Diagnostics and modeling of an inductively coupled radio frequency discharge in hydrogen

Transcription

1 Diagnostics and modeling of an inductively coupled radio frequency discharge in hydrogen Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften in der Fakultät für Physik und Astronomie der Ruhr-Universität Bochum von Victor Anatolievich Kadetov aus Moskau Dissertation eingereicht am:.5.4. Tag der mündlichen Prüfung: Referent: Prof. Dr. rer. nat. Uwe Czarnezki Korreferent: Prof. Dr. rer. nat. Ralf Peter Brinkmann Bochum 4

2 Contents. Introduction...5. Brief review on ICPs Fundamentals RF discharge basics Plasma generation in RF discharges RF discharges classification CCP discharges ICP discharges Diagnostic tools Langmuir probe Fluorescence-dip spectroscopy Ion energy and mass analyzer Emission Spectroscopy Theory Analytical model of a hydrogen plasma Profiles of plasma potential and plasma density (relative values) Electron temperature Energy balance Plasma density (absolute values) Electrical model of an ICP source Plasma configuration in a planar ICP Set of equations for the transformer model Modeling an ICP source The efficiency of the GEC reference cell as a hydrogen plasma source Modification of the antenna design The modified plasma source Sheath theory Static sheath Sheath in ICP Ion energy distribution Experimental setup...75

3 5.. Plasma source ICP setup ICP source characterization Diagnostics Langmuir probe measurements Laser diagnostics Measurement of ion energies Optical measurements Results Gas Temperature Doppler broadening Gas temperature of a hydrogen ICP Plasma bulk parameters Electron energy distribution function Electron temperature Plasma density Sheath dynamics Electric field in the ICP sheath Time-averaged electric field Time-varied electric field in the sheath Sheath parameters Ion Energy Distribution functions Energy distribution of the ion flux Electron temperature at the sheath edge Plasma potential CCP-ICP mode transition ICP emission Intensity modulation Mode transition Mode transition in the pulsed ICP Summary and conclusions...4 Appendix A List of symbols and abbreviations...7 Appendix B Analytical model of a hydrogen plasma... B.. Particle transport equations...3 3

4 B... Diffusion approximation...4 B.. Energy transport equation...4 B... Elementary processes in a hydrogen plasma...4 B... Energy loss due to a particle transport...5 B..3. Ohmic heating...5 B..4. The average density and the density at the sheath edge...6 B..5. Local energy balance and induced electric field...7 B.3. One-dimensional model...8 B.3.. B.3.. B.3.3. B.3.4. B.4. Set of dimensionless variables...8 Particle transport equations...9 Profiles of plasma potential and plasma density (relative values)...9 Electron temperature...3 Spatially resolved model in the diffusion approximation...3 B.4.. Plasma density in the entire discharge volume...3 B.5. Absolute value of the plasma density...33 Appendix C Transformer model...34 C.. Inductive power coupling into the plasma...34 C... Structure of an electromagnetic field induced in a vacuum...34 C... Antenna-plasma transformer...36 C..3. Antenna inductance and transformer impedance...38 C..4. Influence of the antenna inductance on current and voltage...39 C..5. Induced currents in conducting materials of the vacuum chamber...39 C..6. Geometrical assumptions about the planar ICP...4 C..7. Electron density...4 C..8. Skin depth...43 C.. Capacitive power coupling into the plasma...43 C... Capacitive power coupling and transformer impedance...43 C... Simplifications in the electric circuit...45 C.3. ICP matching network...46 C.4. Calibration...47 C.4.. Antenna impedance...47 C.4.. Capacitance between the antenna and plasma...48 C.5. Efficiency of power coupling into plasma...49 Literature...5 4

5 . Introduction The boom in the semiconductor industry has dramatically increased the interest in plasma-assisted material processing. This has prompted a broad range of gas discharge studies, particularly on RF discharges. The inductively coupled plasma (ICP) sources produce high-density, uniform plasmas at low gas pressures and are used for microelectronics production [Hop 9, Eco ]. Although researchers have known about ICPs for over one hundred years [Eck 6], they have not been extensively investigated until recently [Hop 93, Tus 96, Che 96, Lie 98, God 99, Suz, Bog ]. An understanding of plasma physics and surface science is needed to develop plasmaassisted processes. The relationship between the physical and chemical processes occurring in the plasma is generally unclear and complicated. Because of this, processes are often designed using trial and error. The great number of parameters; such as the discharge geometry, gas composition, pressure, incident power, and flow rate; hamper the systematic analysis of experimental data. Therefore, it is important to develop an understanding of the low-pressure ICP in terms of a physical model, which includes the main particularities of the power coupling mechanism, plasma generation and the sheath formation. The model should be simple enough to be calculated analytically, realistic enough to agree qualitatively with measurements, and transparent enough to allow some insight into the physical mechanisms and phenomena occurring in the ICP. A one-component gas simplifies the task by excluding plasma chemistry from the investigation. This orients the plasma model towards a description of electron-molecule interactions. Where as the model of a many-component discharge is more oriented towards the various interactions between atoms, molecules, and radicals. Such complex systems generally only have numerical solutions. In this study, a hydrogen ICP discharge was generated. Hydrogen is widely used for plasma-assisted material processing; it is used as reducing agent for oxidized materials [Got 9], and as a background gas for diamond-like film deposition [Bac 9, Awa 97]. At the time this work was started, there were no investigations on low-pressure ICPs in pure hydrogen. The chief goals of this study were therefore: Design, manufacture, and optimize a hydrogen ICP source. Carrying out a complete set of the plasma diagnostics to study the bulk plasma and the sheath. Model the hydrogen ICP source to gain a better understanding of the possible mechanisms that could be used for controlling the plasma parameters. Analyze the experimental and theoretical results to reconstruct the underlying processes occurring in the RF discharge. 5

