Dissertation. zur Erlangung des Grades eines Doktor-Ingenieurs der Fakultät für Elektrotechnik und Informationstechnik an der Ruhr-Universität Bochum

Size: px
Start display at page:

Download "Dissertation. zur Erlangung des Grades eines Doktor-Ingenieurs der Fakultät für Elektrotechnik und Informationstechnik an der Ruhr-Universität Bochum"

Transcription

1 RUHR-UNIVERSITÄT BOCHUM Characterization of multiple frequency driven capacitively coupled plasmas for ferro-metallic thin film sputter deposition Dissertation zur Erlangung des Grades eines Doktor-Ingenieurs der Fakultät für Elektrotechnik und Informationstechnik an der Ruhr-Universität Bochum Egmont Semmler Bochum 2008

2

3

4

5 Dissertation eingereicht am: Tag der mündlichen Prüfung: Berichter: Prof. Dr.-Ing. Peter Awakowicz Prof. Dr. rer. nat. Achim von Keudell

6

7 Contents i Contents Important symbols and abbreviations List of figures Abstract iii xi xv 1 Introduction Common thin film deposition techniques Multiple frequency driven capacitively coupled plasmas Multiple frequency CCPs for PVD of ferro-metallic / magnetic materials Thesis layout Experimental setup Constructional design properties Electrical characterization by vector network analyzer measurements Evaluation of the impedance matching networks Chamber characterization and equivalent circuit model for the electrical feed Plasma and thin film diagnostics Voltage current (VI) probe Plasma impedance determination in multiple frequency capacitive plasmas Langmuir probe Compensation schemes and application in multifrequency plasmas Phase resolved optical emission spectroscopy (PROES) Self excited electron resonance spectroscopy (SEERS) / Plasma series resonance (PSR) Nonlinear electron resonance heating (NERH) Correlation of measured PSR currents to PROES Comparison of measured SEERS/PSR currents to model calculations Retarding field energy analyzer (RFEA) Ion velocity/energy distribution function measurement Quartz crystal microbalance (QCM) Measurements and discussion Variation of external parameters for VHF / MHz CCP operation Frequency ratio

8 ii Contents Power ratio Pressure variation Influence of the relative phase at integer driving frequency ratios Langmuir probe results PROES and SEERS/PSR measurements Ion energy distribution measurements Voltage ratio Frequency ratio Ferro-metallic thin film deposition study Optimization of sputter deposition rate Estimation of expected deposition rates and comparison to measurements Calibration of quartz-crystal microbalance and determination of film density Identification of sputtered atomic species and relative densities by optical emission spectroscopy Conclusions and outlook 101 Bibliography 105

9 Symbols and Abbreviations iii Important symbols and abbreviations Symbols a A electrode a Fe bcc A i A ik A Probe A q b B PSR C 2M xxx C 13M xxx C acs C Contact C el C Feed C Screws C Sheath C VHF xxx C Vacuum d f d q d QCM D rf (t) ε 0 ε q ε r e E E E i (t) Incident wave amplitudes Area of driven electrode Lattice constant of Iron (body-centered cubic) Effective decay rate of excitation level i Transition rate from excitation level i to k Area of Langmuir probe tip Area of quartz-crystal substrate Outgoing wave amplitudes Plasma series resonance bandwidth Capacitive element of 2 MHz matching network Capacitive element of MHz matching network Equivalent acoustic impedance capacitor Contact capacitance matchbox output to copper feed Capacitance of metallized quartz-crystal substrate Capacitive coupling of vacuum feed-through Capacitive coupling of vacuum feed screws Plasma boundary sheath capacitance Capacitive element of VHF matching network Capacitance of vacuum electrodes Film thickness Quartz-crystal substrate thickness Film deposition rate [Å/s] Electrical displacement field Vacuum permittivity Relative permittivity of quartz Relative permittivity Electron charge Mean (ion/electron) energy IEDF energy spread (peak separation) Excitation function

10 iv Symbols and Abbreviations φ Φ Φ coil Φ float Φ plasma f 2MHz f 13.56MHz f 14MHz f coated f ion (v) f MSRF f pe f PSR f q f v,elec (E) f VHF g ik Γ Ar + Γ Fe γ Fe γ loss η all η chamber η matching η source H power H rf (t) H voltage I i I probe I retard I rf (t) I sat,elec I sat,ion J rf (t) κ k B k q λ Debye L Relative phase angle Potential difference Magnetic flux in Rogowski coil Floating potential Plasma potential Frequency of 2 MHz Frequency of MHz Frequency of 14 MHz Coated quartz substrate oscillation frequency Ion velocity distribution function Motional series resonance frequency Electron plasma frequency Plasma series resonance frequency Quartz-crystal substrate oscillation frequency Velocity distribution function in energy space Variable VHF frequency (60 90 MHz) Escape factor Ion flux density of Argon ions Flux density of Iron atoms Sputtering yield of Iron Flux loss factor Overall electrical system efficiency Vacuum feed-through loss factor Impedance matching network electrical efficiency Maximum amplifier efficiency Power transmission function Magnetic field Voltage transmission function Current at network port i Langmuir probe current Electron retarding current RF current through VI probe Electron saturation current Ion saturation current RF current density (VI probe) Frequency ratio in 2f-CCP operation Boltzmann constant Collisional de-excitation coefficient Debye-Hückel length Effective plasma bulk length

11 Symbols and Abbreviations v L 2M xxx L 13M xxx L acs L Bulk L Rod L Screws L VHF xxx Inductive element of 2 MHz matching network Inductive element of MHz matching network Equivalent acoustic impedance inductor Plasma bulk inductance Copper feed inductance at high frequencies Inductive coupling of vacuum feed screws Inductive element of VHF matching network µ 0 Vacuum permeability µ f Shear modulus of quartz µ r Relative permeability m Ar Atomic mass of Argon M coil Rogowski coil inductance m e Electron mass m Fe Atomic mass of Iron m i Ion mass (general) ν m Effective electron-neutral collision frequency Ground state population density n 0 N coil n e N Fe ṅ Fe mono n i n i (t) ṅ Ph,i n q N q Number of coil turns (Rogowski coil) Electron/Plasma density Number of Iron atoms per monolayer Number of Iron monolayers Ion density Population density of excited state i Observed emission per volume Density of all collision partners q Frequency constant for AT-cur quartz ω 2MHz Angular frequency of 2 MHz (ω 2MHz = 2 π f 2MHz ) ω 14MHz Angular frequency of 14 MHz (ω 14MHz = 2 π f 14MHz ) ω pe Electron plasma frequency (ω pe = 2 π f pe ) ω PSR Plasma series resonance frequency (ω PSR = 2 π f PSR ) P 13.56MHz MHz amplifier power Variable frequency (60 90 MHz) amplifier power P VHF Q(t) Q PSR ρ A,Fe ρ Cr ρ f ρ Fe ρ Mo ρ Ni Time-dependent charge (sheath) Plasma series resonance quality factor Area mass density of Iron atoms (monolayer) Mass density of Chrome Mass density of growing film Mass density of Iron Mass density of Molybdenum Mass density of Nickel

12 vi Symbols and Abbreviations ρ q R 13M xxx R acs R Bulk R Rod R VHF xxx R z s S S 11 S 12 S 21 S 22 S circ S f s HF s VHF T e τ i τ rf Û 2MHz Û 14MHz u Bohm U Bulk U Current (t) U dc bias U i U phase (t) U probe U Q v V 0 V f v q Z 0 Z Z f Z film Z L Z Plasma eff Mass density of quartz Resistive element of MHz matching network Equivalent acoustic impedance resistor Plasma bulk resistance Copper feed resitance at high frequencies Resistive element of VHF matching network Acoustic impedance ratio Mean sheath width Scattering parameter matrix Input reflection coefficient Reverse voltage gain Forward voltage gain Output reflection coefficient 3-Port circulator S-Parameter matrix Sauerbrey constant Mean sheath width contribution HF Mean sheath width contribution VHF Mean electron temperature Ion transit time across the sheath RF period time Voltage amplitude 2 MHz waveform Voltage amplitude 14 MHz waveform Bohm velocity Plasma bulk voltage Current proportional induction voltage DC self bias voltage Voltage at network port i Voltage waveform Langmuir probe voltage Voltage source VNA Velocity vector (3D) Plasma sheath voltage Volume of growing film Velocity of sound for quartz Network port wave impedance Generalized matching network impedances (T-type) Acoustic impedance of growing film Electrical equivalent film impedance Load impedance Effective plasma impedance

13 Symbols and Abbreviations vii Z Plasma HF Z Plasma VHF Z q Plasma impedance HF contribution Plasma impedance VHF contribution Acoustic impedance of quartz

14 viii Symbols and Abbreviations Abbreviations 2f-CCP Dual Frequency Capacitively Coupled Plasma AFM Atomic Force Microscopy ALD Atomic Layer Deposition APS3 Automated Langmuir-Probe System, revision 3 BvD Butterworth - van Dyke equivalent circuit model CCD Charge Coupled Device CCP Capacitively Coupled Plasma CVD Chemical Vapor Deposition DLC Diamond-Like Carbon DRAM Dynamic Random Access Memory DSP Digital Signal Processor DUT Device Under Test EDF Electron Distribution Function EMC Electro-Magnetic Compatibility FTIR Fourier-Transform Infrared Spectrometry GEC Gaseous Electronics Conference GMR HF HiPIMS HPPMS ICCD ICP IED IDF LIF MACOR R MBE MCC MEMS MF MFC MF-CCP MO-CVD MRAM NERH OES OML PE-CVD PIC Giant Magneto Resistance (Effect) High Frequency band (3 30 MHz) High Power Impulse Magnetron Sputtering High Power Pulsed Magnetron Sputtering Intensified Charge Coupled Device Inductively Coupled Plasma Ion Energy Distribution Ion Distribution Function Laser Induced Fluorescence Vacuum compatible and machinable glass ceramic Molecular Beam Epitaxy Monte Carlo Collisions Micro Electro-Mechanical Machining Medium Frequency band (0.3 3 MHz) Mass Flow Controller unit Multiple frequency driven capacitively coupled plasma Metal-Organic Chemical Vapor Deposition Magneto-resistive Random Access Memory Nonlinear Electron Resonance Heating Optical Emission Spectroscopy Orbital Motion Limited theory Plasma Enhanced Chemical Vapor Deposition Particle In Cell (simulation method)

15 Symbols and Abbreviations ix PROES PSR PVD QCM rf RFEA RIE RML SEERS SEM SNR TEM VHF VI VNA XRD Phase Resolved Optical Emission Spectroscopy Plasma Series Resonance Physical Vapor Deposition Quartz Crystal Microbalance radio frequency Retarding Field Energy Analyzer Reactive Ion Etching Radial Motion Limited Self-Excited Electron Resonance Spectroscopy Scanning Electron Microscopy Signal to Noise Ratio Tunneling Electron Microscopy Very High Frequency band ( MHz) Voltage-Current (trace/characteristic/probe) Vector Network Analyzer X-Ray Diffraction Spectrometry

16

17 List of Figures xi List of Figures 2.1 Gas and vacuum layout of the experimental setup Mechanical and electrical layout of the plasma chamber Definition of voltages, currents and wave parameters for a two-port network Generalized impedance network for calculating the input reflection coefficient S 11 and forward voltage gain S Electrical equivalent circuit of the 2 MHz matching network including parasitic components Transmission function S 21 for the 2 MHz impedance matching network Voltage transmission S 21 for a matched 2 MHz impedance network using a real plasma impedance termination Electrical equivalent circuit of the MHz matching network including parasitic components Transmission function S 21 for the MHz impedance matching network Voltage transmission S 21 for a matched MHz impedance network using a real plasma impedance termination Electrical equivalent circuit of the VHF impedance matching network including parasitic components Transmission function S 21 for the VHF impedance matching network Voltage transmission S 21 for a matched VHF impedance network using a real plasma impedance termination Parasitics equivalent circuit model of the top electrode Comparison of fitted voltage-current probe data to a set of reference plasma impedances gained from Langmuir probe measurements Calculated power transmission S 21 for the vacuum feedthrough equivalent circuit Exemplary internal outline of a voltage-current (VI) probe sensor Voltage transmission functions (S 21 ) from the input port to the voltage and current equivalent voltage measurement port Raw VI probe data of a dual frequency discharge Plasma impedance equivalent circuit model Measured current equivalent induction voltage U Current (t) and its discrete amplitude Fourier spectrum Measured single frequency VI probe impedances and proposed combinations thereof Physical explanation for the impedance splitting as performed by a VI probe Comparison of magnitude and phase of an effective plasma impedance to Langmuir probe deduced plasma impedances

18 xii List of Figures 3.9 Characteristic Langmuir probe current-voltage (IV) curve Principal setup and measurement schematic of the APS3 Langmuir probe system Discrete amplitude Fourier spectrum of a plasma current detected by a SEERS/PSR current probe Comparison of compensated to uncompensated probe current Phase resolved optical emission spectroscopy (PROES) setup for a capacitive dual frequency discharge Space and time resolved excitation plot for a 2 MHz/14 MHz dual frequency discharge Typical current signal acquired in a dual frequency discharge Measured dual frequency (13.56 MHz / 67.8 MHz) PSR current with the according discrete Fourier spectrum Simple PSR equivalent circuit model of a capacitive rf plasma discharge Correlation of space and time dependent excitation plots from PROES to simultaneously measured PSR currents Comparison of calculated to experimental PSR currents under equivalent discharge conditions Retarding field energy analyzer (RFEA) used for ion distribution function (IDF) measurements Typically used potential distribution among the grids of the applied RFEA for ion distribution function measurements Characteristic measured current from a RFEA by sweeping the retarding potential Normalized ion distribution function (IDF) calculated as the first derivative of a measured voltage-current trace Functional schematic of a quartz-crystal microbalance Butterworth-van Dyke (BvD) equivalent circuit of a quartz crystal resonator Frequency dependence of electron density n e by varying f VHF Frequency dependence of the plasma and floating potential by varying f VHF Frequency dependence of mean electron temperature T e by varying f VHF Frequency dependence of the dc self bias voltage by varying f VHF Discrete Fourier amplitude spectrum of a measured PSR current at integer frequency ratio Discrete Fourier amplitude spectrum of a measured PSR current at noninteger frequency ratio Comparison of both Fourier amplitude spectra from integer and non-integer driving frequency ratio case Signal energies calculated from acquired PSR current signals Power dependence of dc self bias voltage Power dependence of electron density n e Comparison of weighted MHz and 71 MHz current, both measured at matchbox output Power dependence of mean electron temperature T e Low frequency power dependence of floating potential Pressure dependence of electron density n e Pressure dependence of mean electron temperature T e and dc self bias voltage 77

19 List of Figures xiii 4.16 Discrete Fourier spectra for observed PSR currents at low (3 Pa) and high (20 Pa) pressure PROES excitation plot for a pure 2 MHz discharge in Neon Relative phase dependence of electron density n e and mean electron temperature T e Relative phase dependence of plasma impedance magnitude and phase Relative phase dependence of plasma and floating potential Relative phase dependence of electron distribution function Correlation of the electron excitation dynamics to SEERS/PSR currents at a relative phase angle of -90 and Influence of relative phase on a simple plasma boundary sheath waveform model Influence of relative phase on excitation behavior for PVD-like discharge conditions Influence of relative phase on a simple plasma boundary sheath waveform model, resembling PVD-like conditions Low frequency voltage U 13.56MHz influence on the ion distribution function (IDF) on the target electrode Calculated mean ion energies from measured IDFs for low frequency voltage U 13.56MHz variation Dependence of the ion distribution function on the VHF driving frequency f VHF Pressure dependence of sputter deposition rate Pressure dependence of dc self bias voltage Power dependence on sputter deposition rate in single frequency discharge (13.56 MHz, 71 MHz) Dependence of sputter deposition rate on single frequency MHz and dual frequency discharge operation (13.56/71 MHz) Separate power dependence of MHz and 71 MHz on sputter deposition rate Optical emission spectrum for determination of relative atomic species densities in single frequency VHF operation Optical emission spectrum for determination of relative atomic species densities in dual frequency operation Atomic force microscopy (AFM) picture of a 56 nm Fe-coated silicon wafer. 100

20 xiv List of Figures

21 Abstract xv Abstract Capacitively coupled plasmas driven at multiple frequencies have attracted industrial interest in recent years, because of their attributed advantage of separated tunability of ion flux and ion impact energy. Common examples of these type of plasmas are found in new generations of etching tools utilized in the semiconductor industry branch. The separability is usually achieved by using one frequency out of the VHF band ( MHz) and another out of the HF band (3 30 MHz) or even the MF band (0.3 3 MHz). Within this work, a capacitively coupled plasma setup, intended for physical vapor deposition (PVD) of ferro-metallic materials, is developed, built and evaluated. A thorough electrical characterization is performed, to efficiently suppress mutual amplifier interferences, ensuring stable plasma conditions. Therefore, a detailed analysis of electrical loss mechanisms due to impedance matching networks and electrical vacuum feed-throughs is carried out. As a result the overall electrical system efficiency can be estimated and is found to be comparable to present industrial devices. Furthermore, an electrical vacuum-feed-through description allows for plasma impedance determination during discharge operation, using a standard voltage-current (VI) probe. In a second step, the discharge is studied by several invasive and non-invasive diagnostics, such as Langmuir probe, VI probe, plasma series resonance (PSR) current sensor, optical emission spectroscopy (OES), phase resolved optical emission spectroscopy (PROES) and retarding field energy analyzer (RFEA). In detail, frequency ratio, power ratio, pressure and influence of the relative phase are studied. Anomalous heating at integer driving frequency ratios is observed and explained on the basis of theoretic considerations by Mussenbrock and Brinkmann [1] through nonlinear electron resonance heating (NERH). Furthermore, global model calculations by Mussenbrock and Ziegler [2][3] can be very well matched to experimentally gathered PSR current signals. Thereby, a significant contribution to understanding electron heating in capacitive discharges is achieved, which is a key parameter for dedicated discharge control. Power ratio variation studies verify the influence of VHF power on plasma density. However, also a significant influence of the low frequency (HF) power on plasma density, especially with respect to typical operating regimes in PVD processes, is observed. In general, the aforementioned desirable complete separability of ion flux from ion bombarding energy is possible but limited for typical plasma processing applications. However, for industrial requirements a high enough degree of separate tunability is achievable, as shown in deposition experiments. Investigations on changing the relative phase between driving frequencies unveil a dedicated control of the amount of high energetic electron production (discharge excitation) directly

22 xvi Abstract in front of the target electrode. It is believed to be of high relevance for discharge drift compensation and ion flux optimization, as experimental evidence supports. Furthermore, the optimization becomes electrically regulable through an observed correlation of the localized electron heating as measured by PROES and PSR current resonant structures. These findings also agree very well to aforementioned model considerations. Finally, deposition rate characterization on metallic targets using a quartz-crystal microbalance gives insight into the complex driving frequencies coupling behavior. Although for typical power regimes in PVD applications, with large low frequency power and small high frequency power contributions, most diagnostics predict a decrease in plasma density through the dominating influence of low frequency power, no such observation is made for deposition rate experiments. This is explained by a significant change of the ion energy dependent sputtering yield, compensating losses in plasma density. Simultaneously raising high frequency power verifiably boosts deposition growth rate. However, this effect only works up to a defined threshold power, where discharge behavior starts changing towards single-frequency equivalent operation. Concluding, it can be said that despite an observed strong frequency coupling, prohibiting a complete separation of ion flux and energy, an adequate level of control is achievable for industrial processing.

