). The time evolution of electron density in the dust-containing plasmas experiences a significant change compared to the dust-free mixtures. In the turn-on phase of the argon/acetylene/dust mixture, the electron density increases rapidly within the time scale of approximately 1 µs in the turn-on phase, hence faster than in both dust-free mixtures. This may be related to the higher electron temperatures in dusty plasmas, thus enhanced ionization in the discharge. The experimental results show that the steady-state electron densities n e in argon/ acetylene/dust plasma decrease about 6 7 times compared to n e in argon/acetylene plasma and about 4 5 times compared to n e in the pure argon plasma measured under the same discharge conditions, due to the electron collection by dust particles. In order to accurately determine the steady-state electron densities in argon/acetylene/dust plasmas, the chemistry of acetylene-containing discharge has to be combined with the dust-induced processes (collection and release of electrons, ions or radicals from the dust), as well as the high electron temperatures characteristic for dusty plasmas. In the plasma afterglow phase, an increase of electron density is observed immediately after switching the RF power off, which is consistent with the previous findings by Berndt et al. [32, 5]. The maximal electron density is reached after 5 µs of the afterglow, after which the electron density decays exponentially according to (5.5). The density of electrons produced in the afterglow can be up to 5 times higher than the steady-state electron densities n e in the power-on phase (depending on the applied power). Similar to the argon/acetylene plasmas, the decay time of electrons τ e (estimated after the afterglow peak) is shorter than in the pure argon plasmas, indicating the presence of acetylene in the discharge.

74 76 5 Time resolved electron density in pulsed reactive and dusty plasmas Argon/dust plasma The argon/dust mixture is obtained after stopping the acetylene gas flow from the argon/acetylene/dust discharge. In this manner, the plasma chemistry is simplified compared to the acetylene-containing discharges. Still, the presence of dust particles strongly affects the production and loss mechanisms of plasma components, as well as their dynamics. Beside the production and losses of electrons typical for the pure argon plasmas, electrons may be lost due to their collection by dust particles or may be produced by the release of secondary electrons from the dust surface. All these processes are also impacted by the increase of electron temperature, which compensates the losses of free electrons on dust particles. The experimental results of electron densities measured in pulsed argon/dust plasmas are given in figures 5.2 (curves "Argon/Dust"). The overall electron density measured in argon/dust plasmas is significantly reduced compared to other gas mixtures. However, the time evolution of electron density in argon/dust plasmas stays approximately the same as in the argon/acetylene/dust mixture, having a low steady-state density during the power-on phase and an afterglow peak in the plasma afterglow. After the plasma ignition, the rise time of electron density in argon/dust plasma is in the order of 3 µs, which is comparable to the rise time in the pure argon, but slower than in the acetylene-containing dust-free and dusty plasmas. This indicates that the fast rise time is not only due to the increased electron temperatures, but also due to the C 2 H 2 presence in the discharge. The steady-state electron densities in argon/dust plasmas are reduced about an order of magnitude compared to the dust-free mixtures measured under the same discharge conditions. It is clear that the loss of electrons through the collection by dust particles is responsible for the lower electron densities in comparison to the dust-free discharges. As concerning the comparison with argon/acetylene/dust plasma, the steady-state electron density in argon/dust mixture is smaller about 3 4 times. This decrease of n e can be explained by the lack of the electron production in the reactions with acetylene and other reactants in acetylene-containing discharges. The afterglow peak of electron density is observed also in argon/dust plasmas. After switching the RF power off, the electron density increases, reaching a maximal value after about 5 7 µs. Similar to the argon/acetylene/dust plasmas, the maximal value of the afterglow electron density can overcome the steady-state values several times. After the peak, the electron density decays exponentially with a decay time constant τ e according to (5.5). The decay times τ e in argon/dust plasma are higher than in all other mixtures, indicating the slower decay of electrons due to the presence of dust particles. The dust presence causes a decrease of the ion mean free path and the ambipolar diffusion coefficient, finally causing an increase of ion and electron diffusion times to the walls. However, as previously indicated, the

75 77 consequences of the dust presence are also higher electron and gas temperatures, which also affect the densities of other plasma components, such as argon neutral and metastable atoms. Thus, all these parameters and corresponding collision mechanisms have to be taken into account when investigating a dust-containing discharge. The argon/dust plasma afterglow is described by the global model in chapter 7, setting an emphasis on the electron density decay in relation to the other plasma parameters, such as argon metastable density and electron temperature. The slow electron density decay, obtained in the experiments, does not agree with the generally accepted theory of a fast decay of the electron density in the plasma afterglow due to the dust presence, as suggested by Couëdel et al. [91]. Indeed, the dust presence in the discharge affects the reduction of steady-state electron density due to the electron collection. However, a fast decay of electrons in the plasma afterglow is observed only if acetylene is present in a dust-containing plasma. In absence of acetylene, electrons decay significantly slower, even in dusty plasmas. 5.4 Power dependence of electron density The change of applied RF power is generally not reflected on the change of the electron temperature, but rather on the change of the plasma density, as explained in section 5.1. In CWdriven discharges, an increase of the applied RF power implies the increase of the total energy available in the discharge for the dissociation and ionization processes, consequently leading to the increased electron (plasma) density in the discharge. For the same reason, an increase of electron density is expected in the power-on phase of the pulsed discharge. However, the increase of electron density may cause enhanced losses in the processes such as diffusion to the walls or collisions with other plasma components, which may have a strong effect on the dynamics of electrons during the plasma afterglow. The electron loss processes may become even higher, if reactive gases or dust particles are present in the discharge. The collisions between these additional plasma components with the increased number of electrons (caused by the RF power increase) may also enhance the electron losses and impact the overall plasma dynamics. This section regards the response of electron density in the pulsed RF plasmas with various gas mixtures to the change of the applied RF power. The waveforms of the electron densities, previously presented in figure 5.2, are plotted again in figure 5.3 in a function of the increasing RF power. These graphs enable to observe the time evolutions of electron densities in different gas mixtures in a better resolution. The effect of the increased RF power are followed in the power-on and in the afterglow phase of the discharge. These phases are characterized by different electron temperatures, thus production and loss processes which govern the electron behavior.

76 78 5 Time resolved electron density in pulsed reactive and dusty plasmas Electron density (1 15 m -3 ) Argon P = 1 W P = 2 W P = 4 W P = 6 W P = 8 W power-on afterglow Time (ms) Electron density (1 15 m -3 ) power-on afterglow Time (ms) (a) Power dependence of electron density in pure argon plasma. (b) Power dependence of electron density in argon/ acetylene plasma. Electron density (1 15 m -3 ) Argon / C 2 H 2 / Dust power-on P = 2 W P = 4 W P = 6 W P = 8 W afterglow Time (ms) (c) Power dependence of electron density in argon/ acetylene/ dust plasma. Electron density (1 15 m -3 ) Argon / C 2 H 2 Argon / Dust power-on afterglow P = 1 W P = 2 W P = 4 W P = 6 W P = 8 W P = 2 W P = 4 W P = 6 W P = 8 W Time (ms) (d) Power dependence of electron density in argon/ dust plasma. Figure 5.3: Time evolution of electron density in various mixtures of pulsed plasmas ( f = 1 Hz, duty cycle = 5 %) with the increasing power: P = 1 W ( ), P = 2 W ( ), P = 4 W ( ), P = 6 W ( ), and P = 8 W ( ). Power-on phase For the pulsing frequencies and the duty cycles applied in this work, the electron density reaches its steady-state value n e within 1 ms after the plasma ignition, regardless of the gas mixture and the applied RF power. Moreover, the steady-state electron densities n e grow almost linearly with the applied RF power in each of the gas mixtures, which can be seen in figure 5.4(a). In the pure argon plasma, the linear behavior of the steady-state electron density is an expected result. For instance, a nearly linear electron density increase with the applied RF power is also calculated for the present discharge conditions according to a self-consistent

77 79 Electron density (1 15 m -3 ) Power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust Power (W) (a) Steady-state electron density n e in the power-on phase. Electron decay time (ms) Afterglow Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust Power (W) (b) Electron decay time τ e in the plasma afterglow. Figure 5.4: The dependence of steady-state electron density n e and electron decay time τ e on the applied RF power in different gas mixtures. non-homogeneous model for CC RF discharges, developed by Lieberman and Lichtenberg [1]. A similar increase of electron density has been reported by Overzet and Hopkins in a comparative study performed in a Gaseous Electronics Conference reference cell [98], where the electron densities in argon plasma are measured by microwave interferometer and Langmuir probe. In [98], the linear dependence of the electron density on the applied RF power is related to the linear extension and contraction of the electrode sheath, which actually controls the power input into the discharge and the electron heating. In [99], Godyak et al. show a linear increase of the plasma density with respect to the discharge current for an argon discharge in α mode. A linear increase of the steady-state electron density with applied RF power is observed also in other acetylene-containing or dust-containing gas mixtures (figure 5.4(a)). Thus, both processes of electron production and electron losses are affected by the increase of RF power, in spite of the presence of highly reactive acetylene or the dust particles, finally resulting in the linear increase of the steady-state electron densities with the power. In all of the applied gas mixtures, a slight deviation of the linearity is observed at higher powers, resulting in smaller electron densities than the expected ones. If this characteristic would be related to the discharge transition from α γ mode, characteristic for the capacitively coupled discharges at increased RF powers, an abrupt increase of the electron density would have been seen [99]. However, the experimental results show a slight decrease of n e. Hence, this feature is probably related to some other mechanism. In dusty plasmas, one of the possible processes responsible for the reduction of steady-state electron densities may be a redistribution of dust particles in the plasma volume at higher powers (explained in the "Plasma afterglow" of this section). The change of the dust distribution profile in the

78 8 5 Time resolved electron density in pulsed reactive and dusty plasmas plasma bulk may influence on the metastable production, resulting in the similar saturation of the steady-state metastable density observed at higher powers in dusty plasmas (see section 6.2.3). Hence, due to the reduced metastable densities, the density of electrons produced in the metastable-metastable collisions may be also reduced, finally leading to the reduction of steady-state electron densities at higher powers. Another possible mechanism may be a reduced dissociation of acetylene observed at higher powers, which may influence the electron production in acetylene-associated reactions. Plasma afterglow The response of the electron decay time τ e on the increase of the RF power differs depending on the gas mixtures. In general, the electron decay time τ e is decreasing with power increase in argon and argon/dust discharge, whereas it is slowly increasing in the gas mixtures which contain acetylene: argon/acetylene and argon/acetylene/dust, which can be seen in figure 5.4(b). Similar power and gas mixture dependencies are observed for the decay time of argon metastable atoms performed under the same discharge conditions (figure 6.4(b)). In the afterglow of the pure argon plasma, the electrons decay mainly due to the (ambipolar and free) diffusion to the walls, but also due to the collisions with other plasma components. The experimental results show a faster decay of electron density with an increase of RF power, thus smaller electron decay times τ e (figure 5.4(b)). Assuming the electron temperature is independent on the applied power, as well as the gas temperature in the discharge, the diffusion coefficient and the diffusion frequency of electrons should also stay unchanged after the increase of the RF power, according to (5.3). Thus, the faster electron decay occurring after the RF power increase is probably related to the enhanced electron loss rate in collisions with other plasma components (neutrals or metastable atoms). Besides, electrons may collide with impurities, such as hydrocarbon film, dust residues from the reactor walls/electrodes or oxygen-rich impurities originating from the reactor cleaning. At higher RF powers, the sheath voltage and the ion bombardment energies are increasing, causing a release of impurities from electrodes and enhancing their collisions with electrons. More results on the effect of impurities on the plasma parameters are presented and discussed in chapter 9. In argon/dust mixtures, the electron decay time τ e is generally longer than in a dust-free plasmas due to the presence of dust particles as additional collision partners of electrons and ions in the discharge, i.e. a decrease of mean free paths and diffusion coefficients. With an increase of RF power, the electron decay times τ e are decreasing, similarly to the pure argon plasma. Hence, the increased collisions of electrons with plasma components, including ions, metastable atoms, and dust particles, are probably responsible for the enhanced electron loss rate, causing the faster decay of electrons at higher powers. In the gas mixtures containing acetylene, regardless of the dust presence, the increase of electron decay times τ e with the RF power is observed, indicating their slower decays at higher powers. It can be also noticed that the electrons decay slower (with longer τ e ) in

79 81 argon/acetylene/dust, which is consistent with the conclusions previously set out for the argon/dust mixture. The behavior of electron density decay τ e in acetylene-containing plasmas can be associated to the decay of argon metastable density τ m under the same discharge conditions, showing the same rising tendencies with RF power (figure 6.4(b)). The increase of the applied RF power has also a strong influence on the distribution of dust particles in the plasma volume. The peak of electron density in the plasma afterglow phase can serve as a probe to follow the change in the dust particle distribution. The effect of the increased RF power on dust distribution is pronounced in argon/dust mixtures, where no additional acetylene precursors are supplied to the reactor. In argon/dust plasma, the afterglow peak of electron density is rapidly disappearing at higher powers. For instance, at 8 W the afterglow peak is disappearing already 1 s after changing the pulsing frequency from 8 to 1 Hz, after which the steady state electron density increases and the behavior of the electron density is the same as in a dust-free discharge. At smaller powers, this transition is slower and dust disappears from the central region after approximately 2 minutes (at P = 1 W). Hence, the distribution profile of electrons, metastables and ions is influenced by the power input. The dust disappears from the center of the discharge faster at higher powers, being dragged to the electrodes and staying trapped in the vicinity of electrodes (void formation). The increase of the ion drag force with power may be responsible for the fast disappearance of the dust from the center of the discharge, while the electrostatic force keeps them close to electrodes. This behavior is one of the indicators that the dust particle distribution is non-uniform in the plasma volume when the discharge conditions change, which can also significantly influence on the dynamics of plasma parameters, especially on electron density and electron temperature.

80

81 6 Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms This chapter reports the experimental findings on the density of argon metastable atoms in the 3 P 2 state. The first section 6.1 gives a review of the electronic configuration of argon atom and corresponding energies, and emphasizes the importance of the argon Ar m ( 3 P 2 ) metastable atom in the dust-containing discharges. The second section 6.2 shows the time evolutions of argon metastable densities in pulsed RF plasmas under different discharge conditions, including a power dependence in argon/acetylene gas mixtures before and after the formation of nanoparticles. In section 6.3, a spatial distribution of Ar m ( 3 P 2 ) metastable atoms during a cycle of the nanoparticle formation in a CW-driven argon/acetylene plasma is described. 6.1 Argon metastable states In the plasma processes, various mechanisms may induce the transition of a valence electron from the outermost shell of an atom or a molecule into a higher energetic state. These electronic transition occur radiatively or non-radiatively. In the radiative transitions, the atom or molecule interacts with an electromagnetic radiation, causing an electronic transition due to the absorption or emission of a photon with the appropriate frequency and wavelength. The probability of the electronic transition is determined by selection rules [1], which define the more probable or allowed transitions. The energy levels for which the transitions are allowed are called resonance levels. The transitions for which the selection rules are not satisfied are called forbidden transitions. These transition may occur, but their transition probability is much lower than for allowed transitions. The corresponding energy levels from which the transitions are forbidden are called metastable states, and the atom in such an excited state is a metastable atom. Metastable states cannot (spontaneously) decay to a lower energy level by an emission of radiation, or cannot be reached from a lower level by absorption. Due to the low transition probability, the average lifetime of the metastable state may become very long and can be in the order of seconds. The comparison of average lifetimes of metastable states ( seconds) and nonmetastable states ( 1 8 s) suggests that the metastable atoms have a significant role in the plasma processes, due to their high population densities and high internal energies. The most probable radiative transitions are electric dipole transitions, occurring when the 83

82 84 6 Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms LS Paschen J i J f Radiative lifetime [11] 3 P 2 1s s 3 P 1s 3 >1.3 s 3 P 1 1s ns 1 P 1 1s ns Table 6.1: Measured lifetimes of argon 4s states [11]. J i and J f are the total angular momenta for initial and final state in the transition process, respectively. wavelength of electromagnetic radiation is very large compared to the size of an atom. According to the selection rules for the electric dipole transition, the transition is allowed if there is a change in the total angular momentum quantum number J accompanied by the change in the parity of the wavefunction [1]: J =, ±1 (but is not allowed) (6.1) l = ±1 Non-radiative transitions can happen due to the collisions between atoms and molecules. Such transitions do not have to obey selection rules. In the plasma processing technologies, argon is commonly used as a carrier gas due to the chemical inertness, availability and relatively cheap separation process. In the ground state, argon has 8 valence electrons completely filling its outermost shell. In plasma processes, electronic transitions between 2 excited configurations prevail, 3p 5 4s 1 (marked as 4s) and 3p 5 4p 1 (marked as 4p). The 4s manifold consists of 4 possible energetic levels indexed as 1 P 1, 3 P, 3 P 1 and 3 P 2, which lie more than ev above the ground level. The 4p manifold consists of 1 possible energetic levels, 1 S, 1 D 2, 3 S 1, 3 P,1,2 and 3 D 1,2,3, having the energies approximately ev above the ground state. The ionization energy of an argon atom is E ion = ev. Radiative transitions from the state 3 P 2 with J = 2 (1s 5 in Paschen s notation) and the state 3 P with J = (1s 3 in Paschen s notation) to the ground level of argon atom (J = ) are forbidden, according to the selection rules (6.1), hence these are metastable states. The other two states 1 P 1 (1s 2 ) and 3 P 1 (1s 4 ) in the 4s manifold are resonance states. The measured radiative lifetimes of the 4s energy levels are compared in table 6.1. It can be seen that the radiative lifetimes of metastable states are significantly longer than the lifetimes of resonance states, qualifying the metastables as long-living states. Nevertheless, the lifetimes of resonance states may be prolonged by radiation trapping, reaching the lifetimes of metastables states in systems with high ground-state density [11]. The most populated excited state for the argon atom is the Ar m ( 3 P 2 ) metastable state. Argon metastable atoms have been used as a tool for the investigation of different physical

83 85 properties in various discharge configurations. Due to the long lifetimes of metastable atoms, their velocities in the discharge are comparable to the velocities of the ground-state gas atoms, and Ar m ( 3 P 2 ) atoms can be used for the measurement of neutral gas temperatures from the Doppler width [66, 67]. Excited states are often not included into the global model of investigated discharges [11, 12], although they can be a significant participant in chemical reactions and collisional processes due to high internal energy of ev. This is of particular importance in plasmas containing dust particles. In a study by Do et al. [13], argon metastable atoms are applied to investigate the dust growth in hydrocarbon-containing continuously driven plasmas. The study of pulsed RF discharge, conducted by Stefanović et al. [67], described the argon Ar m ( 3 P 2 ) metastable atom as an excellent probe for the dust particle formation. In the scope of this thesis, the impact of argon Ar m ( 3 P 2 ) metastable atoms on the overall dynamics of pulsed RF discharges is further investigated. It will be shown that Ar m ( 3 P 2 ) metastable atoms are not only the "silent bystanders" in the discharges, but they actively participate in the plasma processes and take the responsibility for specific dynamics of other charged species in dusty plasmas. 6.2 Time-resolved density of argon metastable atoms in pulsed non-reactive and reactive plasmas In order to investigate the role of argon metastable atoms Ar m ( 3 P 2 ) and to find the correlation with other plasma parameters in pulsed RF plasmas, the argon metastable density is measured by laser absorption spectroscopy (section 4.2.1) simultaneously to the electron densities described in chapter 5. The experimental conditions are described in sections 5.2 and 5.3. The argon metastable density is examined under various discharge conditions, changing the gas mixtures and the applied RF power Time evolution of argon metastable densities during one pulsing period The following section presents the time evolution of the argon metastable atoms during a single pulse cycle ( f = 1 Hz, duty cycle = 5 %) in the pure argon plasma, correlating it to the behavior of the electron density measured under the same discharge conditions, reported in section 5.2. A typical time evolution of the argon metastable Ar m ( 3 P 2 ) density in the pure argon plasma is presented in figure 6.1. The applied pulsing frequency and the duty cycle enable the metastable density to reach the steady-state conditions during the power-on phase, and to approach zero density during the plasma afterglow. The power modulation causes the transient turn-on and turn-off intervals at the beginnings of the power-on and afterglow phases, respectively. In these initial phases, the electron temperature is significantly changed, inducing modifications in the metastable production and loss processes, as well as in their dynamics in the discharge.

84 86 6 Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms Argon (P = 6 W) Turn-on Steady-state Turn-off Late afterglow POWER-ON AFTERGLOW Figure 6.1: The characteristic phases in the time evolution of the argon metastable density in a pure argon plasma pulsed with a frequency of f = 1 Hz and 5 % duty cycle. The measurement is performed applying laser absorption spectroscopy. The density of argon metastable atoms during the whole cycle of pulsed plasma is determined by different production P m and loss L m processes of metastable atoms, according to the following balance equation: dn m dt = P m L m. (6.2) The dominating production mechanism of Ar m ( 3 P 2 ) states is direct electron-impact excitation from the ground state of argon atoms, followed by electron-impact de-excitation from higher energy states. The destruction of argon metastable atoms is mostly related to collisions with the background gas or impurities and losses to the walls (chapter 7). In the transient turn-on phase, occurring immediately after the plasma ignition, the production of argon metastable atoms is initiated by the increase of electron temperature and electron density. Because of the rapid overshoot of electron temperature expected in the turnon phase of a discharge (see section 5.2), the production of argon metastable atoms in direct electron-impact excitation of the argon ground-state atoms may be enhanced. However, due to the still relatively small electron density, the rise of argon metastable density is not as rapid as the electron temperature, but it rather follows the slower increase of electron density. The steady-state conditions are achieved within the first 1 2 ms after the plasma ignition, resulting in the constant argon metastable densities n m until the discharge is turned off. Hence, the production of argon metastable atoms by the electron-impact excitation and de-excitation is, in the steady-state, balanced by their losses in collisions with other plasma components or diffusion to the walls.