6 The standard GEC reference cell was used as an ICP source [GEC 94, GEC]. In this cell, an additional planar electrode allows more independent control sheath parameters from other plasma parameters. The GEC reference cell is representative of commercial cells used by the semiconductor industry. In order to perform investigations in pure hydrogen, the efficiency of this plasma source was improved. For this purpose, the GEC reference cell was supplied with a novel, multi-spiral antenna. The range of plasma conditions was further extended by pulsing the discharge. For the experimental investigations, Langmuir probe measurements, measurements of the electric field distribution across the sheath, measurements of the mass and energy spectra of hydrogen ions coming to the electrode surface, and time-resolved optical measurements of plasma radiation were carried out. At the time of writing, The fluorescence-dip spectroscopy (FDS) electric field measurements [Cza 98] were the first experimental study of the Debye sheath dynamics in an RF discharge [Cza ]. The physical model of a one-component, molecular gas discharge can be extremely complex. Several research groups have modeled hydrogen discharges numerically. There is a kinetic model for a microwave discharge [Has 99], a particle in cell (PIC) model for an RF parallel-plate reactor [Cap ], and a global model for the deuterium negative ion source experiment (DENISE) [Zor ]. However, a hydrogen plasma is an almost ideal system for analytical modeling: it has one dominate ion species (H 3 + ) at lower electron temperatures, it has a constant collision frequency when expressed as an E-field-to-pressure ratio, and all relevant cross sections are known. Further, this work demonstrated that in the hydrogen ICP the electron energy distribution function (EEDF) is almost Maxwellian. During the course of this study, an analytical model of a hydrogen plasma was developed. The model consists of three modules linked together. Input parameters are the planar cell geometry, the neutral gas pressure, the neutral gas temperature, the incident RF power, and the antenna resistance. The plasma model module allows the calculation of the electron density, the electron temperature, and the effective electron-neutral collision frequency. The electrical model relates the incident RF power to the power dissipated in the discharge either capacitively or inductively by calculating the respective currents in the plasma. Finally, the sheath model calculates the fields, potentials, currents, and the ion energy distribution function. While the former two models are analytical, the latter integrates Poisson s equation numerically. This model is consistent with measurements. Moreover, the analysis of experimental data using the analytical model extends the capabilities of the plasma diagnostics used in the study. For example, the temporal and spatial modulation of Balmer-α emission from the plasma was measured and then used for finding the ICP mode transition. This is a new method which is applicable for both continuous and pulsed discharges. The results from different diagnostics were rigorously compared. The thesis is organized as follows. A brief history of ICP discharges, investigations of these discharges, and its applications is reviewed in Chapter. Chapter 3 introduces the 6

7 fundamentals of RF plasmas. The first section of Chapter 3 explains the underlying physical principles and contains examples of frequently observed phenomena in RF discharges. The second section describes the analytical methods and the diagnostic tools used in this study. Because of the limited size of the work, a broad variety of historical and scientific facts about RF discharges are not presented here. Therefore, the selected material for Chapters and 3 is subjective. These chapters are not intended as a general review of the subject. A model of the hydrogen ICP is presented in Chapter 4. As was mentioned above, the model consists of three modules. The first two modules, the plasma module and the electrical module, are described in detail in Appendixes B and C. These sections allow one to repeat all calculations from the underling physical laws to the final results. The experimental setup is described in Chapter 5. In addition, this chapter contains the measurement schemes and outlines the calibration of the plasma diagnostics. The neutral gas temperature, the electron temperature, the plasma density, the electron energy distribution (EEDF), the ion energy distribution (IEDF), and the electric field distribution in the sheath were measured. In Chapter 6, these measurements are compared and contrasted with calculations from the ICP model. Chapter 7 summarizes the results and conclusions. The thesis is supported with a list of symbols and abbreviations, Appendix A, and with a bibliography. 7