23 1 1. Introduction Today, low pressure plasmas are a widespread tool for manufacturing micro- and nano-scale devices. Popular examples range from semiconductor manufacturing of well-known computing processors, micro-electromechanical machining (MEMS) and biomedical applications like lab-on-chip and sterilization processes, up to a large industry branch involved in specialized coatings technology. Hereby, thin film solar cells, architectural glass coatings with optimal ecological properties or layers for hardening workshop machining tools are common fields of applications. Several established methods for low pressure plasma processing exist and are discussed in the following. 1.1 Common thin film deposition techniques A number of established low pressure processes for coatings manufacturing are available today. Not all of them necessarily involve the use of plasma technology. Major representatives of this area are deposition tools like chemical vapor deposition (CVD) and the atomic layer deposition (ALD). Chemical vapor deposition (CVD) is a deposition process, solely based on chemical reactions taking place directly at the substrate surface through gaseous reactants. Therefore, a precursor gas is injected into the processing chamber. In most cases the substrate is heated to several hundred degrees Celsius, in order to enable, enhance or otherwise optimize chemical reactions on the substrate surface. The nitrification or carbonization of silicon wafers to produce isolating materials for on-chip capacitors can be stated as an example. As a consequence, heat stress of the substrate material during CVD processing is an issue that needs to be carefully controlled. Especially if previous processing steps have brought sensitive structures (layers) onto the substrate, they could be damaged subsequently. During heat-up and cool-down further temperature stress is brought upon the present and newly generated layers when substrate and layer materials have largely different expansion coefficients. These temperature problems could be resolved by using a plasma to chemically activate all reactants. Thereby, the gas or gaseous precursor molecules are dissociated/fragmented into ions and can thus be deposited on the substrate surface. This method is known as plasmaenhanced CVD (PE-CVD). The plasma s main advantage in reducing substrate heat load resides in the different heating contributions of ions and electrons. Because the electrons are in most cases much lighter than the ions, they heat up more easily (in terms of kinetic

24 2 1. Introduction energy), whereas the ions remain cold (near room temperature). Hence, chemical activation is achieved by kinetic electrons without significantly heating the gas itself. As a CVD equivalent, atomic layer deposition (ALD) recently attracted commercial interest. Because of their close relation, it brings along some of the previously discussed temperature problems. Essentially, ALD works similarly to CVD. The significant difference is, ALD allows for an absolutely dedicated thin film growth control down to monolayer precision. This is achieved by splitting the reactants into two half-reactions. Through purge/injection cycles of the feedstock gases a growth control in atomic layers precision is realizable. Additionally, surface reactions are self-limited, due to a limited number of produced chemical bonds per cycle. Although an absolute film growth control is possible, the numerous purge/injection cycles are time-consuming, depending on the desired film thickness. Two further examples for coatings manufacturing relevant to the scope of this work are related to physical vapor deposition (PVD). The basic working principle in all discharge cases is the production of high energetic ions. On surface impact, they are capable of removing a target atom out of its solid bond, which then diffuses towards the substrate and forming a layer. In very dense plasmas these sputtered atoms can also be ionized, allowing for a controllable directed deposition. The latter is particularly relevant for the filling of contact holes or so-called vias. Two different discharge approaches are interesting to this regard. On the one hand the magnetically enhanced (pulsed) dc cathodes (dc magnetron cathodes) provide high deposition rates due to high plasma densities. On the other hand multiple frequency driven capacitive discharges (2f-CCPs) are considered an adequate competition with advantages on the homogeneity and controllable deposition side. DC magnetron cathodes are magnetically enhanced, and in most cases pulsed, dc discharges. Magnetically enhanced in this context denotes the generation of a magnetic field parallel to the target by placing strong magnets with differing orientation behind it. Through this, bulk electrons and secondary electrons are efficiently captured in front of the target causing a high plasma density, hence ion flux. The combination of high ion flux and easily tunable ion acceleration voltage results in a high rate, high throughput deposition process. But there are three weaknesses to this concept. First, for reactive deposition processes involving isolating films, a committed arc management is obligatory to avoid arcing and thus substantial substrate damage. Second, magnetic target materials short circuit the parallel magnetic field, reducing deposition rate. As a countermeasure, specially prepared and costly targets have to be used. Third, sputtering and deposition homogeneity is disturbed because of preferential erosion along the magnetic field lines. Target utilization is low and frequent replacements are needed. Recently upcoming modifications are the so-called high power impulse magnetron sputtering (HiPIMS), also known as high power pulsed magnetron sputtering (HPPMS). One of their advantage for PVD is through high power pulses circumventing the aforementioned problems of arcing and deposited films tend to have good adhesion properties. A competitive new development with respect to ferro-metallic/magnetic thin film deposition and also high aspect ratio etching are capacitively coupled plasmas (CCPs) driven at multiple frequencies. They have the advantage of separately controlling ion flux and ion density. However the extent of separability and its dependence on external tuning parameters, like e.g. powers and pressure, are an open issue. These and related problems are the main work

25 1.2. Multiple frequency driven capacitively coupled plasmas 3 topic within the presented thesis. 1.2 Multiple frequency driven capacitively coupled plasmas Capacitive discharges experience a come-back prior to have been deemed industrially unattractive in the mid 20 th century. They were first reconsidered by the appearance of single frequency CCPs excited at frequencies in the VHF ( MHz) band [4][5][6]. Hereby, first applications range from PE-CVD deposition of silicon layers [7][8] to the production of diamond-like carbon (DLC) layers [9]. A considerable potential was anticipated by using higher excitation frequencies, because plasma density could be increased to equivalent values as reported from inductively coupled plasma (ICP) sources. Detailed investigations into the driving frequency behavior followed [10]-[15]. It was found that the elementary proportionality n e f 2 VHF (1.1) holds, with n e as the plasma (electron) density and f VHF as the excitation frequency. At the same time it was observed that the dc self bias voltage, as a good ion bombarding energy approximation, decreases. Both effects are equally attractive in plasma processing, because substrate damaging through high energetic particles is still an issue in today s manufacturing, especially in combination with shrinking component dimensions (e. g. reduced layer thickness or layer-to-layer separation). Although, increasing driving frequency possesses advantageous properties a dilemma persists. Ion bombarding energy is not controllable independently from plasma density (ion flux). One of the early experimental reports demonstrating a separate tunability was shown by Goto et al. [16]. It eventually led the way to what is now understood as dual frequency driven capacitive discharges. Theoretical approaches, analyzing the functional separation of ion flux and ion energy followed [17]-[20]. Until today, the most widespread field of application for 2f-CCPs is anisotropic reactive (ion) etching, documented experimentally [21]-[23] and theoretically [24]-[29]. Today, dual frequency capacitively coupled plasmas are generally attributed a full separability of ion flux and ion bombarding energy. However, a strong frequency coupling is observed when excitation frequencies are close together (f VHF /f HF < 10) [3][30]. Unfortunately, experimental evidence is sparse for dual frequency discharges in general. Although numerous theoretical considerations exist, detailed investigations into the frequency coupling and the mutual dependency of other external tuning parameters on discharge characteristics is needed. This topic is a major issue addressed within the frame of this work. Among studying the behavior of relevant stationary plasma parameters, such as electron density and temperature or floating and plasma potential, also detailed analysis into the transient electron heating (high energetic electron production / excitation mechanisms) is done by optical and electrical diagnostics. It is anticipated that by understanding external parameter s influence on electron heating is the most appropriate way of discharge optimization. Therefore not only an experimental but also a theoretical understanding of discharge heating and power deposition in the plasma is desired. Several models, describing dual frequency discharges, are found in literature ranging from

26 4 1. Introduction general scaling laws, (global) nonlinear behavior studies and heating properties [31]-[38] and [3] to specifically sheath related studies [39]-[44]. Recent trends in dual frequency CCP modelling arise from semiconductor manufacturing needs of reported observed inhomogeneities in large area processing of silicon wafers. These effects have also been diagnosed in single frequency VHF driven CCPs [45]. Theoretical approaches [46]-[51] and [52]-[55] deal with the problem of increasing tool and workpiece dimensions at simultaneously reduced excitation wavelengths. Indeed, it is shown by several independent sources that with increased workpiece dimensions in conjunction with dense plasmas (> cm 3 ), processing homogeneity can be seriously compromised through three identified effects. First, the standing wave effect is relevant when reactor dimensions come in range of excitation wavelengths, causing an enhanced heating in the discharge center. Second, the plasma skin effect describes the phenomenon of induced electric fields parallel to the electrodes causing a maximal heating at the plasma edges. It gets more and more relevant with increasing plasma densities. Third, the well-known edge effects in CCPs, denoting an enhanced heating at the discharge edges due to electrostatic field enhancements play a role. Additional edge effects with similar properties are theoretically reported when taking full electromagnetic calculations into account. Commonly, the above effects occur simultaneously. As a result, there are operating regimes where either effect becomes dominant. One possible solution to resolve discharge inhomogeneities are specially shaped electrodes [53]. Thereby, manufacturing and machining requirements are tough. These phenomena however are beyond the scope of this work and are not experimentally addressed, because reactor dimensions are small and densities for intended PVD experiments are moderate. Most commercial dual frequency plasma tools use frequencies which are an integer multiple of each other. By that, the relative phase as a further control parameter becomes available for discharge optimization. Since practical properties of this additional parameter have not been reported before, detailed investigations into the role of relative phase are performed. In order to be able to compare and correlate experimental observations to theory, special care has to be taken in terms of electrical discharge stability. There exist ample evidence on how to construct single frequency CCPs. However, using two frequencies and particularly one within the VHF band might seriously compromise discharge stability, because of mutual amplifier interferences. Thorough investigations into a dedicated suppression of mutual frequency interferences are necessary. Within this work, detailed studies of the transmission characteristics of the impedance matching networks are performed and methods, enhancing the suppression of mutual interferences, are proposed. Similar developments as presented for dc magnetron cathodes move towards magnetic enhancement of dual frequency discharges [56][57]. Depending on magnetic field strength, the same desired effect of boosting plasma density is achievable. By that, plasma densities of m 3 can be realized. However, homogeneity decreases at the same time in favor of preferential heating at the discharge center. Though a further increase in plasma density is desirable, controlling homogeneity problems might become a costly task.

27 1.3. Multiple frequency CCPs for PVD of ferro-metallic / magnetic materials Multiple frequency CCPs for PVD of ferro-metallic / magnetic materials Ferro-metallic films are important especially for their impact on magneto-resistive random access memory (MRAM) research. MRAMs are considered to be the successor of dynamic RAMs (DRAM), because of their advantage of non-volatility when switching off power. Because MRAM cell s space requirements are high and manufacturing, especially of the magnetic layers, is costly, their spread is rather limited. The development of spintronics (=spin-based electronics) is one of the key fields of application for these kind of films. Its major representative is the spin (valve) transistor based on the giant magneto-resistive (GMR) effect. The device is manufactured by common semiconductor processing steps (plasma deposition, etching, UV lithography) and its internal setup resembles that of a silicon transistor. In this case thin ferro-metallic films are used, separated by an aluminium oxide spacer layer. Electrically, the transistor becomes conducting when both magnetic layers have the same magnetic field configuration. Then, electrons can tunnel through the non-conducting material by applying a voltage drop across the transistor. Conversely, it possesses a high impedance when the magnetic field configuration is anti-parallel. Two types of transistor modes are distinguishable. The spin valve transistor is operated with an open base. Switching is accomplished by an externally applied magnetic field. This form of the spin transistor is well-defined and controllable. Another operating mode is the spin transistor, which does not use an open base. In other words, the spin valve transistor can be understood as a subset of the full spin transistor. Hereby, switching is realized by injecting a spin-polarized current into the transistor base. Within this work first experiments characterizing elementary deposition and thin film properties of ferro-metallic layers are performed. First, sputter deposition is characterized using a quartz crystal microbalance (QCM). Results are compared to findings from Langmuir probe and retarding field energy analyzer (RFEA) data. Roughness properties and determination of relative sputtered atomic species densities complete the elementary characterizations. However, the full development of a specific magnetic layer system lies beyond the scope of this thesis. 1.4 Thesis layout The presented thesis is divided into three parts. In the first part (chapter 2), the buildup phase and electrical process chamber characterization is discussed. First, constructional design properties are addressed (section 2.1) and the experimental setup is described in detail. Following in section is the electrical characterization of the transmission behavior of the applied impedance matching networks and electrical vacuum-feed-throughs, which is necessary to ensure stable discharge conditions. Thereby, vector network analyzer (VNA) measurements are performed. For each electrical network a circuit model including parasitics

28 6 1. Introduction is developed and fitted to VNA measurements, obtaining electrical component values. Special focus is laid on the development of an equivalent circuit model resembling electrical vacuum feed-throughs, because they are the main reason for rf losses due to strong capacitive coupling to ground. Combining the investigations result in an accurate estimation of overall electrical system efficiency. More importantly, the question of how much power is deposited in the plasma with respect to applied amplifier powers is clarified. The second part (chapter 3) primarily deals with the detailed description of used plasma diagnostics with respect to error considerations by applying them to multiple frequency driven capacitive discharges. Due to the nonlinear plasma boundary sheath behavior, numerous excitation frequency harmonics are produced, disturbing electrical diagnostics such as VI probe (section 3.1), Langmuir probe (section 3.2) and retarding field energy analyzer (RFEA, section 3.5). Investigations into uncompensated and filtered measurements gives way for the possibility of adequately using those diagnostics on 2f-CCPs. Further investigations involve the plasma impedance determination during plasma operation (section 3.1.1) using a standard available VI probe. On the basis of a previously developed feed-through equivalent circuit, it is calibrated by comparison to plasma impedance data obtained from Langmuir probe measurements. A way is proposed on whether plasma generated harmonics have to be considered or only measured frequency specific plasma impedances suffice for calculating the plasma impedance. More importantly, a method of mathematically combining these impedances is outlined [58]. Another set of diagnostics comprises a plasma series resonance (PSR) current sensor (section 3.4) and phase resolved optical emission spectroscopy (PROES, section 3.3). They are used to monitor the generation of harmonics and their mixing products in 2f-CCPs. The validity of a developed global model by Mussenbrock and Ziegler [3] is verified against experimentally measured PSR currents. Additionally, the possibility of experimental verification of nonlinear electron resonance heating as proposed by Mussenbrock and Brinkmann [1] is discussed. Finally, industrial implications of a found correlation of local excitation phenomena observed by PROES and PSR current resonant structures is discussed. In the third part of this thesis (chapter 4), all diagnostic results are discussed. First, Langmuir probe, VI probe and PSR current studies on a variety of external parameters, such as frequency ratio (section 4.1.1), power ratio (section 4.1.2) and pressure (section 4.1.3) are presented. Thereby, phenomena related to nonlinear plasma heating are outlined. Second, the role of tuning the relative phase is investigated (section 4.2) by PROES, Langmuir probe, VI probe and PSR current measurements. Third, the ion distribution is characterized by RFEA studies (section 4.3) with respect to planned ferro-metallic deposition experiments. Fourth, elementary thin film deposition analysis is performed (section 4.4) and correlated to all previously applied diagnostics. The thesis concludes with a summary comprising all essential results and discusses further topics with respect to a planned scale-up version (section 5).

29 7 2. Experimental setup This chapter outlines the developed experimental setup with its mechanical and electrical properties. First, important constructional design properties with respect to capacitively driven discharges are discussed in section 2.1 followed by a detailed analysis of the electrical rf system. It is a particularly important aspect for multiple frequency driven discharges, since all applied rf generators need to be protected from mutual interference. Usually, this is achieved by investigating transmission behavior in conjunction with possible modifications of the respective impedance matching network. The detailed procedure is described in section 2.2. Especially when using excitation frequencies in the VHF band ( MHz), it is inevitable to consider rf losses between an impedance matching network and the vacuum electrode. In order to quantify these losses, an electrode equivalent circuit model is developed and verified. 2.1 Constructional design properties The experimental setup consisting of the mechanical/vacuum parts and the electrical/radiofrequency (rf) parts is outlined in this section. To begin with, the mechanical and vacuum properties are discussed with figure 2.1 presenting a detailed overview. The process chamber is a modified GEC (Gaseous Electronics Conference) reference cell in a capacitive setup with an approximate volume of 30 liters. Attached is a vacuum pump combination consisting of a 230 l s 1 turbo-molecular pump (TMP1) and a membrane pump (3.3 m 3 h 1 )(FP1). System pressure is controllable by a butterfly valve (BV) assuming a constant gas flow, which is realized by mass flow controller units (MFC) tuned to the specific process gas properties. Although the MFCs are capable of shutting down the gas flow completely, separate manual valves (MV) have been inserted into the gas line for safety reasons. Chamber pressure measurement is performed by two pressure gauges (PG1 and PG2) covering different ranges. PG1 is a Penning cold-cathode pressure gauge, measuring the base vacuum below 10 4 Pa and PG2 is a capacitive pressure gauge (Baratron R ) monitoring the process pressure ( Pa). Available process and diagnostic gases are N 2 (nitrogen), O 2 (oxygen), Ar (argon), He (helium), Ne (neon) and H 2 (hydrogen). In order to allow for sample treatment and preparation without breaking the vacuum a load-lock system is installed connecting load-lock and process chamber. Both chambers are separated by a manual shutter (MV). Evacuation of the load-lock chamber is done by a

30 8 2. Experimental setup Figure 2.1: Gas and vacuum layout of the experimental setup. turbo-molecular/rotary vane pump combination (TMP2/FP2). Since the load-lock chamber is frequently pressurized and evacuated, a pumping bypass is installed that allows for continuous operation of TMP2. For secure bypass operation, it is fully automated by three electro-pneumatic valves (PV). A full range pressure gauge, which is a combination of a hot cathode gauge (Bayard-Alpert) and a Pirani gauge, monitors the load-lock chamber pressure. Sample transfer is performed by a magnetic transfer rod, taking a square silicon sample within a prepared holder, moving it into the process chamber and securing it into a retention mechanism. All exhausts from both vacuum pump stations are combined and fed into a filtering system to prevent gas and particle leakage. This completes the general overview of the gas and vacuum layout and a more detailed introduction of the main chamber s mechanical and electrical properties is addressed. Figure 2.2 shows the main chamber s mechanical (left) and electrical (right) outline. The pressure gauges PG1 and PG2 have been inserted to highlight their respective position. Both electrodes are mounted to the system from above (further denoted as top electrode) and from below (further denoted as bottom electrode) and are equipped with electrical and gas feed-throughs together with backside water-cooling. The electrode plates are made of stainless steel and are isolated from electrical ground by a MACOR R ceramic plate. Both, the stainless steel and MACOR R plates are embedded in a grounded guard ring, surrounding the capacitor stack at a distance of 1 mm. This technique focusses the discharge between the electrodes and prevents conductive coatings of the isolating ceramics, which would eventually lead to arcing and unstable plasma conditions. Gas is fed into the system via a circular shower head, located above the top electrode. An even gas distribution is achieved by numerous submillimeter holes in the shower head.