85 87 In the plasma afterglow phase, the production of metastables is discontinued and the metastable dynamics is governed by the loss processes. Similarly to electrons, the argon metastable atoms cannot follow the rapid decay of electron temperature during the turn-off phase according to (5.4), but their decay is correlated to the slower decay of other plasma components (electrons and ions). Moreover, the argon metastable atoms decay with longer decay times than electrons. Consequently, some residual argon metastable atoms can be found also in the late afterglow phase, resulting in a non-zero metastable density, in spite of the low electron temperatures. Similar to electron densities, the decay of argon metastable density during the afterglow phase may be approximated by an exponential function: where τ m is the corresponding metastable decay time. ( n m (t) = n m exp t ), (6.3) τ m Argon metastable density in pulsed plasmas with various gas mixtures Figure 6.2 reports the argon metastable densities measured in pulsed plasmas with different gas mixtures: pure argon, argon/acetylene, argon/acetylene/dust and argon/dust. It can be seen that the application of different gas mixture induces differences in the time evolution of the argon metastable density throughout the whole pulse cycle. An increase of the RF power induces an increase of the metastable densities in all of the applied gas mixtures, nevertheless keeping their mutual relationships. In this section, the time evolutions of argon metastable densities in different gas compositions are described, followed by a discussion of the possible production and loss processes which may influence the metastable densities and dynamics in a pulsed RF discharge. Pure argon plasma The general behavior of the time evolution of argon metastable densities in the pure argon plasma has been described in the previous section As already mentioned, in the relatively simple chemistry of pure argon plasmas, argon metastable atoms are predominantly produced in excitation processes from the ground-state argon atom or in the de-excitation from the resonance states (4s or 4p manifolds). Several mechanisms may induce their disappearance from the discharge: diffusion to the walls, electron-induced excitations to higher energy resonant states or ionization, and metastable-metastable collisions (see table 7.2 in chapter 7). The time evolution of the argon metastable density in the pure argon plasma is compared to the other gas mixtures which contain reactive gases or/and dust particles in figure 6.2 (curves "Argon"). The rise time of metastable densities after the plasma ignition is about 33 µs (at

86 88 6 Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms Metastable density (1 15 m -3 ) P = 2 W power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust afterglow Time (ms) Metastable density (1 15 m -3 ) Time (ms) (a) Argon metastable densities in various mixtures at P = 2 W. (b) Argon metastable densities in various mixtures at P = 4 W. Metastable density (1 15 m -3 ) P = 6 W power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust afterglow Time (ms) Metastable density (1 15 m -3 ) P = 4 W power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust afterglow Time (ms) (c) Argon metastable densities in various mixtures at P = 6 W. (d) Argon metastable densities in various mixtures at P = 8 W P = 8 W power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust afterglow Figure 6.2: Time evolution of argon metastable densities in pulsed plasmas ( f = 1 Hz, duty cycle = 5 %) in various gas mixtures: pure argon ( ), argon/c 2 H 2 ( ), argon/c 2 H 2 /dust ( ), and argon/dust ( ). P = 2 W), which is in the same order of magnitude as for electron densities under the same discharge conditions (figure 5.2). After the balance of production and loss processes, the steady-state conditions are achieved, resulting in a steady-state metastable density of n m = m 3 (at P = 2 W). In the pure argon plasma afterglow, the argon metastable atoms decay from the discharge volume according to (6.3). The decay constant of metastable atoms is found to be in the range τ m = 1 2 ms, thus it is slower than the decay of simultaneously measured electrons. Taking into consideration the diffusion length and the diffusion coefficient for metastable atoms Ar m ( 3 P 2 ), D m /n g [m 1 s 1 ] [14], the diffusion frequency is in order of 225 s 1. The corresponding decay time of metastable atoms due to the diffusion ν m,di f f

87 89 is about 4.5 s, which is significantly longer than the measured metastable decay time τ m in the plasma afterglow. Besides, the two- and three-body collisions of metastable atoms with argon ground-state atoms contribute negligibly to the decay time because of the significantly smaller collision frequencies (ν 2b K 2b n g = 5.67 s 1 and ν 3b = K 3b n 2 g =.85 s 1 ) 2. Thus, probably the other mechanisms, such as electron-impact collisions or metastable pooling, impact on the decay of metastable atoms from the discharge volume during the plasma afterglow. The possible metastable loss mechanisms are examined by the space-averaged global model for the plasma afterglow in chapter 7. The electrode surface conditions may also impact the steady-state metastable density and metastable decay time in the plasma afterglow, inducing an increase of metastable density in the case when hydrocarbon film covers the electrodes. This process is investigated and discussed in details in chapter 9. Argon/acetylene plasma After adding the highly reactive acetylene into the discharge reactor, the argon metastable density retains the general behavior during one pulsing cycle as in the pure argon plasmas in figure 6.1, having the rise up to steady-state values in the power-on phase and the exponential decay during the plasma afterglow according to (6.3). However, from the waveforms shown in figure 6.2 (curves "Argon/C 2 H 2 "), it can be noticed that both steady-state metastable density n m and metastable decay time τ m experience significant changes in comparison to the ones in pure argon plasmas. These changes are induced by the efficient quenching of argon metastable atoms by acetylene molecules. Moreover, the main production mechanism of argon metastable production, the electron-impact excitation from the ground-state, is competing with the electron-induced excitation or ionization of C 2 H 2, finally leading to the decrease of argon metastable densities in the whole pulsing cycle. In the turn-on phase after the plasma ignition, the initial rise of argon metastable density in the argon/acetylene plasma occurs in the time scale of less than 1 µs, about 3 times faster than in the pure argon plasma. An initial overshoot of argon metastable density can be seen in the turn-on phase of the discharge, similarly to the overshoot of electron density in argon/acetylene plasma (figure 5.2). As previously proposed in section 5.3, these features may be related to the overshoot of the electron temperature immediately after the plasma ignition. The T e -overshoot enhances the electron and metastable production processes, resulting in slightly higher metastable production than losses by acetylene quenching, finally leading to the small elevation of argon metastable density over its steady-state value. After setting the equilibrium between the production and losses of metastable atoms, the metastable density obtains a steady-state value n m. The experimental results show an orderof-magnitude decreased n m compared to the pure argon plasma (n m m 3 at P = 2 Coefficients K 2b = m 3 s 1 and K 3b = m 6 s 1 are taken from Tachibana [15].

88 9 6 Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms 2 W). As previously mentioned, the high losses of metastable atoms arise from their quenching by acetylene present in the discharge. The metastable loss rate in acetylene quenching may be estimated to ν q = k q n C2 H s 1, with the quenching rate coefficient k q = m 3 s 1 [16]. Hence, estimated time of metastable losses in acetylene quenching is about 12 µs. However, not only acetylene present in the discharge, but also the acetylene ions or high-mass hydrocarbon molecules, created in the acetylene polymerization, may impact the losses of metastable atoms and induce their low steady-state values. In the argon/acetylene plasma afterglow, the metastable density decays faster than in the pure argon plasma, with the decay times τ m <.5 ms. The measured decay times τ m are still significantly higher than the predicted time of metastable loss in acetylene quenching (about 12 µs). It is probably not only acetylene, but also other hydrocarbon products which cause the fast decay of metastables in acetylene-containing discharges. A high acetylene dissociation (up to 96 %) is confirmed by monitoring hydrocarbon concentrations simultaneously by mid-infrared laser absorption spectroscopy and Fourier transform infrared spectroscopy on the present experimental setup [17]. Therefore, the fast decay of metastable density in the argon/acetylene plasma is probably related to the collisions of metastable atoms with the products of acetylene-related reactions. Argon/acetylene/dust plasma The increase of electron temperature in dusty plasmas has a significant impact on the production processes of argon metastable atoms in the discharge, as well as their distribution (presented in section 6.3). In addition to the metastable losses characteristic for the pure argon plasma, the presence of acetylene and dust particles may impact the dynamics of argon metastable atoms in the pulsed discharge. However, the general behavior of argon metastable densities in argon/acetylene/dust plasmas (curves "Argon/C 2 H 2 /Dust" in figure 6.2) follows the same time evolution as in the pure argon plasmas (figure 6.1). The turn-on phase of argon metastable density in a argon/acetylene/dust mixture is characterized by a rise time of approximately 2 µs (at P = 2 W), about two times slower than the rise time of the corresponding electron density. Compared to the pure argon plasmas (t rise 33 µs), the metastable rise time in argon/acetylene/dust is larger, due to the metastable quenching by acetylene. In comparison to the argon/acetylene plasmas (t rise 1 µs), this rise time is smaller, because the enhancement of metastable production in dusty plasmas. The steady-state argon metastable density n m is strongly increased in argon/acetylene/ dust: for a factor of 1 compared to pure argon and for a factor of 2 compared to the argon/acetylene mixture. This can be correlated to the strong electron temperature increase in dusty plasmas and the enhancement of the metastable production processes, although in this

89 91 mixture metastable losses in quenching by acetylene might still be high. Moreover, the change of the discharge regime due to the dust presence (α γ transition), causing the spatial redistribution of excitation zones to the whole discharge volume, may be also responsible for the strongly increased argon metastable density. The latter effect will be shown in section 6.3. In the afterglow phase, no peak of argon metastable density is found, in contrast to the electron density in dusty plasmas. In argon/acetylene/dust mixtures, the argon metastable density decays with time constants τ m <.7 ms, i.e. significantly faster than in the acetylenefree discharges. However, the presence of dust particles induces a slightly slower decay time than in the argon/acetylene plasmas under the same conditions. A possible reason for this effect is a decrease of the mean free path of metastable atoms due to the collisions with dust particles in the discharge volume. Argon/dust plasma The actual effect of dust particles on argon metastable density may be observed in the argon/dust mixture, after evacuating acetylene from the discharge. In this manner, the losses of metastable atoms in quenching by acetylene are avoided, inducing a large increase of the metastable density over the whole pulsing cycle. The experimental results of argon metastable densities in argon/dust plasmas are presented in figure 6.2 (curves "Argon/Dust"). The metastable density in argon/dust plasma rises slowly in comparison to other gas mixtures (t rise 8 µs). The metastable rise is also slower than the corresponding rise of electron density in the turn-on phase (about 3 µs). The steady-state metastable density n m of the argon/dust plasma is increased by a factor of 1 compared to the pure argon, which is an expected result arising from the electron temperature increase in dusty plasmas. Compared to the argon/acetylene/dust mixture, n m is about 5 times higher in argon/dust, due to the lack of acetylene and decreased quenching rates. Moreover, the excitation zone is spread over the whole discharge volume, contributing to the large number of metastables produced in the argon/dust mixture. In the plasma afterglow, the metastable atoms decay from the discharge with time constants τ m 1.25 ms. These times are about the same order of magnitude as τ m in pure argon plasma, although having smaller values. This effect might be related to the collisions of metastable atoms with dust particles, with a metastable-dust collision frequency ν md = K md n d (K md = πr 2 d v T d ). Assuming spherical dust particles with r d 5 1 nm, dust temperature T d = T g = 366 K [67], and density n d = m 3, the collision frequency varies between ν md s 1. The corresponding lifetimes (between 1.4 ms and 6 ms) suggest that metastable-dust collisions might be a responsible for the decay of metastable densities in the argon/dust plasma. However, the metastable-dust collisions may effect less on the metastable

90 92 6 Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms decay time, due to the dependence of ν md on dust size or density. Besides the dust particles, hydrocarbon impurities sputtered from the electrodes may influence the metastable decay time. The individual metastable loss processes in the argon/dust afterglow are considered in the global model presented in chapter Power dependence of argon metastable densities Similar to the electron densities (section 5.4), an increase of the applied RF power leads to changes in production and loss processes of argon metastable atoms in the discharge. The production of metastable atoms is predominantly enhanced due to the increase of electron densities with RF power, thus the corresponding electron-induced collisions. However, the increased electron densities may also induce the decrease of argon metastable density through the non-radiative processes, such as excitation to resonant 4s or 4p levels, or ionization. In this section, the possible processes inducing the change of the metastable dynamics with the increase of RF power are discussed. The time evolutions of metastable densities at different applied RF powers are presented in figure 6.3 for each of the investigated gas mixtures. The power-on and the afterglow phase are separately discussed. The steady-state metastable densities n m in the power-on phase and the metastable decay times τ m in the afterglow are presented as functions of RF power in figures 6.4. Power-on phase The steady-state metastable density n m as a function of RF power depends on the applied gas mixture. In the dust-free discharges (argon and argon/acetylene), n m is increasing almost linearly with the power (figure 6.4(a)), but with smaller rates than the corresponding electron densities (figure 5.4(a)). The slow increase of n m with the applied power is probably a consequence of the competition between production and loss of metastable atoms in electron-impact collisions. At lower powers, n m in the pure argon plasma is an order of magnitude higher than in the argon/acetylene plasma. After increasing the power, the difference factor becomes lower (about 2.7 at P = 8 W), which may be due to the faster dissociation of acetylene at higher powers [67]. In dusty plasmas (argon/acetylene/dust and argon/dust), a linear increase of the steadystate metastable density is observed at smaller powers (P < 4 W), whereas it approaches a saturation level at higher powers (figure 6.4(a)). A possible mechanism which induces the saturation of steady-state metastable density might be a redistribution of dust density in the plasma bulk at higher powers, as previously proposed in section 5.4. Plasma afterglow The metastable decay times τ m in the plasma afterglow as a function of RF power in various gas mixtures are reported in figure 6.4(b). It can be noticed that the power dependencies of

91 93 Metastable density (1 15 m -3 ) Argon power-on afterglow P = 1 W P = 2 W P = 4 W P = 6 W P = 8 W Time (ms) (a) Power dependence of the argon metastable density in pure argon plasma. Metastable density (1 15 m -3 ) Argon / C 2 H 2 / Dust power-on P = 1 W P = 2 W P = 4 W P = 6 W P = 8 W afterglow Time (ms) (c) Power dependence of the argon metastable density in argon/acetylene/dust plasma. Metastable density (1 15 m -3 ) Argon / C 2 H 2 power on P = 1 W P = 2 W P = 4 W P = 6 W P = 8 W afterglow Time (ms) (b) Power dependence of the argon metastable density in argon/acetylene plasma. Metastable density (1 15 m -3 ) Argon / Dust power-on P = 2 W P = 4 W P = 6 W P = 8 W afterglow Time (ms) (d) Power dependence of the argon metastable density in argon/dust plasma. Figure 6.3: Time evolution of the argon metastable density in various mixtures of pulsed plasmas ( f = 1 Hz, duty cycle = 5 %) with increasing power: P = 1 W ( ), P = 2 W ( ), P = 4 W ( ), P = 6 W ( ), and P = 8 W ( ). τ m have a similar behavior as the corresponding electron decay times τ e (figure 5.4(b)) in particular mixtures. In acetylene-free mixtures (pure argon and argon/dust), the metastable decay time τ m decreases with an increase of the RF power, i.e. the metastables are decaying faster from the discharge. The fast metastable decay in both mixtures occurs probably due to the increased densities of electrons and metastable atoms with the power, which cause higher metastable losses in non-elastic collisions between metastables and electrons or dust particles. In the mixtures which contain acetylene (argon/acetylene and argon/acetylene/dust), the

92 94 6 Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms Metastable density (1 15 m -3 ) 3 Power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust Power (W) (a) Steady-state argon metastable density n m in the power-on phase. Metastable decay time (ms) 2.5 Afterglow Argon Argon / C 2. 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust Power (W) (b) Metastable decay time τ m in the plasma afterglow. Figure 6.4: The dependence of steady-state argon metastable density n m and metastable decay time τ m on the applied RF power in different gas mixtures. decay time of metastable density becomes longer after the increase of RF power. This might be correlated to the increased dissociation of acetylene with RF power, leading to the reduced quenching rate of metastable atoms by acetylene, hence an increase of the corresponding metastable lifetimes.

93 Space resolved densities of argon metastable atoms during the process of dust particle growth Laser induced fluorescence is employed to follow the spatial distribution and the relative density of argon metastable atoms Ar m ( 3 P 2 ) (section 4.2.2). The Ar m ( 3 P 2 ) distribution is examined along the laser beam perpendicular to the electrodes during one cycle of the dust growth in a continuous argon/acetylene discharge at P = 15 W (Q(Ar) = 8 sccm, Q(C 2 H 2 ) =.5 sccm, p = 1 Pa). The experimental results provide information on the behavior of argon metastable atoms under different discharge conditions during the process of the dust growth, but also on the emission from the surrounding plasma changed by the dust growth. Figure 6.5 reports the recorded LIF images at different times during the dust growth cycle. The central part of the recorded image is the total LIF signal, comprised of the induced fluorescence signal (2s 7 1s 4 transition) together with the plasma emission. All LIF signals in figure 6.5 are normalized to the maximum signal intensity during the dust growth cycle, measured when the dust particles are present in the discharge (figure 6.5(d)). The spatial distribution, i.e. the relative metastable density of argon metastable density along the laser beam is obtained after subtracting the surrounding plasma emission from the total LIF signal according to (4.31). The distributions of metastable atoms between electrodes, corresponding to the particular moments in figures 6.5, are presented in figures 6.6. In the pure argon plasma (figures 6.5(a) and 6.6(a)), the spatial distribution of Ar m ( 3 P 2 ) has a saddle-like shape, characteristic for the α discharge regime [1]. In the α mode, most of the excitation and ionization processes occur in the negative glow regions close to the electrodes, which can be attributed to the acceleration of electrons by the electric field in the presheath. Consequently, the brighter regions near the electrodes can be clearly distinguished from the darker discharge center. The higher electron energies enhance the production of metastable atoms in the negative glow. The sheath size is estimated to s m =.62 cm. The addition of acetylene to the discharge leads to the reduction of the intensity of discharge and the relative metastable density, which can be observed in figures 6.5(b) and 6.6(b), respectively. This is a consequence of the metastable losses in quenching by acetylene. The discharge still glows in the α mode with characteristic excitation/ionization zones in the presheath areas, although a reduction of discharge intensity is observed in the whole plasma volume. In the center of discharge, the metastable density is reduced due to the efficient quenching by acetylene, but also due to a slower metastable diffusion from the negative glow to the discharge center. In an argon/acetylene plasma, the estimated sheath width is s m =.71 cm, i.e. it is larger than in the pure argon plasma. In CW-driven plasmas, the formation of dust particles is a spontaneous process correlated to the formation of the critical concentration of dust precursors [26]. In the presented measurement, the dust is formed approximately 1 minute after supplying the discharge with acetylene. After the formation of dust particles, a discharge mode transition α γ occurs,

94 6 Time and space resolved density of argon Arm (3 P2 ) metastable atoms (a) Argon (t ) 4 3 (b) Argon + C2 H2 (t min). 5 (d) Dust growth (t min). 6 (e) Dust growth (t min). 8 7 (c) Dust formation (t min). (f) Appearance of void (t min) (g) Void (t min). (h) Dust fall (t min). (i) New cycle in argon/c2 H2 (t min). Figure 6.5: Laser induced fluorescence images in different moments during one cycle of the dust growth (false colors). characterized by the enhancement of electron temperature as a response to the dust production (section 2.3). Beside the intensified plasma emission from the whole plasma volume (figure 6.5(c)), the spatial distribution of argon metastable atom is also modified, as shown in figure 6.6(c). In the negative glow region, the relative metastable density is about two times higher than in the dust-free discharges. A significant change occurs in the bulk region, where the metastable density increases by about one order of magnitude in comparison to the metastable density in argon/acetylene mixture. Hence, as soon as the dust particles appear in the discharge, the production of metastables significantly exceeds their losses in acetylene

95 97 Metastable density (a.u.) Upper electrode Electrode distance (cm) (a) Argon (t ) 1Lower electrode Metastable density (a.u.) 1 5 Upper electrode Electrode distance (cm) (b) Argon + C 2 H 2 (t min). 2 Lower electrode Metastable density (a.u.) Electrode distance (cm) Upper electrode (c) Dust formation (t min). 3Lower electrode Metastable density (a.u.) Metastable density (a.u.) Upper electrode Electrode distance (cm) (d) Dust growth (t min). Upper electrode Electrode distance (cm) (g) Void (t min). 4Lower electrode 7Lower electrode Metastable density (a.u.) Metastable density (a.u.) Upper electrode Electrode distance (cm) (e) Dust growth (t min) Upper electrode Electrode distance (cm) (h) Dust fall (t min). 8 5Lower electrode Lower electrode Metastable density (a.u.) Upper electrode Electrode distance (cm) (f) Appearance of void (t min). Metastable density (a.u.) Upper electrode Electrode distance (cm) 6Lower electrode 9 Lower electrode (i) New cycle in argon/c 2 H 2 (t min). Figure 6.6: The spatial distribution of the argon metastable density between two electrodes, corresponding to the LIF images in figure 6.5. quenching. The sheath width in dusty plasmas is estimated to s m =.59 cm. During the growth of dust particles, the discharge glows in the γ mode with the intensified plasma emission in the whole plasma volume. Moreover, the spatial distribution of metastable density shows the shift of metastable production to the center of the discharge. Figures 6.5(d) and 6.6(d) are the measured LIF signals for the dust particles with the radius 7 nm, whereas figures 6.5(e) and 6.6(e) represent the LIF signals for the dust with r d r d 34 nm (both radii are found assuming a growth rate of 24 nm/min [26]). In the discharge center, the metastable density rises by a factor of 2 in comparison to the argon/c 2 H 2 plasma. The sheath width collapses to s m =.36 cm.

96 98 6 Time and space resolved density of argon Ar m ( 3 P 2 ) metastable atoms After approximately 2 minutes of the dust growth, a dust-free void region forms in the central part of the discharge. This is initially manifested by a decrease of the plasma emission (figure 6.5(f)), whereas no significant change can be seen in the spatial distribution of metastable density (figure 6.5(g)). This may be due to the small size of the void and its absence at the place of the laser beam, therefore, no impact on the measured LIF signal. However, the formation of a void causes the redistribution of electron temperature in the plasma volume [18], leading to the change in the production and loss of plasma components. Furthermore, the change in the electron temperature may impact the electron heating processes in the discharge, as well as the electric field and voltage distribution in the plasma bulk and in the electrode sheaths. In the experiments, an expansion of the electrode sheath is noticed as the void appears, having the sheath widths approximately as in the dust-free plasmas (s m >.5 cm). In the further course of the dust growth cycle, the dust-free void grows due to the large particle size and forces acting on them. The spatial distribution of metastable atoms along the laser beam changes and their relative density decreases (figure 6.6(g)). After approximately 27 minutes, the dust particles fall on the electrode (figures 6.5(h) and 6.6(h)) and a new dust growth cycle can begin. In the new cycle, the discharge produced in the argon/c 2 H 2 mixture glows again in the α mode with characteristic high metastable production zones in the presheath (figures 6.5(i) and 6.6(i)). Nevertheless, the relative metastable densities in negative glow and in plasma center are slightly higher than in the argon/acetylene plasma at the beginning of the measurement (figure 6.6(b)), which may be attributed to some residual dust particles in the discharge. In conclusion, the dust presence in the discharge volume strongly affects the spatial distribution of the plasma parameters, such as electron density, electron temperature and metastable density. These changes have to be taken into consideration when studying dusty plasmas. The changes in the distribution of plasma parameters may be even more pronounced in pulsed plasmas, due to the additional losses of plasma components during the plasma afterglow.