8 . Brief review on ICPs The first inductively coupled plasma (ICP) was produced in 884 by J.H. Hittorf by discharging a Leyden jar through a coil surrounding a glass chamber [Eck 6, Mat 3]. At the end of the 9th century, the development of alternating current (AC) sources allowed the stationary generation of ICP discharges. The electrodeless mechanism that sustains ICP generation was disputed until 99 when McKinnen showed that these discharges were usually capacitively sustained by power coupling between the low- and high-voltage ends of the coil. He believed that only at high applied powers and erroneously at high gas pressures the plasma was inductively coupled to the coil [Mac 9]. Mainly due to higher power costs, capacitively coupled plasmas (CCPs) and microwaves were used in place of ICPs for electrodeless discharge technology. In 96, T.B. Reed proposed using an ICP [Ree 6, Reed 6, Ree 6] for atomic emission spectroscopy (AES). In AES, inorganic materials are dissociated and exited using a gaseous discharge. The plasma emissions determine qualitatively the elemental composition of the sample. Direct current plasma (DCP) discharges were used before 964, when Greenfield S. et. al. [Gre 64] and then Wendt R.H. and Fassel V.A. [Wen 65] performed AES using an ICP. The new ICP-AES method was more accurate than the DCP-AES, because impurities from sputtering the walls and electrodes were reduced. ICP-AES has been available commercially since the middle of 97s [Moo 89], and was the most expensive AES technique at the time. In 973, the IBM Corporation experimented with using ICPs for semiconductor manufacturing. Early studies were on ICP-assisted silicon oxidation for the thin-film transistor s (TFT) fabrication on glass for flat panel displays [Pul 73, Pul 74]. They were looking for a low temperature alternative to direct thermal oxidation. A MHz oxygen ICP at about 4 Pa produced similar quality to thermal oxidation. The input power was limited, and kept the gas temperature below 55 K. This study also contained the innovation of using an additional electrode with the ICP source. The silicon substrate was placed on the electrode, and the energy of coming ions was controlled by DC biasing. Widespread use of ICPs in industry began at the end of the 98s after the successful study and commercialization of the helicon discharge [Bos 84]. However, this discharge was developed independently from other ICPs. The interference of ionosphere s whistler waves with telephone communications was firstly observed in 886 [Fuc 57, Sch 98]. In 93s, the phenomenon was intensively investigated [Bar 3, Dar 34, Eck 35]; and in 953, a detailed theory of the whistlers was presented [Sto 53]. Most of the subsequent research on whistler waves was done by solidstate physicists. In 96, P. Aigrain studied the propagation of the whistler waves in materials, and coined the phrase helicon waves [Aig 6]. R.W. Boswell invented a helicon plasma source with waves in the radio frequency (RF) range in 97 [Bos 7]. 8

9 Because of the unusually high ionization efficiency, the plasma densities achieved in the helicon discharge were almost an order of magnitude higher then in other discharges for comparable gas pressures and input powers. The view that ICPs are inefficient had completely changed. However, normal ICPs operate by capacitive coupling at lower powers and then shift to an inductive coupling mechanism at a threshold power. At this threshold, the total power coupling in the plasma has minimum efficiency. To operate a normal ICP efficiently, it needs to be operated at a power lever much higher than the threshold. ICP reactors are therefore only efficient for high-density plasma sources. Today the ICP discharges are widely used for lighting and technological processes, because of their high charged particle density and their low power losses in the sheath. The inductive power coupling mechanism does not generate a large voltage across the RF sheath, and therefore reduces the interaction of the ions with chamber walls. This reduces chemical reactions on the wall surface, sputtering, and etching in comparison to a CCP. Several contemporary applications of ICPs are presented below. In 99s, the DCP-AES was totally replaced by high-density ICP-AES. Increased power costs were compensated by shorter measurement times. This caused a major change in the techniques, methodology, and apparatus used for AES. These changers are recently reviewed [Mon 9, Bou 3, Hen 3]. Today ICP-AES is widely used for the elemental analysis of metallic aerosols and powders, dusts, and fly ashes. A high-density ICP was also used as an ion source for analytical mass spectrometry (ICP-MS) [Hou 8, Mon 98]. In ICP-MS, the test sample is typically converted to an aerosol and injected into the plasma. An argon ICP that is 9% ionized is used. After vaporization, atomization, excitation, and ionization processes an elemental and isotope analysis is performed using a quadrupole mass spectrometer (QMS). ICP-MS can determine trace elements in air, liquids, and dust [Bal 3]. It is the most sensitive means for detecting trace inorganic metals. For example, in 996, Schultz et al. measured lead (Pb) concentrations in blood from smelter workers using ICP-MS [Sch 96]. In 995, ICP-MS was first used to detect U 35 and U 38 in urine [Vit 95]. In 996 Karpas et al. commercialized a fully automatic version for detecting radionuclide [Kar 96]. They simplified sample preparation by diluting urine in % nitric acid. Other chemical treatments or separations were not needed because of the ICP-MS s sensitivity. In 993, D.P. Myers and G.M. Hieftje combined an ICP with time-of-flight mass spectrometry (ICP-TOF-MS). The TOF-MS acquires data at least two orders of magnitude faster than a quadrupole. The application of ICP-TOF-MS for elemental analysis is reviewed in [Bal 3]. Commercial ICP-TOF-MS instruments have been available since 998. The first elecrodeless fluorescent lamp was developed in 98 [Pro 8]. This lamp was based on a CCP RF discharge, but was not commercially viable due to low energy efficiency. The efficiency was increased later when the CCP was replaced with a lowpressure ICP. The first generation of commercial electrodeless lamps were introduced by Philips (QL) and Matsushita (Everlight) in 99. They were later followed by GE Lighting 9