31 2.1. Constructional design properties 9 a a a a aaaaaa aaaaaa aaaaaa aaaaaa Figure 2.2: Mechanical (left) and electrical (right) layout of the plasma chamber including liner, guard ring, gas distribution ring, rf shielding (EMC) meshes and impedance matching networks. Because VHF driven plasmas tend to expand rapidly into the entire chamber, stainless steel rf shielding meshes used for EMC (Electro-Magnetic Compatibility) tests need to be introduced into the system at the indicated positions in figure 2.2 (left). Additionally, meshes are put into the pressure gauge flanges and below the bottom electrode. They ensure an enhanced discharge confinement. The confinement is further enhanced by introducing a metallic sheet (liner) of about 1 mm thickness, into the chamber. It effectively cancels the viewport s and diagnostic flanges parasitic volumes. One viewport for optical diagnostic access is protected from the plasma by a magnetically driven shutter mechanism. In the righthand diagram of figure 2.2, the setup s electrical schematic is depicted. As indicated up to three impedance matching networks, two of which mountable onto the top electrode, can be applied simultaneously. Their respective matching capability spans 2 MHz, MHz and MHz. All networks are prepared to be freely interchangeable among both electrodes, apart from the 2 MHz matching network. It can only be mounted to the bottom electrode, which has a long electrical feed line unfavourable for frequencies larger than 2 MHz. Rapid matching network exchange is realized by quick connectors also providing good rf contacting conditions. Both, matching network and connector are set on top of a copper rod, which is fed into the vacuum system. Figure 2.2 (right) displays the commonly used electrical setup in this work, showing the MHz and MHz matching network installed. Hereby, the bottom electrode is always grounded, apart from special case which are discussed in detail later. Every impedance matching network is connected to its according rf generator. Three different rf generators are experimentally applicable. Two of them, 2 MHz and MHz, are fixed frequency rf sources at 600 W and 700 W respectively. For VHF power delivery an arbitrary function generator combined with a 500 W broadband amplifier ( MHz) is used.

32 10 2. Experimental setup The arbitrary function generator allows for additional plasma operating options such as nonsinusoidal excitation waveforms and phase-locked dual frequency operation. Particularly the latter option is investigated in detail later within this work. 2.2 Electrical characterization by vector network analyzer measurements For multiple frequency driven capacitive discharges it is very important to minimize mutual interference of the high power rf equipment. Otherwise, no stable plasma condition can be ensured and equipment lifetime is strongly reduced. The interferences are usually suppressed by inserting absorption circuits (band-pass filters), tuned to the specific driving frequency of the rf generator. They can be inserted either directly at the matching network s output, or between the generator and matching network connection. Depending on the transmission behavior of each impedance matching network, the necessity of an absorption circuit needs to be determined individually. This is performed by vector network analyzer (VNA) measurements. A vector network analyzer is a device, which probes a device under test (DUT) with respect to its frequency response. Prior calibration is needed to accurately eliminate systematic errors [59]. Those errors mainly include cables and connectors. Results are saved in the form of scattering parameters or S-parameters, which are assembled into a n n S-parameter matrix for a n-port network. It fully describes the frequency dependent rf transmission and reflection behavior of a n-port network after equation (2.1) with n = 2. Hereby, the vector a describes the incident wave and b the reflected wave out of a given two-port network. ( b1 b 2 ) ( ) ( ) S11 S = 12 a1 S 21 S 22 a 2 (2.1) Figure 2.3: Definition of voltages, currents and wave parameters for a two-port network. The vector elements of a and b describe the wave amplitudes with respect to a known wave impedance Z 0i and are defined as depicted in figure 2.3. Defining the wave amplitudes in

33 2.2. Electrical characterization by vector network analyzer measurements 11 quantities of voltage and current at a port i yield a i = b i = U a i Z0i = Z 0i I ai (2.2) U b i Z0i = Z 0i I bi. (2.3) The connection between the wave amplitudes a i and b i to measurable values of port voltages U i and currents I i can be written as U i = U ai + U bi = Z 0i (a i + b i ) (2.4) I i = I ai + I bi = 1 (a i b i ) Z0i. (2.5) Rearranging equations (2.4) and (2.5) and solving for the wave amplitudes a i and b i yield a i = U i + Z 0i I i 2 Z 0i (2.6) b i = U i Z 0i I i 2 Z 0i. (2.7) The S-parameters can be understood by one of the following descriptions: S 11 is the input reflection coefficient describing the ratio between a wave b 1 coming out of and a 1 going into the input port of a two-port network, without a wave a 2 traversing from the output port. S 12 is the reverse voltage gain describing the ratio of a wave a 2 traveling from the output to the input port being detected as b 1, with no incident wave a 1 at the input port. S 21 is the forward voltage gain describing the ratio of a wave a 1 traveling from the input to the output port being detected as b 2, without a wave a 2 traversing from the output port. S 22 is the output reflection coefficient describing the ratio between a wave b 2 coming out of and a 2 going into the output port of a two-port network, with no incident wave a 1 at the input port. Several simplifications can be applied to the S-parameter matrix if the DUT satisfies one or more of the following conditions: Reciprocity A network is considered reciprocal if it is passive. Passivity of an electrical circuit is defined as only consisting of passive components such as resistors, capacitors and inductances. For the S-parameter matrix this implies the secondary diagonal elements to be equal such that S mn = S nm with m n, and for a two-port network S 12 = S 21.

34 12 2. Experimental setup Symmetry When in addition to the reciprocity condition also the main diagonal elements S mm of the S-parameter matrix elements are equal, a network is considered to be symmetric. Loss-free For loss-free networks the condition S H S = I holds, where S H is the conjugate transpose of the S-parameter matrix and I the identity matrix. In mathematical terms the S-parameter matrix is called unitary. In this work, each investigated impedance matching network is reciprocal, but not symmetric implying S 21 = S 12 S 11 S 22. Since only transmission behavior is relevant for the performed matching network investigations, only S 21 is considered. All measurements are performed using a HP8714ET vector network analyzer and the S-parameters are expressed in terms of voltages, meaning e.g. forward voltage gain and input (voltage) reflection coefficient Evaluation of the impedance matching networks In order to identify the necessity of absorption circuits, the matching network s transmission behavior is examined by measuring the forward voltage gain S 21. To quantify parasitic components, S 21 is additionally modeled and compared to these measurements. A direct comparison of modeled and measured S-parameters becomes possible if the complete circuit including the VNA s frequency tunable voltage source U Q as shown in figure 2.3 is accounted for. Figure 2.4: Generalized impedance network for calculating the input reflection coefficient S 11 and forward voltage gain S 21. Therefore, general solutions of the input reflection coefficient S 11 as well as the forward voltage gain S 21 are derived on the basis of the circuit in figure 2.3, applied to the generalized impedance network in figure 2.4, with Z as freely definable impedances. These results are used in all further calculations and comparisons to VNA data. The S-parameters S 21 and S 11 are defined by the wave amplitudes as S 21 = b 2 and S 11 = b 1. (2.8) a 1 a2 =0 a 1 a2 =0

35 2.2. Electrical characterization by vector network analyzer measurements 13 Substituting Z 01 = Z 0 (input port impedance) and Z 02 = Z L (output port impedance) the wave amplitudes can be written as a 1 a2 =0 a 1 = U 1 + Z 0 I 1 2 Z 0 = U Q 2 Z 0 a 2 = 0 (2.9) b 1 = U 1 Z 0 I 1 2 Z 0 = 2 U 1 U Q 2 Z 0 b 2 = U 2 ZL. (2.10) Inserting the wave amplitudes from equations (2.9) and (2.10) into equation (2.8) and expressing the voltage ratios as a function of the impedances Z and Z L yields S 21 = b 2 Z0 a 1 = 2 U2 Z0 Z 2 (Z 3 + Z L ) = 2 a2 =0 Z L U Q Z L Z 0 + Z 1 + Z 2 (Z 3 + Z L ) Z L (2.11) Z 3 + Z L S 11 = b 1 = 2 U1 Z 1 + Z 2 (Z 3 + Z L ) 1 = 2 U Q Z 0 + Z 1 + Z 2 (Z 3 + Z L ) 1. (2.12) Finally, the S-parameters are successfully expressed in terms of the matching network impedances Z 1...3, allowing for a comparison to measured VNA data. Furthermore in this work, all S-parameters are plotted in the form 20 log 10 ( S mn ), which always denote voltage dependent functions. In case the plotted S-parameters are power dependent, it is noted separately. Further references to the above representation are denoted as transmission function (S 21 ) and reflection coefficient (S 11 ). Simulations are performed using equal input and output impedances Z 0 = Z L = 50 Ω, representing real VNA measurement conditions. Portability to experimental plasma operation conditions however need further considerations, because the output impedance changes from 50 Ω to an arbitrary complex-valued output impedance. With some constraints (see section for more details), it can be regarded as the plasma impedance. Figure 2.5: Electrical equivalent circuit of the 2 MHz matching network including parasitic components. Therefore, comparisons of VNA data to simulated transmission functions with a 50 Ω output impedance, provide a basis for matching network (stray) component determination. Repeating the same simulation in a second step with a precalculated load impedance (e.g. plasma impedance), the transmission function valid for experimental operation is derived. Additionally, the impedance matching networks (2 MHz, MHz and MHz) are investigated with respect to their capability of attenuating other driving frequencies components. For easier understanding, the electrical components of each impedance matching network are named according to the following defined scheme: (i) The major letter denotes the type of

36 14 2. Experimental setup electrical part (capacitor, inductor or resistor). (ii) The index s first letters indicate to which type of impedance matching network the electrical part belongs (2M = 2 MHz impedance matching network). (iii) All remaining letters give information about whether this particular part is a parasitic component (denoted as stray) or not (denoted otherwise). Hence, e.g. C 2M parallel is the parallel capacitor of the 2 MHz impedance matching network. Figure 2.6: Comparison of measured and simulated voltage transmission S 21 impedance matching network. for the 2 MHz First, the 2 MHz impedance matching network is examined. By examining and transferring the matching network s topography, an equivalent circuit model is gained. The transmission function is calculated according to equation (2.11) with the impedances Z chosen after the modeled circuitry in figure 2.5. The resulting expressions are exemplarily written down below. The stray inductance L 2M stray = 40 nh was inserted after simulations failed to reproduce measured VNA data. The influence of a series resonance to electrical ground in this branch cannot be neglected. Z 1 = 0 Ω 1 Z 2 = + j ω L 2M stray j ω C 2M parallel 1 Z 3 = j ω L 2M out + j ω C 2M out Values for the electrical parts of the simulated network are found by fitting simulation to measurement. The results are plotted in figure 2.6. Both graphs compare well, however the fine structure as well as the rising slope for frequencies above 40 MHz are not reproducible by the small number of components in the equivalent circuit. Nevertheless, further simulations as well as test measurements using a voltage-current probe show the given equivalent circuit model to behave accurately for needed considerations in this work. As an exemplary value, the output inductance is estimated to L 2M out = 23.6µH using the fit to the 2 MHz resonance matching peak (indicated in figure 2.6). Taking the fitted component values and repeating the simulation for a changed load impedance with Z L 50 Ω produces the result shown in figure 2.7. It is noticeable, that the impedance

37 2.2. Electrical characterization by vector network analyzer measurements 15 Figure 2.7: Voltage transmission S 21 for a matched 2 MHz impedance network using a real plasma impedance termination. The voltage gain at 2 MHz is indicated. matching network causes a net voltage gain for an arbitrary complex load impedance. The explanation is, that whenever an impedance matching network attunes itself to an optimum match, the reactive elements of the load impedance go into resonance with the reactive matchbox elements. A typical load impedance has a value of (2 j100)ω for a dual frequency discharge. Due to this voltage resonance, significantly higher output voltages compared to the input voltages are detectable. For plasma ignition and operation this is a desired effect, because the gas breakdown condition defined in Paschen s law is easily met [60]. Because a matching network does not consist of ideal components the peak s resonant enhancement is limited by resistive parasitic internal and external elements. Typically, the output voltage of such an impedance matching network acquires a two to three times higher value compared to the input side when matched. For the 2 MHz matching network a 7.8 db gain can be derived from figure 2.7, which is 2.45 times higher than on the input side of the network. Furthermore, information about the network s attenuation at the remaining driving frequencies of MHz and MHz are important. Referring to the measured VNA transmission function in figure 2.6 gives a minimum 35 db attenuation for MHz and a mean attenuation of 40 db for MHz. This spans a range of two orders of magnitude for backward voltage transmission. Relating the attenuation values to corresponding measured peak voltages of 800 V (13.56 MHz) and 300 V (60 90 MHz) results in a net backward power of < 3 W dissipated in Z 0 underlying ideal matching conditions and Z 0 = 50 Ω. This contribution is mainly produced by the MHz frequency component. For the used amplifiers this represents an uncritical value, because they are designed to operate at a much larger amount of reflected power, which normally is on the order of magnitude of their rated forward power. However, in scaled-up applications where delivered powers are larger, considerations of integrating an additional absorption circuit for generator protection might become necessary. To verify simulations, VI probe measurements at the input port

38 16 2. Experimental setup Figure 2.8: Electrical equivalent circuit of the MHz matching network including parasitic components. of the matching network have been performed and no significant voltage components were detectable. Figure 2.9: Comparison of measured and simulated voltage transmission S 21 for the MHz impedance matching network. Second, the MHz matching network is investigated. Again the initial equivalent circuit, consisting of C 13M parallel, C 13M out and L 13M out in figure 2.8 is gained by transferring the network topography. Trying to fit this simple equivalent circuit to VNA data however is unsuccessful, since the dip at 24 MHz in figure 2.9 is not reproducible by one LC resonator. Hence, a second LC-resonator needs to be inserted, whose property is to reduce transmission at 24 MHz. Two possibilities are reasonable to this regard: (i) adding an additional inductance into the parallel capacitor C 13M parallel branch or (ii) putting a parallel RC-circuit into the output branch of the inductance L 13M out to additionally control the resonance s bandwidth and Q-factor. Trying option (i) does not reproduce the low frequency (< 20 MHz) part correctly. Option (ii) on the other hand produces a matching fit with experimentally verifiable component values. The completed equivalent circuit model including parasitics is shown in figure 2.8. R 13M stray and C 13M stray as additional components can be attributed to resistive losses in the inductance s coil and capacitive coupling between the coil turns.

39 2.2. Electrical characterization by vector network analyzer measurements 17 Figure 2.10: Voltage transmission S 21 for a matched MHz impedance network using a real plasma impedance termination. The voltage gain at MHz is indicated. In a next step the effective operational transmission function is determined. Similarly a complex-valued load impedance is assumed and the existing transmission function is resimulated with the previously estimated component values. The result is depicted in figure As with the 2 MHz impedance matching network a net voltage gain at the output port is observed. Expressed in absolute numbers the output voltage is approximately 5.8 db ( 1.95 times) higher than the input voltage. Concerning the need of an absorption circuit, 2 MHz voltages are attenuated by at least 20 db and MHz voltages are attenuated by at least 35 db on average. This is sufficient for existing experimental conditions, but enhancing the 2 MHz damping must be considered in a scaled-up process. Finally, the VHF broadband matching network is investigated. The initial electrical components derived from the matchbox topography are C VHF in, L VHF parallel and C VHF out as seen in figure Figure 2.11: Electrical equivalent circuit of the VHF impedance matching network including parasitic components. Theoretically, these elements are sufficient for obtaining an adequate match. However, trying to fit the resulting function to measured VNA data is not possible for two reasons. On the

40 18 2. Experimental setup one hand the absorption peak at 7.4 MHz cannot be adequately modeled, because of too few passive components. On the other hand the broad high pass behavior is similarly lacking model components. To resemble the transmission minimum at 7.4 MHz additional capacitive coupling C VHF stray to ground is inserted into the L VHF parallel branch. Furthermore, resistive losses R VHF stray play an important role, because they limit the minimum impedance at the series resonance frequency, which otherwise would represent a short circuit to ground. But the parasitic (L VHF stray ) is responsible for broadening the high pass behavior of the matching network. Completing the given network with above parasitic elements and refitting the measured data to the modified circuit yields a very good agreement as seen in figure Figure 2.12: Comparison of measured and simulated voltage transmission S 21 impedance matching network. for the VHF Reevaluating the simulation with a plasma impedance equivalent load, produces the effective transmission function plotted in figure Hereby, the net voltage gain is 5.75 db which implies a 1.94 times higher output voltage than the input voltage, which is in agreement with VI probe measurements. As to the necessity of an absorption circuit, 2 MHz voltages are damped by at least 70 db and MHz by at least 45 db. Underlying the maximum rated output voltages of 550 V (2 MHz) and 800 V (13.56 MHz) result in a net backward power of < 1 W, assuming ideal matching conditions and a source resistor Z 0 = 50 Ω. Comparing the matching networks, the broadband VHF matching network is most efficient in suppressing interfering frequency components. Also the necessity of absorption circuits are eliminated for all networks. However, one remaining problem commands a protection mechanism nevertheless. Because the plasma itself is a nonlinear medium it produces harmonics of the excitation frequency. The amplitudes of these harmonics are negligible (sufficiently damped) for the 2 MHz and MHz networks, but not for the VHF network because of its high pass characteristic. An inspection of figure 2.13 reveals a constant gain above 100 MHz of 0 db. Estimating the amplitude of the first harmonic to be 30% of the basic frequency, allows generator

41 2.2. Electrical characterization by vector network analyzer measurements 19 Figure 2.13: Voltage transmission S 21 for a matched VHF impedance network using a real plasma impedance termination. The voltage gain at 67.8 MHz is indicated. loading with more than 120 W of harmonic power at a maximum generator forward power of 500 W assuming an ideal match. This is important, because this amount of backward harmonic power, coming solely from the VHF excitation, can seriously influence plasma process stability and amplifier lifetime. A solution is inserting an rf broadband circulator into the power line between the generator and impedance matching network. It is complex to construct a circulator for a frequency range fitting the given matching network. Hereby, the difficulty lies in the corresponding wavelength range and resulting circulator dimensions. Realizable bandwidths are ± 10% of the center frequency of this particular frequency range. In the experimental setup a circulator ranging from 67 MHz to 82 MHz is used. In general, a circulator is a three or more port network where power transfer is only possible in a fixed port order from e.g. PORT 1 PORT 2 PORT 3 PORT 1. By terminating port 3 with a 50 Ω load, which is practically realized by a 40 db (1 kw maximum power rating) attenuator and a 5 W load, the circulator is transformed into an rf isolator. Terminating PORT 3 prohibits any power transfer to PORT 1 by full power consumption into the 50 Ω load. The ideal S-parameter matrix of such a three-port circulator without crosstalk and insertion losses is represented by ( ) S circ = (2.13) From (2.13) it follows that a circulator is a non-reciprocal rf component. Its internal structure consists of a Faraday-rotator relying on the non-reciprocal Faraday-effect. This effect describes the polarization plane change of an electromagnetic (EM) wave under the influence of an applied magnetic field. Practically it allows the directed guidance of an EM wave from one port to another by constructive interference and disallows the direct return path by destructive interference. Concluding, all impedance matching networks have been investigated for the option of an absorption circuit. Results show that no modifications on the standard components need to