97 7 A global model for the afterglow of pure argon plasma and argon plasma containing dust particles A spatially-averaged, global model, developed by Denysenko et al. [19], is described in the following chapter. The global model provides an insight into the dynamics of different plasma parameters in pulsed discharges. In particular, the temporal evolutions of electron density, argon metastable density and electron temperature are examined during the afterglow phase of a pure argon plasma and of an argon plasma which contains large densities of dust particles. Various loss mechanisms are observed in order to determine which of these processes could be responsible for the increase of electron density at the beginning of the afterglow phase of argon/dust plasmas. In section 7.1, the global model is described, including the experimental conditions, the balance equations for different plasma species and for the power in the discharge. The following sections 7.2 and 7.3 describe the theoretical results for the afterglow of pure argon argon/dust plasmas, respectively. 7.1 Model description The response of electron and argon metastable densities to the formation of hydro- carbonaceous nanoparticles in pulsed RF discharges has been reported in the previous chapters 5 and 6. The experimental results show an unusual increase of the electron density at the beginning of the afterglow phase of dusty plasmas. The appearance of dust particles in the discharge is accompanied by the increase of density of argon metastable atoms, which carry large internal energies, hence they may influence the plasma properties. In order to explain the behavior of pulsed plasma parameters during the afterglow phase, a theoretical global model is developed, following the global model of Ashida et al. [11]. The model investigates different processes and mechanisms which can influence the production and losses of various species in the pure argon plasma and in the argon plasma with nanoparticles. By comparing the theoretically calculated electron and argon metastable densities with experimentally obtained values, it can be concluded, which of the observed processes may have the largest significance for explaining their behavior in the plasma afterglow phase. 99

98 1 7 A global model for plasma afterglow Experimental conditions The experimental conditions applied in the model correspond to the conditions used for the measurements of electron and metastable densities in this work (section 5.3). The argon gas flow (Q = 8 sccm) is supplied to the discharge reactor, having a total pressure of p = 1 Pa. The RF power delivered to the electrodes (radius R =.15 m and distance L =.7 m) is modulated by a square-wave signal with pulsing frequency f = 1 Hz and duty cycle 5 %. The dust particles are formed by adding acetylene (Q =.5 sccm) into the reactor. The argon/dust mixture is obtained by evacuating acetylene from the discharge. The gas temperatures of T g = 294 K in the pure argon plasma and T g = 366 K in the argon/dust plasma are taken from the previous measurements by laser absorption spectroscopy [67]. The initial conditions are found from the steady state conditions (power-on phase). In argon/dust plasmas, the steady-state values for dust density n d = m 3 and charge per dust particle Z d = 1e 21 are calculated according to OML theory (section 2.1.1), taking the initial electron density n e () = m 3 and positive ion density n i () = m 3 from the experiment and assuming the electron temperature to be T e = 2.6 ev. The initial argon metastable density is n m () = m Model assumptions In the model, it is assumed that the plasma is composed of: electrons with density n e, singly charged positive argon ions with density n i, negatively charged dust particles with density n d, charge Z d, and fixed dust radius r d = 5 nm, argon metastable atoms with density n m (including 3 P 2 and 3 P metastable states), argon atoms in resonance 4s state (including 3 P 1 and 1 P 1 resonance states) with total density n r, and argon atoms in 4p state with total density n 4p. The density of argon neutrals is denoted as n g. The density of free electrons is smaller than the density of dust charge n e < Z d n d. The dust density n d is considered to be constant in the plasma afterglow. The electron energy distribution function is assumed to be Maxwellian, while the ions and dust particles have the same temperatures T i = T d = T g. Furthermore, it is assumed that the plasma species are uniformly distributed over the plasma volume and that the reactor surfaces surrounding the plasma are at the same floating potential Balance equations The model consists of balance equations for electrons, ions, argon metastable states and argon resonant states, the equation for dust charge and the electron energy balance equation. The balance equation for individual species accounts for different reactions and mechanisms responsible for the production and losses of these species in the plasma. The electron energy balance equation follows the changes of the energy exchanged in different processes, having 21 e - elementary charge

99 11 the major role for the determination of rate coefficients for these processes. The calculation of different parameters according to the proposed model is performed in two steps. The first step requires the determination of initial values of these parameters for the steady-state conditions ( / t = ). In the second step, the time evolutions of various plasma parameters during the afterglow phase are calculated. In this manner, the production and loss mechanisms of the plasma species are estimated during the afterglow of argon and argon/dust plasmas. The densities of electrons n e and ions n i are determined from the balance between their production and loss processes. The production and loss processes of electrons and ions in dust-free and dusty plasmas, accounted in this model, are given in table 7.1. The balance equation for electrons takes the form: n e t = K 7 n g n e + γ i K i d n in d + γ m K m d n mn d + k m n 2 m + (n m + n r )n e K 8 + n 4p n e K 9 (7.1) n e /τ ew K e d n en d, and the balance equation for ions: n i t = K 7 n g n e + k m n 2 m + (n m + n r )n e K 8 + n 4p n e K 9 (7.2) n i /τ iw K i d n in d. The rate coefficients for ionization and metastable pooling (K 7, K 8, K 9 and k m ) are given in table 7.4. The coefficients for the secondary electron emissions in ion-dust collisions γ i [9] and metastable-dust collisions γ m [11] are varied in order to determine their impact on the electron density development in the plasma afterglow. The diffusion time of ions to the walls τ iw is calculated assuming the ambipolar diffusion to the walls: τ iw = Λ2 D a, (7.3) where Λ = ((π/l) 2 + (2.45/R) 2 ) 1/2 is the effective diffusion length [11] and D a = λ i v Ti (1 + T e /T i )/3 the ambipolar diffusion coefficient (v Ti is the thermal velocity of ions given by (2.5)). The collisions of ions with argon neutral atoms and with dust particles have to be accounted for the determination of the ion mean free path λ i : λ i = (n g σ ig + n d σ id ) 1, (7.4) where σ ig 1 18 m 2 is the cross section for ion-neutral collisions [1] and σ id is the cross section for ion-dust collisions [25].

100 12 7 A global model for plasma afterglow Production process Reaction Rate Ground state ionization Ar + e Ar + + 2e K 7 Secondary emission in ion-dust collisions dust(z d ) + Ar + dust(z d γ i ) + γ i e + Ar γ i K 7 Secondary emission in metastable-dust collisions dust(z d ) + Ar m dust (Z d + γ m ) + γ m e + Ar γ m Km d Metastable pooling Ar m + Ar m Ar + e + Ar k m Ionization of 4s state atoms Ar 4s + e Ar + +2e K 8 Ionization of 4p state atoms Ar 4p + e Ar + +2e K 9 Loss process Reaction Rate Diffusion to the walls e wall 1/τ ew Collection by dust particle e + dust(z d ) dust(z d 1) Kd e Table 7.1: Electron production and loss processes accounted for in the presented model. Production process Reaction Rate Ground-state excitation Ar + e Ar m + e Km De-excitation from a 4s resonant state Ar r + e Ar m + e K rq De-excitation from a 4p state Ar 4p + e Ar m + e.5k 6 Radiative de-excitation from 4p states Ar 4p Ar m + hν.5ν rp Loss process Reaction Rate Diffusion to the walls Ar m Ar (wall) D m /Λ 2 Electron impact de-excitation Ar m + e Ar + e K 2 Electron impact ionization Ar m + e Ar + + 2e K 8 Electron quenching Ar m + e Ar r + e k quen Metastable pooling Ar m + Ar m Ar + e + Ar 2k m Excitation to a 4p state Ar m + e Ar 4p + e K 5 Atom quenching Ar m + Ar 2Ar K 2b Metastable-dust collision dust(z d ) + Ar m dust(z d ) + Ar Km d Table 7.2: Metastable production and loss processes accounted for in the presented model. Production process Reaction Rate Ground-state excitation Ar + e Ar r + e K r Electron quenching Ar m + e Ar r + e k quen De-excitation from a 4p state Ar 4p + e Ar r + e K 6 Ground-state excitation Ar + e Ar 4p + e K 3 Excitation from a 4s state Ar m (Ar r ) + e Ar 4p + e K 5 Loss process Reaction Rate Radiative de-excitation Ar r Ar + hν ν rs Radiative de-excitation Ar 4p Ar r (Ar m ) + hν ν rp De-excitation from a 4s to a metastable state Ar r + e Ar m + e K rq Ionization of 4s (2p) state atoms Ar r (Ar 4p ) + e Ar + + 2e K 8 (K 9 ) De-excitation to the ground state Ar r (Ar 4p ) + e Ar + e K 2 (K 4 ) Table 7.3: Production and loss processes of 4s resonant and 4p state atoms accounted for in the presented model.

101 13 The rate coefficient for the collection of electrons Kd e and ions Ki d by a dust particle are obtained from the orbital motion limited theory (equations (2.4) in section 2.1.1): ( Kd e = πrd 2 v T e exp Kd i = ( πrd 2 v T i eϕ(r d) k B T e 1 eϕ(r d) k B T i ). ), (7.5) In (7.5), ϕ(r d ) = e Z d /(4πε r d ) is the potential of a spherical dust particle. However, a modification proposed by Khrapak et al. [111] is applied for determination of K i d,: K i d = πr2 d v T i (1 + ξτ + Hξ 2 τ 2 λ s n g σ ig ), (7.6) where ξ = e 2 Z d /(4πε r d k B T e ), τ = T e /T i, and λ s λ D. The function H takes asymptotic values: Here, β = e 2 Z d /(4πε λ s k B T i )..1,.1 β 1 H = β, β 1 β 2 (ln β) 3, β 1 The rate coefficient for the metastable-dust collisions is calculated by: (7.7) K m d = πr2 d v T i. (7.8) The equation for dust charge Z d determines a number of elementary charges e per single dust particle: Z d t = K e d n e K i d n i(1 + γ i ) γ m K m d n m. (7.9) In (7.9), the number of elementary charges, gained by electron collection by dust particles, is balanced by the loss of elementary charges through the collection of positive ions by dust particles, or through the secondary electron emission in ion-dust or ion-metastable collisions. Taking into account the plasma quasineutrality n i = n e + Z d n d and combining it with the balance equations for electrons (7.1), ions (7.2), and dust charge (7.9), the relation between the ion and electron diffusion times is found to be n e /τ ew = n i /τ iw. Hence, the electron diffusion time can be calculated according to τ ew = τ iw n e /n i. The balance equation for the argon metastable atoms is described by: n m t = D m Λ 2 n m (K 2 + K 5 + K 8 + k quen )n m n e 2k m n 2 m K 2b n m n g K d mn d n m (7.1) + K mn g n e + K rq n r n e K 6n 4p n e ν rpn 4p.

102 14 7 A global model for plasma afterglow Rate coefficient Reference K 2 = T.74 e [11] K 3 = T.71 e exp ( 13.2/T e ) [11] K 4 = T.71 e [11] K 5 = T.51 e exp ( 1.59/T e ) [11] K 6 = T.51 e [11] K 7 = T.68 e exp ( 15.76/T e ) [11] K 8 = T.67 e exp ( 4.2/T e ) [11] K 9 = T.61 e exp ( 2.61/T e ) [11] k m = [14] k quen = [14] K 2b = [15] K rq = [112] ν rs [113] ν rp = [114] Table 7.4: Rate coefficients for the production and loss processes applied in this model. The electron temperature T e is given in electron volts (ev), the rate coefficients in m 3 /s, and frequencies in s 1. The reactions in which the argon metastable atoms can be produced or destroyed are given in table 7.2. The diffusion of argon metastable atoms is described by the metastable diffusion coefficient D m /n g [m 1 s 1 ] (n g is given in m 3 ) [14]. The rate coefficients for the electron impact collisions (K 2, K 5, K 6, K 8, k quen ) are electron temperature dependent functions given in table 7.4, along with the rate constants for the two-body collisions K 2b and for the deexcitation from 4s state K rq. The rate coefficient for the ground-state excitation to metastable states Km are calculated using the argon inelastic cross sections provided by Alves et al. in [115] and Maxwellian EEDFs are calculated according to Gudmundsson [81]. The production and loss processes for the resonant 4s and for the 4p states of argon atom, given in table 7.3, determine the densities n r and n 4p through the following balance equations: n r t n 4p t = K r n g n e + k quen n m n e K 6n 4p n e ν rpn 4p (7.11) + ν rs n r K rq n r n e (K 2 + K 5 + K 8 )n r n e, = K 3 n g n e + K 5 (n m + n r )n e ν rp n 4p (K 4 + K 6 + K 9 )n 4p n e. (7.12) The rate coefficient K r for the ground-state excitation to 4s resonant state is also calculated taking the cross sections from Alves et al. [115]. The T e -dependent rate coefficients of different processes are given in table 7.4. To solve the previously presented balance equations, it is necessary to know the evolution of electron temperature T e in the plasma afterglow. The following electron energy balance

103 15 equation is applied: 3 T e 2 t = W coll W w, (7.13) where electron energy losses in different collisional processes are described by W coll and energy losses on the walls by W w. The collisional integral W coll includes the energy losses in the collisions of electrons with neutrals, with excited states and with dust particles: W coll 3m e m i ν eg (T e T g ) + ν j U j + S ed. (7.14) Here, ν eg is the momentum transfer frequency for electron-atom collisions, ν j and U j are the non-elastic collision frequencies and excitation threshold energy for the j-th energetic level, respectively. The electron energy lost in electron-dust collisions S ed takes the form [54]: ( ) S ed 2 3/2 πrd 2 n T e eϕ(rd ) d exp (2T e eϕ(r πm d )). (7.15) e The total energy lost in the collisions of electrons and ions with the walls W w can be determined from: T e W w = 1 τ ew (E e + E ion ). (7.16) The mean energy lost per electron lost to the walls can be calculated by E e = 2T e, assuming the Maxwellian EEDF [1]. The mean energy lost per ion lost to the walls E ion accounts for the energy of ion E i entering the sheath with the Bohm velocity u B and the energy V s gained by the ion as it traverses the sheath (equal to the sheath voltage given by (1.4)): E ion = E i + V s = 1 2 T e + 1 ( ) 2 T mi e ln. (7.17) 2πm e Finally, it is assumed that the electron temperature stays constant in the plasma afterglow after reaching T aft =.5 ev.

104 16 7 A global model for plasma afterglow 7.2 Pure argon plasma afterglow In the case of pure argon plasmas, the system of balance equations (7.1) - (7.17) has been solved neglecting the dust-related reactions. The numerically obtained time evolutions of electron and argon metastable density in the plasma afterglow are compared to the experimental results. The impact of different production and loss processes on the behavior of plasma parameters in the dust-free plasma afterglow is examined. Figures 7.1(a) and 7.1(b) show the comparisons between experimental (squares) and numerical (dashed curve) results of electron and argon metastable densities, respectively, in the afterglow of a pure argon plasma. The numerical functions for both n e and n m agree well with the experimental decays in the plasma afterglow. In the results of the model, the decay of electron temperature is accounted for the calculation of rate coefficients of different production and loss processes in the plasma afterglow. Figure 7.2 compares the loss rates of electron energy in different processes during the afterglow of the pure argon plasma. The following processes are compared: elastic electron-atom collisions (term 3m e /m i ν eg (T e /T g 1) in (7.14)), electron energy lost in diffusion to the walls (term W w /T g ), and in non-elastic electron-atom collisions (term νj U j /T g). The numerical results show that the electron energy losses in the non-elastic collisions, such as excitation to resonant and metastable states and ionization (curve 3 in figure 7.2), dominate in the first 2 µs after switching the RF power off. After this initial phase, the energy losses in non-elastic collisions decrease rapidly and become negligible compared to energy losses in other processes. The losses of electron energy through the diffusion to the walls (curve 2 in figure 7.2) become dominant after t > 2 µs. They are about an order of magnitude higher than the 8 Argon 4 Argon 6 3 n e (1 9 cm -3 ) n m (1 1 cm -3 ) Time (ms) (a) Electron density in pure argon plasma Time (ms) (b) Argon metastable density in pure argon plasma. Figure 7.1: Time evolutions of electron (a) and argon metastable (b) densities in the afterglow of pure argon plasma. The comparison is performed between experimental data (Curve 1 - ) and numerically calculated data (Curve 2 - dashed) (after [19]).

105 17 Electron energy loss rates (1/s) Time (ms) 2 3 Argon Figure 7.2: Different electron energy loss rates in the afterglow of pure argon plasma: elastic electron-neutral collisions (curve 1), electron energy lost to the walls (curve 2), and non-elastic electron-neutral collisions (curve 3) (after [19]). Metastable loss rates (1/s) Argon Time (ms) Figure 7.3: Loss rates of argon metastable atoms in different processes: in electron collisions (curve 1), in diffusion to the walls (curve 2), in metastable pooling (curve 3), and in quenching with groundstate atoms (curve 4) (after [19]). 2 losses of electron energy in the elastic electron-neutral collisions (curve 1 in figure 7.2). It has to be noted that the term W w (electron energy losses to the walls) has to be included in the model calculations in order to obtain the longer decay times of electron density in the plasma afterglow. Figure 7.3 reports about the losses of argon metastable atoms in different processes during the afterglow of pure argon plasma. Previously calculated electron energy losses are included into estimation of the metastable loss rates. The following loss processes are taken into account: losses in electron-induced collisions (term (K 2 + K 5 + K 8 + k quen )n e in (7.1)), losses in diffusion to the walls (term D m /Λ 2 ), losses in metastable pooling processes (term 2k m n m ), and losses in quenching with argon neutrals (term K 2b n g ). The model predicts a dominance of metastable losses in collisions with electrons (curve 1 in figure 7.3) for t <.6 ms in the plasma afterglow. This can be correlated to the relatively high electron temperature in the initial phase of the afterglow, which enables high-energetic collisions. After the first t.6 ms, the electron-metastable losses diminish and the metastables are predominantly lost in the diffusion to the walls (curve 2 in figure 7.3). The metastable diffusion is constant throughout the afterglow phase, since it depends only on the gas density n g. This is also valid for the losses in quenching with neutrals (curve 4 in figure 7.3). For the applied experimental conditions, the loss rate in two-body quenching are about 2 orders of magnitude smaller than the diffusion loss rate. The loss rate in metastable pooling (curve 3 in figure 7.3) is about one order of magnitude smaller than the diffusion loss rate. However, with an increase of the applied RF power, the densities of electrons and argon metastable atoms increase, which could induce a larger loss rates of metastables in collisions with electrons (curve 1) or with other metastable atoms (curve 3).

106 18 7 A global model for plasma afterglow 7.3 Dusty plasma afterglow The experimental results of the decay of electron and argon metastable densities in the afterglow of argon/dust plasma are compared to the numerical decays calculated according to the proposed model from the set of balance equations (7.1) - (7.17). The comparisons of experimental and calculated electron and argon metastable densities during the afterglow of argon/dust plasma are presented in figures 7.4(a) and 7.4(b), respectively. The initial parameters for densities and temperatures are given in section The calculated evolution of dust charge Z d corresponding to n e and n m is shown in figure 7.5. The secondary emission coefficients are set to γ i = γ m =.1, where γ i =.1 corresponds to the secondary emission measured in the case of stainless steel electrodes covered by dust particles [9]. The agreement between numerical and experimental results for electron and metastable densities in argon/dust plasma is less satisfactory than in the pure argon. However, their analysis may provide a better understanding of the relevant processes occurring in dusty plasma afterglow. The agreement between the experimental and numerical electron densities, presented in figure 7.4(a), is good for t < 2 ms, after which a larger disagreement is observed. For t > 2 ms, the calculated electron density decays faster than the experimental n e. Such behavior of n e could be the consequence of a decrease of the dust charge Z d, hence the decrease of the dust potential ϕ(r d ). This may lead to the enhanced electron losses on dust particles compared to the electron diffusion to the walls. The fast decrease of calculated n e in argon/dust plasma can also originate from the assumption of the Maxwellian EEDF. The EEDF in dusty plasma may considerable differ from the Maxwellian EEDF, due to the collection of high-energetic n e (1 9 cm -3 ) Argon / Dust Time (ms) (a) Electron density in argon/dust plasma. n m /n m () Argon / Dust Time (ms) (b) Argon metastable density in argon/dust plasma. Figure 7.4: Time evolutions of electron (a) and normalized argon metastable (b) densities in the afterglow of an argon/dust plasma. The comparison is performed between experimental data (Curve 1 - ) and numerically calculated data (Curve 2 - dashed). The input parameters are: n e () = m 3, n d = m 3, γ i = γ m =.1 (after [19]).

107 Argon Z d (e) 1 T e / T g 1 Argon / Dust Time (ms) Time (ms) Figure 7.5: The charge of a dust particle Z d in the units of elementary charge e calculated according to the proposed model. The input parameters are the same as for the curve 2 in figure 7.4 (after [19]). Figure 7.6: The ratio of electron to gas temperatures T e /T g during the plasma afterglow of: pure argon plasma and argon/dust plasma. The input parameters for argon correspond to the conditions in figure 7.1. For argon/dust, input parameters are the same as for the curve 2 in figure 7.4 (after [19]). electrons by dust particles, their deposition to the walls or release of high-energetic electrons in metastable pooling, which should be also accounted for the dusty plasma modeling. A better qualitative agreement if found for the experimental and calculated values of argon metastable densities during the plasma afterglow. The comparison between normalized values of n m in experiment and model is presented in figure 7.4(b). However, the numerical n m are about 3 times lower than the measured ones (initial values relate n m (exp)/n m (model) = 17.5/5.85). Similar as for the electron densities, the difference between measured and calculated n m may originate from the assumption of Maxwellian EEDF. Beside this, the discrepancy may be a consequence of an underestimated density of dust particles n d, whose increase would enhance the Ar m metastable atom production. The assumption of a uniform distribution of dust particles in the plasma volume may also be compromised in real systems. The decay of electron temperature T e (t) during the afterglow phase of both pure argon and argon/dust plasma is presented in figure 7.6. Due to the additional losses of electron energy in collisions with dust particles, the electron temperature decays faster in dusty plasmas. The loss rates of electron energy in the argon/dust plasma due to different mechanisms are reported in figure 7.7. Here, the loss rate of electron energy in electron-dust collisions (term S ed /T g in (7.14)) is compared to loss rates also present in dust-free plasmas. It can be noticed that the electron-dust collisions are the dominating electron energy loss mechanism for the time interval between 2 µs and.1 ms (curve 4 in figure 7.7). After t.1 ms, the rate of electron energy lost on the dust particles becomes approximately equal to the loss rate to the walls (curve 2 in figure 7.7). The loss rates of argon metastable atoms in different processes are reported in figure 7.8.

108 11 7 A global model for plasma afterglow Electron energy loss rates (1/s) 1 7 Argon / Dust Time (ms) 1 Metastable loss rates (1/s) 1 3 Argon / Dust Time (ms) 3 1 Figure 7.7: Different electron energy loss rates in the afterglow of argon/dust plasma: elastic electron-neutral collisions (curve 1), electron energy lost to the walls (curve 2), non-elastic electronneutral collisions (curve 3), and energy lost in electron-dust collisions (curve 4) (after [19]). Figure 7.8: Loss rates of argon metastable atoms in different processes: in electron collisions (curve 1), in diffusion to the walls (curve 2), in metastable pooling (curve 3), in quenching with ground-state atoms (curve 4), and in metastable-dust collisions (curve 5) (after [19]). For the calculation of metastable loss rates, the time evolution of T e (figure 7.6) is applied. In addition to the processes which are present in dust-free discharges, the losses of Ar m on dust particles are included (term Kmn d d in (7.1)). The metastable losses in the diffusion to the walls (curve 2 in figure 7.8) dominate in comparison to other loss processes during the most of the plasma afterglow period. The losses in diffusion are about 3 times larger than the losses of argon metastable atoms in collisions with dust particles (curve 5 in figure 7.8). Only in the very beginning of the plasma afterglow (t < 2 µs), the metastable losses in the electron-impact collisions (curve 1 in figure 7.8) are increased, as a consequence of still high electron temperature. The two-body collisions between metastables and neutrals (curve 4 in figure 7.8) are significantly lower than other loss processes. The losses in the metastable pooling (curve 3 in figure 7.8) may have a role only in the initial phase of the afterglow when the density of Ar m is still high. The figure 7.9 regards the roles of individual processes in the formation of an electron density peak at the beginning of the afterglow phase. The following processes are observed: 1. electron-impact ionization ( n e / t = (K 7 n g + K 8 (n m + n r ) + K 9 n 4p )n e ), 2. secondary electron emission caused by ion-dust interaction ( n e / t = γ i Kd i n in d ), 3. secondary electron emission caused by metastable-dust interaction ( n e / t = γ m Kd mn mn d ), 4. metastable-metastable pooling ( n e / t = k m n 2 m). Due to the fast decrease of electron energy, i.e. electron temperature in the afterglow of

109 111 Electron density (1 9 cm -3 ) Argon / Dust Experiment Ionization Ar + - dust ( i =.1) Ar + - dust ( i =.4) Ar m - dust ( m =.1) Ar m - dust ( m =.5) Metastable pooling Time (ms) Figure 7.9: The comparison of experimental electron densities (curve "Experiment") with the estimated electron densities produced in various processes: ionization (curve "Ionization"), ion-dust collisions with γ i =.1 and γ i =.4 (curve "Ar + -dust"), metastable-dust collisions with γ m =.1 and γ m =.5 (curve "Ar m -dust"), and metastable pooling (curve "Metastable pooling") (after [19]). argon/dust plasmas, the electron production in ionization processes is significantly smaller than in other processes. The ionization may contribute to the electron production only in the very beginning of the plasma afterglow phase. The production of electrons in the processes of secondary electron emission caused by interaction between dust particles and both ions or metastable atoms strongly depends on the coefficients γ i and γ m. In figure 7.4(a), experimental electron density is compared with the calculated electron density assuming γ i = γ m =.1. However, such small coefficient yield a very small contribution to the final electron density. An increase of these coefficients indeed may lead to the increased production of electron density in the beginning of the plasma afterglow, which can be seen in figure 7.9. However, the afterglow peaks obtained by applying higher values for γ i and γ m are more shifted towards the beginning of the afterglow phase, which excludes them as the possible electron production sources. Electrons can be also released in the process of re-ionization through metastable pooling. The metastable pooling relates to the rate of electron production proportional to the square of argon metastable density. It can be noticed that the electron density obtained only by metastable pooling approaches closest to the experimental electron density. The metastable pooling also provides an afterglow peak of electron density which agrees well with the measured one. Moreover, the decay time of electron density produced in metastable pooling processes is highest compared to other processes, thus approaching to the decay time of the measured electron density. In summary, the proposed global model for argon/dust plasma afterglow offers a good

110 112 7 A global model for plasma afterglow qualitative agreement with the measured plasma parameters. The time evolutions of different plasma parameters are calculated taking into account the evolution of electron temperature during the plasma afterglow. A good agreement between the experimental and theoretical electron densities is found in the argon/dust plasma afterglow. The peak of electron density in the plasma afterglow can be attributed to the electron production by metastable pooling, assuming small coefficients for secondary electron emission in ion-dust and metastable-dust collisions. An increase of the secondary electron coefficients would induce a larger effect of the secondary electrons on the electron density in the argon/dust plasma afterglow. Although calculated argon metastable densities are smaller than in the experiment, their decay times in the plasma afterglow are in a good agreement. Besides the densities, the model provides the time evolution of dust charge during the plasma afterglow, showing that dust particles retain a small negative charge in the late afterglow. For the better understanding of the changes in electron density and other parameters of the pulsed dusty plasmas, it is necessary to improve the proposed model by introducing the new electron energy distribution function which corresponds more to the realistic systems, to take into account possibly nonuniform distributions of plasma components (electrons, ions, metastable states or dust particles), or to study the role of other negative ions which may have an impact during the plasma afterglow.