10 (Genura) in 994 and OSRAM SYLVANIA (ENDURA, ICETRON) in 998 [Lis ]. All of these products are used for lighting of large areas, where higher applied powers and operated times cannot be met by conventional fluorescent lamps. The electrodeless design allows the use of gases that would normally corrode an electrode, and eliminates wall blackening or the deposition of electrode materials on the wall. The use of high pressure ICPs as a replacement for high intensity discharge (HID) lamps is still being investigated. The major challenge is the matching between the RF power supply and the plasma impedance as it changes through the lamp s starting, ramp up, and stationary modes [Ino 98]. The plasma-assisted thin-film deposition, etching, surface cleaning, oxidation, and hardening play a crucial role in the multibillion-dollar semiconductor industry. The requirements of this industry has and continues to spawn a large variety of different ICP source designs. For example, the efficiency of ICPs generated by the internal and external antennas was investigated by several research groups [Lis 9, Suz 98]. In 995, an ICP source with a neutral magnetic loop inside the plasma cell was developed [Tsu 95]. The presence of magnetic field gradients inside the vacuum chamber increases the power coupling efficiency at low pressures. The etching rate of the neutral loop discharge (NLD) was several times higher than a conventional ICP for otherwise identical conditions. A number of particular improvements for ICP sources can also be found in the literature, and ICP generation is now available for powers as low as several Watts and at gas pressures below. Pa. Up until 99, almost all ICPs had a cylindrical, barrel-like geometry with the antenna wrapped around the diameter. This monopoly ended with the introduction of planar antennas [Ogl 9]. These new discharges had reduced plasma loss, better power coupling, and were more uniform for flat surfaces. Since silicon wafers are flat, planar ICPs are almost exclusively used in the microelectronics industry. It is interesting that early research in using ICPs for spectra-chemistry did not vary the geometry from the original 884 design. They varied the cell dimension, the gas composition, the power, and the pressure; but it was always a cylindrical coil surrounding the reactor vessel. For ICP lamps, cylindrical antennas placed within re-entrant cavities have been used since 936 [Bet 36]. Most innovations in ICP design have been for materials processing. It seems as though this is the most flexible, complicated, and progressive application for ICPs, and an area where many technological requirements still need to be satisfied.

11 3. Fundamentals 3.. RF discharge basics Since the discovery of RF discharges, a broad variety of experimental data and theoretical facts about this phenomenon have been collected. Today this allows a detailed interpretation of the physical processes occurring in RF plasmas. Of course, all of this material cannot be reviewed in the framework of this dissertation. In this chapter, the underlying physical principles, the fundamentals, and analytical solutions for RF plasma sources operated at low pressures, p < Pa are briefly considered Plasma generation in RF discharges Gas-discharge plasmas are produced when the electromagnetic energy released in a discharge is sufficient to ionize the gas and maintain the density of charged particles. RF discharges are excited by applying an oscillating electromagnetic field across a discharge gap. Under regulations set up by the International Telecommunication Agreements (ITA) and the Industrial, Scientific and Medical use (ISM), the standard frequency that should be used in commercial RF generators is f RF = 3.56 MHz and its higher harmonics. Systems using non ITA/ISM frequencies must be fully shielded to emissions to ensure that they will not interfere with communications equipment. However, also nonstandard frequencies below this limiting frequency are used [Tus 96]. In a qualitative sense, we can distinguish two operating regimes for RF discharges which are distinguished by the ratio between the exciting-field frequency ω and the electron ω e and the ion ω i plasma frequencies: ω e = nee m ε e, ω i = n e i M i ε (3.) In a low-frequency regime, where ω << ω i << ω e, the motion of all charged particles is governed by electromagnetic-field oscillations. In a high-frequency regime, where ω i << ω << ω e, the spatial positions of ions vary only slightly in time. This simple qualitative picture does not apply to RF discharges at 3.56 MHz. For example, in hydrogen plasmas dominated by H 3 + ions, the condition ω ω i is fulfilled even for ion densities on the order of n i = cm -3. Breakdown of a neutral gas is an avalanche-like process. The gas always contains a small quantity of free electrons produced by cosmic rays. These primary electrons are accelerated by the applied electric field to high energies and collide with neutrals and walls of the chamber producing more charged particles. This gives rise to an avalanche, resulting in the gas breakdown. The final state of the produced plasma and its parameters are determined by a balance between the input and loss power and a particle balance. The processes outlined above is based on energy transfer from electrons accelerated in an RF E-field to the background gas, and is an illustration of the dominant role of electron-

12 neutral collisions in a plasma. Therefore, it is named collisional or Ohmic heating. The electron elastic collision frequency, v m, is proportional to the gas density and, at a constant gas temperature, to the gas pressure: v m N p. (3.) Fig.3. shows the dependence of the ratio v m /p on the electron energy ε e for hydrogen and argon. In particular, the value of v m /p for hydrogen is constant over a wide range of electron energies: v m = αp, where α = Pa - s -. (3.3) 4 ν e / p ( 7, s - Pa - ) m Ar H ε e (ev) Fig.3.. Collision frequency versus electron energy for hydrogen and argon gases [Rai 97]. Fig.3.. Experimental determination of the effective collision frequency in the RF discharge at f RF = 4,8 MHz in mercury [Pop 85]. In RF discharges collisionless or stochastic heating is an additional heating mechanism. In order account for stochastic heating, the effective electron collision frequency, v eff, is used instead of the elastic-collision frequency, v m. Fig.3. shows measurements of v eff in an RF discharge at a frequency of f RF = 4.8 MHz in mercury [Pop 85], and demonstrates that the stochastic heating is more efficient at low gas pressures. Theoretical descriptions of the stochastic heating are still been disputed. Two models are encountered in the literature. One model is based on Fermi acceleration, where electrons gain additional energy due to their reflections from the moving edge of the sheath [Lie 98]. The alternative model is based on the effect of repetitive compression and rarefaction of the electron cloud at the sheath edge [Goz,Goza, Goz, Tur 93]. The stochastic heating in this case is attributed to pressure variations.