42 20 2. Experimental setup be performed. An exception is made for the broadband VHF matching network. Thereby, a broadband circulator is inserted to absorb plasma generated backward harmonic power. For a planned scaled-up version these investigations have to be carefully repeated, because individual matching network behavior and exact amplifier power specifications need to be considered in conjunction. Furthermore, not only impedance matching networks need to be characterized, but also the behavior of the plasma chamber itself especially with respect to rf losses. Regarding backward harmonic power and an equivalent circuit model for the electrical feed, a circulator might become irrelevant, because of the additionally considered transmission function Chamber characterization and equivalent circuit model for the electrical feed The overall electrical efficiency of any type of rf driven discharge crucially depends on loss factors and how they can be minimized. The most important loss factors are identifiable as Impedance matching networks RF contacts and connectors Vacuum feed-throughs The impedance matching networks have been characterized previously in section and network efficiency is determined by the respective measured transmission function. Regarding rf contacts, only losses at the network outputs are relevant. Other contacts are realized by available low-loss coaxial connectors and cables, where no significant losses could be experimentally identified. Finally, the vacuum feed-throughs are considered in conjunction with rf contacts, since both effects are closely linked and can also be recorded simultaneously by VNA measurements. Figure 2.14: Parasitics equivalent circuit model of the top electrode. In order to find an appropriate way of describing discussed losses, an equivalent circuit model is developed on the basis of common methods. In literature, similar equivalent circuits exist and are well established [61]-[65]. Among those, the equivalent circuit proposed by Sobolewski [61] is most adequate for given experimental conditions. He thoroughly characterized stray parasitic effects by voltage and current measurement on a GEC reference cell. Based on

43 2.2. Electrical characterization by vector network analyzer measurements 21 these findings, the equivalent circuit is adapted to represent given mechanical properties. Following, each electrical component is assessed for its validity. All concentrated electrical components are gained theoretically by considering the mechanical properties between an impedance matching network and the vacuum electrode plate. Figure 2.14 shows all components that could be derived from mechanical properties. The validity of each component is verified by fitting VNA and real plasma impedance data to measured input impedance data. Each component is explained by one of the following descriptions: R Rod represents ohmic losses on the electrical line (copper rod) between the matching network and the vacuum feed-through connector. Due to the skin depth at higher frequencies this component rapidly grows in magnitude. L Rod represents an equivalent coaxial inductance calculated from geometric data. C Contact represents the stray capacitance of the connector between a matching network and the electrical line (copper rod). L Screws and C Screws represent twelve individual screws holding the vacuum stack of the electrode and MACOR R ceramic plate together. Additionally they are responsible for tightening the vacuum seals. C Feed represents the coaxial capacitance of the vacuum feed-through. A crucial task is to gain related values for above listed components. Some components like L Rod, C Feed and C Screws can be adequately estimated from geometric data and later refined iteratively. The most important calculated values are L Rod 60 nh C Screws 140 pf C Feed 130 pf The contact capacitance C Contact and vacuum screws inductance L Screws are evaluated separately in the fitting process with respect to feasibility. Initially, they are introduced for completeness of the circuit model, but play a negligible role as is seen later. In order to derive values for all electrical components, the equivalent circuit parameters are determined by iteratively adapting measured voltage-current (VI) probe data to known plasma impedances. These plasma impedances are derived from Langmuir probe measurements on the basis of a plasma impedance model, which incorporates relevant plasma parameters, such as electron density and mean electron temperature [60]. Both impedance magnitudes are depicted in figure The VI probe is located between the impedance matching networks and the electrical feed-through as indicated in figure 2.2 (right). It measures the complex impedance as seen from its position towards the vacuum electrode. The Langmuir probe derived plasma impedances are calculated from plasma parameters by applying an appropriate equivalent circuit model by Lieberman and Lichtenberg [60]. A more detailed outline is found in section ([58]).

44 22 2. Experimental setup Figure 2.15: Comparison of fitted voltage-current probe data to a set of reference plasma impedances gained from Langmuir probe measurements. The Langmuir probe derived plasma impedance is assumed as an accurate goal of estimation. By iteratively fitting VI probe data to Langmuir probe data, all component values are found to be R Rod = 1.03 Ω L Rod = nh C Contact = nf C Feed = pf L Screws = ph C Screws = pf Comparing these results to previous approximations, they show a good agreement. L Rod, C Feed + C Screws and R Rod have reasonable values with respect to mechanical considerations. However, the component values for L Screws and C Contact need to be validated. During the fitting process C Contact was found to adopt a comparably high value of nf giving way for two implications. On the one hand C Contact is in series to the output capacitor of a matchbox, which typically ranges from several pf to a few hundred pf. The combination of both produces an even lower capacitance than from the matchbox alone. On the other hand such a high value indicates a very good contacting condition, which in an ideal case would be C Contact. Testing these assumptions by eliminating C Contact and reevaluating the simulation delivers no detectable deviation in the calculated complex impedances. Similar considerations apply for L Screws. Calculating the resonance frequency for L Screws and C Screws gives f res Screws = MHz which is one order of magnitude larger than the driving frequencies in question. Even the resonance frequency for C Feed + C Screws gives f res Screws = MHz, which still is significantly larger. Similarly, the simulation is repeated with L Screws left out and no change was observable. Essentially, the developed

45 2.2. Electrical characterization by vector network analyzer measurements 23 and verified equivalent circuit model consists of three relevant component R Rod, L Rod and C Feed +C Screws, which is in good agreement with Sobolewski s findings [61]. Using this refined equivalent circuit model allows for accurate interpretation of voltage and current measurements and ensures stable, reproducible plasma conditions. Furthermore the possibility is given to predict the overall electrical efficiency of a plasma setup, by considering the transmission functions from the impedance matching networks and equivalent circuit model. This means, deposited power within the plasma can be directly correlated to VI probe measurements at the matching network output. It is also stated by Sobolewski [61] that implications for commercial use of this diagnostic method for plasma impedance monitoring are delicate. A significant drawback is the determination of exact stray component values, which needs to be performed for each plasma chamber individually. Above calculations have unveiled the derived plasma impedance magnitude to be very sensitive to small stray component value deviations ( 10%). Additionally, depending on mechanical chamber properties, the validity of the equivalent circuit model needs to be verified and modified if applicable. Both arguments prevent a wider use of this diagnostic method. The availability of cheaper and more efficient plasma monitoring tools supersedes impedance measurements (see next chapter). Estimation of electrical system efficiency For an accurate estimation of the overall electrical system efficiency, all loss mechanisms need to be known. Major losses have been identified in the impedance matching networks, rf contacts and feed-throughs (see equivalent circuit model). Voltage transmission functions have been determined for all networks. They are transferable into equivalent power transmission functions under the following conditions: (i) the impedance matching network is terminated with a 50Ω load during measurement or simulation and (ii) the DUT is reciprocal. Both conditions are met in this work, so that power transmission functions are derived from voltage transmission functions by H power = 10 log 10 ( S 21 ) = 1 2 H voltage = 1 2 (20 log 10( S 21 )). (2.14) On this basis, also the power transmission function of the electrode equivalent circuit model is calculated. The result is shown in figure As it is seen, the equivalent circuit model acts as a low-pass filter with a cut-off frequency ( 3 db point) at 53 MHz. Related to a typical operation frequency of 71 MHz, power transmission is reduced by approximately 5 db. Exemplarily considering the measured VHF broadband matching network transmission in figure 2.12 at 71 MHz gives an approximate voltage reduction of 3 db or = 1.5 db in power. To calculate the overall electrical efficiency the power source s efficiency needs to be known. From the maximum power transfer theorem this is derived to be η source = 1. Combining all sub-efficiencies yields the overall electrical 2 efficiency η all to be η all = η source η matching η chamber = %. (2.15)

46 24 2. Experimental setup Figure 2.16: Calculated power transmission S 21 for the vacuum feedthrough equivalent circuit. Nonetheless, overall system efficiency is very low at 11.2%. Depending on the given matching networks an efficiency range is calculated to 5% η all 13%. These calculations clearly indicate the generator power readout to be an unsuitable external tuning parameter for plasma processes. Only the impedance matching network s output voltage is an adequate controlling parameter, because it represents the discharge voltage to a very good extent. For asymmetric capacitively coupled plasmas exist an easy approximation in the dc self bias voltage. In stationary state it acquires a value, which results from balancing ion and electron current at the grounded walls. Thus it is dependent on the electrode to ground ratio, used gases and grounding conditions (e.g. non-conducting liners for enhanced discharge confinement). Usually, every type of impedance matching network measures the dc self bias voltage by acquiring the dc voltage drop between the blocking capacitor and electrical ground. This concludes the electrical characterization of the applied impedance matching networks and the plasma chamber. It was found, that the measured transmission functions are accurate and applicable to further calculations of the overall electrical efficiency. Furthermore no modifications in the prototype system are necessary to prevent mutual generator interference. However, harmonic power was discovered to be a potential source of process instability if left unfiltered. Hence, a broadband circulator was inserted into the power line between amplifier and matching network. An equivalent circuit model for the electrode was developed considering different loss mechanisms. Results are in good agreement with literature. Despite a favorable transmission function of the electrical feed with respect to plasma generator backward harmonic power, a circulator is used to ensure stable amplifier operation. Finally, the results are combined to estimate the electrical system efficiency to be η all = 11.2%, which means only a small amount of amplifier power is deposited in the plasma.

47 25 3. Plasma and thin film diagnostics This chapter outlines the different experimentally applied plasma and thin film diagnostics. To this regard and within the frame of this work they are categorized into four groups invasive electrical diagnostics non-invasive electrical diagnostics optical diagnostics thin film diagnostics As an non-invasive electrical plasma diagnostic, a voltage-current (VI) probe is used. A further such diagnostic is a vector network analyzer applied without plasma operation. The VI probe s working principle including transmission behavior and theory of calibration will be presented. A number of plasma diagnostics are counted to the group of invasive electrical diagnostics. Experimentally applied are a Langmuir probe, a self-excited electron resonance spectroscopy current sensor and a retarding field energy analyzer. Each diagnostic covers a range of measurable plasma parameters. Third, optical diagnostics are presented. Among the range of available optical diagnostics, those working on the basis of optical emission have been experimentally applied. In contrast, not applied are absorption methods like laser induced fluorescence (LIF) or cavity ring down spectroscopy (CRDS). The focus of this section concentrates on phase resolved optical emission spectroscopy (PROES). Compared to simple optical emission spectroscopy (OES), PROES gives insight into transient plasma processes, whereas OES as a time-averaged technique gives information about stationary plasma processes. Therefore, PROES is used to study discharge heating mechanisms with respect to external parameter variations. On the other hand, OES is applied for investigating atomic species (relative densities) in sputter deposition experiments. Finally, thin film deposition diagnostics are briefly addressed by using a quartz crystal microbalance (QCM). The theory of operation is discussed and possible problems with respect to metallic film deposition are considered. Furthermore, the microbalance is classified and compared to equivalent thin film diagnostics as e.g. ellipsometry.

48 26 3. Plasma and thin film diagnostics 3.1 Voltage current (VI) probe Voltage-current probes or VI probes are used in industrial plasma processing tools as a means of passive discharge diagnostic. Usually, a VI probe is therefore installed between the impedance matching network output and vacuum feed-through connector. At this position, the discharge voltage is accurately measurable and the discharge current is not. Hence, reproducible plasma conditions are achievable by tuning to this voltage value. As presented in section 2.2.2, an adequate description of electrode loss mechanisms in the form of an equivalent circuit model is needed to convert measured VI probe currents into realistic discharge currents. Such a model also allows for the plasma impedance determination. In the experiment a standard available VI probe (MKS/ENI VI Probe R 4100) with a specified frequency range of MHz is used. The calibration procedure is explained theoretically and verified experimentally. Figure 3.1: Exemplary internal outline of a voltage-current (VI) probe sensor. To describe the measurement principle of a VI probe, figure 3.1 is used. Measurement of voltage and current are realized by a capacitive voltage divider and a Rogowski coil respectively. Two precautions need to be considered for realizing the voltage divider. On the one hand, the voltage measurement has to be performed highly resistive, so as not to draw significant rf current. On the other hand, the voltage has to be reduced down to low amplitude levels for easier post-processing by the evaluation electronics. Current measurement is more complex, since only a current equivalent induction voltage U Current is measurable. Similarly, the induction voltage measurement has to be realized highly resistive, because counter-induction would otherwise introduce significant measurement errors. A correlation from the rf current to the induction voltage is derived next. Generally, the rf current I rf (t) is correlated to the time-dependent magnetic field H rf (t) through Ampère s law H rf (t) d s = J rf (t) d A A } {{ } conduction current + t D rf (t) d A A } {{ } displacement current (3.1)

49 3.1. Voltage current (VI) probe 27 where J rf (t) is the current density, D rf (t) the electric displacement field, d s the line element of the magnetic field and d A the normal vector on the conductor s cross-sectional area. The normal vector s orientation needs to be chosen in the same direction as the current. In this case, the total rf current is carried by conduction, eliminating the second summand. Integrating around the outer rf conductor at a radius r in cylindrical coordinates gives 2 π r H rf (r, t) = I rf (t). (3.2) Multiplying both sides with the permeability µ 0 µ r and reforming equation (3.2) to the magnetic flux density B rf (r, t) yields B rf (r, t) = µ 0 µ r 2 π r I rf(t). (3.3) Assuming the Rogowski coil to be ideal (neglecting magnetic stray fluxes) and only considering field contributions at a constant radius r, the expression 2πr equals the coil s mean length l coil. Furthermore, multiplying equation (3.3) with the turn s cross sectional area A coil gives the total magnetic flux Φ coil (t) in the inner coil to be Φ coil (t) = µ 0 µ r A coil l coil I rf (t). (3.4) Finally, the measurable induction voltage U Current (t) is described by Lenz s law U Current (t) = N coil dφ coil(t) dt = µ 0 µ r A coil N coil di rf(t) l } {{ coil dt } coil inductance M coil. (3.5) Since no magnetic materials are used within the Rogowski coil, the relative permeability is µ r = 1 in above equations. The coil inductance has been determined experimentally in a calibration measurement to M coil = ± 9.9 nh. Figure 3.2: Voltage transmission functions (S 21 ) from the input port to the voltage and current equivalent voltage measurement port.

50 28 3. Plasma and thin film diagnostics A crucial task is to calibrate the transmission characteristics from the rf current input connector to the voltage and current measurement ports. Figure 3.2 displays the voltage and current transmission function measured by a vector network analyzer. Although the working principle is comparably easy, calibration is not. Because voltage and current transmission are strongly frequency dependent due to nonlinear coupling and stray elements, the calibration needs to be a customizable part of a digital signal processing (DSP) unit. By that means, measured voltage and current values are correctable. The shown transmission functions from figure 3.2 are needed if the commercial evaluation electronics, wherein calibration results are integrated, is not used and direct oscilloscope measurements are performed. In this case, all time-domain signals have to be transferred into frequency space, corrected, and transferred back to time-domain in order to obtain realistic current and voltage amplitudes Plasma impedance determination in multiple frequency capacitive plasmas As discussed previously, a VI probe s main application is discharge impedance monitoring. Several attempts are found in literature for single frequency discharges [66]-[72]. One suitable method correlating measured impedances to true plasma impedances has been presented in section This procedure is further explained in detail in the following paragraphs. Additionally, investigations into the plasma impedance determination for multiple frequency driven plasmas are presented. Figure 3.3: Raw VI probe data of a dual frequency discharge operated at f HF = MHz and a variable frequency f VHF = MHz. Left: absolute impedance magnitudes. Right: corresponding phase information. Figure 3.3 shows raw VI probe data of a dual frequency discharge operated at f HF = MHz and a variable frequency f VHF = MHz. On the left-hand side, absolute impedance magnitudes of Z VIProbe HF and Z VIProbe VHF are drawn. On the right-hand side, corresponding phase information is found. Since these data are gained from a capacitive discharge where the plasma boundary sheath capacitance always dominates the plasma impedance, a phase angle near 90 is expected. This holds for Z VIProbe HF resulting from f HF = MHz but not for Z VIProbe VHF resulting from f VHF = MHz. The VHF

51 3.1. Voltage current (VI) probe 29 impedance clearly expresses an inductive behavior which does not fit considerations for a capacitive discharge. This problem is solved by comparing given VI probe impedances to realistic plasma impedance values. By that, all component values of an equivalent circuit model can be determined. These plasma impedances are obtained from simultaneously performed Langmuir probe measurements, which are described in chapter 4 in more detail. From those measurements, the electron density n e and mean electron temperature T e are derived. In turn, both parameters n e and T e are used to calculate true plasma impedances by the following set of equations from Lieberman and Lichtenberg [60] C Vacuum = ε 0 A electrode L s (3.6) 1 L Bulk = ωpe 2 C Vacuum (3.7) R Bulk = ν m L Bulk (3.8) C Sheath = ε 0 A electrode s in conjunction with the plasma impedance equivalent circuit in figure 3.4. (3.9) Figure 3.4: Plasma impedance equivalent circuit model from Lieberman and Lichtenberg [60]. In above equations, the electrode radius r electrode, electrode separation L and electron-neutral collision rate ν m are experimentally given as r electrode = 70 mm, L = 45 mm and ν m = 10 8 s 1. The electrode area is defined as A electrode = π relectrode 2. Electron-neutral collision rate is assumed to be constant for all calculations. Additionally, definitions for the mean sheath expansion s and the electron-plasma frequency ω pe are given as 50 s = λ Debye ( 2 e V0 k B T e ) 3 4 (3.10) ε0 k B T e λ Debye = (3.11) e 2 n e e ω pe = 2 n e (3.12) ε 0 m e where λ Debye is the Debye-Hückel length, V 0 the voltage drop across the plasma boundary sheath, k B the Boltzmann constant, ε 0 the vacuum permittivity, e the electron charge and m e the electron mass [60]. One problem of directly comparing Langmuir probe derived impedances to VI probe data is an indeterminate frequency reference. On the one hand, a Langmuir probe as an electrostatic plasma diagnostic determines time-averaged frequency-insensitive (dc) plasma parameters.

52 30 3. Plasma and thin film diagnostics On the other hand, VI probe impedances and their respective plasma impedances can only be gained with respect to a dedicated frequency. Moreover, they are usually determined for the multitude of available driving frequencies but not for the entire frequency spectrum, including e.g. discharge harmonics. Thus, it needs to be determined first, whether discharge harmonic contributions have to be included in VI probe measurements. And second, if and in which way all frequency-discrete plasma impedances are to be combined to an effective plasma impedance. Addressing the role of harmonics for VI probe measurements, it is found by considering figure 2.16 that most generated discharge harmonics larger than 50 MHz are not accessible by a VI probe because they are significantly damped by the vacuum feed-through. An exemplarily acquired current-equivalent induction voltage signal U Current (t) and its discrete Fourier spectrum are shown in figure 3.5. Figure 3.5: Measured current equivalent induction voltage U Current (t) (left) for a MHz and 71 MHz discharge with its according discrete amplitude Fourier spectrum (right). Clearly visible are the two main excitation frequencies of 71 MHz and MHz and only two additional harmonic components at 142 MHz (= 2 71 MHz) and 213 MHz (= 3 71 MHz) can be detected. Other frequency components have too low amplitudes to be useful for impedance calculations. Hence, because driving frequency harmonics are strongly attenuated by the feedthrough s transmission function they are not available for plasma impedance calculations and only the excitation driving frequencies are used further. Eventually, the question of combining all frequency-discrete plasma impedances remains and whether realistic results can be obtained. Therefore, an empirical approach is used. Two simple possibilities of generating an effective frequency-independent plasma impedance are a series or a parallel combination according to Z Plasma eff1 = Z Plasma VHF + Z Plasma HF (3.13) = + Z Plasma eff2 Z Plasma VHF Z Plasma HF. (3.14) Applying above equations to measured VI probe impedances produces figure 3.6 showing the resulting impedance magnitudes.