111 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas determined by a non-invasive technique In this chapter, a non-invasive diagnostic technique for the determination of ion fluxes and ion densities in pulsed reactive and non-reactive plasmas is described. The ion flux towards an electrode is found from the change of the electrode DC-bias voltage during the plasma afterglow. Taking into account the ion density profile between the electrodes, the ion density can be estimated from the measured ion flux. After the introductory sections 8.1 and 8.2, the diagnostic method for measurements of DC-bias voltage is described in the section 8.3. The following section 8.4 introduces the principles for the determination of ion flux to the electrode from the measured electrode voltage and for the estimation of ion fluxes, with the discussion on the conditions necessary for their successful determination. The experimental results are reported and discussed in the final section Introduction In the plasma processing industry, the quality of the deposition or etching processes greatly depends on the fluxes of ions arriving to the target surface and on their bombarding energies. The ion fluxes and the ion bombarding energies are influenced by the dynamics of the RF sheath and the voltages across the sheath, as previously mentioned in chapter 1. In particular, a negative DC-bias (self-bias) voltage formed on the electrode is responsible for pulling the ions out from the plasma bulk and their acceleration through the sheath region. The investigation of electrode DC-bias voltages may provide some information on the fluxes of electrons and ions flowing to the electrode. Many diagnostic techniques have been used in the past to determine the ion fluxes,currents, and ion densities in plasmas. However, the accurate determination of these parameters is often influenced by problems accompanying the measuring procedure, such as a deposition of insulating films on the diagnostic tools or a drift of control parameters. A commonly applied diagnostics is the Langmuir probe technique, in which the ion densities are determined from the I/V characteristics of the probe inserted in the discharge. Ion currents can be also measured by a calibrated ion-sampling orifice incorporated into an electrode [116], or applying a large negative DC-bias voltage on electrode [117]. In reactive plasmas, these techniques could 113

112 114 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas provide inaccurate results for ion fluxes, due to deposition of insulating films on the reactor or probe surfaces (electrodes, targets or wires), etching processes on these surfaces or plasma perturbation due to the presence of diagnostic device. An electrostatic probe method, developed by Braithwaite et al. [118], proved to be tolerant to deposition of insulating films. According to this technique, the ion flux in a continuously driven discharges can be determined from discharging of an RF-biased capacitance in series with a large-area planar electrostatic probe. In addition, Braithwaite introduces a possibility to use a driven electrode of a pulsed discharge as the probe, hence to measure the ion flux to the driven electrode. Braithwaite further investigated this possibility in [119], using the blocking capacitance of the matching network in the role of the RF-biased capacitance. However, he suggested "it is not feasible to use the driven electrode directly as an ion flux probe because it can only sample the afterglow phase" [119]. In the scope of this work, ion fluxes have been determined in pulsed plasmas by applying a non-invasive method based on the analysis of a DC-bias electrode voltage. A simple external circuit with a large capacitance is used to measure the DC-bias voltage on the electrode, providing a non-invasive and non-disturbing diagnostic technique. The ion flux toward a driven electrode is determined from the discharging of the capacitance in the external LC circuit during the afterglow of the pulsed plasma, in a similar way as the Braithwaite s electrostatic probe. Beside the ion fluxes, a method for estimation of ion densities is proposed, taking into consideration the discharge dimensions, ion transport and ion profile in the discharge. In the following sections, the principles of the diagnostic technique and the applied external circuit are described in detail. The proposed methods for measurements of ion fluxes and densities are tested under various discharge conditions, which include the dependence on the applied RF power and gas compositions with or without dust particles in the discharge volume. 8.2 DC-bias voltage Formation of a negative DC-bias voltage in a capacitively coupled RF plasma is a consequence of electron and ion fluxes flowing to electrodes and their tendency to equalize in order to sustain the plasma and to prevent the electron escape [8, 1]. The DC-bias voltage can be formed when a blocking capacitor is connected between the RF power supply and the electrode, which prevents the DC current flow to the external circuit. An insulating film deposited on the electrode can also take the role of the blocking capacitor. Figure 8.1 presents the principle scheme of the formation of negative DC-bias voltage in a capacitively coupled RF discharge. In absence of an RF voltage across the electrode (figure 8.1a), the electrode acquires a a floating potential ϕ f (1.4), at which the electron and ion fluxes are equal and zero net current flows into the external circuit. After applying the RF voltage across the electrodes, the equality of fluxes is disrupted. The ion flux Γ i depends on the plasma

113 115 V t e( ) (a) V t e( ) (b) f t t V DC t ions t electrons t ions t electrons Figure 8.1: The RF voltage on electrode before (a) and after (b) the formation of DC-bias voltage V DC in capacitively coupled RF plasmas. The floating voltage is denoted as ϕ f. Times t ions and t electrons denote the time intervals in an RF cycle during which the ion and electrons, respectively, can leave the plasma. density at the plasma-sheath boundary n s and the Bohm velocity u B at which ions enter the sheath [1]: Γ i = n s u B. (8.1) The electron flux Γ e is a function of the voltage across the sheath, determined by the electrode voltage V e and the plasma potential V p, and the kinetic energy of electrons, described by their thermal speed v Te : Γ e (V e ) = 1 ( ) 4 n Ve V p sv Te exp. (8.2) The expression (8.2) is derived assuming the Maxwellian electron energy distribution [1]. The sign of the applied RF voltage determines which species arrive to the electrode. In a positive half-period, electrons are accelerated to the electrode, hence the electrode voltage becomes negative. During a negative half-period of the RF voltage, the electrode is charged by the positive ion flux and the electrode voltage shifts to positive values. However, due to higher mobility of electrons compared to ions, the electrode voltage stays negative with respect to the floating potential. During the subsequent RF cycles, the process is repeated until reaching the steady-state, in which Γ i = Γ e. The negative voltage developed on the electrode (with respect to the ground) is the DC-bias voltage (V DC in figure 8.1b). Due to the negative electrode voltage, the electrode is bombarded by electrons for a significantly shorter time than by positive ions t electrons < t ions (figure 8.1), resulting in an nearly continuous bombardment of electrodes by ions. The DC-bias voltage is characteristic for the systems in which the RF powered surface and the grounded surface differ in size, i.e. in geometrically asymmetric systems. In common arrangements, the smaller electrode is powered, whereas the larger one is grounded. Due to different electrode sizes in such systems, the voltage on the smaller electrode is higher than T e

114 116 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas the voltage on the larger electrode. The difference between these voltages gives a negative DC self-bias voltage at the powered electrode with respect to the ground. In a system with electrodes of equal sizes (with or without blocking capacitance), both electrodes obtain the same amount of charge during one RF cycle, resulting in a symmetric voltage distribution and no DC-bias voltage [1]. The ion bombardment in such systems is usually controlled by adding an external DC voltage on one electrode. 8.3 The non-invasive diagnostics for measurement of DC-bias voltages In the present experiment, two electrodes of equal size are symmetrically driven by an RF power supply (with a phase shift of 18 ) and surrounded by a large grounded reactor surface. Each electrode acquires a negative DC voltage with respect to the grounded walls. Due to equal electrode areas, the negative DC voltages developed at each electrode are approximately equal. The formation of these voltages resembles to the formation of a DC-bias voltage in asymmetric systems. In the following text, the measured negative DC voltages on electrodes will be referred to as DC-bias voltages. Figure 8.2 shows a simplified scheme of the electrical circuit applied for the measurement of the DC-bias voltage. The RF signal from the generator is modulated by a square-wave signal provided by a pulse generator. The pulse generator enables to control the pulsing frequency and duty cycle. A square-wave signal is transferred through the matching box to both of electrodes. The DC-bias voltages at each electrode are measured by external LC circuits (red boxes in figure 8.2). The LC circuit consists of a large input inductance L (choke) and an output capacitance C. The output voltage v OUT is measured by an oscilloscope with an internal resistance R, connected in parallel with the capacitance C. Due to the presence of the large inductor L, the LC circuit acts as a low-pass filter, strongly attenuating the high frequency RF component of the input electrode voltage v IN and passing only the slow changing component. The inductor L prevents the rapid change of the voltage on capacitance C. The charge time of the capacitance C depends on the impedances of the electrode voltage (plasma impedance and sheath capacitance), the DC resistance of inductance L, and the capacitance C itself. The discharge of the capacitance C occurs through the resistance R, with a discharge time constant τ dis = 2RC. For typically used large C and R, the discharge time τ dis is long enough to disable the total discharging of the capacitance C and to provide an oscillation of the output voltage around the average value of the input electrode voltage. In the electrical engineering approximation, the LC filter can be represented as a voltage divider formed by L and C, which share the input voltage v IN oscillating at frequency f. The

115 117 LC filter Oscilloscope v IN L = 4 µh RF f = MHz + Pulse generator Matching box Plasma C LC filter L = 4 µh R = 1 M Oscilloscope v OUT v IN C R = 1 M v OUT Figure 8.2: A simplified scheme of the electric circuit for measurements of the DC-bias voltage. relation between impedances Z C = jx C (X C = (2π f C) 1 ) and Z L = jx L (X L = 2π f L) at different frequencies determines the filtering effect of the LC circuit. At high frequencies, X C X L, causing a strong attenuation of the high-frequency component of the input voltage. At low frequencies, X C X L, thus the output voltage follows the input electrode voltage, i.e. v OUT v IN. In this work, the inductance of L = 4 µh is used, while the capacitance C is changed between C = 4.7, 47, and 47 nf. The internal oscilloscope resistance is R = 1 MΩ. Examples of DC-bias voltages on an electrode during one period of a pulsed plasma ( f = 1 Hz, duty cycle = 5 %), measured by 3 different capacitances in the LC filter, are reported in figure 8.3. During the power-on phase, the steady-state DC-bias voltages are approximately equal for all three capacitances. The small voltage differences may arise from the change of the impedance matching when exchanging the capacitors. This result suggests that the DC-bias voltage depends primarily on the electron and ion fluxes flowing to the electrode and not on the size of the measuring capacitance C. Nevertheless, the capacitance C can affect the rise time of the DC voltage immediately after the plasma ignition: the voltage measured on the smallest capacitor C = 4.7 nf reaches a steady state faster than the voltage on larger capacitors C = 47 and 47 nf (figure 8.3). In the afterglow phase, the differences between the measured voltages become more pronounced. The electrode voltage discharges most slowly for the largest capacitance C = 47 nf, with a discharge time in the millisecond range. The measured DC voltage stays negative during the whole afterglow phase. A decrease of the capacitance C leads to the faster discharge of the electrode voltage, due to the smaller discharge time. For C = 47 nf, the discharge time is reduced to τ.5 ms, but the electrode voltage still stays negative during the plasma afterglow. Using the smallest capacitance C = 4.7 nf, the electrode voltage is discharging rapidly with the smallest time constant (τ 1 µs), after which it has a slightly positive

116 118 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas Voltage (V) Argon C = 4.7 nf C = 47 nf C = 47 nf power-on afterglow Time (ms) Figure 8.3: The electrode DC-bias voltage during one pulsing cycle ( f = 1 Hz, duty cycle = 5 %) measured by the LC filter with 3 different capacitances: C = 4.7 nf, C = 47 nf, and C = 47 nf. value (about 3 5 V). It has to be noted, that the measured discharge time constants (denoted as τ C in the following text) are significantly smaller than the predicted discharge times τ dis = 2RC (94 ms, 94 ms and 9.4 ms, respectively), i.e. τ C τ dis. It can be concluded that the capacitance C does not discharge only through the resistance R, but also through the decaying afterglow plasma. In the equivalent electrical circuit, the plasma can be modeled with plasma impedance R pl and sheath capacitance C sh. Assuming zero plasma potential in the plasma afterglow and solving the corresponding differential equation, the discharge time τ C of the voltage v OUT can be found from: ( 1 τ C = 2R pl + 1 ( 1 + R )) 1 pl. (8.3) C sh C R Hence, τ C depends on the parameters of the external LC circuit and on the internal parameters of the decaying plasma in the afterglow. According to (8.3), τ C increases with an increase of C, which is consistent with the experimental findings. Assuming R pl R(= 1 MΩ), the last expression can be simplified to τ C = 2R pl (1/C sh + 1/C) 1. Furthermore, assuming C sh C, the discharge time constant can be calculated from the plasma impedance R pl and the sheath capacitance C sh of the decaying plasma, i.e. τ C R pl C sh. In [56], Godyak et al. calculate the plasma resistance by R pl = R ν + R st, where R ν = m e Lν/(Ae 2 n e ) is the plasma resistance due to electron-neutral collisions with frequency ν and R st 2v Te m e /(Ae 2 n s ) is the plasma resistance due to stochastic heating. The equivalent sheath capacitance is C sh ε A/s. Though derived for the CW-driven discharges, these expressions may provide a guidance to understand the behavior of discharge time τ C in the plasma afterglow as a function of different parameters.

117 Determination of ion fluxes and ion densities from the DC-bias voltage The following section describes the procedure for determination of ion fluxes and ion densities. In the first part, a time evolution of the electrode DC voltage during one pulsing cycle for the typical conditions applied in this work is reported. The discharge of the electrode voltage in the plasma afterglow can be correlated to the electron and ion fluxes to the electrode. In the second part, the procedure for determination of ion flux from the electrode DC voltage is presented, along with the necessary conditions which have to be accounted for. In the final part, we present the method for estimation of ion densities from the calculated ion fluxes Time evolution of the electrode voltage during one pulsing period Plasma pulsing leads to the modulation of the electrode DC-bias voltage. This is manifested by a successive charging and discharging of the electrode voltage during the power-on and afterglow phases, respectively. The formation of a bias voltage in a pulsed RF argon discharge and the time constants involved in its development have been previously studied by Boswell et al. [85, 87], both experimentally and theoretically. These works focus on different stages of the bias formation after the plasma ignition, i.e. in the power-on phase, setting the relations between the electron temperature, electron density, plasma potential and charging times of the blocking capacitor. In the scope of this thesis, the evolution of the DC-bias voltage in the power-on phase is only briefly described. The focus is primarily set on the plasma afterglow and the behavior of the DC-bias voltage during this phase. Figure 8.4 shows a typical waveform of the DC-bias voltage during one pulsing cycle ( f = 1 Hz, duty cycle = 5 %) measured for the discharge conditions used in this work (section 5.1). The voltage is measured on the capacitance C = 47 nf of the external LC circuit. During the power-on phase, the electrode DC-bias is charging to negative voltages, whereas it discharges to zero in the plasma afterglow. In order to correlate the time behavior of the DC voltage with the time behavior of electron density (figure 5.1) and argon metastable density (figure 6.1), the same characteristic phases are observed: power-on, afterglow, and transient turn-on and turn-off phases. After the plasma ignition, the process of formation of a negative DC-bias voltage is initiated, according to the mechanisms described in section 8.2. However, a small increase of the DC voltage can be seen in the turn-on phase, particularly in pure argon plasmas at lower RF powers. The increase of DC electrode voltage (from 38.8 V to 38 V in figure 8.4) may be induced by a electron temperature overshoot in the turn-on phase (section 5.1). Due to the T e overshoot, the escape of ions and electrons from the discharge by the ambipolar diffusion should be slightly increased (D a T e from (7.3)). The fast electrons escape predominantly to

118 12 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas Argon (P = 2 W) Turn-on Steady-state Turn-off Late afterglow V f ~exp(- t/ C ) V f POWER-ON AFTERGLOW Figure 8.4: The time evolution of DC-bias voltage in the pure argon plasma pulsed by frequency f = 1 Hz and 5 % duty cycle. Characteristic parameters are given: V f - steady-state DC-bias voltage in the power-on phase, V f - amplitude and τ C - discharge time constant of the voltage decay in the plasma afterglow. the grounded walls (the floating voltage on the walls is still smaller than the electrode voltage ϕ f < V f ). Due to their mass, the heavy positive ions diffuse mostly to the electrodes, rather than to the reactor walls (L/2 < R reactor ). Thus, in the turn-on phase, the plasma is more positively charged. The higher (positive) plasma potential prevents the flux of electrons to the electrode and enhances the ion flux, finally resulting in the increase of electrode DC voltage in the turn-on phase. In the following milliseconds of the power-on phase, the electrode DC voltage gradually becomes more negative, due to the increased electron flux to the electrode in comparison to ion flux. The constant negative DC-bias voltage V f is obtained when Γ i = Γ e over a single RF cycle. Only electrons with the energies E e > ev pl ev f can reach the electrode and escape from the discharge. In the plasma afterglow, the electrode voltage and the external capacitance C are discharging. As shown in figure 8.3, the discharge rate of the electrode voltage depends on the size of the applied capacitance C. When applying a large external capacitance C, the discharge of electrode voltage during the plasma afterglow is slower. The decay of electrode DC voltage during the plasma afterglow can be parameterized by an exponential function: ( V f (t) = V f + V f (1 exp t )). (8.4) τ C Here, V f is the steady-state voltage at the end of the power-on phase, V f the amplitude and τ C the discharge time constant of the DC-bias during the plasma afterglow phase.

119 Calculation of ion fluxes After switching the RF power off, electrical conditions in the reactor change. The ion and electron fluxes, flowing from the plasma bulk to the electrodes, start to discharge the electrode DC voltage according to the following expression [118]: dv f (t) dt = ea C (Γ i Γ e (V f )), (8.5) where A is the electrode area. The electron flux Γ e strongly depends on the measured electrode voltage V f and the plasma potential V p according to (8.2). The Langmuir probe measurements show rapid decreases of electron temperature T e and plasma potential V p in the plasma afterglow, with the decay time constants τ ε 1 µs (figure 8.5). Hence, the electrode voltage stays significantly higher than the electron temperature V f T e and the plasma potential V f V p during the most of the afterglow phase. The energy of electrons in the plasma afterglow is not high enough to enable their escape from the discharge to the electrodes. Consequently, the electron flux to the electrode can be considered as negligible compared to the ion flux Γ i Γ e (V f ). Substituting this result into (8.5), the ion flux can be determined from the change of the electrode voltage according to: Γ i (t) C ea dv f (t). (8.6) dt Assuming the electrode voltage decays in the plasma afterglow according to (8.4), a time evolution of ion flux during the plasma afterglow phase can be calculated by: Γ i (t) C V f ea τ C ( exp t ). (8.7) τ C The ion flux at t = can be calculated from the parameters of the measured electrode DC voltage in the plasma afterglow, using a simple expression: Γ i () C V f. (8.8) ea τ C Several conditions have to be fulfilled in order to be able to calculate the ion flux from the change of the electrode voltage during the plasma afterglow: (a) The condition Γ i Γ e (V f ) is fulfilled for t > τ ε in the plasma afterglow, where τ ε is a decay time constant of electron temperature by T e = T e exp ( t/τ ε ). Within the turnoff phase [, τ ε ], some electrons may still posses enough kinetic energy to overcome the sheath voltage and to escape from the plasma. In this interval, the electron flux Γ e (V f ) may contribute to the discharge of the electrode voltage according to (8.5). The decay time τ ε is estimated to be in the range of 1 µs (figure 8.5) in a pure argon plasma. In

120 122 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas 25 5 Plasma potential (V) power-on afterglow V p T e Time (ms) 4 Electron temperature (ev) Figure 8.5: The time evolution of the plasma potential V p ( ) and the electron temperature T e ( ) during the power-on phase (last 1 ms) and the plasma afterglow (first 3 ms). The measurement is performed by the Langmuir probe in pure argon plasma at P = 2 W. dusty plasmas, τ ε might be even smaller due to electron energy losses in collisions with dust particles (figure (7.6)). (b) During the plasma afterglow, the difference between electrode DC voltage and plasma potential should stay much larger than electron temperature V f V p T e. In an opposite case, the ion and electron fluxes to electrode might become comparable Γ i Γ e (V f ). Due to collection of electrons, the proposed method to determine ion fluxes could not be applied. The condition V f V p T e is always fulfilled when a large capacitance in the external LC circuit is used (C = 47 nf). (c) The insulation of electrode by a deposited film has to be taken into account. According to Braithwaite et al. [118], the formation of a DC bias voltage on an insulated electrode is possible if the external capacitance C stays in the following relation to the sheath capacitance C sh and the film capacitance C f : C sh C < C f. (8.9) For the experimental conditions applied in this work, the film capacitance is found in the range of 1 µf (section 9.2.2), whereas the sheath capacitance is estimated to C sh 1 pf. Hence, the criterion (8.9) is fulfilled.