13 3... RF discharges classification Conventionally, RF discharges are classified according to the mechanism of RF power coupling to a plasma, i.e. they are either inductive or capacitive. The RF discharge classifications are shown in Fig.3.3. capacitively coupled plasma (CCP) E-discharge Classification of RF Discharges RF RF discharge applied electro-magnetic field hybrid CCP/ICP H-discharge with with an an additional powered electrode E-mode inductively coupled plasma (ICP) capacitive Fig.3.3. Schematic of conventional RF discharge classifications. H-discharge power coupling hybrid mode capacitive/inductive H-mode inductive For electrodeless RF discharges G.I. Babat [Bab 47] first introduced in 947 the terms E- and H-discharges to differentiate between plasma generation by electric or magnetic fields. The term E-discharge was adopted by V.A. Godiak [God 76] who applied it to capacitively coupled plasma (CCP) sources containing electrodes. In inductively coupled plasma (ICP) sources, the electromagnetic field maintaining a discharge is induced by oscillating currents in the antenna. In addition, antenna can directly generate an electric field, in which case it acts as an electrode. Both the inductive and capacitive mechanisms of power coupling are present in the ICP sources, and there are two modes of operation known respectively as E-mode and H-mode [Lie 94]. Between the E- and H-modes a transition regime, where the dominant power coupling mechanism is difficult to determine, exists. This ICP regime is named the hybrid mode. Besides the purely inductive or capacitive discharges mentioned above, there are hybrid ICP/CCP discharges. In the latter case, the design of an ICP source includes an additional RF-biased electrode typical of CCP sources, so that it becomes possible to independently control the generation of a plasma and the properties of the plasma sheath. 3

14 3..3. CCP discharges A basic diagram of a simplified CCP cell and its equivalent circuit are shown in Fig.3.4 A discharge is excited between two electrodes which are usually placed inside the plasma cell. Sometimes the surface of either one or both of the electrodes is coated with an insulator. If the electrodes are placed outside the plasma cell, the chamber is made from a dielectric material. Cell sizes are usually chosen to meet the requirements of a particular material processing, and they can be varied within wide limits. The electrode shapes and surfaces can be the same or different. Power Sheath Plasma Sheath R S C S R S R pl L pl R S Fig.3.4. Basic diagram of the simplified CCP cell and its equivalent circuit. R S, R S, C S and C S are resistances and capacitances of the sheaths. R pl and L pl are the resistance and the inductance of the plasma bulk. R pl L pl C S The bulk of the plasma forms in the central region of the cell. The bulk is characterized by quasineutrality, an Ohmic resistance, R pl, and inductance, L pl. Two space change sheaths form near the electrodes. Here electrons are moving in and out periodically while the ions form a practically constant background charge. These time varying sheaths characteristically have high resistances, R S and R S and capacitances, C S and C S : C A d, (3.4) S S S where A S, d S are the sheath area and the sheath gap. In simplified equivalent circuits, the bulk plasma is considered as a resistance, whereas the sheath is considered as a capacitance because of a large difference (in magnitude) between of the complex impedances at frequencies of the RF range: Rpl << ωl pl and RS >> ωcs. (3.5) CCP discharges can be operated in either the α-mode or the γ-mode. The α-mode is the initial state and occurs just after breakdown. As the power applied to the electrodes is slowly increased, the discharge abruptly changes above a threshold power and enters a brighter state, the γ-mode. The discharge behaves as if a secondary breakdown is occurring in the gap. This effect was studied experimentally in [Lev 57, Levi 57]. This experiment shows that the transition from one mode to another is abrupt in hydrogen, where in argon it is more transitional. A physical explanation of α-mode and γ-mode was put forward by the authors of [Rai 97]. When the plasma density is low, a discharge operates in the α-mode. The current through the nonconducting sheath is in fact a displacement current and new charges are produced in the plasma bulk only. As the plasma density increases the current through the sheath increases substantially, and the discharge changes to the γ-mode. Now, the electrons 4

15 are produced predominantly by secondary ion-electron emission at the electrode. While passing through the sheath, the secondary electrons are accelerated and multiplied by ionizing collisions with neutrals. When they enter the bulk plasma, they contribute efficiently to ionization and excitation of neutral gas particles, and the average plasma temperature is reduced. Taking into account stochastic heating, the classification of CCP discharges was extended by Boeuf et. al. [Boe 9]. For the γ-mode discharge, the authors distinguished a positive column regime where the stochastic heating is negligible and an electron-sheath collision regime where the stochastic heating is essential. The CCP source is powered by an RF-oscillator combined with a matching network. Minimum power loss due to internal resistance of the RF-oscillator, R RF (typically 5 Ω), and due to a power reflection is achieved if the load impedance is equal to R RF. The matching network transforms the plasma complex impedance, Z eff, to R RF. So the circuit operates with maximum efficiency. If the condition Re(Z eff ) R RF is fulfilled, the impedance matching can be provided by a passive matching network. This network consists of two variable capacitors and an inductor. If the plasma resistance is high, Re(Z eff ) > R RF, then the impedance matching becomes a complicated engineering problem. In this case, it would be better to use an RFoscillator with high internal resistance (R RF = kω) instead of an active matching unit. CCPs are often asymmetric, typically with one of the electrodes grounded. If a CCP is symmetrical, it means that both electrodes are powered. Such a circuit complicates realization of the experiment, but allows one to simplify interpretation. If the electrodes in the discharge have different sizes, then sheaths will differ from one another. An additional voltage drop occurs at the smaller, usually powered electrode. This effect, known as self-biasing, was explained in [Lie 94]. It is assumed that the density of the current flowing across the sheath j i is proportional to some power of the voltage across the sheath and inverse proportional to a different power of the sheath thickness. Mathematically, this can be formulated as U m S ji n ds, (3.6) where the powers m and n are specified by the particular sheath conditions. For homogeneous plasma, the current density is the same at both electrodes: j = j. (3.7) S S In this case, equation (3.4) and the Ohm law applied to the impedances of both sheaths give the ratio between the voltage drops across these sheaths: U SCS = U S CS, (3.8) ( A A ) γ U. (3.9) S U S = S S In available theoretical models of colissionless and collisional sheaths the value of the power γ = ( - m/n) - is predicted to lie between.3 and 4. Experimentally γ is often found to be about. 5