53 3.1. Voltage current (VI) probe 31 Figure 3.6: Measured single frequency VI probe impedances of MHz ( ) and MHz ( ) and proposed combinations in series ( ) and parallel ( ) compared to the Langmuir probe deduced plasma impedance ( ). Additionally, the pre-calculated Langmuir probe plasma impedances are plotted for comparability. A significant deviation is observed for adding up each plasma impedance contribution according to equation (3.13). This is explainable by the significantly differing impedance magnitudes of Z Plasma VHF and Z Plasma HF. Summing over all components yields an even larger value as seen in figure 3.6. Building the effective plasma impedance out of a parallel combination of the frequency contributions, according to equation (3.14) shows a very good agreement to pre-calculated impedance values gained out of Langmuir probe measurement parameters. Figure 3.7: Physical explanation for the impedance splitting as performed by a VI probe. Arrows in the electrical line indicate the corresponding rf current direction. The voltage drop across the discharge is considered as U Plasma. Physically, this is explained as follows. Consider multiple power sources at different operating frequencies connected to the input port of a VI probe, assuming each current passing through the VI probe and the plasma. Thereby, it is unimportant how they are connected (in series or parallel), because the frequency-specific current contributions add up according to Shannon et al. [20], implying a parallel circuitry. Consequently only one dedicated voltage drop

54 32 3. Plasma and thin film diagnostics U Plasma is found across the plasma. Figure 3.7 resembles the experimental situation for easier understanding. Practically, a VI probe is capable of detecting frequency-specific impedances Z Plasma (ω). In case of multiple frequency components, each single impedance is recorded. Relating this to plasma impedance determination in multiple frequency driven plasmas, all measured frequency-specific VI probe impedances have to be combined in parallel in order to gain the plasma impedance as derived from Langmuir probe determined plasma parameters. Figure 3.8: Comparison of magnitude and phase of an effective plasma impedance ( ) after equation (3.14) to Langmuir probe deduced plasma impedances ( ). From the effective plasma impedance the mean sheath ( ) width is deducible using equation (3.18) and a fit to the mean sheath width ( ) is performed. From the gained plasma impedances, several important plasma parameters are deducible, such as the mean sheath thickness s [64][65], electron density n e [64][73] and ion current [64]. Exemplarily, the mean sheath thickness s is derived and compared to simulations from literature [10][19]. In a dual frequency capacitive discharge, the total mean sheath thickness can be expressed by s = s VHF + s HF (3.15) with s VHF and s HF representing the mean sheath thickness for each frequency component [20]. Since only f VHF is varied in this particular measurement series, the contribution of s HF is constant. Accordingly, equation (3.15) is rewritten to s(ω VHF ) = s VHF (ω VHF ) + s HF. (3.16) Consequently, also the plasma impedance magnitude can be written as Z Plasma eff = 1 ω VHF C Sheath (s(ω VHF )). (3.17) Rearranging equation (3.17), substituting ω VHF = 2 π f VHF and solving for s(ω VHF ) yields s(ω VHF ) = 2 π Z Plasma eff A electrode f VHF ε 0. (3.18) Plotting equation (3.18) by using the previously derived plasma impedances Z Plasma eff results in figure 3.8. For completion, Z Plasma eff and the pre-calculated Langmuir probe plasma

55 3.2. Langmuir probe 33 impedance magnitudes and phases are incorporated, both agreeing well. Also, the respective phases agree well underlining the equivalent circuit model validity. Furthermore, a fit to the mean sheath thickness on the basis of simulation predictions [10] is performed. Results exhibit a proportionality of s f 0.8 VHF which is in very good agreement to findings of Vahedi et al. [10]. They predict a scaling of the mean sheath width with frequency of s f Langmuir probe Langmuir probes belong to the category of invasive plasma diagnostics and the measurement principle works as follows. A thin wire electrode, typically several µm in diameter, is brought into the plasma. Then, voltage is applied between the wire and a grounded electrode. This voltage is scanned in a specified range and the probe current is sampled at each voltage step. The resulting current-voltage characteristic (IV-trace) is evaluated and plasma parameters such as plasma- and floating potential, mean electron temperature, electron density and electron distribution function are gained. Despite the method s simplicity several evaluation difficulties need to be considered: Subtraction of the ion current from total current, to obtain the electron current. Accurate determination of the plasma potential. Calculation of the IV-curve s second derivative for estimating the electron distribution function (EDF ). Filtering of discharge harmonics and excitation frequency components in the VHF band. To quantify the above statements a more detailed description is needed. Therefore figure 3.9 depicts a measured typical IV-trace, described in the following. The shown IV trace is formally dividable into three distinct regions with different physical meanings. However, in reality the transition between each region cannot be pinpointed exactly to the indicated positions. At large negative voltages only ions and very fast electrons can traverse the probe electrode s sheath. This part of the IV curve is denoted as ion saturation current. Because the number of very fast electrons is small compared to the number of ions, the resulting current is assumed to be carried by ions only. The second region is denoted electron retarding current. Here, a significant number of electrons begin to traverse the sheath, but still have to overcome the probe sheath potential. It describes the transition from ion current to a mixed ion/electron current. At the point where the total current becomes zero, the probe voltage U Probe equals the floating potential Φ float with respect to electrical ground. Every isolated (electrically floating) object in a plasma acquires that potential, because ion and electron current have to balance. The plasma potential Φ plasma is derived from the curve s inflection point, where the ion current is assumed to be zero and electrons are no longer repelled. Increasing the applied voltage further, only the electron saturation current remains. However, the term saturation only applies for planar probe

56 34 3. Plasma and thin film diagnostics Figure 3.9: Characteristic Langmuir probe current-voltage (IV) curve. Three regions are identifiable: I ) ion saturation current, II ) exponential electron current or electron retarding current, III ) electron saturation current. tips, whereas the electron saturation current increases with increasing voltages for cylindrical probe tips. There are two different behaviors for the electron saturation current. First, with planar probe electrodes the current stays constant above plasma potential and second, with cylindrical electrodes the current increases as shown in figure 3.9. The difference is explainable by additionally considering angular momentum and a different sheath expansion for cylindrical geometries. By further assuming a collisionless sheath all currents can be defined by the orbital motion limited (OML) theory. Within this work only cylindrical electrodes such as tungsten wires ( 50µm, length 5 mm) are used. A detailed derivation of the OML theory is found in [74] and [75]. Resulting from this theory are mathematical descriptions for all currents, from which the plasma parameters electron temperature T e, electron density n e and the electron distribution function (EDF) can be calculated. An elementary equation describes the relation between electron retarding current and a measured IV trace. It was described by Druyvesteyn [76] and is known as Druyvesteyn s relation. 8 me E f v,elec (E) = A Probe e d2 I retard and E = e U 3 d UProbe 2 Probe (3.19) Thereby, e represents the electron charge, m e the electron mass, E the equivalent probe energy, U Probe the applied probe voltage, I retard the electron retarding current and A Probe = 2 πr wire l wire the probe tip s surface area with R wire as the tip radius and l wire the tip length. Interpreting equation (3.19) directly correlates the electron distribution function (EDF) to measured current-voltage characteristics. This is very important, because no additional assumptions on the distribution s mathematical form are made. Therefore, an arbitrary EDF is the result of applying equation (3.19). Calculating all plasma parameters directly from an EDF resulting from Druyvesteyn s relation is the most accurate way, because other formulas explicitly or implicitly underly a Maxwellian distribution. Within this work all IV

57 3.2. Langmuir probe 35 trace evaluations are performed using equation (3.19). To give a complete overview the possible methods are explained in the following. To begin with, the three regions of a probe characteristic need to be described. Assuming an isotropic Maxwellian distribution of the form f( v ) = n e ( me ) 3/2 exp[ m ] e v 2 2 π k B T e 2 k B T e (3.20) where, n e is the electron density, T e the mean electron temperature and v the velocity vector, the electron retarding current I retard can be written as [ ] kb T e e UProbe I retard (U Probe ) = e A Probe n e exp 2 π m e k B T e (3.21) and describes the behavior of electrons capable of traversing the potential barrier larger than U Probe [77]. Similarly the electron saturation current I sat with kb T e 2 I sat,elec (U Probe ) = e A Probe n e π 1 + e U Probe (3.22) 2 π m e k B T e is derivable. Equation (3.22) holds under the following constraints: (i) the probe radius r Probe needs to be small against the surrounding sheath radius r Sheath, so that r Probe r Sheath. (ii) Only for sufficiently high values of U Probe > ( Φ Plasma + 2 kb T e ) e, the electron retarding current can be expressed in closed form. Finally, the ion saturation current is found in analogy to the electron saturation current by introducing the Bohm velocity, which gives with I sat,ion (U Probe ) = e A Probe n i u Bohm 2 π 1 e U Probe k B T e (3.23) u Bohm = kb T e m i (3.24) where n i and m i represent the ion density and mass. As with the electron saturation current the applicability begins for sufficiently low values of U Probe < (Φ float 2 kb T e ). The Bohm e velocity u Bohm is the minimum ion velocity when entering the plasma sheath region. Coming from the plasma bulk, they are accelerated to the Bohm speed within the so-called pre-sheath region. If they would not attain this speed, energy conservation within the space charge sheath would be violated. As a countermeasure the pre-sheath would extend accordingly to achieve sufficient acceleration. Having introduced the equations for describing the different IV trace current contributions, leaves open the determination of plasma parameters. Different ways are presented on how to derive the plasma parameters mean electron temperature T e, electron density n e and electron distribution function (EDF). Beginning with the mean electron temperature T e

58 36 3. Plasma and thin film diagnostics which is obtained by taking the natural logarithm of the electron retarding current I retard provides ( ) kb T e ln(i retard (U Probe )) = ln e A Probe n e + e U Probe 2 π m e k B T e (3.25) = C 1 + m 1 U Probe which is a linear relation. Hence, the mean electron temperature T e is calculable by determining the slope of the logarithmic of the electron retarding current I retard yielding the electron temperature to be d ln(i retard (U Probe )) du Probe = m 1 = e k B T e (3.26) T e = e du Probe k B d ln(i retard ). (3.27) Instead of taking I retard, using d2 I retard yields exactly the same equation as (3.27), only replacing I retard with d2 I retard duprobe 2. However the original electron retarding current (3.21) is gained, duprobe 2 based on the assumption of a Maxwellian distribution, which might not be the case for any type of discharge. The most general way of determining the mean electron temperature, is using Druyvesteyn s relation (3.19) to obtain the electron distribution function (EDF). Since no assumptions are made on the gained distribution, the term mean temperature needs to be reconsidered. The mean electron temperature T e correlates to the mean electron energy by E = 3 2 k B T e. (3.28) From the calculated EDF f v,elec (E) the mean energy of an arbitrary distribution is E f 0 v,elec (E) de E =. (3.29) f 0 v,elec (E) de In the following sense the term mean temperature is defined as the equivalent Maxwellian temperature found by inserting equation (3.29) into equation (3.28) and solving for T e. Solely this method is applied within this work to obtain the mean electron temperature T e, unless stated otherwise. T e = 2 3 k B E (3.30) Summing up, there basically exist two important ways of finding the mean electron temperature. Both methods focus on the electron retarding region of an IV trace. One technique uses the slope of the semi-logarithmic IV-trace representation and the other applies a general approach by using the EDF gained from Druyvesteyn s relation, which is proportional to the current s second derivative. Besides electron temperature, electron density is an important plasma parameter. Essentially there exist three methods for calculating the electron density out of measured IV traces. Two

59 3.2. Langmuir probe 37 of them implicitly assume a Maxwell distribution, whereas the third follows a general approach. First, one way of gaining the electron density n e is looking at the electron saturation current I sat,elec. Squaring equation (3.22) ( I sat,elec (U Probe ) 2 = e 2 A 2 Probe n 2 k B T e 4 e 1 + e U ) Probe (3.31) 2 π m e π k B T e and building the first derivative with respect to U Probe di 2 sat,elec (U Probe) du Probe produces an estimation for the electron density π n e = 2 m e 2 e 3 A 2 Probe = e 3 A 2 Probe n 2 e 2 π 2 m e (3.32) di2 sat,elec du Probe. (3.33) In short, the electron density n e can be obtained from the slope of the squared saturation current. However, it is important to keep the prerequisites of using the saturation current in mind. Therefore only values of I sat,elec (U Probe Φ Plasma ) are applicable. A second method involves the exact current value of I retard (U Probe = Φ Plasma ) at the plasma potential Φ Plasma. Thereby, Φ Plasma needs to be determined by finding the root of d 2 I retard (U Probe ) d U 2 Probe = 0 (3.34) which is the curve s inflection point. Solving equation (3.21) for n e and using the current I retard at the plasma potential Φ Plasma gives 1 2 π me n e = I retard (U Probe = Φ Plasma ). (3.35) e A Probe k B T e Hereby, the accuracy of n e crucially depends on the accuracy of the plasma potential estimation (3.34). When using the second derivative of I retard for plasma potential determination numerical instabilities occur. Measured data always include statistical uncertainties, which worsen when applying derivatives. Thus, using the second derivative on I retard can lead to large errors in the plasma potential. This is circumvented by applying a statistical method developed by Schulze and Wenig [78][74] to smoothen the IV trace prior to differentiation, which works as follows. A numerically stable smoothing algorithm calculates local polynomial approximations at each data point p = (U Probe, I Probe ). Therefore, a number of points, defined by the smoothing function s bandwidth, around p are included to calculate the desired polynomial approximation. Depending on the mathematical distance to p, all additional points are weighed and included. By supporting adaptive bandwidths the different slopes of a Langmuir probe characteristic can be described separately. Resulting is a smoothed curve with significantly reduced measurement noise that can be differentiated twice. This algorithm ensures a stable and reproducible estimation of the plasma potential and is solely used in this work. A detailed description of this algorithm and its requirements is found in the works of Schulze and Wenig [78][74].

60 38 3. Plasma and thin film diagnostics Finally, the most general way of calculating the electron density n e is presented. Both previously discussed methods rely on the assumption of a Maxwellian distribution, whereas the following does not. It is based on the prior calculation of the electron energy distribution function (EDF) from Druyvesteyn s relation (3.19) and correlates to the electron density as n e = 0 f v,elec (E) de. (3.36) Because of its general applicability only this method is used in this work for electron density determination. Returning to the difficulties of Langmuir probe measurements mentioned earlier in the introduction, the first three arguments have been addressed. Regarding the plasma potential determination and the IV trace s second derivative, a newly developed algorithm by Schulze and Wenig [78][74] is applied in the evaluations of Langmuir probe current-voltage characteristics. From the smoothed curve the EDF is calculated and the electron density n e and mean electron temperature T e are derived. To qualify the influence and necessity of ion current correction on plasma parameter determination, investigations performed by Wenig [74] are referenced. He unveiled in simulations, also supported by measurements, that ion current correction is only possible in IV traces with nearly ideal properties (without noise). He also exemplarily performed ion current correction on measured IV traces, showing that even in near ideal measurements, the noise level is high enough to disallow useful ion current correction. Because noise reduction to the required extent is not feasible, ion current correction is not applied within this work. Finally, the filtering of discharge harmonics in the VHF band remains to be discussed, which is done in the following section Compensation schemes and application in multifrequency plasmas As discussed in the previous section, a Langmuir probe is a useful diagnostic for obtaining several relevant plasma parameters. In practice, taking measurements in rf driven discharges is made difficult by the oscillating plasma and floating potential, which is detected as an averaging effect for the IV trace. In turn, particularly the mean electron temperature is overestimated by above equations. As a consequence, the probe tip needs to follow the rf oscillation, which is achieved by capacitive coupling of the probe tip to a large floating electrode. In figure 3.10, the measurement principle of the used Langmuir probe system APS3 is shown. A capacitive coupling between the probe tip and the floating probe head encasing is visible. In general, the better the capacitive coupling is realized, the more accurate the resulting Langmuir probe characteristic will be obtained. However, filters are needed to protect the measuring electronics. For the floating voltage measurements this is realized by a low-pass filter, and in the probe tip branch by a passive filter concept. Further details of the APS3 Langmuir probe system are found in literature [79][74][78]. When discussing rf filtering, a frequency (range) needs to be specified to work efficiently in a band-stop array. For the case within this work the fundamental frequency MHz

61 3.2. Langmuir probe 39 Figure 3.10: Principal setup and measurement schematic of the APS3 Langmuir probe system [75]. and four of its harmonics are filtered in the probe tip branch. Nevertheless, dual frequency VHF driven capacitive plasmas produce more high frequency components with additional side-bands depending on the used frequencies. These high frequency components can have two origins. On the one hand, they are generated by the nonlinear plasma boundary sheath itself as harmonics of the excitation frequency. Depending on geometric properties of the discharge vessel, the harmonic distortion is differing in strength for individual frequencies. A more detailed explanation of this is found in section 3.4. On the other hand, the investigated VHF dual frequency discharge applies critical frequencies directly as the plasma s excitation frequency. Hence, their amplitude is large compared to amplitudes resulting from plasma generated harmonics. Additionally, all fundamentals and harmonics of each excitation frequency produce mixing frequencies leading to numerous components in frequency space as shown in figure Filtering every component given in figure 3.11 using passive band-stop filters is unfeasible, because of the resulting number of elements needed. Other passive filters like low-pass filters cannot be used because of their strong capacitive coupling to electrical ground. In that way a significant amount of current does not reach the evaluation electronics. A further possibility is active filtering using operational amplifiers, however these sensitive components cannot be incorporated into the probe head mechanics, because of size and temperature specifications. The last option involves putting an inductance into the probe head, but the needed magnitude and the permeability s strong frequency dependence at VHF frequencies are not realizable. This only leaves the option using band-stop filters of the most significant frequency components. Those have been built into the applied filter array.