121 Estimation of ion densities Following the arguments on derivation of ion fluxes, it can be assumed than the electrode DC-bias voltage discharges in the plasma afterglow mostly by collecting the positive ions, simultaneously repelling negatively charged electrons. The positive ions (mass m i ) from the discharge enter the sheath with the Bohm velocity u B : u B (T e ) = et e m i. (8.1) The ion flux at the plasma sheath boundary Γ i = n s u B (8.1) depends also on the plasmasheath boundary density n s. Assuming the negligible ionization and recombination within the sheath region, the ion flux can be considered as continuous throughout the whole sheath region [1]. Therefore, the ion flux on the electrodes is equal to the ion flux at the plasma-sheath boundary Γ i = n s u B. The density at the plasma-sheath boundary n s is determined by the conditions in the discharge, such as gas pressure and gas temperature, discharge dimensions, and electron temperature [1]. These conditions determine the transport processes of electrons and ion, affecting their distribution in the discharge. In [12], Godyak calculated an approximate expressions for the ratio of plasma densities at the plasma-sheath boundary n s and in the plasma center n = n e n i. For the low to intermediate pressure range, the ratio of densities in the axial direction (between the electrodes) is given by: h l = n ( s L 2s ) 1/2. (8.11) n 2λ i Here, L is the distance between the electrodes, s is the sheath width, and λ i is the ion mean free path. The ion mean free path can be calculated according to (7.4), neglecting the term n d σ id in the dust-free case. The neutral-ion momentum transfer cross section is assumed to be constant σ ig 1 18 m 2 for the range of the experimental ion energies [1]. The sheath width s is a function of electrode voltage V f and ion flux Γ i [1]: s(t) = ( ε ( 4πeλi M i ) 1/2 V 3/2 f (t) eγ i (t) )2/5. (8.12) The time evolution of the sheath width s(t) during the plasma afterglow can be estimated taking into account the experimental electrode DC voltage (8.4) and the calculated ion flux (8.7). After calculating the sheath width s(t), the density ratio h l can be found from (8.11). Knowing the density ratio h l and the ion flux to the electrode Γ i, the density of ions in the

122 124 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas plasma center can be calculated by: n i (t) = Γ i h l u B (T e ). (8.13) Hence, the ion density in the bulk center can be followed from the experimental change of the electrode DC voltage during the afterglow phase. The expression (8.13) is valid for the time t > τ ε in the plasma afterglow. Moreover, for t > τ ε, the Bohm velocity stays approximately constant u B (T aft ), assuming the constant electron temperature in the late afterglow T aft. Therefore, the time evolution of n i (t) depends predominantly on the behavior of the electrode voltage, the ion flux and the sheath size for t > τ ε. Due to the slower decay of electron and ion densities compared to the T e decay in the plasma afterglow, it can be expected that the ion density does not change significantly in the turn-off interval [, τ ε ], i.e. n i () n i (τ ε ). Consequently, the ion density at the end of power-on phase (t = in the afterglow) can be estimated from the change of the electrode DC voltage during the plasma afterglow: n i () Γ i () h l ()u B (T aft ). (8.14) The expression (8.1) for the Bohm velocity is valid for the collisionless ion dynamics within the sheath [1]. For collisional plasmas, the effects of the collisional processes in the discharge and the sheath can be included through a modified Bohm velocity. A heuristic solution for the ion velocity at the edge of a collisional sheath is calculated by Godyak and Sternberg [57]: u s (t) = u B (T e ), (8.15) (1 + πλ Ds /(2λ i )) 1/2 where λ Ds is the electron Debye length at the sheath edge, calculated in this work using the experimental electron density. Furthermore, assuming the Druyvesteyn EEDF in the discharge, the Bohm velocity can be calculated by u B (T e ) =.457 3eT e /m i [81]. Finally, the ion density in the center of the discharge can be determined from: n i () = Γ i () h l ()u s (T aft ) C V f eaτ C h l ()u s (T aft ). (8.16)

123 Results and discussion Dependence of electrode DC-bias voltage on gas mixture and applied RF power The electrode DC voltages, presented in this section, are measured simultaneously with the electron densities described in section 5.1. The simultaneous measurements between electron densities and electrode DC voltages under the same experimental conditions may provide information on their mutual depencence. The time evolutions of electrode DC voltages during one period of plasma pulsing ( f = 1 Hz, duty cycle = 5 %), measured on the external capacitance C = 47 nf, are reported in figures 8.6. The DC voltages correspond to the electron densities reported in figures 5.2. The power-on and afterglow phases of the pulsed discharge are considered separately. Power-on phase During the power-on phase, the electrode is charging by the electron and ion fluxes towards the DC-bias voltage. For C = 47 nf, the steady-state conditions are established within 1 3 ms after the plasma ignition, which exceeds significantly the rise time of electron density. After establishing the steady state, the negative DC-bias electrode voltage V f stays constant until the RF power is switched off. The power dependencies of the DC-bias voltages in different gas mixtures are shown in figure 8.7(a). It can be noticed that absolute value of electrode DC-bias voltage V f follows the behavior of steady-state electron densities n e for all investigated discharge conditions (figure 5.4(a)). With an increase of RF power, V f becomes larger due to to the increased electron densities, hence the higher electron fluxes flowing to the electrode. The increase of DC-bias voltage with power is also predicted by the time-averaged sheath model of Raizer et al. [1] and by the model for CC RF asymmetric discharges by Lieberman and Lichtenberg [1]. In these models, the DC-bias voltage is directly proportional to the amplitude of the applied RF bias voltage and it depends on the ratio of areas of the powered and grounded surfaces. In the measurements presented in figure 8.7(a), the DC-bias voltage slightly deviates from the linear behavior at higher powers, similarly to the decrease of n e observed for the same powers and gas mixtures (figure 5.4(a)). In different gas mixtures, the DC-bias voltage follows the steady-state electron densities n e in the same manner as for the applied RF powers. The absolute DC-bias voltage V f is the largest for the argon/acetylene plasma, due to the increased n e in comparison to other mixtures (figure 5.4(a)). In plasmas containing dust particles (argon/acetylene/dust and argon/dust), the absolute DC-bias voltages V f is decreased due to smaller electron densities n e in the presence of dust particles. The absolute DC-bias V f is the smallest for the argon/dust mixture due to the lowest electron densities.

124 126 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas Voltage (V) Voltage (V) P = 2 W Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust power-on afterglow Time (ms) (a) Electrode DC voltages in various mixtures at P = 2 W P = 6 W Argon / C 2 H 2 / Dust Argon / Dust Argon Argon / C 2 H 2 power-on afterglow Time (ms) (c) Electrode DC voltages in various mixtures at P = 6 W. Voltage (V) Voltage (V) P = 4 W Argon / C 2 H 2 / Dust Argon / Dust Argon Argon / C 2 H 2 power-on afterglow Time (ms) (b) Electrode DC voltages in various mixtures at P = 4 W P = 8 W Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust power-on afterglow Time (ms) (d) Electrode DC voltages in various mixtures at P = 8 W. Figure 8.6: Time evolution of electrode DC voltage in pulsed plasmas ( f = 1 Hz, duty cycle = 5 %) with various gas mixtures: pure argon ( ), argon/acetylene ( ), argon/acetylene/dust ( ), and argon/dust ( ). Plasma afterglow Figure 8.7(b) presents the discharge time constants τ C of the electrode DC voltage decay during the plasma afterglow phase, obtained by fitting the experimental data in figure 8.6 by the function (8.4). The behavior of discharge constant τ C with power depends on the gas mixture. In dust-free discharges (argon and argon/acetylene), the time constant decreases with the increasing power. This can be related to the decrease of plasma resistance R pl n 1 e with power, hence a smaller τ c according to (8.3). It can be noticed that τ C in the argon/acetylene plasma is larger than in the pure argon plasma. This may arise from the faster decay of electron density in the argon/acetylene plasma afterglow (figure 5.2), leading to the higher dis-

125 127 Voltage (V) Power-on Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust Power (W) (a) Electrode DC-bias voltage V f in the power-on phase. Discharge time (ms) Afterglow Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust Power (W) (b) Discharge time constant of the electrode voltage τ C in the plasma afterglow. Figure 8.7: The dependence of electrode DC-bias voltage V f and discharge time τ C on the applied RF power in different gas mixtures. The applied capacitance of the LC circuit is C = 47 nf. charge times τ C ( R pl n 1 e ). In dusty plasmas, the electrode DC voltage is reduced due to the smaller electron densities, as shown in figure 8.6. However, the discharge time τ C stays in the same time span (1 2 ms) as in the dust-free discharges. In argon/dust mixtures, the discharge of the capacitance C is slightly slower for all applied RF powers (larger τ C ), due to the additional losses of ions and electrons on dust particles. In argon/acetylene/dust plasmas, τ C even increases with the applied RF power, similarly to the electron decay time (figure 5.4(b)). In such plasmas, the discharge of the electrode voltage is probably not only to the flow of positive argon ions, but also the ions produced in the reactions with acetylene, which have to be also accounted for the proper interpretation of the experimental data. Moreover, no dip of DC voltage is measured at the beginning of the dusty plasma afterglow, which could correspond to the electron density afterglow peak. This confirms that the positive ions predominantly arrive to electrode during the plasma afterglow Dependence of ion flux on gas mixture and applied RF power Figure 8.8 reports the power dependence of the calculated ion fluxes at the beginning of the afterglow phase Γ i () in pure argon plasma, measured by two different external capacitances C = 47 nf and C = 47 nf. The ion fluxes Γ i () are calculated from the measured DC voltages using the simple expression (8.8). Although the DC voltages measured by different capacitances C differ significantly in the plasma afterglow (figure 8.3), the calculated ion fluxes Γ i () are approximately equal for the same discharge conditions (discharge power, gas mixture). Hence, regardless of the size of the external capacitance, the same number of pos-

126 128 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas Ion flux (1 15 m -2 s -1 ) Argon C = 47 nf C = 47 nf Power (W) Ion flux (1 15 m -2 s -1 ) Argon Argon / C 2 H 2 Argon / C 2 H 2 / Dust Argon / Dust Power (W) Figure 8.8: The ion flux Γ i () in pure argon plasma calculated for the change of electrode DC voltage applying 2 different capacitances C in external LC circuit: C = 47 nf ( ) and C = 47 nf ( ). Figure 8.9: Power dependence of ion flux at the beginning of the plasma afterglow Γ i () in various gas mixtures: pure argon ( ), argon/acetylene ( ), argon/acetylene/dust ( ), and argon/dust ( ). itive ions arrives to the electrode during the afterglow phase if the discharge conditions do not change. In figure 8.9, the ion fluxes at the beginning of the afterglow phase Γ i () are presented for different gas mixtures as functions of the applied RF power. The calculated ion fluxes correspond to the electrode DC voltages shown in figure 8.6. In all gas mixtures, the ion fluxes Γ i () rise almost linearly with the increasing power in an expected manner, because of the increase of the plasma density. In dust-free mixtures (argon and argon/acetylene), Γ i () follows the changes of the plasma (electron) density, with slightly larger values for the argon/acetylene plasma. The difference between the ion fluxes in dust-free mixtures is smaller than between the corresponding electron densities n e in figure 5.4(a). This is probably a consequence of the assumption Γ i Γ e at t = of the plasma afterglow, which fails due to the high electron temperature still present in the discharge. The results for Γ i () prove that the electrode DC voltage follows the dynamics of plasma parameters for different discharge conditions in non-reactive and reactive plasmas without the presence of dust particles. In dusty plasmas, the losses of free electrons on dust particles enhance electron and ion production through an increase of electron temperature. The ion fluxes Γ i () in dusty plasmas are higher than in dust-free mixtures (figure 8.9), in spite of the significantly lower electron densities (figure 5.4(a)) and steady-state DC voltages (figure 8.6). This is consistent with the expected increase of ion densities in dusty plasma. The high ion flux to electrodes might also originate from the increased Bohm velocity u B T e 1/2 in dusty plasmas. Figure 8.9 also shows that the positive ion flux Γ i () is higher in the argon/acetylene/dust discharge, probably due to the additional flux of positive ions created in a variety of reactions with acetylene. In dusty plasmas, the ion flux Γ i () shows a tendency of saturation at higher applied RF

127 129 powers. A similar saturation is observed in the power dependence of argon metastable density in dusty plasmas (figure 6.4(a)). Such behavior may be attributed to the change of dust density distribution at higher powers. The laser light scattering experiments, presented in chapter 1, show a rapid redistribution of dust particles at higher applied RF powers. After the increase of RF power, the dust particles migrate faster from the discharge center to the presheath regions. Due to the collection of ions by a larger number of dust particles in the presheath regions, the density of ions flowing to the electrodes might decrease. Hence, the dust redistribution could be a possible reason for the observed saturation of ion fluxes at higher powers Estimated ion densities under various discharge conditions The ion fluxes, determined from the analysis of the electrode DC voltage in the plasma afterglow, are used to estimate the steady-state ion densities in the center of the plasma following the principles described in section The ion densities at the beginning of plasma afterglow n i () are calculated for different gas mixtures and RF powers using two approaches: (8.14) and (8.16). The gas temperatures for dust-free and dusty plasmas are T g = 294 K and T g = 366 K, respectively. The dust density at the afterglow beginning is assumed to be n d () = 1 14 m 3 and the dust charge Z d = 1 (corresponding to the assumptions for the global model in chapter 7). The ion-dust collision cross section σ id, necessary to determine the ion mean free path λ i from (7.4), is calculated according to Bouchoule [25]. The sheath width s() and plasma density ratio h l (), necessary for the estimation of ion densities n i (), are obtained from the measured electrode DC voltage (8.4) and ion flux (8.6), taking their values at t =. Both parameters show only a slight dependence on the applied RF power. The calculated values for s() and h l (), are in a good agreement with the results of the self-consistent non-homogeneous model for CC RF discharges, developed by Lieberman and Lichtenberg in [1], applied for the present discharge conditions. It is also necessary to estimate the electron temperature in the late plasma afterglow T aft. The afterglow electron temperature is used primarily as a fitting parameter when estimating the ion densities according to the proposed method. Figures 8.1 show the comparisons between the electron densities in the plasma center n e, measured independently by microwave interferometry, and estimated ion densities n i () at different applied RF powers and in various discharge mixtures. The ion densities in the discharge center are calculated for Bohm velocity u B according to (8.14) (denoted as n i (u B )) and for modified Bohm velocity u s according to (8.16) (denoted as n i (u s )). At the plasma-sheath boundary, the ion density n s is estimated from (8.1). For all presented calculations, the afterglow electron temperature is set to T aft.5 ev. In dust-free discharges (argon in figure 8.1(a) and argon/acetylene in figure 8.1(b)), a

128 13 8 Ion fluxes and ion densities in pulsed non-reactive and reactive RF plasmas Ion density (1 15 m -3 ) Ion density (1 15 m -3 ) Argon Te =.5 ev n i (u B ) n i (u s ) n s n e Power (W) (a) Pure argon plasma. Argon / C 2 H 2 / Dust Te =.5 ev n i (u B ) n i (u s ) n s n e Power (W) (c) Argon/acetylene/dust plasma Electron density (1 15 m -3 ) Ion density (1 15 m -3 ) Electron density (1 15 m -3 ) Ion density (1 15 m -3 ) Argon / C 2 H 2 Te =.5 ev n i (u B ) n i (u s ) n s n e Power (W) Argon / Dust Te =.5 ev n i (u B ) n i (u s ) n s n e (b) Argon/acetylene plasma Power (W) (d) Argon/dust plasma. Figure 8.1: The comparison between the steady-state electron density n e ( ) and ion densities estimated by different approaches: n i (u B ) ( ) according to (8.14), n i (u s ) ( ) according to (8.16), and plasma-sheath boundary density n s ( ) according to (8.1). The afterglow electron temperature is set to T aft.5 ev Electron density (1 15 m -3 ) Electron density (1 15 m -3 ) very good agreement between electron and ion densities is obtained assuming the afterglow electron temperature T aft.5 ev. This result coincides with the afterglow electron temperatures predicted in the global model for plasma afterglow (chapter 7). The density ratio between the sheath edge and the plasma center is calculated to be h l.1 for all applied RF powers. The estimated ion densities n i (u B ) and n i (u s ) are increasing almost linearly with the applied RF power. This result is consistent with the observed increase of the ion flux Γ i () (figure 8.9), as well as the increase of the steady-state electron densities n e with the power (figure 5.4(a)). The discrepancy between calculated n i (u B ) and n i (u s ) arise from the dependence of the modified Bohm velocity u s on the electron density according to (8.15). In the pure argon plasma, the ion densities calculated using the modified Bohm velocity u s have a better agreement with the measured electron densities. In argon/acetylene plasmas, a larger discrepancy is noticed between the measured n e and

129 131 the estimated n i (), assuming the fitting electron temperature stays T aft.5 ev for all applied powers. The reason for this disagreement may be the simplicity of the proposed model, which neglects the collisions of neutrals and electrons with other ions beside the argon ions. In addition, no other significant losses of ions are accounted for, which may be incorrect for the plasmas with highly reactive gases such as acetylene. Nevertheless, the agreement between the measured n e and estimated n i () is still in a satisfactory level, considering all possible processes and model assumptions which could impact the result. In dust-containing discharges, the dust charge has to be taken into consideration, besides ions and electrons. Due to the unknown dust density n d and dust charge Z d, the ion density calculated according to the proposed method is inaccurate. However, the order of magnitude and the tendency of the ion density can be estimated. For the afterglow electron temperature of T aft =.5 ev, the ion densities are estimated in the argon/acetylene/dust (figure 8.1(c)) and in argon/dust plasmas (figure 8.1(d)). An assumption of higher T aft would impose a decrease of the ion densities. Keeping T aft =.5 ev constant, the estimated ion densities increase with the RF power, as expected due to the increase of ion fluxes Γ i () and electron densities n e. A saturation of n i () is observed at powers higher than 4 W, which can be correlated to the saturation seen in the corresponding ion fluxes. In dusty plasmas, the difference between the ion densities n i (u B ) and n i (u s ) is more pronounced than in the dust-free mixtures. This is a consequence of the increased Debye length λ Ds n 1/2 e and the decreased ion mean free path λ i n 1 d. Hence, the modified Bohm velocity u s (8.15) is smaller in dusty plasmas, causing n i (u s ) > n i (u B ). Additionally, the spatial distribution of dust particles in the plasma volume has to be considered. In dust-free discharges, the ratio of densities h l at the plasma-sheath boundary n s and in the plasma bulk center n is found from the electrode DC voltage according to (8.11), giving the power-independent value (h l.1). This approach to calculate h l is not applicable in dust-containing discharges, due to a significant change in the distribution of electron temperature (α γ transition). Therefore, another approach for estimation of the density ratio h l = n s /n has to be applied. The ion densities presented in figures 8.1(c) and 8.1(d) are estimated using the density ratio h l found from the kinetic model for capacitively coupled RF discharges with mobile charged particles developed by Schweigert et al. [92]. Taking into account the sheath width, electric field distribution and ion density distribution for the nanoparticles with radius r d = 3 nm (figures 6 and 8 in [92]), the density ratio is estimated to h l.24. Using this value, the calculated ion densities (figures 8.1(c) and 8.1(d)) are found to be an order of magnitude higher than the electron densities. In conclusion, the ion distribution in the discharge volume has to be known for the proper estimation of ion density. However, the ion fluxes to the electrode, measured from the change of the electrode DC voltage, allow the estimation of ion densities at the plasma-sheath boundary n s in the dustcontaining plasmas.

130

131 9 Dynamics of the pulsed reactive discharge in response to thin film deposition This chapter reports on the effect of a thin hydrocarbon film deposited on electrodes on time evolutions of electron densities, argon metastable densities and electrode DC voltages in a pulsed argon plasma. After introductory section 9.1, section 9.2 describes experimental conditions and experimental results of the plasma parameters for different thicknesses of the deposited film. In section 9.3, possible mechanisms responsible for the behavior of plasma parameters are discussed, considering also the effect of the impurities present in the discharge volume. 9.1 Introduction The conditions on reactor surfaces, particularly electrodes, play a significant role in sustaining the discharge by secondary electron emission [7, 121]. In DC glow discharges, a release of secondary electrons emitted from the cathode is responsible for sustaining the discharge. Insulation of electrodes can, therefore, cause a prompt extinction of a DC glow discharge [7]. In RF discharges, insulation of electrode surfaces becomes less important, since an RF discharge is sustained by oscillation of electrons in an alternating electrical field [1, 7]. However, application of reactive gases in an RF discharge can lead to the insulation of electrodes, but also the diagnostic tools in contact with reactive gases, which may affect the accuracy of the applied diagnostic technique. The deposition of a thin dielectric layer on an electrode surface causes an accumulation of the charge particles impinging on it. Charged particles impinging on a metallic electrode recombine immediately [2]. Raizer et al. [1] suggest that no new effects occur in the discharge after the insulation of electrode by a dielectric material, justifying this claim by the absence of a significant change in plasma potential for metallic and dielectric-coated electrodes. Sobolewski [121] classifies the electrode surface conditions among the main factors which affect the reproducibility of a plasma produced in a Gaseous Electronics Conference (GEC) reference cell, next to the external circuit effects and gas impurities. He also shows that an oxygen-rich surface layer on electrodes induces a slow decrease of plasma impedance due to increased emission of secondary electrons. The influence of secondary electrons has been also studied by Kawamura et al. [122], who show that secondary electrons may increase the ionization efficiency in a capacitively coupled RF discharge, thereby reducing the RF voltage 133

132 134 9 Dynamics of the pulsed reactive discharge in response to thin film deposition amplitude for the same input power. A correlation of surface conditions on the powered electrode and the formation of dust particles is suggested by Massereau-Guilbaud et al. [123, 124], reporting also changes in the secondary electron energy and a decrease of electron temperature. In the previous chapters, it has been shown that the presence of reactive gases and dust particles in the plasma volume causes significant changes in the time evolutions of plasma parameters during a pulsing cycle in power-modulated plasmas. Besides, it has been noticed that the plasma parameters also respond to the deposition of a thin hydrocarbon film on electrode surfaces. Differences are observed in the time evolutions of electron density, argon metastable density and electrode DC voltage measured under the same discharge conditions (gas pressure, applied RF power, impedance matching), prior and after the thin film deposition on electrodes. The chapter presents the systematic measurements of electron density, argon metastable density and electrode DC voltage, performed in order to investigate the effect of a thin film gradually deposited on the electrodes. Acetylene is used as a precursor gas for the thin film deposition. However, the measurements of the plasma parameters are performed in a pure argon plasma after removing acetylene from the discharge, in order to avoid the complicated acetylene-induced chemistry. The dust particle formation is prevented by plasma pulsing, in order to exclude the effect of dust particles on the investigated plasma parameters. The changes of plasma parameters, observed in both power-on and afterglow phase of the pulsed discharge, can help to understand the mechanisms of production and loss of the plasma species. 9.2 Effect of deposited thin film on various plasma parameters: Experimental results Experimental conditions The investigation of thin hydrocarbon film deposition on electrode surfaces is performed for the typical experimental conditions used in this work. Argon with a flow rate of Q = 8 sccm and at a pressure of p = 1 Pa is used as the carrier gas. Acetylene with a flow rate of Q =.5 sccm is supplied to the discharge reactor only during the deposition process, keeping the total pressure constant at p = 1 Pa. The hydrocarbon dust particles formation is prevented by plasma pulsing at f = 1 Hz and a duty cycle 5 %. In the course of experiments with highly reactive acetylene, an amorphous hydrocarbon film (a-c:h) is deposited on the reactor surfaces, which can be efficiently removed from the electrodes by chemical sputtering with oxygen plasmas (section 3.1). In order to investigate the effect of the thin film growth on various parameters, the electrodes are, in the first place, cleaned from the deposited film by an O 2 plasma exposure between.5 and 2 hours, depending on the contamination on the elec-

133 135 MW antenna 26.5 GHz Laser absorption spectroscopy = nm PD MWI Electronic unit 3 E 9 Oscilloscope / Data acquisition Langmuir probe MW antenna DO APS3 Data Acquision System Figure 9.1: Experimental setup (MWI - microwave interferometer, PD - photodiode, DO - digital oscilloscope). trodes in the previous experiments. However, the application of oxygen plasma introduces a large amount of oxygen residues which stay in the plasma volume or bond on the electrode surfaces. Two steps are taken to remove the oxygen from the discharge chamber. First, the chamber is pumped until the background pressure reaches about 1 6 mbar (about 3 min). Second, the argon sputtering at high RF powers is applied for several hours. In this manner, the oxygen content is presumably diminished. The first measurement of the plasma parameters is performed in a pure argon plasma with "clean" electrodes, i.e. the electrodes which are film-free, but they may still contain some oxygen-rich residues. The film growth is initiated by adding the acetylene flow into the discharge reactor, at the same time preventing the dust particle growth by plasma pulsing. The thickness of the deposited film is controlled by stopping the acetylene flow into the chamber after a chosen deposition time t dep. The measurement of the plasma parameters is performed approximately 1 minute after stopping the acetylene flow, which corresponds to the gas residence time. Hence, the plasma parameters are measured in the pure argon plasma with a layer of the thin film on the electrode. The next layer is deposited by adding acetylene to the discharge reactor and repeating the previously described steps, which results in the increase of the film thickness in each subsequent cycle. Figure 9.1 shows a simple scheme of the experimental setup and diagnostic techniques used for the measurements. The microwave interferometry (section 4.1.1) is employed to follow the time evolution of averaged electron densities. The measurements of line-of-sight averaged argon metastable density are simultaneously performed using the laser absorption spectroscopy (section 4.2.1). Ion fluxes and ion densities are estimated from the decay of the DC electrode voltage measured on the capacitance C = 47 nf in the external LC circuit (chapter 8). The Langmuir probe is used to determine the time evolutions of local electron densities, electron temperatures, and plasma potentials in the midplane between the elec-