16 The concept of a standardized CCP source was proposed in 988. This furnishes an opportunity to compare results of studies carried out by various research groups. Fig.3.5 shows a schematic diagram of this standard plasma cell, known as the Gaseous Electronic Conference (GEC) reference cell [GEC 94]. Fig.3.5. Schematic diagrams of the plasma cell and the pump-out manifold for the GEC reference CCP source. The standard plasma cell contains two identical plane electrodes with radius r el = 5 cm which are placed parallel to one another at a distance of h cell =.5 cm. Typical discharge parameters are: operating frequency f RF = 3.56 MHz, gas pressure p = - Pa, applied power P = - W, electron density n e = 9 - сm -3, electron temperature T e = - 4 ev. Since a reproducibility of the parameters of a low-pressure plasma depends on the design of the discharge chamber, the identical geometry of plasma cells is important for the standardization of RF discharges. 6

17 3..4. ICP discharges The alternative form of maintaining an RF discharge is by inductive coupling [Hop 9]. An ICP is used for technologies where a low-temperature, dense and uniform plasma is needed. A typical diagram and the equivalent electric circuit of the ICP source are presented in Fig.3.6 [God 99, Lie 94]. quartz RF power L gas inlet to pump plasma r η Ant D Ant R pl R S C q L L L (e) R C S antenna L pl L matching unit RF generator C S R S R Fig.3.6. Diagram of the ICP cell and the equivalent electric circuit of an antenna-plasma transformer. R and L are the antenna resistance and induction. R, L and L (e) are the plasma resistance, geometrical plasma inductance and inductance due to inertia of electrons. L and L are the interactive inductions between an antenna and a plasma. In an ICP, energy coupling into the plasma is through a transformer whose circuit consist of the antenna and the plasma. The ICP mechanism of capacitive power coupling is equivalent to a CCP. Because of this, we should include the CCP equivalent circuit from Fig.3.4 in the ICP equivalent circuit by connecting the CCP circuit in parallel to the antennaplasma transformer. When an external antenna is used, we should modify the circuit by adding the capacitance of the dielectric separator, C q. The antenna has the inductance, L, and resistance, R. Since the antenna is usually made from a conductor, the following inequality holds: ωl >> R. The plasma serves as the secondary coil of a transformer. In contrast with CCP discharges, the plasma inductance, L, is primarily determined by the geometry of the induced currents. The plasma inductance due to the inertia of electrons L ( e) contributes only insignificantly to the total inductance: L >> L (3.) ( e) The relation between R and ωl depends on many parameters and can vary with changing discharge conditions. As was mentioned above, the ICP discharge can operate in the E- and H-modes, which are distinguished by the dominant power coupling mechanism. In the E-mode, the antenna acts as a powered electrode like in CCP discharges. Capacitive power coupling into a plasma can be illustrated by a simple model proposed in [Lie 94]. In this model, the voltage 7

18 drop across the sheath can be determined by assuming the plasma potential to be zero. This is a reasonable approach, because the plasma potential is usually much lower than the antenna voltage. The antenna-plasma voltage divider formed by the capacitances of the dielectric separator and the sheath is strongly nonlinear. The dependence of the sheath potential on the antenna potential scales with the fourth power: 4 U.8 ε e U S = en ( ) 4 ub M i hq ε, (3.) where n is the electron density at the sheath edge, u B is the Bohm velocity, and h q is the dielectric-separator thickness [Lie 94]. Energy losses due to particle transfer through the sheath increase as the potential U S increases. Through the energy balance, these additional losses lead to the density decrease. It will be shown later in Subsection Iteratively, the sheath potential increases according to equation (3.), and the electron density decreases again. Finally, this leads to a deterioration of conditions favorable for the H-mode. On the other hand, if the plasma density increases or the antenna voltage decreases, the efficiency of capacitive power coupling into the plasma decreases. In the H-mode, ICP discharges are electrodeless. The efficiency of the power coupling into the plasma is determined by the plasma-cell geometry and the plasma parameters, particularly by the conductivity. It is well known that a transformer in which the secondary circuit is open or shorted dissipates the input power totally in the primary circuit. Reasoning from this knowledge, we can distinguish three characteristics inherent to ICP discharges: The plasma cannot be self-ignited using the inductive coupling mechanism alone. The E-mode always precedes the H-mode. Therefore, it is reasonable to consider the formation of the H-mode discharge as a mode transition rather than an ignition process. A maximum efficiency of power coupling into ICP discharges is reached at plasma densities that are one order of magnitude higher than typical plasma densities of CCP discharges. Consequently, a higher incident power is required. Metal near the antenna can couple to it. As a result, a major cause of power loss in the ICP source can be by high conductivity material used to construct the vacuum chamber. The H-mode is dominant for ICP sources. There is an optimum plasma density that ensures a maximum power coupling into the plasma. On one hand, a discharge is maintained by Ohmic heating which increases as the electron density increases: < S Ω > =< j E > ~. (3.) e n e On the other hand, the penetration of the electric field into the plasma is characterized by a skin depth, δ, which decreases as the plasma density increases. Thus, although the efficiency of heating increases, the heating region decreases. A maximum efficiency is achieved when the value of δ is smaller than the plasma cell size, but is still comparable with it. The skin 8