62 40 3. Plasma and thin film diagnostics Figure 3.11: Discrete amplitude Fourier spectrum of a plasma current (excitation with f = MHz and 5 f = 67.8 MHz) detected by a SEERS/PSR current probe. The strongest harmonic content is found at 12 f = MHz with a three times larger amplitude than the base frequency f. Consequently, not all frequency components are filtered and the remaining oscillation of the Langmuir IV trace needs to be characterized. Therefore two IV traces are compared in figure The compensated IV trace results from a MHz/13.56 MHz discharge, whereas the uncompensated is measured in a 83 MHz/13.56 MHz discharge. Considering the realized passive filtering concept, it becomes clear that the compensated case is effectively filtered in the fundamental VHF frequency, whereas the uncompensated case is not. In that way the influence of filtering the strong VHF excitation component is determined. Analyzing figure 3.12 (left) only a minor change is observable between compensated and uncompensated measurement. The uncompensated case exhibits a more averaged behavior. The most sensitive plasma parameter affected by this averaging is the electron temperature. As a first approximation linear fits in the semi-logarithmic plot of figure 3.12 (right) deliver the mean electron temperature from equation (3.27). Results for both cases are an equal mean temperature. Reanalyzing the IV traces with the new algorithm by Schulze and Wenig delivers a deviation of 5% between both cases. The result is in good agreement with findings of Oksuz et al. [80]. They investigated and compared fully uncompensated to compensated Langmuir probe measurements in rf driven discharges. Since in this work at least a partial compensation is always achieved, the results show less errors. Summarizing, in multiple frequency driven capacitive plasmas only a partial rf compensation can be achieved. However, a comparison of compensated to uncompensated measurements show minor differences using the improved algorithm by Schulze and Wenig. Consequently, Langmuir probe measurements can be performed without producing errors attributed to compensation problems. With respect to the presented different methods of determining plasma parameters out of IV-traces, only Druyvesteyn s relation is applied within this work. To support Langmuir probe measurements additional optical diagnostics have been applied.

63 3.3. Phase resolved optical emission spectroscopy (PROES) 41 Figure 3.12: Comparison of compensated (81.36/13.56 MHz) to uncompensated (83/13.56 MHz) probe current. Left: Measured Langmuir probe IV traces in absolute voltages with respect to electrical ground. Right: Semi-logarithmic plot with fits to the electron retarding current for mean electron temperature determination. 3.3 Phase resolved optical emission spectroscopy (PROES) The Langmuir probe as an invasive diagnostic was presented in the previous section. Within this section a non-invasive optical diagnostic is addressed. Phase resolved optical emission spectroscopy (PROES) relies on the same working principle as optical emission spectroscopy (OES), with the difference that PROES is time (phase) resolved and OES is time-averaged. Its main feature is the determination of the time-dependent excitation and ionization dynamics. Both play an important role for capacitive discharges, because they are a key mechanism for discharge sustainment and control. As seen later, also an alternative diagnostic method exists capable of capturing the same transient excitation and ionization behavior, although spacial information is lost in this particular case. Prior to going into more details on the evaluation scheme, some problems and specialties of the diagnostic setup are addressed. Figure 3.13 shows the applied PROES diagnostic setup. An intensified CCD camera (ICCD) (LaVision PicoStar R ) is placed in front of a viewport recording the plasma s light emission. By that means, a specific wavelength is monitored, corresponding to the Ne 2p 1 state at λ Neon = nm with an excitation energy level of 19.0 ev. Within this work PROES measurements are only performed on neon discharges. The wavelength selection is achieved by an electrically tunable wavelength filter (CRI VariSpec R ). Its transmission behavior is calibrated prior to measurements to avoid optical artefacts, minimizing distortions. Since PROES is a time-resolved plasma diagnostic the camera needs to be synchronized with the plasma excitation. In dual frequency discharges this is usually the lowest available frequency. Hereby, the complete discharge behavior can be captured. However, when scanning the low frequency cycle, the step width has to be sufficiently small to allow for an adequate resolution of the high frequency cycle. Furthermore, the two applied frequencies need to be an integer multiple of each other and it is important to synchronize both frequency (signals) as well. In this work only the combination of 14 MHz and 2 MHz are used for PROES

64 42 3. Plasma and thin film diagnostics Figure 3.13: Phase resolved optical emission spectroscopy (PROES) setup for a capacitive dual frequency discharge. diagnostics as seen in figure Practically, source synchronization is difficult because both frequency signal sources are different with respect to signal generation. The 2 MHz source uses an internal generator with a combined amplifier and the 14 MHz source consists of a signal generator and a broadband power amplifier. Synchronization is achieved by feeding the 2 MHz clock signal into the 14 MHz signal generator. Although the signal generator produces discrete programmable frequencies internally, also an external clock reference signal can be supplied. Consequently, the signal generator derives the 14 MHz frequency from the 2 MHz clock reference signal, such that there is only one master oscillator from which all signals are derived. The according signal path is shown in figure Additionally the clock reference signal is fed into a trigger delay unit, which allows for scanning the 2 MHz signal at different phases by adjusting the delay between input and output signal. The unit s output signal triggers the ICCD camera. With this concept the phase position of the 2 MHz cycle is shiftable and can be captured at each point. The ICCD camera is set to a gate width of 2 ns. Accurately sampling the entire 14 MHz cycle at 2 ns gives approximately 35 points per period, which complies with the Nyquist- Shannon sampling theorem. Additionally the lifetime of the monitored excited state needs to be shorter than a 14 MHz period (71.43 ns), otherwise temporal resolution is lost. For the chosen Ne 2p 1 transition the lifetime is gained from databases to be 14.5 ns [81]. The measured fluorescence signal is accumulated over every rf cycle at a specified phase position for a large number of rf cycles. Especially for plasmas with low light emission (e.g. 2 MHz discharge in single frequency operation), this is useful for obtaining evaluable data. Sweeping the relative phase by adjusting the delay with the trigger delay generator, an entire set of discrete time snapshots is gained. Nevertheless, one has to keep in mind, that those data do not represent the excitation or ionization directly. They have to be deconvoluted with the temporal behavior of the chosen Ne 2p 1 transition. Therefore an appropriate model describing the (de-)excitation needs to be developed. The presented model has been developed by Gans et al. and will be presented comprehensively. Full details can be found in literature [82].

65 3.3. Phase resolved optical emission spectroscopy (PROES) 43 The required model description needs to capture the time-dependent excitation dynamics. Essentially it is based on the so-called Corona model in combination with appropriate rate equations. In its simplified case used within this work only electron impact excitation out of the ground state and de-excitation by spontaneous emission are taken into account. Because other (de-)excitation processes like inelastic collisions, cascades, excitation out of metastable states or reabsorption of radiation might also be of importance, possible sources of errors quickly become apparent. However, the used Ne 2p 1 emission line was chosen for several reasons. First, an exact knowledge of electron impact excitation cross sections and optical transition rates are available from literature and databases. Second, the expected influence of cascading processes and collisional de-excitation is generally low, which has been investigated and verified in detail by Gans et al. [82]. Third, the chosen transition exhibits enough intensity for diagnostic purposes and has no superposition with other possible emission lines. Most importantly, the chosen neon line relaxes fast enough for a high temporal resolution and furthermore, due to its excitation energy level of 19 ev gives access to the strongly rfmodulated high energetic tail of the EDF. Finally the time-dependency is incorporated by using rate equations as an adequate description of the transient excitation behavior. Because the diagnostic interest lies in determining the transient excitation one has to correlate it to the observed emission. This can be written as ṅ Ph,i (t) = A ik n i (t) (3.37) where ṅ Ph,i (t) is the observed emission per volume and time from level i, A ik the transition rate of the observed emission and n i (t) the population density of an excited level i. Next, the time-dependent (de-)population of the used Ne 2p 1 transition needs to be described by a rate equation. Therefore only excitation from ground state and spontaneous emission are considered, yielding the relation d n i (t) d t = n 0 E i (t) A i n i (t) (3.38) where n 0 is the ground state density, E i (t) the excitation function with E i (t) = n e X 0i and X 0i as a rate coefficient. Furthermore A i is defined as an effective decay rate by A i = k A ik g ik + q k q n q (3.39) with k A ik g ik describing the radiation by spontaneous emission and q k q n q describing radiation-less de-excitation by inelastic collisional processes. Hereby, g ik is the so-called escape factor, k q the collisional de-excitation coefficient and n q the density of all collision partners q. For more details on the determination of k q please refer to Gans et al. [83]. Inserting equation (3.37) into (3.38) and solving for E i (t) correlates the excitation directly to the observed emission. E i (t) = 1 ( ) d ṅph,i (t) + A i ṅ Ph,i (t) (3.40) n 0 A ik d t Because, de-excitation by inelastic collisions is found to be low for the chosen Ne 2p 1 transition the term q k q n q becomes negligible in equation (3.39).

66 44 3. Plasma and thin film diagnostics Figure 3.14: Space and time resolved excitation plot for a 2 MHz/14 MHz dual frequency discharge. Conditions are Neon, 10 Pa, 7 sccm, equal voltage contributions, no counter electrode (electrode=grounded wall) installed. A typical plot resulting from such a measurement is shown in figure This plot incorporates a full set of time-discrete images recorded at dedicated phases, such that a one dimensional spatial and temporal resolution is achieved. Figure 3.14 depicts the distance from the electrically driven electrode versus a 2 MHz cycle and the following is observed. In the first half (0 250 ns) of the 2 MHz cycle the formation of high energetic ( 19 ev) electrons, moving outward from the electrode into the plasma bulk is evident. In the second half ( ns) no such electrons are detectable. This group of hot electrons are further denoted as electron beams [84]. The electron beam concept, with respect to electron heating in rf driven capacitive discharges, was investigated experimentally and theoretically by Schulze, Heil et al. [84]. The production of high energetic electron beams is explainable by electrons being reflected at the expanding plasma boundary sheath gaining additional energy, which in a low pressure regime ( 10 Pa) is recognized as a form of stochastic heating. Since the discharge is operated in such a pressure regime, stochastic heating is considered the main mechanism of electron heating and thus discharge sustainment. By reducing pressure the intensity of the high energetic electron beams becomes more pronounced, indicating the electron beams acquire an increased amount of energy. In contrast, within the second half of the 2 MHz cycle, during the phase of maximum sheath expansion, no high energetic beams are recorded. For a near symmetric industrial dual frequency capacitive setup, Schulze et al. found the electron beams being reflected at the opposite electrode s sheath performing additional heating as they traverse the plasma bulk several times [85]. The discussed phenomenon of electron beams is more easily detectable by electrical means, which is of relevance for industrial process monitoring as seen later in section 3.4. Normally, in a single frequency rf discharge only one beam of high energetic electrons is produced each frequency cycle. However in a dual frequency discharge the plasma boundary

67 3.4. Self excited electron resonance spectroscopy (SEERS) / Plasma series resonance (PSR) 45 sheath is modulated with two frequencies such that more than one beam can be produced as seen in figure Theoretically, for the given discharge conditions (2 MHz/14 MHz), a maximum of seven outgoing beams could be produced by the electrode s sheath expansion. Tuning the relative phase between both excitation frequencies also has a direct influence on the number of produced beams, which is explained in more detail later on in section 4.2. Generally it can be stated, that the observed high energetic electron beams are not only the key mechanism for discharge sustainment, but also a directly accessible discharge optimization parameter. Summing up, PROES as a plasma diagnostic is used for the time-resolved determination of excitation mechanisms. With respect to capacitively coupled dual frequency discharges this diagnostic method is important for determining effects resulting from changing the relative phase between excitation frequencies. Therefore a phase-locked synchronization has to be ensured. Practically, this is achieved by supplying the 2 MHz source s reference clock signal into the 14 MHz rf source. In that way, only one dedicated clock signal exists and the relative phase becomes adjustable. Additionally synchronizing the camera system with the 2 MHz cycle through a trigger delay generator enables the acquisition of time-discrete discharge snapshots at a set of dedicated phases. An evaluation scheme developed by Gans et al. [82] is applied to correlate the measured light emission to excitation. Typical results exhibit the generation of high energetic beams of electrons by reflection at the expanding plasma sheath edge. The role of relative phase change between the excitation frequencies is further investigated in section 4.2. Since optical diagnostics of the discussed scale are unsuited for industrial plasma processing another possibility of investigating discharge excitation mechanisms is presented next. 3.4 Self excited electron resonance spectroscopy (SEERS) / Plasma series resonance (PSR) In the previous section the observation of high energetic electron beams by phase resolved optical emission spectroscopy (PROES) was discussed. In industrial plasma processes however, where realtime process monitoring is desired, PROES is expensive and unmanageable to be applied on numerous processing tools. As mentioned previously, an alternative way of detecting those electron beams can be used. By introducing a metallic sensor plate isolated from electrical ground, a part of the total rf current to the wall can be recorded. It is measured by a current equivalent voltage drop across a 50 Ω resistor. An exemplary acquired current signal is seen in figure 3.15 (right). Additionally, the scaled purely sinusoidal excitation voltage waveform is plotted (figure 3.15 (left)). Both waveforms were not sampled synchronized, such that their relative phase relation is arbitrary. What becomes apparent is, despite the excitation voltage consisting only of sinusoidal waveforms, the measured plasma current obviously contains more frequency components. This is explained by the generation of harmonics and their mixing frequencies due to the nonlinear nature of the plasma boundary sheath in front of the driven electrode. But especially highlighted is the appearance of resonant structures at each MHz period, as illustrated in

68 46 3. Plasma and thin film diagnostics Figure 3.15: Typical current signal acquired in a dual frequency discharge (right). Additionally the arbitrarily scaled (purely sinusoidal) excitation voltage waveform is plotted for comparison (left). Discharge conditions are 67.8 and MHz, electrode gap 35 mm, Argon, 5.4 Pa, 10 sccm. Figure 3.16: Measured dual frequency (13.56 MHz / 67.8 MHz) PSR current from figure 3.15 with the according discrete Fourier amplitude spectrum. figure 3.16 (left). Also the current s discrete Fourier spectrum is shown in figure 3.16 (right). Clearly, the presence of harmonics and their mixing frequencies are visible. However a theoretical explanation for the exhibited resonance is needed. Mussenbrock et al. developed a simple nonlinear global model and a sophisticated analytic model capable of addressing this missing link [3]. Later the simple model was theoretically verified by Czarnetzki et al. [86]. Basically this model builds on the standard electrical equivalent circuit representation of a capacitive discharge [60], with the difference of introducing nonlinear capacitors for the respective sheaths in front of the grounded and conducting electrode as shown in figure For the case of a dual frequency driven plasma two voltage sources U RF1 (t) and U RF2 (t) are used. Mussenbrock s et al. model separates the mathematical description of plasma bulk and plasma boundary sheath, because in capacitive discharges the Debye-Hückel length λ Debye as defined by equation (3.11) is typically much smaller than the electrode separation. In this case, the plasma bulk can be described by the concentrated electrical components L Bulk and

69 3.4. Self excited electron resonance spectroscopy (SEERS) / Plasma series resonance (PSR) 47 Figure 3.17: Simple PSR equivalent circuit model of a capacitive rf plasma discharge. R Bulk. They represent electron inertia and ohmic power dissipation in the plasma. Within the bulk, quasi-neutrality holds (n e = n i ) and the current is carried solely by conduction. Hence, the resulting total current through the plasma bulk can be written in time-domain representation as ( ) m e L d I U Bulk = e 2 n e A electrode d t + ν m I (3.41) where ν m is the electron-neutral collision frequency, n e the average plasma density in the bulk, A electrode the area of the driven electrode, L the effective bulk length (electrode gap minus both sheath extensions) and U Bulk the voltage drop across the plasma bulk [87]. By regrouping above equation values for the electrical components L Bulk and R Bulk can be derived as m e L L Bulk = (3.42) e 2 n e A electrode R Bulk = L Bulk ν m. (3.43) Thereby, the description of the plasma bulk is complete and the plasma boundary sheaths are described next. For the sheath description a matrix sheath is assumed. A matrix sheath describes the divergence of electron and ion density in the sheath region as a hard wall (non-continuous) concept. That means, the electron density n e drops to zero at the sheath edge. Overall, it is the simplest concept of formulating the charge density divergence. An alternative possibility involves the Child law sheath assumption, which uses a uniformly continuous function for n e and n i. For the given model description by Mussenbrock et al. no electrons are present within the sheath region. Hence, the total discharge current is carried solely by displacement. Figure 3.17 includes both plasma sheath regions in front of the driven electrode C Sheath electrode and the grounded wall C Sheath ground. Additionally, a dc current blocking capacitor C Block is introduced into the system. The voltage drop across this component is the plasma s dc self bias voltage. The standard case for capacitive discharges, which also holds for the experiment within this work, assumes a strongly asymmetric operation (A Sheath ground A Sheath electrode ), which makes C Sheath ground large compared to C Sheath electrode such that the

70 48 3. Plasma and thin film diagnostics voltages are U Sheath electrode U Sheath ground. Because both capacitors are in series, the total capacitance in the circuit is expressed as C Sheath total C Sheath electrode. In the following step, expressions for the voltage drops across both capacitors need to be determined. As mentioned earlier the main cause for harmonics generation lies with the nonlinear nature of the sheath capacitances. Hence, no linear formulation, such as e.g. I C (t) = C d U C is allowed. On the d t basis of a self-consistent simulation, Mussenbrock et al. propose a voltage-charge relation for the nonlinear plasma sheath region in front of the driven electrode as follows U Sheath electrode (Q(t)) = U Sheath electrode + s ε 0 A electrode Q ε 0 e n i,sheath A 2 electrode Q 2. (3.44) It has been shown, that even for large sheath modulations the quadratic-order voltage-charge approximation remains reasonable [88]. For the sheath in front of the grounded electrode a simple description is found, because the voltage drop remains constant as U Sheath ground (Q) = U Sheath ground. (3.45) Additionally the dc components within both voltage equations are recognized to be the dc self bias voltage U dc bias = U Sheath electrode U Sheath ground = U Block U Sheath electrode. (3.46) Using the fundamental relation d Q d t = I (3.47) to couple bulk and sheath model and further applying Kirchhoff s law on the complete equivalent circuit from figure 3.17 yields a differential equation with respect to discharge current U RF1 (t) + U RF2 (t) = ÛRF1 cos(ω RF1 t) + ÛRF2 cos(ω RF2 t) = ( ) ( ) d I L Bulk d t + ν s 1 m I Q + Q 2. (3.48) ε } {{ } 0 A electrode 2 ε 0 e n i,sheath A 2 electrode } {{ } U Bulk U Sheath electrode Finally, equation (3.48) represents the desired nonlinear global model for a dual frequency driven capacitive discharge, capable of describing the generation of harmonics by the nonlinear plasma sheath. Also the appearance of the resonance-like structures in figure 3.16 (left) are explainable. Despite the model s simplicity, calculated and measured current signals are comparable to a very good extent as outlined in more detail in section Obviously, by taking a closer look, the given equivalent circuitry is determined to be a series resonance circuit, which is the main reason for the naming of plasma series resonance (PSR). By solving the differential equation (3.48), a characteristic geometric resonance frequency ω PSR, often referred to as self-excited electron resonance spectroscopy, is found. It is formulated as ω PSR = e 2 n e s ε 0 m e L = ω pe s L. (3.49) Using a characteristic set of plasma parameters for the presented dual frequency setup with n e = m 3, T e = 3.0 ev, L = 35 mm and V 0 = 500 V yields a plasma series resonance