134 136 9 Dynamics of the pulsed reactive discharge in response to thin film deposition Film thickness (nm) C f d f d f (linear fit) Deposition time (min) Film capacitance (µf) t dep = 2 min 3.4 t dep = 4 min 3.3 t dep = 6 min 3.2 t dep = 8 min 3.1 t dep = 1 min 3. t. dep = 12 min Photon energy (ev) Figure 9.2: The film thickness d f ( ) for thin film deposition times varying between t dep = 2 12 min. The linear fit of the film thickness (dashed line) results in a growth rate of 1.5 nm/min. The film capacitance C f ( ) is estimated according to (9.1). Figure 9.3: Optical constant ε 1 (hν) for film deposition times varying between t dep = 2 12 min. The dielectric constant ε r is estimated by extrapolation of the presented optical constants. trodes at r = 1 cm from the discharge center (section 4.1.2). Due to the limitations of the experimental setup, the Langmuir probe measurements are performed separately, nevertheless applying the same procedure. A separate set of measurements is also performed to deposit the thin hydrocarbon film on silicon wafers positioned on the lower electrode. The thickness of a-c:h film deposited on silicon wafers is determined ex situ by means of optical ellipsometry [125] Deposition rate of a-c:h films The silicon wafers placed on the lower electrode are coated by the hydrocarbon film produced from acetylene as a precursor gas. The film is deposited in the 1 Hz pulsed discharge applying an input power of P = 2 W. After the film deposition, one silicon wafer is extracted from the discharge reactor and its properties are measured by optical ellipsometry. The same procedure is repeated for various discharge times t dep, varying between 2 and 12 minutes. Figure 9.2 reports the ellipsometric measurements of the thin film thickness d f as a function of deposition time. An almost linear increase of film thickness with the deposition time is observed for the hydrocarbon film grown under given discharge conditions, resulting in a deposition rate of about 1.5 nm/min. In the time scale between and 2 minutes, a data extrapolation is applied in order to emphasize the linear growth of the film thickness. The film deposited on the electrode, with the film thickness d f, can be treated as a capacitance connected in series between the electrode and the external circuit. The film capacitance C f

135 137 Electron density (1 15 m -3 ) Power-on P = 8 W P = 5 W P = 2 W Film thickness (nm) (a) Steady-state electron density n e in the power-on phase. Electron decay time (ms) Afterglow.4 P = 2 W.2 P = 5 W P = 8 W Film thickness (nm) (b) Electron decay time τ e in the plasma afterglow. Figure 9.4: The influence of the increase of a-c:h film thickness on the steady-state electron density n e and electron decay time τ e at different RF powers: P = 2 W ( ), P = 5 W ( ), and P = 8 W ( ). Measurements are performed in pure argon plasma after the film deposition. can be estimated using the parallel-plate model: C f = ε ε r A d f, (9.1) where A is the surface of the electrode covered by the thin film (approximately equal to the total electrode surface) and ε r is the dielectric constant of the film. The complex index of refraction ñ, obtained from the ellipsometric measurements, is related to the complex dielectric function ε by ε = ñ 2. The real part of the complex dielectric function ε = ε 1 + iε 2 is presented in figure 9.3 for each of the investigated films. Extrapolating ε 1 (hν) at a photon energy of hν =, the relative dielectric constant ε r can be found in the range between 2.6 and 2.8 for the measured samples. Thus, the film capacitances C f is in the range of 1s µf, i.e. C f > C, C s h. The voltage drop across the deposited film can be considered as much lower than on the capacitance C, allowing the determination of ion fluxes from the decay of DC voltage in the plasma afterglow, according to the method proposed in chapter The effects of deposited thin films on electron densities, electron temperatures and plasma potentials After depositing the hydrocarbon film on the electrodes, the electron density still behaves in a usual manner (figure 5.1), characterized by a fast rise to steady-state electron density n e during the power-on phase and an exponential decay n e (t) = n e exp ( t/τ e ) during the plasma afterglow. However, it has been noticed that the values of n e and τ e change after the film deposition.

136 138 9 Dynamics of the pulsed reactive discharge in response to thin film deposition Plasma potential (V) V p T e Film thickness (nm) 5 4 Electron temperature (V) Figure 9.5: The decay of steady-state plasma potential V p ( ) and steady-state electron temperature T e ( ) in pure argon plasma (P = 2 W) due to the thin film deposition. Figure 9.4(a) shows the changes of the steady-state electron densities n e in the pure argon plasma at different applied RF powers, induced by the deposition of the hydrocarbon film on electrodes and the increase of the film thickness d f. A difference can be observed between n e measured in the case of clean electrodes (d f = ) and in the case when the film thickness increases, regardless of the applied RF power. Compared to the initial values at d f =, the steady-state densities n e increase for about 2 % at larger film thicknesses. The density n e saturated after 1 minutes of deposition, corresponding to d f 15 2 nm. In the plasma afterglow, the deposition of the thin film on electrodes induces an increase of electron decay time τ e, reported in figure 9.4(b). The increase of τ e with the film thickness is measured at all applied RF powers. With the increase of RF power, the decay times τ e are reduced, which is consistent with the experimental results (figure 5.4(b)). At smaller film thicknesses, the power dependence of τ e is almost negligible, whereas it is pronounced at larger film thicknesses. Figure 9.5 presents the steady-state electron temperatures T e and the steady-state plasma potentials V p during the power-on phase of the pulsed argon plasma as a function of the increasing film thickness. A decreasing trend of both T e and V p is observed already for d f 5 nm, after which the parameters stay approximately constant. In the plasma afterglow, both electron temperature and plasma potential decay rapidly with approximately equal decay times τ ε 1 µs (figure 8.5). With an increase of the film thickness, the experiments show no significant change in the decay times of electron temperature and plasma potential, which stay in the same order of magnitude τ ε 1 µs.

137 139 Metastable density (1 15 m -3 ) Power-on P = 2 W P = 5 W P = 8 W Film thickness (nm) (a) Steady-state metastable density n m in the power-on phase. Metastable decay time (ms) Afterglow.5 P = 2 W P = 5 W P = 8 W Film thickness (nm) (b) Metastable decay time τ m in the plasma afterglow. Figure 9.6: The influence of the increase of a-c:h film thickness on the steady-state argon metastable density n m and metastable decay time τ m at different RF powers: P = 2 W ( ), P = 5 W ( ), and P = 8 W ( ). Measurements are performed in pure argon plasma after film deposition The effects of deposited thin films on argon metastable densities The gradual deposition of the thin film on electrodes leads to the change of the steady-state argon metastable densities n m during the power-on phase and the metastable decay times τ m in the plasma afterglow. Figure 9.6(a) reports the measured steady-state argon metastable densities n m as a function of the applied RF power and deposited film thickness d f. The steady-state metastable densities n m increase with higher input powers. Regardless of the RF power, the gradual deposition of the hydrocarbon film results in an increase of n m. Unlike the electron densities n e, the steady-state metastable densities do not saturate at larger d f. Compared to the initial values with no film on the electrodes (d f = ), n m is larger by about 5 % at P = 2 W and about 4 % at P = 5 and 8 W at larger d f. In the plasma afterglow phase, the metastable decay time τ m increases with the thickness of the deposited film at all applied RF powers, as shown in figure 9.6(b). For d f = const, τ m is reduced with an increase of RF power, indicating the faster decay of metastables from the discharge. The behavior of metastable decay time τ m corresponds to the behavior of electron decay time τ e with increased power and film thickness (figure 9.4(b)) The effects of deposited thin films on average electrode voltages, ion fluxes, and ion densities The deposition of a thin a-c:h film on the electrodes also reflects on the behavior of electrode DC voltage V f measured on the capacitance C of the external LC circuit. The electrode voltage V e is shared between the external capacitance C and the film capacitance C f in series

138 14 9 Dynamics of the pulsed reactive discharge in response to thin film deposition Voltage (V) Power-on P = 2 W P = 5 W P = 8 W Film thickness (nm) (a) Steady-state DC-bias voltage V f in the power-on phase. Discharge time (ms) Afterglow P = 2 W P = 5 W P = 8 W Film thickness (nm) (b) Capacitance discharge time τ C in the plasma afterglow. Figure 9.7: The influence of the increase of a-c:h film thickness on the steady-state electrode DCbias voltage V f and the discharge time τ C at different RF powers: P = 2 W ( ), P = 5 W ( ), and P = 8 W ( ). Measurements are performed in the pure argon plasma after the film deposition. connected between the LC circuit and the electrode: V f = V e 1 + C/C f, (9.2) where V f is the voltage measured on the external capacitance C. After the film deposition, the film capacitance C f is reduced, resulting in a decrease of the (absolute) electrode DC voltage V f according to (9.2). Due to C C f, the voltages V e and V f can be considered as approximately equal V f V e. Consequently, the voltage V f follows the dynamics of the pulsed discharge, i.e. electron and ion densities and fluxes which respond to the thin film deposition. Figure 9.7(a) presents the dependence of the electrode DC-bias voltage V f in the power-on phase induced by the increase of film thickness d f and applied RF power. With an increase of the applied RF power at the same electrode conditions (d f = const), an increase of V f is measured, expected due to higher electron densities. However, at a single RF power, the DCbias voltage V f is reduced after the film deposition, which is in fact opposite to the increase of V f expected due to higher electron densities (figure 9.4(a)). The possible mechanisms for such behavior will be discussed in the following section. During the plasma afterglow, the electrode voltage decays exponentially with the discharge time constant τ C. The response of τ C on the increase of film thickness at different applied RF powers can be seen in figure 9.7(b). It can be noticed that the discharge time τ C increases with the film thickness. Furthermore, τ C is reduced with the increase of RF power. The behavior of τ C corresponds to the behaviors of the decay times of electrons τ e (figure 9.4(b)) and metastable atoms τ m (figure 9.6(b)).

139 141 Ion flux (1 15 m -2 s -1 ) P = 8 W P = 5 W P = 2 W Film thickness (nm) Figure 9.8: The ion flux Γ i () in the pure argon plasma calculated from the change of electrode DC voltage at different RF powers: P = 2 W ( ), P = 5 W ( ), and P = 8 W ( ). Ion density (1 15 m -3 ) Thin film n e n i (T aft =.1 ev) No film n i (T aft =.5 ev) Power (W) n e Electron density (1 15 m -3 ) Figure 9.9: The comparisons between ion densities n i () (open symbols) and steady-state electron densities n e (solid symbols) in the case of clean electrodes ("No film" - squares) and with a thin deposited film ("Thin film" - circles). Figure 9.8 shows the ion fluxes Γ i () in argon plasma calculated by (8.8) from the measured electrode DC voltages for different applied RF powers and film thicknesses. The ion fluxes Γ i () follow the increase of the steady-state electron density n e (figure (9.4(a))). This is consistent with the expected behavior of the ion flux according to Γ i = h l n e u B. The correlation between the calculated ion fluxes and independently measured electron densities confirms that the proposed method for ion flux determination can be performed also when the insulating layers cover the powered electrode. Along with the ion fluxes, the ion densities are calculated from the electrode DC voltage decay in the plasma afterglow, following the principles described in section Calculating the sheath width s() by (8.12) and the density ratio h l () by (8.11), the ion densities at the beginning of the plasma afterglow n i () can be estimated according to (8.16). Figure 9.9 shows the comparisons between the estimated ion densities n i () and the independently measured steady-state electron densities n e at different RF powers and different film thicknesses. The comparisons are presented for two cases: clean electrodes with d f = and electrodes covered by the thin hydrocarbon film with d f = 9 nm. In both cases, the estimated ion densities n i () increase almost linearly with the applied RF power in an expected manner. For the case of clean electrodes, a good agreement between n i () and n e is found by fitting with the afterglow electron temperature of T aft =.5 ev, also predicted by the global model in chapter 7. After the thin film deposition, an agreement between n i () and n e is found for slightly increased electron temperature T aft =.1 ev, which is also in a range of predicted afterglow electron temperatures [95, 96].

140 142 9 Dynamics of the pulsed reactive discharge in response to thin film deposition 9.3 Discussion The possible mechanisms responsible for the changes of the measured plasma parameters are discussed in this section. These mechanisms may impact the production and loss processes of the plasma species and the energy exchange in the discharge. Due to the difference in the available electron temperatures, production and loss mechanisms differ significantly in the power-on and afterglow phase. However, certain mechanisms, such as the presence of impurities or reactive gases and their residues, may affect the production and loss processes throughout the whole pulsing cycle Electron density and electron temperature Power-on phase In the power-on phase of the discharge, the steady-state electron density n e is determined by the balance between the electron production and loss processes. After the deposition of the thin film, an increase of the steady-state electron density is observed (figure 9.4(a)), which suggests the appearance of a new equilibrium in the electron production/loss balance. In section 5.3, it has been shown that only a small amount of reactive acetylene may impact the steady-state density of electrons, as well as their decay in the plasma afterglow. Traces of molecular gases, such as oxygen and nitrogen, can change the plasma chemistry and introduce additional reactions (e.g. electron attachment). The impurities (oxygen, nitrogen) appear in the reactor when exposing it to the surrounding atmosphere during the cleaning process. In the present work, the concentration of oxygen-rich impurities is increased because of the reactor cleaning by oxygen plasma, in order to remove hydrocarbon film residues from the electrodes. However, the oxygen-containing residues remain in the reactor after several cycles of the dust production and their deposition on the electrodes despite argon sputtering. This behavior is confirmed by Fourier Transform Infrared Spectroscopy (FTIR), performed on the same experimental setup in a previous study of Kovačević et al. [7]. It can be assumed that the gradual deposition of a-c:h film on the electrodes lowers the content of oxygen and OH radicals on the electrodes and in the plasma volume, which leads to the reduced probability of electron losses in reactions with argon and electronegative oxygen (the reaction set for oxygen/argon reactions is reported in [126]). Therefore, the reduced concentration of oxygen impurities could be a possible mechanisms for the increase of steady-state electron density in the power-on phase of pulsed discharge. The secondary electron emission in the discharge is also influenced by the amount of oxygen present on the surface of the electrodes. In the work by Stefanović et al. [9], performed on the same experimental setup as in this thesis, the secondary electron yield for the "clean" stainless-steel electrodes is found to be higher than for the stainless-steel electrodes covered by a thin hydrocarbon film. A similar result is found by Sobolewski in [121], where the sec-

141 143 ondary electron yield is increased for the oxidized aluminium electrodes in a GEC reactor. We conclude that the high oxygen content is responsible for high secondary electron emission from clean electrodes. Due to the enhanced secondary electron emission, a higher electron density is expected in the case of clean electrodes. This expectation, however, contradicts the experimental results for the steady-state electron densities n e presented in figure 9.4(a), which show an actual decrease of n e for the smaller film thicknesses. Obviously, the electron density is influenced rather by the oxygen-related reactions which occur in the plasma volume than the reactions on the electrode surface. Oxygen in the gas phase increases the equivalent plasma impedance [121], which corresponds to the measured decrease of the steady-state electron density. Film deposition on the electrodes affects the reduction of oxygen concentration in the discharge, finally decreasing the equivalent plasma impedance. The conditions on the electrode surface can also play a role in the initiative phase of the dust particle formation. In the study by Massereau-Guilbaud et al. [124], it is suggested that the sputtering of electrodes is responsible for the initial nucleation phase of the dust clusters, which later coagulate to the particles of larger size. In the investigations performed in this work, it is noticed that the spontaneous dust formation is not possible directly after cleaning the reactor by oxygen plasma. Moreover, an acetylene flow for a longer period (several minutes) after the reactor cleaning is necessary for the initialization of the dust particles formation. It is possible that the oxygen residues participate in the formation of negative ions, which is a competitive process with the formation of negative ions from the acetylene monomer (section 2.2.1). Hence, the coverage of the electrode surface by the thin film and the elimination of oxygen residues from the plasma volume can enhance the dust particle formation in the discharge. Figure 9.5 reveals the decrease of steady-state electron temperatures T e and steady-state plasma potential V p after the thin film deposition, which can also be correlated to the corresponding reduction of electron losses in the discharge. The steady-state electron temperature depends on the balance between the electron production and losses in the discharge [1]. The increased electron losses (such as in the case of increased concentration of oxygen impurities) have to be compensated by an increased electron temperature in order to enhance the electron production rate and to sustain the discharge. In contrast to it, the reduction of electron losses would lead to the decrease of electron temperature. Thus, for the presented measurements, the increase of steady-state electron temperature at low film thicknesses can be explained by the high electron losses and a need for enhanced production of electrons. Similar results are reported in [123] for a hydrogen-methane RF plasma, where a decrease of electron temperature is measured and attributed to the coatings on the powered electrode. The steady-state plasma potential V p follows the decrease of the steady-state electron temperature with the increase of film thickness. At smaller d f, the plasma potential is increased to prevent the escape of fast electrons from the discharge. After the film deposition, the electron losses are decreased and a lower plasma potential is sufficient to sustain the plasma.

142 144 9 Dynamics of the pulsed reactive discharge in response to thin film deposition Additionally, the plasma potential decrease at larger d f may be related to the decrease of the plasma resistance due to R pl 1/n e. Plasma afterglow A change of the applied RF power and the deposition of hydrocarbon film on the electrodes influence the electron decay time τ e, as shown in figure 9.4(b). With an increasing RF power, the decay time of electrons decreases, which has been previously observed (section 5.4). The electron decay time τ e increases with an increase of film thickness at each of the applied RF powers, hence electrons escape slower from the discharge. As a result, the electron density is higher also in the plasma afterglow phase, corresponding to the overall increase of electron density after the thin film deposition on the electrodes. The increase of the oxygen-rich impurities in the discharge, such as O 2 /OH, may cause the additional losses of electrons due to the electron attachment, as indicated for the poweron phase. The process of electron attachment may become an important loss process in the late afterglow, after the relaxation of electron energy. In this phase, mean electron energies approach the electron affinities for oxygen (E ea (O 2 ) =.45 ev [127]), inducing the formation of negative ions. In the case of clean electrodes and the increased concentration of oxygen impurities in the discharge, electrons decay faster due to their additional attachment by the impurities. After the film deposition, the concentration of impurities is reduced, the electron attachment is smaller, leading to the slower electron decay from the discharge and higher decay times τ e. The experimental results in figure 9.4(b) show only a small power dependence of the electron decay times τ e at smaller film thicknesses (d f < 15 nm). The difference becomes evident and significantly pronounced at larger film thicknesses. As proposed, the concentration of oxygen impurities is probably decreased after the deposition of the film, leading to the increase of the electron decay time τ e at higher d f. Thus, the decrease of τ e with the increased power might originate from some other process occurring in the discharge. In chapter 7, diffusion of electrons to the walls is designated as the main electron loss process in the discharge. With an increase of the RF power, the electron and ion temperature are supposed to stay unchanged, hence the electron diffusion should not experience any significant change over the range of the applied RF powers 22. One of the possible mechanisms which induce the decrease of electron decay time with the increase of RF power might be the hydrocarbon film residues sputtered away from the electrodes. At higher powers, the sputtering energy is increasing, leading to the more efficient release of the hydrocarbon or carbon film previously deposited on the electrodes. Hence, the sputtered material may pollute the pure argon plasma, collecting the electrons in the way similar to the dust particles in dusty plasmas and finally inducing the faster decay of electrons at higher powers. 22 The electron temperature is approximately power-independent [1]. The ion/gas temperature, measured by laser absorption spectroscopy in [67], also shows only a slight dependence on the applied RF power.

143 Argon metastable density Power-on phase The balance between production (P m ) and loss (L m ) processes determines the density of argon metastable atoms Ar m ( 3 P 2 ): n m (t) t = P m L m = K(T e )n e n g n m(t). (9.3) τ The first term K(T e )n e n g corresponds to the metastable atom production through the electronimpact excitation from the argon ground-state, where K(T e ) is the excitation rate coefficient. The second term n m (t)/τ corresponds to the losses of metastable atoms by diffusion to the walls and by electron-induced collisions, with the equivalent metastable lifetime denoted as τ. For a steady state ( n m (t)/ t = ), the metastable density n m is given by: n m = K(T e )n e n g τ. (9.4) The experimental results of the steady-state argon metastable density n m, presented in figure 9.6(a), show its increase with applied RF power and deposited film thickness. At a given power, the steady-state metastable density increases with the film thickness. For smaller film thicknesses d f < 3 nm, a steep increase of n m is measured, which can be related to the steep increase of steady-state electron densities for the same d f. In this phase, the experimental results show the decrease of the electron temperature T e (figure 9.5), thus K(T e ) should also decrease. However, reduction of impurity concentration leads to the prolonged metastable lifetime τ, which balances the reduced production by excitation. Thus, prevailing increase of steady-state electron density appears to be the process responsible for the steep increase of the steady-state metastable density for smaller film thicknesses. For larger film thicknesses, the increase of steady-state metastable density is continued, although with a slower slope. Due to the constant steady-state electron temperature T e and almost constant steady-state electron density n e for larger d f, no significant change of the the metastable production by excitation coefficient is expected. Following (9.4), we can conclude that the steady-state metastable density is higher at larger d f due to the reduced concentration of oxygen-rich impurities, resulting in longer metastable lifetimes τ. Plasma afterglow In the plasma afterglow phase, an increase of metastable decay time τ m is measured after the film deposition (figure 9.6(b)). With an increase of the applied RF power, the argon metastable atoms decay from the discharge faster with smaller decay time constants τ m. Within the global model (chapter 7) the diffusion and the electron-induced collisions are designated as the dominating metastable loss processes in the discharge. However, the model does not account for impurities in the discharge volume. The diffusion of metastable atoms is

144 146 9 Dynamics of the pulsed reactive discharge in response to thin film deposition described by the diffusion frequency ν di f = D m /Λ 2, whereas the collision frequency ν coll = (K 2 + K 5 + K 8 + k quen )n e describes the collisions between the electrons and metastable atoms (see (7.1)). With an increase of the applied RF power and the film thickness, the diffusion frequency stays constant, since it depends only on the neutral gas density and the dimensions of the discharge. Hence, the changes introduced in the reactor by the film deposition do not affect the diffusion of the argon metastable atoms to the walls. The thin film deposition modifies the collision frequency ν coll, predominantly because of the change in the electron density available in the discharge. At higher RF powers, the density of electrons in the discharge is increased, causing higher collision frequencies ν coll. The metastable losses in collisions with electrons may thus become comparable with their losses in diffusion to the walls (see figure 7.8), resulting in their faster decay in the plasma afterglow, i.e. the smaller decay times τ m at increased RF powers. With the increasing film thickness, the electron-metastable collision frequency should be higher because of the higher electron densities, whereas the diffusion frequency stays constant. Following theses arguments, a decrease of the metastable decay time would be expected due to the higher electron-metastable collision rate. However, the experimental results show an increase of τ m with the film thickness, similarly to the electron decay times τ e. Such behavior could be correlated to the amount of the impurities present in the plasma volume or on the electrode surfaces before and after the deposition of thin hydrocarbon films. Due to the additional electron energy losses through mechanisms such as electron attachment by impurities present in the discharge, the decay of the electron temperature during the plasma afterglow may differ from the one calculated by the global model (figure 7.6). Consequently, the production and loss processes of electrons and argon metastable atoms may be modified, resulting in the change of their decay during the plasma afterglow phase. For smaller film thicknesses, still large concentration of oxygen-rich impurities leads to an enhanced metastable loss rate due to the efficient quenching of metastable atoms by impurities (a similar metastable quenching is observed when acetylene is present in the discharge). After the deposition of hydrocarbon films on the electrodes, the quenching rate is reduced due to the reduced concentration of impurities, which then leads to the slower decay of argon metastable atoms from the discharge and longer decay time constants τ m Electrode voltage Power-on phase The deposition of thin hydrocarbon films also shows an unexpected behavior of the electrode DC voltage measured on the capacitance C of the external circuit. In figure 9.7(a), it can be seen that the absolute DC-bias voltage V f decreases with the increase of the film thickness, in contrast to the expected increase due to higher steady-state electron densities. Comparing the results of V f with the change of the steady-state electron temperature T e

145 147 (figure 9.5), the inflection point for both d f -dependent functions occurs at approximately the same film thickness d f 5 nm. Hence, the slight increase of V f may be related to the increased electron temperatures available in the plasma for clean electrodes or the smallest film thicknesses, which increase the Bohm velocities of ions and the thermal velocities of electrons. Due to the enhanced velocities of the species, their fluxes are also increased, thus providing a larger (negative) DC-bias voltage. After the decrease of electron temperatures due to the thin film deposition, the velocities of electrons and ions are also reduced. This might be a reason for the decrease of the absolute DC-bias voltage V f, in spite of the enhanced electron and ion densities. Plasma afterglow Discharge of the electrode DC voltage in the plasma afterglow follows the decay dynamics of electrons and ions. As previously discussed in chapter 8, the electrode is discharging predominantly by the positive ion flux. However, the discharge time τ C is, in fact, an effective value corresponding to all processes which drive both ions and electrons during the plasma afterglow (e.g. ambipolar diffusion). Figure 9.7(b) shows a decrease of τ C with the RF power and its increase with the film thickness, following the similar behavior of the electron decay times τ e. Hence, this resemblance between τ e and τ C might be explained by the mutual correlation between the electron and ion dynamics in the discharge. Accounting for the film capacitance C f, the discharge time constant τ C of the equivalent electrical circuit in the plasma afterglow, previously given by (8.3), can be found from: ( 1 τ C = 2R pl ( 1 + R )) 1 pl. (9.5) C sh C f C R Since C f C, C sh, the film capacitance C f itself does not impact significantly on τ C according to (9.5). Following the expression (9.5), we conclude that the decrease of τ C with increasing power is correlated to reduced plasma impedance R pl n 1 e. After the deposition of the thin film, the electron losses are decreased due to the removal of oxygen-rich residues, leading to the slower electron decays in the discharge, i.e. higher τ C. Figure 9.8 reports the calculated ion fluxes at the beginning of the plasma afterglow Γ i (), showing their increase with the applied RF power and the film thickness. This can be related to the similar changes in the plasma (electron) density occurring under the same discharge conditions. The ion densities at the beginning of the plasma afterglow n i () show a linear power dependence in the case of both clean electrodes and the electrodes with the deposited film (figure 9.9). Thus, the results for ion fluxes and ion densities in the discharge prove that the non-invasive method of analysis of electrode DC voltage can be applied even in the case of insulated electrodes.