19 depth in ICP discharges is typically of the order of several centimeters, which is substantially smaller than the RF wavelength (λ RF = m). To analyze the mechanism for the transition between E- and H-modes in ICP discharges, one first assumes that the transition occurs, when the coupling efficiencies of both mechanisms are equal. In this case, the transition should occur at a definite (threshold) power. However, experimental evidence indicates that this interpretation is not always valid. In publications about ICPs, the value of the threshold power varies within rather wide limits. This is typical even when the same gas was used and the discharges were produced in similar plasma sources. Secondly, the presence of some residual features of an alternative power coupling mechanism after the transition leads to the conclusion that a Fig.3.7. Experimental confirmation of a hysteresis at the transition between the modes of an ICP discharge [Loc ]. hybrid CCP/ICP mode is a more adequate description for discharge conditions near the transition of one mode to another. Some research groups have even observed a type of hysteresis. The E-to-H transition occurred at a higher RF power in comparison with the H-to-E transition. For example, Fig.3.7 shows this hysteresis in an experiment carried out by Y. Lokurlu in a hydrogen ICP discharge [Loc ]. The explanation of the hysteresis effect at the transition between modes using the hydrogen ICP model is given in Subsection An alternative model which includes nonlinear effects in the energy balance due to electron collisions and multistep ionization can be found in [Tur 99, Elf 98]. The geometry of the electromagnetic field and, therefore, the plasma heating depend heavily on the design of the antenna. Follow the particular requirements of the plasmaassisted material processing, the different antennas have been introduced and successfully used at the time. They are classified using follow types. The antenna may be external or internal. If an external antenna is used, the vacuum chamber must be made of a dielectric material or have a dielectric window. An internal antenna is usually insulated from the plasma by a nonconducting coating. There is also a hybrid type called the quasi-internal antenna. The coil is placed into a dielectric holder, which is then placed in a vacuum chamber [Lee ]. The antenna may consist of a one turn coil or may have a more complicated geometry, which could be difficult to classify. For example, in [Tus 96] the authors proposed a hemispherical antenna with twenty turns which is capable of generating a homogeneous plasma in a relatively large volume. One special type of ICP sources which uses cylindrical antennas is a helicon discharge [Che 96]. A helicon plasma discharge is generated in a cylindrical vacuum cell, has 9

20 a homogeneous magnetic field, and electrons are heated by Landau damping. The helicon waves have a frequency between ωci << ω << ω ce, (3.3) where ω ci and ω ce are the ion and electron cyclotron frequencies, respectively: eb eb ω ci =, ωce =. (3.4) M m Helicon sources have gained wide acceptance for their high Fig.3.8. Examples of antennas used in helicon discharge. efficiency in comparison with other ICP sources. Several types of helicon antennas [Che 9] are shown in Fig.3.8. There are also many other antenna designs that deserve attention. Industrial devices usually have cylindrical and planar antennas. Cylindrical and planar ICP discharges are named according to the antenna type. ICP sources can also have more than one antenna. Such a design makes it possible to solve several engineering problems at once. For example, in [Col 99] two coaxial antennas were operate at different frequencies f RF = 3.56 MHz and f HF = khz in order to generate a plasma and to heat a substrate simultaneously. In another device, used for sterilization of large tree-dimensional objects, two plane antennas are placed parallel to one another [Mes 3]. This allows to achieve a high plasma density and homogeneity in the radial and vertical directions. i e Fig.3.9. Example of a low induction antenna with several parallel coils [Kim ]. Fig.3.. Example of an ultra-low induction antenna [Wu ]. Oppositely directed currents diminish the antenna inductance. Antennas can be divided into groups depending on the value of their inductance [Men 96]. One group contains antennas in which the direction of current is the same in all coils. This group in turn is subdivided into normal induction antennas containing a single coil and low induction antennas consisting of several parallel coils. An example of a low