71 3.4. Self excited electron resonance spectroscopy (SEERS) / Plasma series resonance (PSR) 49 frequency of f PSR = MHz. Hereby, equation (3.10) was used to calculate an accurate mean sheath extension of s = mm. At the same time the Debye-Hückel length λ Debye = µm and the electron plasma frequency f pe = 1.27 GHz can be exemplarily calculated. One has to keep in mind that although the PSR frequency is calculable to high precision, there always exist experimental deviations. The resulting values should be understood as an approximation of the PSR only. Hence, all calculated PSR frequencies within this work are intended to be reasonable approximations. Before returning to the original question of correlating the dynamic electron excitation recorded by PROES measurements with the harmonic loaded plasma rf currents, another interesting mechanism for heating a plasma discharge is discussed. Since a capacitive discharge can be understood in a simplified sense to be a series resonance circuit with a resonance frequency ω PSR, the question of heating the plasma directly at this frequency arises. Godyak et al. [89] and Qiu et al. [90] closely investigated the possibility of heating a capacitive discharge at the plasma series resonance frequency. They found it to be a highly efficient way of heating the plasma. However, a further possibility can be thought of which is presented in detail in the following section Nonlinear electron resonance heating (NERH) As outlined in the last section a direct heating at the plasma series resonance is feasible, but not aimed for within the frame of this work. An alternative way is shown by theoretical considerations of Mussenbrock and Brinkmann [1]. They propose a further explanation for low pressure ohmic heating. It works as an indirect plasma series resonance heating, termed nonlinear electron resonance heating (NERH). The indirect heating is achieved by the fact that the nonlinear plasma boundary sheath generates numerous harmonics of various amplitudes out of the main excitation frequencies. Especially with dual frequency driven plasmas, mixing of those frequency components is added. As a result, the plasma series resonance can be excited by a set of harmonic frequency components, within a certain vicinity. Further works, related to electron heating phenomena can be found in literature [91][92][93][38][94]. For this principle to work, the vicinity needs to be put into mathematical terms. From electrical engineering the concepts of Q-factor or quality-factor and bandwidth of a resonance are well established. Thereby the Q-factor Q PSR denotes the maximum rise of magnitude at the exact resonance frequency, and the bandwidth B PSR the resonance broadening (width). Generally, they are defined as follows Q PSR = ω PSR L Bulk R Bulk (3.50) B PSR = f PSR Q PSR. (3.51) By above equations, the vicinity is now adequately described through the bandwidth B PSR. Inserting equation (3.50) into (3.51) and simplifying for relevant plasma parameters yields B PSR = ν m 2 π (3.52)

72 50 3. Plasma and thin film diagnostics and also for the Q-factor Q PSR = ω PSR ν m. (3.53) It is a remarkable result, because the PSR bandwidth only depends on the electron-neutral collision rate ν m. Exemplarily calculating B PSR for typical experimental values of ν m, with 10 8 s 1 ν m 10 9 s 1, yields MHz B PSR MHz. Similarly a range for the Q-factor is given by Q PSR This result strongly emphasizes the possibility of an indirect heating at the plasma series resonance (NERH), because even for low electronneutral collision rates ν m all mixing/harmonic frequency components satisfying (f PSR B PSR 2 ) f harmonic (f PSR + B PSR 2 ) (3.54) contribute to the resonance magnitude. It solely depends on the individual type of discharge, whether an additional heating at the series resonance frequency ω PSR by harmonics is provided at a small bandwidth but with a steep magnitude rise or at a broad bandwidth with a much reduced magnitude rise. This finding is also the self-limiting factor of additional harmonic heating, because the more efficient a plasma is heated (resulting in increased ohmic power dissipation, thus increasing also ν m ), the more reduced Q PSR will get. Hence, the magnitude rise is reduced, which in the extreme case becomes Q PSR = 1, which in turn implies the bandwidth becomes equal to the resonance frequency. In this special case, no additional resonance heating is possible. Later in section an experimental example of nonlinear electron resonance heating (NERH) is presented Correlation of measured PSR currents to PROES Continuing the discourse on process monitoring, this section will discuss implications of correlating SEERS to PROES measurements. Figure 3.18 (top) displays the same PROES plot as shown in figure Again the spatiotemporal structures of the electron beam concept are visible. Recapitulating, the two electron beams around t = 100 ns are formed by electrons being reflected at the expanding plasma boundary sheath. Because of the lack of a true counter electrode, in this case the grounded wall acts as the counter electrode, no reflected beams are observed within the second 2 MHz half-period. Correlating a synchronously measured PSR current 3.18 (bottom) to the PROES excitation plot, provides a strong similarity. Although the PSR signal neglects spacial resolution, comparable structures are recognizable in the current signal. More exactly, each resonant peak in the PSR current is directly matchable to an outbound (away from the driven electrode) electron beam. This includes not only their respective position in the timeline, but also the signal magnitude, which correlates with the recorded amount of emission. Also the second 2 MHz half-cycle as measured by PROES can be compared well with the current signal structure, exhibiting no resonances where PROES accordingly shows no excitation. Since the SEERS diagnostic method [95][96] is in wide-spread commercial use, this additional information provide a deeper insight into fine-tuning plasma processes, so as to optimize ex-

73 3.4. Self excited electron resonance spectroscopy (SEERS) / Plasma series resonance (PSR) 51 Figure 3.18: Correlation of time and space dependent excitation plots from PROES to simultaneously measured PSR currents. Discharge conditions are 2/14 MHz, Neon, 10 Pa, 7 sccm, no counter electrode (electrode=grounded wall) installed. citation behavior within certain limits. These limits are set e.g. by a needed plasma chemistry recipe spanning a certain parameter space. An illustrative example for the fine-tuning controllability by PSR current monitoring is provided within this work in section 4.2. Thereby the relative phase between the excitation frequencies is varied and both, PROES as well as PSR measurements unveil a noticeable and tunable effect. The commercially available system is produced by the German company Plasmetrex GmbH, in the form of Hercules R PMX. In its standard version it provides real-time access to the effective electron-neutral collision rate ν m and volume-averaged plasma density n e. These parameters are found by a real-time capable method of either determining the equivalent circuit elements R Bulk and L Bulk or frequency-space analysis, determining ω PSR and B PSR. The following final section verifies the validity of the previously presented global model by Mussenbrock et al. [3] by comparing measured PSR currents to calculated current signals. For the calculations realistic experimental input parameters are used.

74 52 3. Plasma and thin film diagnostics Comparison of measured SEERS/PSR currents to model calculations In this section the applicability for dual frequency discharges of the presented model by Mussenbrock et al. [3] is verified by comparing measured PSR currents to simulated current signals. Therefore the model needs to reproduce the measured PSR currents by setting off with realistic experimental discharge conditions. Those have been 67.8/13.56 MHz with an electrode separation of 35 mm, Argon at 5.4 Pa and 10 sccm. The PSR current sampling is realized by an integrated wall sensor with a diameter of 5 mm, isolated from electrical ground and connected to a digitizer card. Sampling conditions are at a sampling frequency of 2 GHz and a bandwidth of 1 GHz. Most of the above listed external discharge parameters can be directly integrated into the model. However, the model equation (3.48) takes voltages as input parameters and not generator powers. Experimentally, the power ratio has been set to P 67.8 MHz : P MHz = 2 : 1. As input parameters for model calculations the equivalent voltage ratio results to U 67.8 MHz : U MHz = 2 : 1. Consequently using all given external discharge parameters and calculating the expected PSR current signal yields figure All plots on the left-hand side denote measured PSR currents and on the right-hand side represent calculated PSR currents. What becomes apparent first is a very good agreement of both time-domain signals. They exhibit the same resonance structures and also individual peak behavior matches well. A close inspection by performing a discrete Fourier transformation on both current signals provides insight into the differences between model and measurement. As seen in figure 3.19 (bottom), the first ten harmonics of MHz compare reasonably well. Harmonics larger than ten times MHz are different. This is explained by using simplified initial model assumptions. It is assumed from the beginning, that only one overall plasma series resonance exists. However, a more realistic consideration would involve a multitude of these so-called resonant modes. Including these additional modes would lead to very good agreement also for harmonics larger than the tenth harmonic of MHz [2]. This is subject to a current research topic of Ziegler and Mussenbrock [2]. Nevertheless, in spite of the model s simplicity, the results compare remarkably well. For further explanations and a detailed outline of above presented calculations please refer to [2]. Summarizing, a direct connection between excitation plots recorded by PROES measurements and electrical PSR current measurements can be established. On the basis of a global model developed by Mussenbrock, Ziegler et al. it becomes possible to reach a very good comparability between measured and simulated PSR current signals [3][98]. Essentially, this model leads to a deeper understanding of the nature of the plasma series resonance concept. Furthermore it opens up another possible description of the stochastic heating phenomenon observed in low-pressure discharge operation, namely through nonlinear electron resonance heating (NERH). In section the experimentally observed effects of NERH are discussed. The previously discussed diagnostics address the topic of electron heating in capacitive discharges and their correlated plasma parameters. For the following two applied diagnostics the focus moves to ions and neutral species behavior, which is directly relevant for surface modifications and sputter deposition characterization. Therefore a retarding field energy analyzer

75 3.5. Retarding field energy analyzer (RFEA) 53 Figure 3.19: Comparison of calculated to experimental PSR currents under equivalent discharge conditions. Simulation input parameters correspond to experimental tuning parameters. Plots showing simulation results on the righthand-side are taken from [97]. An even better agreement is achieved in a refined model by Ziegler et al. [98] (RFEA) and a quartz-crystal microbalance (QCM) are used and presented next. 3.5 Retarding field energy analyzer (RFEA) A retarding field energy analyzer (RFEA) is used for determining the ion (velocity) distribution function. In general, its working principle is also transferrable to the determination of electron distributions by changing the direction of the retarding potential. It can be seen a mass-integrated ion energy analyzer. The theory of operation is explained by considering figure Physically, an RFEA works as an electrostatic probe. This means negative dc voltages are applied to attract ions and repel electrons. Sweeping the dc voltage produces different detectable current magnitudes. Evaluating the acquired (ion)current/voltage characteristic yields the ion distribution function (IDF). In principal, one sweeping voltage should be sufficient. How-

76 54 3. Plasma and thin film diagnostics a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a Figure 3.20: Retarding field energy analyzer (RFEA) used for ion distribution function (IDF) measurements. ever, as practical applications show, there may arise several problems like secondary electron emission within the analyzer and the ion s angle of acceptance. Figure 3.20 depicts the electrical and mechanical setup of an RFEA. The mechanical layout consists of an entrance orifice, three grids and a collector area. Schematically only one entrance orifice is plotted, however the applied commercial system by Impedans Ltd. consists of multiple 800 µm holes evenly distributed across an area of 1 cm 2, ensuring a sufficient amount of collected ion current. Grids 1-3 are made out of nickel, each having 18 µm holes. Furthermore, they are electrically separated against each other by insulators (quartz, ceramic etc.). More detailed information about the sensor s internal build-up are described in literature [99]. Electrically, the sampling orifice and Grid 1 are on the rf driven electrode s potential. Both, electrons and ions are allowed to pass the sampling orifice and Grid 1 at a small angular distribution. The only objective of Grid 1 is narrowing the effective angle of acceptance for either charged species. All ions and electrons having passed the entrance orifices and Grid 1 encounter the negative (with respect to floating potential) potential U 1 of Grid 2. Its purpose is to filter out the incoming plasma generated electrons, which is particularly relevant at the time of sheath collapse in capacitive discharges, when a large amount of electrons can enter the analyzer. Conversely, ions are attracted and accelerated towards Grid 2. Hence, the potential of Grid 2 needs to be sufficiently negative (at least twice as negative as k B T e ) to effectively filter most of the incoming electrons. Traversing the gap between Grid 2 towards Grid 3, ions are discriminated by the variable voltage U 2. Usually, the potential range for U 2 is scanned between the dc potential of Grid 1 (retarding potential of 0 V) to V above the plasma potential. Thereby, one has to keep in mind that in asymmetric capacitive plasmas the dc self bias voltage needs to be added (in absolute values) to the plasma potential, such that ions can gain a maximum energy of

77 3.5. Retarding field energy analyzer (RFEA) 55 e (Φ Plasma + 2 U dc bias ). This makes an increase in the scanning range for U 2 necessary. In that way all possible ion energies are covered. Eventually, ions with sufficient energy passing Grid 3 are attracted by a small negative potential U 3 towards the collector plate where the resulting ion current is detected. An important condition for the attracting potential U 3 is to not bias it too negatively, so as to largely accelerate the ions. In this case the ions would gain sufficient kinetic energy, bridging the collector material s work function (typically only several electronvolts), producing secondary electron emission. In an extended concept a further Grid 4 is introduced between the collector and Grid 3 to cope with secondary electron emission, by biasing it slightly more negative with respect to the collector potential. This restrains secondary electrons to the volume between Grid 4 and the collector, not disturbing the sensitive ion current measurement. For the measurements within this work, the design shown in figure 3.20, without an additional Grid 4 is used. Carefully adjusted collector voltages circumvent the problem of secondary electron emission. Test measurements have shown that the acquired voltage-current characteristic exhibits no distortions of the kind measured by Böhm and Perrin [100], who thoroughly investigated secondary electron emission in RFEAs. Figure 3.21 depicts an exemplary potential distribution within the used RFEA with three grids. Figure 3.21: Typically used potential distribution among the grids of the applied RFEA for ion distribution function measurements. The presented RFEA is used for ion energy measurements on the electrically rf driven electrode, which on the one hand enforces additional considerations of suppressing rf influence on the electrostatic probe parameters. On the other hand a synchronous modulation of Grid 2 and Grid 3 need to be realized to suppress distortions of the voltage-current trace. Similar to the presented Langmuir probe compensation scheme in section a passive filter concept is incorporated into the commercial solution. Low-pass filters are inserted between the electrical circuit of Grid 2, Grid 3 and the collector to ensure that all grids and the collector maintain electrode rf potential. They also prevent rf voltages from building within the RFEA measurement electronics. A detailed analysis of the applied filter concept is found in literature [99]. In the following section the derivation of the ion velocity distribution out of measured voltage-current traces is discussed.

78 56 3. Plasma and thin film diagnostics Ion velocity/energy distribution function measurement With the given RFEA measurements on the rf driven electrode are performed. An exemplary measured and post-processed (smoothed) voltage-current trace is depicted in figure As smoothing algorithm a Savitzky-Golay scheme with a third order polynomial and a fixed bandwidth is used. Resulting are smoothed curves which can be numerically stable derived. Figure 3.22: Characteristic voltage-current trace from an RFEA by sweeping the retarding potential in a dual frequency discharge at 67.8/13.56 MHz. Experimental conditions are U 13.56MHz = 35 V RMS and U 67.8MHz = 70 V RMS, Argon, 3.5 Pa, 10 sccm. Increasing the retarding potential to positive values, repels more and more ions. Consequently the measured current amplitude reduces from 630 na down to zero. A two-slope-like behavior of the curve is observable. From the obtained voltage-current curve the ion velocity/energy distribution is directly calculable. A detailed derivation by Böhm and Perrin is presented in a comprehensive form to illustrate the scheme [100]. Assuming a one-dimensional velocity distribution function evolving in the ion flight path into the analyzer, the total ion density n i is set to n i = 0 f ion (v) dv. (3.55) The conversion from velocity to energy distribution is achieved by substituting the velocity with E = 1 2 m i v 2 and hence also de = m i v dv, with m i as the ion mass, v the one-dimensional ion velocity (only the ion s preferential direction is considered), n i the ion density and E the ion energy. The total ion current density at the analyzer entrance is defined by I = e vf(v) dv = e ( ) 2E f de (3.56) m i m i

79 3.5. Retarding field energy analyzer (RFEA) 57 with the additional transformation of the ion velocity distribution into the ion energy distribution function [100]. Deriving expression (3.56) with respect to energy E, the ion distribution function is gained ( ) 2E f = m ( ) i di(e) e. (3.57) de m i Expression (3.57) shows the ion distribution function to be directly proportional to the first derivative of the voltage-current characteristic. It can further be rewritten by replacing the energy E with the retarding potential φ ret given as E = e φ ret. ( ) 2 e φret f = m ( ) i di(e e φret ) (3.58) 2 m i dφ ret Finally, applying equation (3.58) to the sample voltage-current trace shown in figure 3.22 provides the ion distribution function depicted in figure Figure 3.23: Normalized ion distribution function (IDF) calculated as the first derivative of the voltage-current trace shown in figure In figure 3.23 the characteristic bimodal structure of an ion distribution function (IDF) typical for rf driven discharges can be seen. Information that is gained from an IDF include the bimodal structure in general and the peak separation E. The reason for the two peaks becomes apparent by considering an ion s incident energy on the electrode. Its energy strongly depends on the relative phase of the sheath s rf electric field. For a sinusoidal modulation, the rf electric field remains long at its minimum and maximum amplitude. Thus, more ions corresponding to those energies are collected, resulting in the characteristic bimodal structure. A further parameter is the time an ion needs to pass the sheath region, denoted as the ion transit time τ i. Relating the ion transit time and the rf period τ rf gives rise to two separate regimes. First, if τ i τ rf the ions are able to cross the sheath in less time than an rf period,

80 58 3. Plasma and thin film diagnostics hence they are able to follow the instantaneous sheath modulation. As a result, a broad IDF is observed. Furthermore, the energy spread E is found to be independent of ion mass, because ions of all masses are able to respond to the rf electric field. The maximum energy ions can gain is the sum of the dc self bias voltage (in asymmetric capacitive discharges) and the rf amplitude, which approximately is twice the rf amplitude, neglecting the plasma potential. Second, if τ i τ rf the ions need multiple rf cycles to cross the plasma boundary sheath. Therefore, they are not able to follow the rf sheath modulation, which implies that the maximum gainable ion energy is solely governed by the dc self bias voltage (in asymmetric capacitive discharges). Consequently, the IDF narrows, leaving the energy gap E at smaller values. This second regime holds for all considerations and evaluations within this work, because the excitation frequencies are much larger than the ion plasma frequency. An analytic expression for the energy spread E in this regime was derived by Benoit-Cattin and Bernard [101] and shows E = 4 π where U rf is the rf sheath voltage and τ rf = 2 π ω rf defined as τ i = 3 s τ rf τ i e U rf (3.59) the rf period time. τ i is the ion transit time mi 2 e U dc bias (3.60) with s as the mean sheath width defined by equation (3.10), m i the ion mass and U dc bias as the dc self bias voltage. It can be seen that the energy spread E is proportional to the ion mass with m 1/2 i. This implies, that for light elements such as e.g. hydrogen the peak separation is proportionally larger than for e.g. argon. Inserting equation (3.60) into (3.59) gives access to the plasma sheath voltage in case all remaining variables are known. Therefore the voltage drop across the sheath can be estimated from the energy spread E of both peaks. Since the presented dual frequency setup is constructed for thin film sputter deposition, only argon IDFs are investigated in section 4.3. A more detailed theoretical approach for calculating ion distribution functions in dual frequency discharges is derived by Wu et al. [102]. Further recent investigations involve the excitation by arbitrary (nonsinusoidal) waveforms for dedicated manipulation of IDFs [103]. Considerations on ion energy distribution control are outlined by Lee et al. [104] and Georgieva et al. [105].