146

147 1 Dust density distribution in symmetrically driven RF discharges This chapter reports on the results of the laser light scattering on dust particles grown in the process of plasma polymerization from acetylene monomers. The performed measurements provide information on the distribution of dust particles under the experimental conditions typically used in this work. The dust density distribution is investigated in the continuously driven and in the pulsed plasmas containing argon/acetylene/dust mixture with different sizes of dust particles. In the continuously driven plasmas, the formation of a void within one cycle of dust growth is observed. After the introductory section 1.1, section 1.2 reports the dust density distribution during one cycle of the dust particle growth in the continuously driven argon/acetylene plasma. In section 1.3, the dust distribution is investigated in pulsed plasmas. 1.1 Introduction The formation of a dust-free void region within the dust cloud is one of the common characteristics of dusty plasmas (section 2.1.3). In a model proposed by Goree et al. [39], the presence of void is attributed to the balance between the ion drag and the electrostatic force acting on dust particles. According to this model, an instability develops in the uniform dust cloud as a consequence of a spontaneous dust density fluctuation. A region with less dust particles has an increased electron density, hence enhanced ionization rates. Due to the positive charge in this dust-free region, an electrostatic field directed towards the surrounding negativelycharged dust particles is formed. The negatively charged dust particles found in the electrostatic field experience two forces: an electrostatic force driving the particles inwards and an outward ion drag force. Depending on the dust size, these forces act differently. The inward electrostatic force is dominating until the dust particles reach a critical size. After that, the outward ion drag force pushes the dust particles away from the initial instability, causing the formation of dust-free void region. A further growth of dust particles enhances the expansion of the void region. When the particles become large enough, they get expelled from the plasma. This general scheme proposed by Goree may be applied for the dust fall on the electrodes or their expulsion away from the plasma bulk, regardless on the experimental conditions. 149

148 15 1 Dust density distribution in symmetrically driven RF discharges In the following sections, experimental results on the distribution of dust particles are reported. The measurements are performed applying the laser light scattering described in section under the discharge conditions typically used within this work. The dust density distribution and the formation of void is observed in CW-driven discharges and pulsed discharges containing argon/acetylene gas mixtures. In this manner, the behavior of dust particles and their dynamics can be distinguished in different phases of their growth or presence in the discharge reactor. 1.2 Dust distribution during a cycle of the dust particle growth Laser light scattering is employed to follow the spatial distribution of hydrocarbon dust particles during one cycle of dust growth in the continuously driven argon/acetylene plasmas. The technique allows to monitor the dust density distribution in the discharge volume with high spatial and temporal resolutions. Besides the light scattering on dust particles, the plasma emission from the discharge volume is measured in different phases of the dust growth cycle. By subtracting the plasma emission from the total scattering signal, it is possible to distinguish the effects of the dust particles in the discharge volume. Figure 1.1 shows the recorded laser light scattering signals in different phases during a cycle of the dust growth at an applied RF power P = 2 W. Argon and acetylene are added to the discharge chamber with typical flow rate ratios of 8 and.5 sccm, respectively, and at a total pressure of p = 1 Pa. The experiment is performed in the cleaned reactor, after the removal of hydrocarbon film residues from the electrodes by oxygen plasma and several hours of a high argon flow to remove the impurities (section 9.2.1). The recorded two-dimensional light scattering images in figure 1.1 show a side-view of the discharge chamber, with the center of the chamber denoted as R = on the R axis (right side of images). The reflections of the laser light on upper and lower electrode with mutual separation of L = 7 cm show the positions of the electrodes as bright lines at the top and at the bottom of each image. A dark circle shows the position of the reactor windows (left side of images). The images in figure 1.1 are recorded with different exposure times (6.5 ms to.6 ms), because of the significant difference in the scattered light intensity in various phases of the dust growth cycle. The final distribution of dust particles in the axial direction (between two electrodes) is calculated by subtracting the background signal and the plasma emission from the total recorded signal shown in figure 1.1, thereby reducing the effects of reflections on the final dust distribution. The axial dust distributions, corresponding to the particular moments of the growth cycles given in figures 1.1, are presented in figure 1.2, with the upper electrode at l = and lower electrode at l = 7 cm. The relative dust distributions are calculated at 4 different radii from the reactor center: 1. in the center ("Center"), 2. at R = 5 cm, 3. at R = 8 cm (corresponding to the position where the void formation is initiated), and at R = 1 cm (corresponding to the axial distribution of argon metastable atoms measured by

149 151 R (cm) R (cm) R (cm) (a) t (b) t (c) t + 9 R (cm) R (cm) R (cm) (d) t (e) t (f) t R (cm) R (cm) R (cm) (g) t (h) t (i) t R (cm) R (cm) R (cm) (j) t (k) t (l) t Figure 1.1: The spatial distribution of dust particles in the argon/acetylene plasma continuously driven at P = 2 W during one cycle of the dust growth. The center of the discharge reactor is at R =. The electrodes with equal radii (R = 15 cm) are separated by L = 7 cm. laser induced fluorescence in section 6.3). The dust growth is initiated after adding reactive acetylene to the pure argon plasma, denoted as the time t in figure 1.1(a). In the pure argon and argon/acetylene plasma before the dust formation, the plasma emission has the largest intensity in the presheath regions, i.e. in the negative glow, as previously noticed in the laser-induced fluorescence measurement of argon metastable density (section 6.3). The calculated distributions in figure 1.2(a) correspond to the light emission due to the reflections on reactor surfaces. The presence of dust particles in the discharge reactor is first noticed at t = t after adding acetylene to the discharge (figure 1.1(b)). This is manifested by the change in the plasma emission from the negative glow regions to the whole plasma volume, which is related to the α γ transition characteristic for the dusty plasmas. Slightly longer times needed

150 152 1 Dust density distribution in symmetrically driven RF discharges Dust density (a.u.) 4 2 R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) 1 5 R = 1 cm R = 8 cm R = 5 cm Center Electrode distance (cm) Electrode distance (cm) Electrode distance (cm) (a) t (b) t (c) t + 9 Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) 1 5 R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Electrode distance (cm) Electrode distance (cm) Electrode distance (cm) (d) t (e) t (f) t Dust density (a.u.) 1 5 R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) 1 5 R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) 1 5 R = 1 cm R = 8 cm R = 5 cm Center Electrode distance (cm) Electrode distance (cm) Electrode distance (cm) (g) t (h) t (i) t Dust density (a.u.) 1 5 R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) 1 5 R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Electrode distance (cm) Electrode distance (cm) Electrode distance (cm) (j) t (k) t (l) t Figure 1.2: The spatial distributions of dust particles during one cycle of dust growth in the CWdriven argon/acetylene plasma at P = 2 W, corresponding to the recorded images in figure 1.1.

151 153 for the dust formation can be attributed to the combination of two effects. First, it takes about t = 58 s that acetylene fills in the space between the electrodes under the applied experimental conditions. Second, it is possible that the critical concentration of precursor molecules necessary for the dust formation is reached at a slower rate due to the higher amount of impurities in the discharge (oxygen/oh residues) after cleaning the reactor with oxygen plasma. In a "dirty" chamber with argon/acetylene in the discharge volume, the dust formations occurs already t 3 s after the plasma ignition. The axial distribution of dust density at t = t , shown in figure 1.2(b), does not differ significantly from the distribution in argon/acetylene plasma in figure 1.2(a), which is due to the low dust density in the initial moments. After the initiation phase, the dust particles continue to grow and to fill the whole discharge volume. In this interval, the distribution of dust particles in both radial and axial direction is rather homogeneous. At approximately t = t after the dust formation, a small dust density redistribution can be observed in the midplane between the electrodes at R = 8 cm, as presented in figure 1.1(c). Besides, dust waves appear in the vicinity of the sheath region. Both effects can be seen in the corresponding relative distributions of dust particles in figure 1.2(c). At R = 8 cm, a deviation from the flat, homogeneous profile of the dust distribution is found between l = 3 4 cm. The dust waves can be recognized as peaks in the dust distribution profile, arising from the intensive light scattered on dust particles. The dust wave s oscillating structure is more pronounced in the vicinity of the lower electrode sheath, which may be correlated to the larger particles usually present at the lower electrode. The dust redistribution, found at R = 8 cm in the midplane between the electrodes, is a position where the development of void is initiated. The void is first observed at t = t , hence approximately 8 minutes after the appearance of dust redistribution. Figure 1.1(d) shows the light scattering signal and figure 1.2(d) the corresponding dust distributions at t = t The void presence is manifested as a dip in the dust density distribution at R = 8 cm. The profiles of dust distribution at R = and R = 5 cm stay approximately flat. All profiles have pronounced wave structures in the vicinity of the sheaths. A change in the homogeneity of the dust distribution is also observed in the radial direction, which is manifested as a darker and more homogeneous region for R < 12 cm, and a brighter zone with more waves for R > 12 cm. This dust redistribution is a result of the ion drag and neutral drag forces acting on dust particles and pushing the larger particles in the radial direction to the outer regions of the discharge volume. The further development of the void occurs on a slower time scale within the next 8 minutes of the dust growth cycle. The void radius is slowly enlarged (see figures 1.1(e) and 1.1(f)). The amplitudes and the frequencies of dust waves are reduced when approaching the end of the dust growth cycle. In the corresponding dust distributions shown in figures 1.2(e) and 1.2(f), respectively, the dips in the density profiles at R = 8 cm become broader, whereas the dust-induced waves are pushed towards the sheaths.

152 154 1 Dust density distribution in symmetrically driven RF discharges Sheath width (cm) CW (P = 2 W) Argon / C 2 H 2 / Dust Upper electrode sheath Lower electrode sheath Time (min) Figure 1.3: The estimated sheath width during one cycle of dust growth in the CW-driven argon/acetylene/dust plasma. Figures 1.1(g)-1.1(l) and 1.2(g)-1.2(l) show a rapid development of the void occurring within about 1.5 min in the final phase of the dust growth, approximately 24 minutes after the dust formation. At this stage, the void has spread in the midplane between the electrodes, covering an area with a radius of approximately 1 cm and being slightly shifted to the upper electrode. The total duration of the dust growth is about 25 minutes. Residual dust particles can be found at the plasma-sheath boundary at the end of the dust growth cycle, visible as the peaks in figure 1.2(l). A new cycle of dust formation begins within the following 1 2 s. Figure 1.3 shows the time evolution of the sheath width during the dust growth cycle, hence in argon/acetylene plasma with dust particles. They are estimated from the recorded laser light scattering images. The estimated sheath widths decrease with the growth of dust particles, which is consistent with the laser induced fluorescence measurements presented in section 6.3. In the first 1 minutes of the growth cycle, the sheath width is reduced from the initial s m.86 cm to s m.35 cm. Afterwards, the time evolution of the sheath width is strongly influenced by the dust-induced waves, oscillating around.35 cm. It can be also noticed, that the sheath width stays approximately constant at the end of the dust growth cycle, which is due to the presence of residual dust particles at the plasma sheath boundary.

153 155 R (cm) R (cm) (a) t (b) t s R (cm) (c) t s R (cm) R (cm) R (cm) (d) t + 47 s (e) t + 9 s (f) t s R (cm) R (cm) R (cm) (g) t s (h) t s (i) t s Figure 1.4: The spatial distribution of dust particles in the pulsed argon/acetylene/dust plasma ( f = 1 Hz, duty cycle 5 %) at P = 1 W. The particles are produced by increasing the pulsing frequency to 8 Hz for 5 minutes. The time t corresponds to the time when the frequency is set back to 1 Hz. 1.3 Dust distribution in pulsed plasmas The hydro-carbonaceous dust particles are produced in the argon/acetylene gas mixture (gas flows 8/.5 sccm and pressure p = 1 Pa) by increasing the pulsing frequency to 8 Hz for 5 minutes. Afterwards, the pulsing frequency is reduced to 1 Hz, to achieve the standard conditions applied throughout this work, and the laser light scattering signals are recorded. The laser, the plasma pulsing and the camera recordings are synchronized (see experimental setup in section 4.2.4). The same procedure is repeated for RF powers varying between 1 and 8 W, which enabled to observe the dust particle distribution with respect to different powers. Figure 1.4 reports the laser light scattering on dust particles applying the RF power P = 1 W. The scattered light images, recorded with an exposure time of 3 ms, show spatial distributions of dust particles in various phases during their presence in the discharge volume of a pulsed plasma. The corresponding dust distributions, obtained after subtracting the plasma emission and the background signal from the total scattering signal, are presented in figure 1.5. These relative dust distributions are calculated at 4 different radii: in the center, and at

154 156 1 Dust density distribution in symmetrically driven RF discharges Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Electrode distance (cm) Electrode distance (cm) Electrode distance (cm) (a) t (b) t s (c) t s Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Electrode distance (cm) Electrode distance (cm) Electrode distance (cm) (d) t + 47 s (e) t + 9 s (f) t s Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Dust density (a.u.) R = 1 cm R = 8 cm R = 5 cm Center Electrode distance (cm) Electrode distance (cm) Electrode distance (cm) (g) t s (h) t s (i) t s Figure 1.5: The spatial distribution of dust particles in the pulsed argon/acetylene/dust plasma ( f = 1 Hz, duty cycle 5 %) at P = 1 W, corresponding to the recorded images in figure 1.4. R = 5, 8 and 1 cm from the discharge center. It can be noticed that the time of the dust presence in pulsed plasma is significantly shorter than the time of the dust growth cycle presented in the previous section 1.2. The dust particles manage to stay in the discharge reactor for about 2 minutes after setting the pulsing frequency back to 1 Hz. After this period, they are ejected away from the plasma volume. The dust distribution in the initial moment t is shown in figure 1.4(a). A darker zone is observed in the midplane between the electrodes, suggesting the lower density of dust particles in this region. In the vicinity of the sheaths, the dust particles induce waves in a similar manner as for the CW-driven discharges. The dust distribution profiles, reported in figure 1.5(a), exhibit a dip in the midplane between the electrodes for radii R = 5, 8 and

155 157 Sheath width (cm) Pulsed plasma (P = 1 W) Argon / C 2 H 2 / Dust Upper electrode sheath Lower electrode sheath Time (s) Figure 1.6: The estimated sheath width in the pulsed argon/acetylene/dust plasma. 1 cm from the discharge center, and wave peaks near the plasma-sheath edge. A significant change can be observed in the light scattering signal already after 1 seconds, as shown in figure 1.4(b). Three zones of different scattered light intensity appear in the discharge volume. The darkest region, positioned centrally in the midplane between the electrodes, probably corresponds to the lowest density of dust particles or to the concentration of particles with the smallest radii. This region is surrounded by two regions of higher scattered intensities. In the following 1 seconds of the measurement, all of the three zones are shrunk to the central region between the electrodes, which can be seen in figure 1.4(c). Due to the increase of scattered light intensity, the dust density appears to increase compared to the initial moment t (figures 1.5(a)-1.5(c). The formation of the dust-free void occurs approximately t = 47 s after setting the pulsing frequency to 1 Hz. Figure 1.4(d) shows the void formed at R = 8 cm, but also the darker zones in the midplane between the electrodes with the smaller densities of dust particles. The axial distribution of dust particles between two electrodes has a relatively flat profile, however with a large void-induced dip in the central region (figure 1.5(d)). Figures 1.4(e)-1.4(i) show that the void is growing more slowly immediately after its appearance, occupying only the central region of the discharge volume. Towards the end of the cycle, the void is spreading, i.e. the dust particles diffuse to the electrodes. The inhomogeneities of the dust particle profile in the radial direction cause the redistribution of the electron and argon metastable densities in this region. The axial distributions of dust densities, reported in figures 1.5(e)-1.5(i), show the rate of the void growth. The dust particles fall on the electrodes approximately 2 minutes after changing the pulsing frequency form 8 Hz at 1 Hz. However, a thin layer of residual dust particles can be still found in the presheath regions, especially at the lower electrode.

156 158 1 Dust density distribution in symmetrically driven RF discharges R (cm) R (cm) R (cm) (a) P = 2 W (b) P = 5 W (c) P = 8 W Figure 1.7: The spatial distribution of dust particles in the pulsed argon/acetylene/dust plasma ( f = 1 Hz, duty cycle 5 %) at different powers: P = 2 W, P = 5 W, and P = 8 W. The particles are produced by increasing the pulsing frequency to 8 Hz for 5 minutes. The images (exposure time 3 ms) correspond to the first moment after setting the pulsing frequency back to 1 Hz. The width of the electrode sheaths in the pulsed argon/acetylene/dust plasma (P = 1 W) are again estimated from the recorded light scattering signals. The time evolutions of the sheath widths on upper and lower electrodes are presented in figure 1.6. In the pulsed dusty plasma, the smallest sheath width is found at the beginning of the measuring cycle with s m.4 cm. This result is consistent with the experimental findings in the CW-driven plasmas (figure 1.3). In the further course of the cycle, the sheath widths are rising towards the widths characteristic for dust-free discharges s m.7 cm. Hence, the plasma pulsing is additionally influencing the ejection of the dust particles from the discharge volume. This is probably the reason why the sheath width becomes larger and resembles more to the sheath width in argon/acetylene mixtures. With an increase of the applied RF power, the duration of the dust presence in the discharge volume is significantly reduced. Figure 1.7 shows the spatial distributions of dust particles in the pulsed argon/acetylene/dust plasma ( f = 1 Hz, duty cycle 5 %) at three different powers: P = 2, 5, and 8 W. At each of the applied RF powers, the dust particles are produced by increasing the pulsing frequency to 8 Hz for 5 minutes. The laser light scattering images in figure 1.7 are recorded at the first moment t after changing the pulsing frequency from 8 Hz to 1 Hz (hence, it is comparable to figure 1.4(a)). It can be noticed that the initial distribution of the dust particles at time t is strongly changed with the power increase. At a lower power P = 2 W (figure 1.7(a)) the dust distribution resembles to the distribution of particles produced at 1 W (figure 1.4(a)). However, the intensity of the scattered light is slightly reduced, which suggests that the smaller concentrations of dust particles are produced in the discharge at higher powers, applying the same time of the dust production. At P = 5 W (figure 1.7(b)) and P = 8 W (figure 1.7(c)), the change of the dust distribution is even more pronounced, manifested by the lack of dust particles in the central region of the discharge volume. This may be related to the increase of the ion drag force with power (due to the increase of ion density in expressions (2.15) and (2.14) in section 2.1.2), which pushes the high-mass precursor molecules out of the discharge volume, thereby diminishing the concentration of dust particles. Hence, at higher applied RF powers, the dust

157 159 dynamics is accelerated. At P = 1 W, the dust particles are present for about 2 minutes in 1 Hz pulsed argon/acetylene plasmas. At higher powers, the dust particles produced under the previously given experimental conditions fall on the electrodes more rapidly: after about 1 s at P = 2 W, about 4 s at P = 4 W, about 2 s at P = 5 W, and after about 7 s at P = 8 W. As previously suggested in section 5.4, such fast escape of the dust particles from the discharge center can explain the rapid disappearance of the electron density peak in the beginning of the plasma afterglow at higher RF powers. To summarize, the presented experiments of the laser light scattering on dust particles show the large differences of the dust distribution in the discharge reactor in both continuously driven and pulsed discharges. Such inhomogeneity in the dust density profile will strongly affect other plasma parameters, especially electron density and electron temperature, and have to be accounted for in future investigations.