21 induction antenna is presented in Fig.3.9 [Kim ]. The second group contains ultra-low induction antennas. Their inductance is substantially reduced because the current in the adjacent coils flows in opposite directions. An example of this antenna is presented in Fig.3. [Wu ]. Coil designs, such as that shown in the figure, are typically very complicated for low-pressure (p Pa) discharges. Generally, the ICP source efficiency can be optimized using the following principle. Examing equation (3.), the efficiency of capacitive power coupling depends strongly on the antenna voltage. Therefore, by decreasing the antenna voltage and increasing the antenna current, it is possible to reduce the mode transition power. According to the Ohm law, the ratio of voltage U to current I at the antenna is proportional to its impedance which is primarily determined by the antenna inductance Z ωl. This is why a low-inductance antenna operates at lower voltages and higher currents in comparison with a high-inductance antenna. U I ~ L. (3.5) Consequently, by modifying the antenna in order to decrease its inductance, it is possible to achieve optimum operation of the ICP source in the H-mode. Like the CCP source, the ICP device contains a power supply and an impedance matching network. The current in the matching network is higher than in the capacitive discharge. Since the power losses increase in this case, a correct matching of the antenna impedance to the output resistance of a RF generator becomes of crucial importance. Stable discharge parameters can be achieved with the use of a commercial matching network with an auto-matching function. Thus, it is usually the equipment that limits the maximum antenna current. A standard matching network uses the L-matching circuit shown in Fig.3.(a). The device contains two adjustable capacitors. One of them is connected in parallel to the power supply, and is called the load capacitor C load. Another capacitor is connected in series to the antenna, and is called the tune capacitor C tune. The current in the antenna is constant along its length. According to the Ohm law, the potential profile is proportional to the impedance profile. For this reason, a potential along the radius of a planar antenna is described by a parabola. Whereas the potential along the length of a cylindrical antenna is described by a line. The antenna voltage relative to ground can be minimized by correctly tuning the phase shift between potentials at its terminals. Two types of passive matching networks aid in solving this problem. One type is a π-matching unit with interchanged positions of C Tune and L. When this unit is used, at ωl > R RF the antenna voltage is lower in comparison with the L-matching unit. When ωl < R RF, the L-matching unit is preferable. Suzuki et. el. proposed a version of the electric circuit for matching network called an antenna coil capacitance termination [Suz ]. The advantage of this device is illustrated by Fig.3. which shows antenna potential profiles sampled during one RF period. As can be

22 seen, the maximum value of the antenna potential in the case of a standard L-matching unit doubles in comparison with the unit shown in Fig.3.(b). Z Ant / Z Ant / Z Ant /4 Z Ant V / I V / I -/ Z Ant -/4 Z Ant - Z Ant -r Ant -/r Ant /r Ant r Ant radial position -/ Z Ant -r Ant -/r Ant /r Ant r Ant radial position Z Ant / Z Ant / Z Ant /4 Z Ant V / I V / I -/ Z Ant -/4 Z Ant - Z Ant -/ Z Ant /4h Ant /h Ant 3/4h Ant h Ant vertical position (a) L-matching unit and /4h Ant /h Ant 3/4h Ant h Ant vertical position (b) antenna capacitance termination in the matching unit Fig.3.. Basic equivalent electric circuits and the antenna potential profiles sampled during one RF period for a planar and a cylindrical antennas. It should be mentioned that an antenna terminated by a capacitance has zero potential at the point corresponding to one-half of its inductance, and electron currents in the plasma are not strongly disturbed by the antenna potential. Indeed, the maximum current corresponds to this region because induced electromagnetic field has also a maximum here. In the case of the L-matching unit, the antenna potential at this point is equal to half the applied voltage. On the other hand, the circuit shown in Fig.3.(b) has two disadvantages. First, the inclusion of an additional capacitor connected in series results in additional energy losses in the capacitor itself and its contacts. Second, the rating of each capacitor in this matching network is twice as large as the rating of a capacitor in a L-matching unit, substantially increasing its cost.

23 Fig.3.. Faraday shield [God 99]. Another way of improving the ICP operation in the H-mode is by using a grounded Faraday shield to isolate the antenna from the plasma. An example of this device is shown in Fig.3. [God 99]. The Faraday shield suppresses the electric field due to the antenna potential, whereas the magnetic field penetrates through radial slits almost without loss. After the transition to the H-mode, the use of the Faraday shield excludes any residual capacitive power coupling to the plasma. However, a current between the antenna and the Faraday shield introduces an additional power loss in the system. With the Faraday shield, there arise two engineering problems: A strong suppression of the initial E-mode makes self-ignition hardly possible. This is acceptable for plasma sources operating in a continuous mode, whereas the use of a Faraday shield in pulsed discharges is a complicated engineering problem. The voltage between the antenna and the Faraday shield limits the maximum incident power because of the danger of high-voltage breakdown. The Gaseous Electronic Conference, GEC, introduced a standard ICP source in 995 [Mil 95]. The GEC reference cell was designed initially as a CCP, and was later modified for use as a planar ICP [GEC]. The modified design, sketched in Fig.3.3, is also by convention. The upper electrode of the CCP was exchanged for a spiral antenna placed inside a metal cylinder with a quartz window with thickness h q = cm. The antenna radius is r ant = 5 cm, and the Fig.3.3. Schematic diagram of the standard ICP cell. number turns is N ant = 5. The antenna is made from a copper tube with an outer diameter of d Cu = 3 mm and is water-cooled. The lower electrode of the CCP was modified by placing a metal plate with radius r el = 8 cm on the top of it. The distance between the quartz window and the lower electrode is h cell = 5 cm. Typical working conditions of the ICP are: frequency f RF = 3.56 MHz, gas pressure p =. - Pa, applied power P = - W, electron density n e = 9 - cm -3, and electron temperature T e = - 5 ev. 3