158

159 11 Investigation of the interaction of ultraviolet radiation with plasma-suspended nanoparticles In this chapter, the influence of nanoparticles on the ultraviolet (UV) radiation is examined. Section describes the UV absorption in different gas mixtures typically used throughout this work. In section , the UV absorption is measured during the course of the dust particle growth in the plasma volume, hence for dust particles of different sizes Introduction Dust particles are significant constituents of interstellar media (ISM) and their composition and structure is of a key importance. The production of astroanalogues, dust particles with specially tailored properties, in low temperature plasmas in laboratory conditions may provide knowledge about some of the characteristics of dust present in the interstellar media. The optical properties, in particular the absorption and extinction in infrared (IR) and ultraviolet (UV) spectral range, play an important role in the characterization of the laboratory dust particles. By comparing the IR and UV absorption and extinction spectra on the laboratory dust particles with the interstellar extinction curves, it can be determined whether the proposed laboratory dust is a suitable candidate for an astroanalogue. In the past, Kovačević et al. [48] proposed a candidate analogue for carbonaceous interstellar dust, produced by reactive plasma polymerization using acetylene as a precursor material. The experimental IR fingerprint of the proposed candidate has shown a good match to the data obtained from astrophysical observation [7], according to the set of criteria given by Pendleton and Allamandola [128]. The presence of the dust particles in the ISM can cause several different processes, such as reflection, absorption or polarization of the incident light radiation from the surrounding objects (e.g. stars). The dust particles can interact with the light radiation, causing total or wavelength-selective extinction of the light due to the combined effect of the light absorption and scattering on dust particles. The extinction depends on different properties of dust particles, such as their composition, density, size, shape and orientation, but also on the properties of incident light (frequency and polarization state) [8]. The intensity of light radiation after 161

160 Interaction of ultraviolet radiation with plasma-suspended nanoparticles passing the dust cloud I(λ) is related to the intensity of the incident light I (λ) by [129]: I(λ) = I (λ) exp ( τ(λ)). (11.1) Here, τ(λ) is the optical thickness, representing the total extinction cross section of all particles along the line of sight. The interstellar extinction is given by [129] : A(λ) = 2.5 ln I(λ) 1.86τ(λ). (11.2) I (λ) The optical thickness τ(λ), hence the interstellar extinction A(λ), are related to the dust density n d and dust size according to: τ(λ) = S d Q ext (m, r d, λ)n d x, (11.3) where S d and r d are cross section and radius of a dust particle, respectively, m is refractive index, x is light path distance, and Q ext is the wavelength-dependent extinction efficiency [129]. Thus, the investigation of the transmitted light radiation and the extinction on dust particles can provide knowledge on the chemical composition, as well as density and shape of the dust particles. The presence of the interstellar dust determines the structure of the interstellar extinction curve in the UV, visible, IR, and far IR spectral range. Several different features have been observed in the interstellar extinction curve, although their origin is not fully understood: silicate features at 9.7 µm (attributed to the S = O stretching), diffuse interstellar bands in visible range 57 nm < λ < 67 nm, 3.4 µm feature (attributed to aliphatic C H stretching mode), interstellar ices at 3.1 µm (attributed to O H stretching in solid H 2 O), and polycyclic aromatic hydrocarbons [13]. However, a most prominent and well-exposed feature of the extinction curve is a broad bump in the UV region at the central wavelength of nm. Since its discovery in 1965 by Stecher [131], the nm feature has been a topic of investigation in the astrophysical and dusty plasma community, because of the controversy regarding its origin. Generally, there is an agreement that the nm UV feature originates from carbon in graphitic form, i.e. from the π π electronic transition induced by the photon absorption [13]. However, other carbon-containing structures, such as hydrogenated amorphous carbon, polycyclic aromatic hydrocarbon or hyper-fullerene carbon have been also regarded as candidates responsible for this UV feature (see e.g. [71, 13, 132]). In this work, the interaction of ultraviolet radiation with nanoparticles suspended in plasmas is investigated. An emphasis is set on the hydro-carbonaceous dust particles produced by plasma polymerization from acetylene as a precursor gas. The UV extinction on these dust particles should complement previously measured IR extinction [7]. The first step of the study required the installation and testing of the UV spectroscopic experimental system,

161 163 which has been described in details in section In the second step, the absorption on hydro-carbonaceous dust particles in the UV spectral range is measured under different discharge conditions, depending on the dust size, gas composition (with and without reactive acetylene) or applied RF power. The purpose of the study is to observe the nm UV extinction bump in the case of the applied astroanalogue Results and discussion The investigated dust particles were produced by plasma polymerization using acetylene (flow rate Q =.5 sccm) as the precursor gas and argon as a carrier gas (flow rate Q = 8 sccm). The total gas pressure is kept constant at p = 1 Pa. The optical thickness τ(λ) is determined from the relation between the incident and transmitted light radiation, according to (11.1). Thereby, the total signal PL(λ), corresponding to the intensity of the transmitted light, and L(λ), corresponding to the intensity of the incident light radiation, are measured. The effects of the emission coming from the plasma itself PE(λ) (without the light from the source) and the background B(λ) (noise of the detecting system) have to be also accounted for. Finally, the optical thickness is calculated by: τ(λ) = ln ( ) ( ) I (λ) L(λ) B(λ) = ln. (11.4) I(λ) PL(λ) PE(λ) UV extinction on dust particles suspended in reactive and non-reactive gas mixtures The UV radiation is examined in the discharges containing argon, acetylene, and dust particles. The control of the plasma polymerization process is achieved by pulsing the plasma with the standard pulsing frequency f = 1 Hz and duty cycle 5 % at the applied RF power of P = 2 W. The dust particles are created by increasing the pulsing frequency to f = 8 Hz for 3 minutes, in order to grow the particles of about 5 7 nm in radius. The formation and presence of dust particles is monitored by simultaneous measurements of the infrared extinction spectra using the Fourier Transform Infrared Spectroscopy and observing the IR fingerprint characteristic for the hydro-carbonaceous dust particles [7]. Figures 11.1 show the intensities of the incident light radiation I (λ) coming from the deuterium lamp, the transmitted light radiation PL(λ) after the extinction, and the plasma emission PE(λ) recorded in different gas mixtures, with the corresponding optical thicknesses ln (I (λ)/i(λ)). The spectral range between nm is observed, previously calibrating the wavelengths according to the known spectral response of the deuterium lamp (figure 4.11). The error of the performed wavelength calibration is estimated to δλ = 2 nm. The exposure time of the CCD camera chip is set to 3 s, whereas the signal-to-noise ratio is improved by increasing the number of accumulations to 5. A noise reduction is achieved by cooling the

162 Interaction of ultraviolet radiation with plasma-suspended nanoparticles Intensity (a.u.) I Argon Argon/C 2 H 2 Argon/C 2 H 2 /Dust Argon/Dust Wavelength (nm) (a) Incident radiation I and the transmitted radiation PL(λ). ln(i /I) Intensity (a.u.) Argon Argon/C 2 H 2 Argon/C 2 H 2 /Dust Argon/Dust Wavelength (nm) (b) Plasma emission PE(λ). Argon Argon/C 2 H 2 Argon/C 2 H 2 /Dust Argon/Dust Wavelength (nm) (c) Optical thickness ln (I (λ)/i(λ)). Figure 11.1: Intensity of (a) the incident radiation I and the transmitted light radiation PL(λ), (b) the plasma emission PE(λ), and (c) the optical thickness ln (I (λ)/i(λ)) in different gas mixtures: argon, argon/acetylene, argon/acetylene/dust, and argon/dust. The production of dust particles is controlled by pulsing the plasma with frequency f = 1 Hz and duty cycle 5 % at P = 2 W. camera down to 4 C. The signal of plasma emission PE is recorded by using a mechanical shutter to cover the radiation from the deuterium lamp. The final calculation of the optical thickness is performed according to (11.4). In figure 11.1(a), the initial radiation from the deuterium lamp I is compared to the intensities of the transmitted light PL in different gas mixtures. In the pure argon plasma, the intensity of the transmitted light PL is not significantly changed in comparison to the incident light I. However, several peaks are observed in the transmitted signal PL, which can be attributed to the emission coming from the plasma, as presented in figure 11.1(b). The strongest

163 165 peak is found at the central wavelength of nm ± δλ, whereas the other strong peaks correspond to the wavelengths of nm, nm, nm, and nm. The origin of these peaks remains an open question. They might originate from the hydro-carbonaceous content, sputtered away from the electrodes or the reactor walls. A possible source of these emission peaks might be also molecular impurities in the discharge (for instance, the traces of nitric oxygen γ system [133]). The plasma emission peaks, however, do not affect the optical thickness, hence the UV extinction (figure 11.1(c)). Furthermore, the optical thickness stays approximately constant in the observed wavelength range. In the pure argon plasma, the optical thickness is approximately zero, suggesting no extinction occurs. In argon/acetylene plasma, a reduction of the transmitted light PL is observed in comparison to the pure argon plasma. Hence, a portion of the incident light is probably absorbed or scattered due to the presence of the acetylene molecules in the discharge, as well as the high-mass molecules created in the process of polymerization. The most striking difference is noticed in the plasma emission signal PE (figure 11.1(b)), which is decreased about an order of magnitude compared to the pure argon plasma. This is consistent with the previously observed reduction of the plasma emission in the visible spectral range, which is due to the high quenching rate of argon metastable atoms by acetylene (see laser induced fluorescence in section 6.3). After the formation of dust particles in the discharge volume, the intensity of the transmitted light PL is further significantly reduced due to the extinction by dust. A slight elevation can be observed in the baseline of the plasma emission PE, corresponding to the overall increase of the plasma emission arising from the presence of dust (section 6.3). Still, the plasma emission lines remain small. The UV radiation is absorbed or scattered on the dust particles, inducing an increase of the optical thickness compared to the dust-free mixtures (figure 11.1(c)). The optical thickness/extinction stays approximately constant in the observed UV spectral range. However, the UV extinction on dust particles produced under given discharge conditions (with estimated radii of about 7 nm) does not result in the appearance of the UV feature at nm. After the removal of acetylene from the reactor, the mixture of argon and dust particles remains in the discharge volume. The presence of the dust particles leads to the expected extinction in the observed UV spectral range. The intensity of the transmitted light PL is higher than in the argon/acetylene/ dust mixture, due to the absence of acetylene. In the absence of acetylene, the increase of the plasma emission at wavelengths previously detected in the pure argon plasma is noticed. The plasma emission is slightly higher as expected due to the particles present in the discharge. Similarly to other gas mixtures, the optical thickness stays approximately constant over the investigated UV spectral range. The UV feature at the central wavelength of nm is again absent in argon/dust plasma. It is possible that the density or size of the dust particles in discharge volume is not sufficient for the detection of the UV nm bump.

164 Interaction of ultraviolet radiation with plasma-suspended nanoparticles Intensity (a.u.) Argon/C 2 H 2 /Dust CW (P = 2 W) t + 12 min t + 16 min t + 25 min t + 3 min Wavelength (nm) I t t + 3 min t + 5 min (a) Incident radiation I and the transmitted radiation PL(λ). ln(i /I) Argon/C 2 H 2 /Dust CW (P = 2 W) t t + 3 min t + 5 min t + 12 min t + 16 min t + 25 min t + 3 min Wavelength (nm) (b) Optical thickness ln (I (λ)/i(λ)). Figure 11.2: Intensities of (a) the incident radiation I and the transmitted radiation PL(λ), and (b) the corresponding optical thickness ln (I (λ)/i(λ)) during a dust growth cycle (CW-driven plasma at P = 2 W) UV extinction on dust particles during one cycle of dust growth In the following experiment, the dust particles are grown in continuously driven discharges, using the typical gas flow rates and total pressure. Under these conditions, the growth rate of dust particles is about 24 nm/min [26]. However, the dust density distribution in the line of sight is changing depending on the phase in the dust growth cycle, as previously shown by the laser light scattering experiments in section 1.2. The radiation intensities I(λ) are recorded with the exposure time of 1 s and 1 accumulations. The camera is cooled down to 4 C. Due to the presence of acetylene in the discharge, the plasma emission PE(λ) is accounted for less than.1 % in the total transmitted light radiation PL(λ), hence it can be neglected. The optical thickness is calculated according to (11.4), taking into consideration the background signal. Figure 11.2(a) shows the intensities of the transmitted light radiation PL(λ) in the observed UV spectral range during a cycle of dust growth, with respect to the incident light radiation I (λ). Immediately upon the formation of dust particles in the discharge, a decrease of the transmitted light intensity PL is initiated, arising from the extinction of the incident radiation. After the formation of void and the decrease of dust density in the midplane between the electrodes, the intensity of the transmitted radiation is slowly rising towards the initial radiation intensity at t. Such temporal behavior of the transmitted light radiation is reflected on the behavior of the optical thickness, hence the UV extinction, during the dust growth cycle. The optical thicknesses in different phases of the dust growth cycle, corresponding to PL in figure 11.2(a), are shown in figure 11.2(b). Similarly to the results obtained using various gas mixtures (fig-

165 P = 2 W P = 6 W.6 ln(i /I) Time (min) Figure 11.3: Temporal evolution of the average optical thickness in the observed UV spectral range between nm during a cycle of dust growth at different applied RF powers P = 2 W and P = 6 W. ure 11.1(c)), the optical thicknesses ln (I (λ)/i(λ)) are nearly wavelength-independent in the observed UV spectral region during each phase of the dust growth cycle. Figure 11.3 shows the temporal evolution of the averaged optical thickness ln (I (λ)/i(λ)) during one cycle of the dust growth. The averaging of the measured signal is possible due to the nearly constant value of the optical thickness in the observed UV spectral range. The optical thickness is initially increasing corresponding to the growth of dust particles, whereas the later decrease is related to the development of the dust-free void region in the central region of discharge volume. The further cycles of the dust growth induce the periodical behavior of the optical thickness, which is consistent with the previously measured absorbencies in the infrared spectral region [7]. With an increase of the applied RF power, the optical thickness retains its characteristic temporal evolution. However, a slight difference can be noticed by comparing the temporal evolutions of optical thicknesses at P = 2 W and P = 6 W, which is probably related to the dynamics of dust particles at higher powers. From the analysis of the measured data, it can be seen that the change of the dust size does not affect the appearance of the requested UV feature at nm. Even by removing acetylene from the discharge and stopping the further growth of particles, the UV extinction bump at nm does not appear. The same set of measurements of the UV extinction spectra has been performed using helium as a carrier gas and acetylene as a dust precursor gas. In this case, the general behavior of the UV extinction is the same as for the mixtures with argon, with additional peaks in the plasma emission. Nevertheless, the UV bump at nm is also not detected in helium/acetylene gas mixtures. Therefore, the requested UV feature is not found in the UV extinction on the particles produced by plasma polymerization from acetylene as precursor gas.

166

167 12 Summary The dynamics of reactive and non-reactive capacitively coupled radio-frequency driven discharges in response to the formation of nanometer-sized dust particles was investigated in the presented work. An emphasis was set on the dynamics of pulsed discharges containing the mixtures or argon and acetylene with nanoparticles. Plasma pulsing was applied to provide an efficient control of the dust particle formation in the process of plasma polymerization from acetylene monomers. Secondly, the behavior of plasma and its parameters in different stages of a pulse cycle may provide a knowledge on the dominating production and loss processes in the discharge. An afterglow phase of the pulsed discharge may be of a particular importance to monitor the losses of different plasma components (such as electrons, ions, or metastable atoms), which are, in the power-on phase, masked by a large production. Various diagnostic methods were applied to characterize the pulsed argon/acetylene plasmas prior and after the formation of nanometer-sized dust particles. Electron densities and electron temperatures were monitored by microwave interferometry and Langmuir probe method. Argon metastable atoms in the 3 P 2 state were examined by the means of laser absorption spectroscopy and laser induced fluorescence. The dynamics of positive ions was deduced from the analysis of electrode DC-bias voltages. The laser light scattering was employed to monitor the distributions of dust particles in the discharge volume in different phases of their growth. The simultaneous measurement of various plasma parameters enabled to establish their mutual relation under various discharge conditions, including the changes of gas composition, power input and electrode surface conditions. The simultaneous measurements of electron and argon Ar m ( 3 P 2 ) metastable densities in different discharge conditions revealed a mutual correlation between these plasma parameters. It was shown than the densities of electrons and argon metastables in both power-on and afterglow phase of a pulsed discharge depend strongly on the applied gas mixture. The presence of dust particles in the discharge volume was reflected on the steady-state values of electron and argon metastable densities in an expected manner: the electron density was reduced about one order of magnitude due to their collection by dust particles, whereas the steady-state metastable density increased significantly as a consequence of the electron temperature rise in dusty plasmas. The argon metastable densities, however, showed a significant decrease upon adding acetylene in the discharge regardless of the dust presence, which was attributed to the high quenching of metastables by acetylene. The effect of the acetylene pres- 169

168 17 12 Summary ence was pronounced in the plasma afterglow, inducing the fast decay of both electrons and argon metastables from the discharge. Moreover, even with the dust particles in the discharge, a significantly faster decay of electron and argon metastable densities decay was found in an acetylene-containing discharge. Thus, although the dust particle presence in the discharge is responsible for the reduction of electron density in the power-on phase, the decay of electrons in the plasma afterglow is predominantly determined by the presence of reactive acetylene. Furthermore, an anomalous behavior of the electron density, manifested by its rapid increase in the initial phase of the plasma afterglow, was observed in both dust-containing mixtures, argon/acetylene/dust and argon/dust, and at all of the applied RF powers. However, with an increase of the RF power, the dust particles diffused rapidly from the discharge center, leading to an immediate disappearance of the electron density afterglow peak. The origin of the electron density afterglow peak was investigated by the space-averaged global model for the afterglow of the pure argon and argon plasma containing large densities of dust particles. In the model, different production and loss process of electrons and argon metastables were taken into account to observe their temporal evolution during the plasma afterglow phase. In the afterglow of a dust-free plasma, electrons were predominately lost due to their diffusion to the walls, whereas the diffusion to the walls and the collisions with electrons governed the losses of argon metastable atoms. In the afterglow phase of the argon/dust plasma, different mechanisms, which might induce the appearance of the afterglow peak of electron density, were observed: electron-impact ionization, secondary electron emissions in ion-dust and dust-metastable interactions, and the reionization in metastable-metastable collisions (metastable pooling). It was found that the electron production in metastable pooling might have the largest impact on the electron density afterglow peak. The electron density and argon metastable densities in pulsed plasmas reacted not only on the formation of dust particles in the discharge, but also on the deposition of hydrogenated amorphous carbon film on electrodes. Both electron and argon metastable densities experienced increases of their steady-state densities in the power-on phases, appearing after the increase of the deposited film thickness on electrodes. Furthermore, the lifetimes of electrons and argon metastables in the plasma afterglow were prolonged upon the film deposition on electrodes. Such behavior was attributed to the change in the production and loss processes in the discharge, probably due to the removal of oxygen-containing impurities from the discharge. The oxygen/oh impurities in the discharge volume and on the electrode surface, appearing after the reactor cleaning by the oxygen plasma, induced an increase of electron losses in the discharge volume. Due to the higher electron losses directly after the reactor cleaning, an increase of the electron production was imposed through the higher electron temperatures, experimentally confirmed by the Langmuir probe measurements. Thus, the gradual deposition of the thin film on electrodes reduced the amount of impurities in the discharge, finally leading to the increase of measured electron and argon metastable densities.

169 171 A non-invasive diagnostic method for determination of ion fluxes and ion densities in low pressure radio-frequency driven plasmas was proposed in this work. The ion flux towards the electrodes was deduced from the change of the DC-bias voltage during the plasma afterglow phase. The measurement of the electrode DC-bias voltage was conducted using an external LC circuit with a large capacitance C, thus making the proposed diagnostics noninvasive and applicable in the case of reactive plasmas. The measured electrode DC voltage reacted sensitively on the change of discharge conditions (applied RF power, gas mixtures or electrode surface conditions), corresponding to the expected dynamics of positive argon ions in the discharge. Taking into account the profile of the ion density between the electrodes, the ion density could be deduced from the measured ion flux. Good agreements with the independently and simultaneously measured electron densities were obtained in the dust-free plasmas, assuming the electron temperature in the late afterglow T aft.1 ev. In dusty plasmas, the proposed method could be applied to find the fluxes and densities of ions on the plasma-sheath boundary, whereas the accurate profile of ion density have to be known for the determination of ion densities in the central region of the plasma bulk. Furthermore, the dynamics of dust particles in the discharge could be of a great importance for the distribution of other plasma parameters, in particular electron density and electron temperature, but also the densities of ions and argon metastable atoms. The axial distribution of argon metastable atoms, measured during a cycle of the dust growth in continuously driven argon/acetylene discharge, showed an α γ transition as a response to the dust particle formation. Hence, the production of the argon metastable atoms in dusty plasma occurred in the whole plasma volume, in contrast to the dominant production in negative glow regions characteristic for the dust-free discharges. The distribution of dust density during a cycle of the dust growth and in the pulsed plasma was investigated by means of laser light scattering. The measurements revealed the time scales of the particular events characteristics for the dust growth, such as the sole production of dust particles, their filling of the whole plasma volume, dust-induced waves, and the formation and development of a dust-free, void, region. Moreover, it was shown that the time scales of the dust presence in the pulsed discharges was significantly faster in comparison to the CW-driven discharges, being expressed in seconds, rather than minutes. Finally, the impact of the ultraviolet radiation on the hydro-carbonaceous dust particles produced by the plasma polymerization from acetylene monomers was investigated. The UV extinction measurements on dust particles showed an increase of the extinction with the size of the dust particles and their density. After the development of a dust-free void region in the midplane between the electrode, a decrease of the measured UV extinction is noticed, corresponding to the lower density of dust particles on the pathway of UV light. However, no significant fingerprint of the investigated dust particles in the UV region was noticed.

170 Summary Moreover, the prominent UV feature on nm, characteristic for the interstellar extinction curves, was not found, suggesting that some other component or gas composition might be responsible for its appearance.

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180 182 Bibliography [123] V. Massereau-Guilbaud, I. Géraud-Grenier, and A. Plain, Determination of the electron temperature by optical emission spectroscopy in a MHz dusty methane plasma: Influence of the power, J. Appl. Phys., vol. 16, no , 29. [124] V. Massereau-Guilbaud, J. Pereira, I. Géraud-Grenier, and A. Plain, Influence of the power on the particles generated in a low pressure radio frequency nitrogen-rich methane discharge, J. Appl. Phys., vol. 15, no. 3, p. 3332, 29. [125] S. Hong, From Thin Films to Nanoparticles: Investigation of Polymerization Processes in Capacitively Coupled Hydrocarbon Plasmas. PhD thesis, Ruhr-Universität Bochum, 24. [126] J. Gudmundsson and E. Thorsteinsson, Oxygen discharges deluted with argon: dissociation processes, Plasma Sources Sci. Technol., vol. 16, pp , 27. [127] NIST, [128] Y. Pendleton and L. Allamandola, The organic refractory material in the diffuse interstellar medium: Mid-infrared spectroscopic constraints, Astrophys. J. Suppl. Ser., vol. 138, no. 1, p. 75, 22. [129] N. Voshchinnikov, Optics of Cosmic Dust 1. Astrophysics and Space Physics Reviews, 24. [13] B. Draine, Interstellar dust grains, Annu. Rev. Astron. Astrophys., vol. 41, pp , 23. [131] T. Stecher, Interstellar extinction in the ultraviolet, Astrophys. J., vol. 143, p. 1683, [132] A. Li, Interaction of nanoparticles with radiation, ASP Conference Series, vol. 39, pp , 24. [133] R. Pearce and A. Gaydon, The indentification of molecular spectra. Chapman & Hall Ltd London, 1968.

181 Acknowledgements Hereby, I would like to kindly acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG) within the granted project WI17/3 and the Ruhr University Research School funded by Germany s Excellence Initiative. I would like to express my sincerest gratitude to the colleagues from the Institute of Experimental Physics II and Research Group Reactive Plasmas at Ruhr Universität Bochum for the comfortable working atmosphere and wonderful time spent here. I would like to thank to Prof. Dr. Jörg Winter, for the given opportunity to conduct this doctoral thesis at the Institute for Experimental Physics II, for the support and backup in scientific communications and motivation for further achievements. It was a honor and pleasure to work under his supervision. To Prof. Dr. Henning Soltwisch I thank for the willingness to cooperate and accept the supervision of this thesis. To Dr. Ilija Stefanović, I would specially like to thank for the introduction into the world of dusty plasmas, for the countless discussions and patience, as well as for all the support and advices in administrational and "life" stuff at University and out of it. My sincerest gratitude goes to Prof. Dr. Igor Denysenko and Prof. Dr. Nader Sadeghi for the joint collaboration, valuable scientific discussions and results arising from it. To Dr. Andreas Aschinger I thank for the selfless help in experiments, for advices and brainstorming about dusty plasmas and for the nice office atmosphere. To Dr. Jan Benedikt and Dr. Benedikt Niermann I would like to thank for the help in the optical ellipsometry measurements. To Dr. Marc Böke, Dr. Volker Schulz-von der Gathen, Dr. Teresa de los Arcos, and Dr. Ante Hećimović I would like to thank for the assistance in experimental work, discussions on scientific and other subjects, as well as for the good atmosphere at the Institute, which could not exist here without their great attitudes. Special thanks go to Mr. Axel Lang, Mr. Michael Konkowski, Mr. Kai Fiegler and Mr. Björn Redeker for construction of the experiment and help on all technical questions. I would also like to thank to Ms. Margot Ocklenburg, for the help and patience in the sea of administrational difficulties. Finally, I dedicate this work to my family.

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183 Curriculum Vitae Personal data: Name: Brankica Sikimić Date of birth: 11/2/1981 Place of birth: Novi Sad, Serbia Education: Since 1/29 Doctoral studies at Ruhr Universität Bochum, Germany Research field: Dusty plasmas 9/27-7/28 School of Information Technology Application Development Programming 9/1999-7/27 Faculty of Electrical Engineering, University of Belgrade, Serbia Department: Physical Electronics Study group: Optoelectronics and Laser Engineering 9/1995-7/1999 X Belgrade Gymnasium "Mihailo Pupin", New Belgrade, Serbia 9/1987-7/1995 Elementary School "Ratko Mitrović", New Belgrade, Serbia

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