81 3.6. Quartz crystal microbalance (QCM) Quartz crystal microbalance (QCM) A typical field of application for quartz-crystal microbalances (QCM) is film thickness monitoring in various kinds of deposition processes, by detecting the change of mass under the assumption of a known film density. Figure 3.24: Functional schematic of a quartz-crystal microbalance. Arrows indicate the electrode contacts (black) and the deposited thin film (gray). Furthermore the thickness shear mode oscillation direction (dashed line) is included. The measurement principle is based on piezoelectricity and illustrated in figure Hereby, a quartz crystal substrate is electrically excited at its motional series resonance frequency (MSRF) or better known as acoustic resonance frequency, which practically ranges from 4 6 MHz for common applications. Therefore, usually gold-plated contacts are brought onto the crystal substrate from both sides. By applying an alternating voltage between both contacts, the crystal starts oscillating due to the piezoelectric effect. Depending on the crystal structure a predefined resonance mode, in this case the so-called thickness shear mode, is excited. It solely produces a lateral displacement as indicated in figure??. Because the resonance is strongly temperature dependent, a special crystal cut, the so-called ATcut, is used to optimize temperature stability. Thereby, a quartz crystal block is cut under a certain angle to the crystallographic axis. An alternative type of crystal cut is able to compensate mechanical stress (SC-cut). Further details on crystal cuts, piezoelectricity and related quartz material properties can be found in literature [106]. The resonance itself has a very low bandwidth, which in turn results in a large Q-factor (using the fundamental relation Q = fres, also see equation (3.51)). Realistic Q-factor values can be B as high as 10 6, denoting a very sharp resonance. This condition provides a stable resonance and a high accuracy in the determination of the resonance frequency and changes thereof. From materials physics it is known that the resonance frequency is inversely proportional to the thickness. By loading the crystal with a material, two changes are observable. First, the resonance shifts to lower frequencies and second the resonance magnitude is damped. Due to the aforementioned resonance s nature the frequency shift from the unloaded case to the loaded case can be precisely determined and directly correlated to the change of total mass. This relation was formulated by Sauerbrey [107] and is given as f = 2f 2 q Z q m A q (3.61) where f q is the uncoated quartz resonance frequency, A q the electrode area and Z q the quartz acoustic impedance defined by Z q = ρ q µ q = ρ q v q (3.62)

82 60 3. Plasma and thin film diagnostics with ρ q as the quartz mass density, µ q as the quartz shear modulus and v q the velocity of sound. The fraction S f = 2f 2 q /Z q is purely material specific and commonly denoted as Sauerbrey constant. If the mass density of the growing film ρ f is known, equation (3.61) can be expressed in terms of thin film thickness d f or more exactly by its change d f using the elementary relation expressing mass in terms of mass density and volume m = ρ V f = S f ρ f V f A q = S f ρ f d f. (3.63) Regrouping equation (3.63) to d f yields the film thickness change to be d f = f S f ρ f = f q f coated 2f 2 q ρ q v q ρ f. (3.64) However, relation (3.64) is only applicable when the following three conditions are met: (i) the film must be evenly distributed on the crystal substrate, (ii) the deposited mass must be rigid and (iii) the frequency change (f q f coated )/f q must be smaller than < 5%. For vacuum coating processes conditions, assumptions (i) and (ii) are easily met. But depending on the atomic weight of the deposited material, condition (iii) is usually not met. As a result a more sophisticated load approximation was derived by Lu and Lewis [108] to d f = N q ρ q 1 ρ f f coated π R z [ ( arctan R z tan π f q f coated f q )] (3.65) where N q is the frequency constant for AT-cut quartz crystals and R z the acoustic impedance ratio given by R z = Z q ρq µ q = (3.66) Z f ρ f µ f with the respective mass densities and shear moduli of the quartz and film material. This final equation (3.65) is the standard method applied in available QCM equipment. To quantitatively correlate electrical to physical properties of quartz and film a mathematical description is needed. It is given by the Butterworth-van Dyke equivalent circuit model of a quartz-crystal resonator as shown in figure 3.25 [109]. Therein, two impedance categories can be identified. First, the electrical and the acoustic impedance branch and second, the perturbed and unperturbed case. Beginning with the representation for the unperturbed crystal, the electrical capacitance C el originates from the contact electrodes and is calculated by C el = ε 0 ε q A q d q (3.67) with ε q and d q as the permittivity and the quartz crystal substrate thickness. Describing the series resonance circuit of the acoustic branch in the unperturbed case, a linear differential equation of second order is used m d2 x dt 2 + α dx dt + k x = 0 (3.68)

83 3.6. Quartz crystal microbalance (QCM) 61 Figure 3.25: Butterworth-van Dyke (BvD) equivalent circuit of a quartz crystal resonator. The acoustic branch parts represent the electrically equivalent behavior of the piezoelectro-mechanical crystal behavior expressed in equations The acoustic film impedance Z Film also consists of an inductance L Film and a resistor R Film. with m as the oscillating mass, k the spring constant and α the attenuation constant. A direct connection to electrical equivalent series resonators is given by replacing the mechanical displacement x with the charge Q. Consequently, the electrical components R acs, L acs and C acs can be written in terms of mechanical variables. All of them depend on the real electrical capacitor C el as found by Bechmann [110]. The validity of these findings was verified by Sauerbrey [111]. They are defined as C acs = 8 K2 0 C el (3.69) (n π) 2 1 L acs = (3.70) ωq 2 C acs R acs = η ( ) 2 q ω (3.71) c q C acs ω q where K 0 is the piezoelectric coupling factor, n the excitation frequency harmonic order, η q the dynamic viscosity and c q the quartz constant for AT-cut crystal substrates (incorporating the speed of sound). Initially only the contribution of the unperturbed crystal exists and no load impedance Z Film is present. By depositing a material onto the crystal substrate, a load impedance of the form Z Film = R Film + j ω L Film is added to the system as shown in figure Hereby, the resistive component R Film describes the resonance amplitude s attenuation and the inductive component causes the change of resonance frequency. Finally, this detectable frequency shift can be used to calculate the film growth by using equation (3.65). The QCM is an invasive diagnostic which in some cases might not be desired, because of its disturbing nature regarding plasma homogeneity. In that case, alternatively an ellipsometer as a non-invasive film monitoring diagnostic is available. With respect to the planned metallic film deposition however, several problems arise by using ellipsometry. First, thin metallic films usually exhibit a low roughness when deposited onto silicon wafers. Simultaneously the reflectivity becomes large, such that only the top monolayers of the film can be investigated. Conversely, depending on deposition and plasma conditions, if the roughness of the resulting layers significantly increase, the probing polarized light is depolarized, caused by scattering effects on the rough surface. Experiments with thin metallic films deposited onto silicon

84 62 3. Plasma and thin film diagnostics wafers show ellipsometry to be difficult in application for these specific materials. Although under certain conditions, such as e.g. only a few monolayers thick films, ellipsometry is applicable for investigations. This finalizes the discussion on the experimentally applied plasma and thin film diagnostics within the frame of this work. The following chapter 4 is concerned with the application of the aforementioned diagnostics to different relevant plasma and thin film tasks. Most relevant investigations for this work involve the optimization and characterization of discharge parameters with respect to frequency coupling and observations in electron heating mechanisms.

85 63 4. Measurements and discussion This chapter discusses investigations into various parameter studies on the introduced dual frequency driven capacitively coupled plasma. Thereby, three dedicated fields of interest with technological relevance to commercial plasma processes are subject to research. As motivated in the introduction, 2f-CCPs are particularly interesting for their attributed property of separated influence on ion flux and ion energy through a high and low frequency contribution. Hence, the first and most thoroughly investigated parameters are the realizable separability of ion flux and energy by tuning respective frequencies and powers. Therefore, the frequency ratio is characterized in detail by Langmuir probe, PROES and PSR measurements. However, not only the frequency ratio is of interest, but also the tunability of the relative phase between both excitation frequencies is examined. Additionally the theoretical investigations of Mussenbrock and Brinkmann [1] concerning nonlinear electron resonance heating are addressed. The correlation between measured PSR currents and PROES excitation plots is outlined in further detail. Furthermore, in a second parameter study, the behavior of ions impinging on the sputter target electrode are investigated using a retarding field analyzer (RFEA) capable of being mounted onto the electrically driven electrode. To this regard, especially the power variation/ratio of both excitation frequencies is most important, because the frequency ratio s effect on the expected ion energy is low. This is also experimentally verified. Finally, detailed investigations and findings from the aforementioned plasma diagnostics is brought to application by performing physical vapor deposition (PVD) experiments with metallic materials. Because of their increasing relevance for memory applications in the form of magneto-resistive random access memories (MRAM), they pose a new industrially relevant field of application for 2f-CCPs. Thus, for initial studies of the sputter deposition rate and deposition homogeneity ferro-magnetic equivalent materials are used. 4.1 Variation of external parameters for VHF / MHz CCP operation Within this section three parameter studies are performed, which include the variation of frequency ratio, power ratio and system pressure. As plasma diagnostics, Langmuir probe and a PSR current sensor are applied to the experiment. The Langmuir probe tip position

86 64 4. Measurements and discussion for all measurements is situated in the discharge center, symmetrically placed between both electrodes. Measurement conditions holding for all investigations within this section are a constant gas flow rate of 5 sccm argon and an electrode separation of 45 mm. The two excitation frequencies are MHz denoted as f 13.56MHz and one discrete frequency out of the range MHz denoted as f VHF. Both excitation frequencies are fed to the top electrode in the way described in section 2.1. All further applicable discharge parameters are mentioned individually for each parameter study. To begin with, the frequency ratio is presented Frequency ratio In this section the frequency ratio is studied by varying the high frequency component f VHF in the range of MHz, while leaving the low frequency component f 13.56MHz constant. The given range for f VHF is chosen to assure an equal matching quality of the VHF matchbox, eliminating effects originating from a poor matching. In this case the generator powers are fixed to P 13.56MHz = 50 W and P VHF = 100 W. The condition P VHF > P 13.56MHz ensures the plasma characteristics to stay dominantly influenced by the high frequency contribution. Discharge pressure is held constant at 3 Pa. Figure 4.1: Frequency dependence of electron density n e by varying f VHF. Experimental conditions are P 13.56MHz = 50 W, P VHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. The nonlinear fit validates the quadratic scaling of n e with f VHF. Figure 4.1 displays the dependence of electron density n e on f VHF and a non-linearly increasing electron density is observed. It is well known from theoretical approaches by Surendra and Graves [5], Vahedi et al. [10] and Meyyappan and Colgan [6] that the electron density approximately scales with the square of the driving frequency in the system. To verify this elementary scaling law for 2f-CCPs, a parametric estimator of the form n e f β VHF is fit to the measured data in the least-squares sense. The exponent β is estimated to β =

87 4.1. Variation of external parameters for VHF / MHz CCP operation 65 This result agrees well with findings from [5][6][10], who predict the exponent β to lie between 1.5 and 2.2, depending on whether radially averaged or peak electron densities from the discharge center are regarded. Figure 4.2: Frequency dependence of the plasma and floating potential by varying f VHF. Experimental conditions are P 13.56MHz = 50 W, P VHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. Also resulting from Langmuir probe measurements are the floating potential Φ float and plasma potential Φ plasma. Both are shown in figure 4.2. As discussed in section 3.2, Φ float is found at the current zero-crossing and Φ plasma is gained from the inflection point of the Langmuir probe current-voltage characteristic. Interpreting the results in figure 4.2 gives an approximately linear increase in the plasma potential by increasing f VHF. The floating potential exhibits a similar behavior, but at a much larger variance. A rough approximation of the mean electron temperature, adapted to argon in the following case, is known to be T e Φ with Φ = (Φ plasma Φ float ) and T e [ ( )] ln mar Φ = Φ 2 π m e (4.1) giving T e directly in Volts [60]. By applying above information to the approximated linear behavior of Φ plasma and Φ float in figure 4.2 an estimation of the mean electron temperature is gained. Since the potential difference Φ remains approximately constant at 12.5 V, it in turn implies a constant mean electron temperature of T e = 2.7 ev. For verification purposes, above estimation is compared to evaluations of T e from measured Langmuir probe characteristics. Thereby, equation (3.30) is used and the outcome is displayed in figure 4.3. It becomes apparent, that the determination of T e on the measured probe characteristics using equation (3.30) yields a large variance ( 0.8 ev) of the mean electron temperature. This fact is clearly visible in figure 4.3. Nevertheless, combining aforementioned rough approximation and shown results for T e leads to the conclusion, that changing the excitation frequency ratio has a negligible influence on the mean electron temperature. This is

88 66 4. Measurements and discussion Figure 4.3: Frequency dependence of mean electron temperature T e by varying f VHF. Experimental conditions are P 13.56MHz = 50 W, P VHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. in accordance with global model considerations, because discharge confinement (mean sheath extension) is only weakly affected and hence no significant changes in electron temperature are expected. Further analyzing floating potential behavior on the basis of a global model can be understood such that the amount of high energetic electrons > 10 ev increases. These assumptions are experimentally verified later by optical measurements in section Returning to figure 4.1, local maxima in the electron density are observed. They reproducibly appear at integer driving frequency ratios for 67.8/13.56 MHz and 81.36/13.56 MHz and even more pronounced in the dc self bias voltage plotted in figure 4.4. Figure 4.4: Frequency dependence of the dc self bias voltage by varying f VHF. Experimental conditions are P 13.56MHz = 50 W, P VHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm.

89 4.1. Variation of external parameters for VHF / MHz CCP operation 67 Hereby, the dc self bias voltage drops strongly in magnitude to an amount of approximately 10%. To describe this phenomenon two possible explanations are deemed adequate. On the one hand, it has been discovered in recent experiments, that this effect becomes much less pronounced if both excitation frequencies are mounted onto separate electrodes. Mounting both rf sources onto one electrode always produces a stronger mutual coupling than having the plasma impedance separating both frequencies. Also, the effect only occurring at integer frequency ratios is physically reasonable, because available power from f VHF is directly deposited into available harmonics of f 13.56MHz, generated by the plasma itself. Conversely, in the case of non-integer frequency ratios the generation of side-bands and mixing products is caused, leaving the delivered powers of f VHF and f 13.56MHz spectrally more distributed. This last explanation gives way for the discussion in section 3.4.1, describing the possibility of electron heating by plasma generated harmonics through nonlinear electron resonance heating (NERH) as proposed by Mussenbrock and Brinkmann [1]. An experimental approach to nonlinear electron resonance heating (NERH) Figure 4.5: Discrete Fourier amplitude spectrum of a measured PSR current at integer driving frequency ratio f VHF /f 13.56MHz = 67.8 MHz/13.56 MHz. The PSR frequency is calculated to be f PSR = MHz using equation (3.49) with the Child-Langmuir sheath (3.10). Experimental conditions are P 13.56MHz = 50 W, P 67.8MHz = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. When discussing the observed phenomenon of local electron density maxima occurring at integer frequency ratios, nonlinear electron resonance heating (NERH) has been deemed one of the possible explanations. Besides other electron heating effects commonly accumulated under the term stochastic heating, NERH proposes an alternative approach to efficient power dissipation in the low pressure regime (< 10 Pa) due to discharge harmonics [113]. Experimental conditions within the frequency ratio investigations meet this pressure prerequisite. Nonlinear electron resonance heating, as explained in detail in section 3.4.1, describes an indirect excitation of the plasma series resonance (PSR) through plasma generated harmon-

90 68 4. Measurements and discussion Figure 4.6: Discrete Fourier amplitude spectrum of a measured PSR current at non-integer frequency ratio f VHF /f 13.56MHz = 63 MHz/13.56 MHz. The PSR frequency is calculated to be f PSR = MHz using equation (3.49) with the Child-Langmuir sheath (3.10). Experimental conditions are P 13.56MHz = 50 W, P 63MHz = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. ics laying close to the PSR. Therefore, the PSR s proximity was mathematically described by the resonance bandwidth B PSR and calculations for the predicted bandwidth have been determined to be at least 16 MHz at given experimental conditions. To quantify and correlate the indirect PSR heating to local electron density maxima, discharge currents have been recorded for a non-integer and integer frequency ratio. The according PSR frequencies have been calculated from acquired Langmuir probe plasma parameters. Figure 4.5 shows the discrete Fourier spectrum for the integer ratio case and figure 4.6 the spectrum for the non-integer ratio case. In order to evaluate the effect of indirect PSR heating, separate zoomed plots for the measured PSR currents at the approximate PSR frequencies have been additionally inserted. For calculating PSR frequencies the rf-corrected Child-Langmuir mean sheath width approximation according to equation (3.10) is used, although other sheath width approximations exist. Depending on the used approximation, considerable differences may arise in the calculated PSR frequencies. Using for example the simpler matrix sheath approximation given as s = λ Debye 2 e V0 k B T e (4.2) would result in PSR frequencies ranging from 200 MHz to 300 MHz. In comparison to the values given in figures 4.5 and 4.6 a non-negligible difference becomes apparent. As to the question of which is the correct calculation method, the Child law approximation yields experimentally verifiable sheath widths, whereas the matrix sheath approximation does not. It also has to be noted that the matrix sheath approximation (4.2) is originally used to derive the PSR frequency expression (3.49). Hence, the limits of this easy resonance frequency concept quickly become apparent. To cope with this, more sophisticated multi-mode PSR

91 4.1. Variation of external parameters for VHF / MHz CCP operation 69 models are needed, which are recently developed by Ziegler and Mussenbrock [98]. Figure 4.7: Comparison of both Fourier amplitude spectra from integer and non-integer driving frequency ratio case. Amplitudes (arrows indicated) for the 67.8/13.56 MHz dual frequency operation tend to be higher than in the 63/13.56 MHz case (left). Arrows in the zoomed plot (right) indicate the possible locations of the PSR frequency depending on used sheath width approximations. Experimental conditions are P 13.56MHz = 50 W, P 63MHz = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. Returning to and interpreting the discrete Fourier spectra for both cases draws attention to the difference in the amount and magnitudes of generated harmonics. In the integer ratio case only dedicated harmonics of MHz are produced, whereas in the non-integer case numerous more are generated due to nonlinear frequency mixing. A comparison of both spectra is shown in figure 4.7. Focussing on the proximity of the pre-calculated PSR frequencies shows an amplitude increase per frequency component for the integer ratio case. This also holds for the remaining frequency components. Hence, the transition from non-integer to integer ratio goes together with a reduced number of frequency components at detectably increased amplitudes. As a consequence, less but stronger frequency components are found within the resonance bandwidth contributing to the plasma series resonance and leading to the increased local electron density maxima. The mathematical concept is a redistribution of the available signal energy among the number of present frequency components. Considering e.g. a constant amount of signal energy and distributing it among only a few frequency components leaves more amplitude per frequency component (integer ratio case) than by distributing the same amount among numerous frequency components (non-integer case). The term signal energy in literature is often misleading since usually, depending on the type of signal, it is not expressed in units of energy. It only becomes a true energy in physical terms by additionally relating physical quantities (e.g. a resistor) with the signal energy. In mathematical terms the signal energy is calculated from the time-discrete signal x( T n), N which in this case is the sampled PSR current, by N ( ) T E sig = x 2 N n (4.3) n=1 where N is the total number of sampled points and T being the length in time of the continuous analytic signal. A true physical energy is gained by correlating equation (4.3)

92 70 4. Measurements and discussion with the oscilloscope s internal resistor to Ẽ sig = E sig 50.0 Ω. (4.4) Above equation is applied for calculations shown in figure 4.8. Further considerations on signal energy and related signal processing concepts are found in detail in literature [114]. Figure 4.8: Signal energies calculated after equation (4.4) from acquired PSR current signals. Experimental conditions are P 13.56MHz = 50 W, P VHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. Figure 4.8 illustrates the calculated signal energy for each frequency f VHF. It can be seen that up to 75 MHz the signal energy can be considered constant. For frequencies above 75 MHz it rapidly reduces, which is explained by increasing losses due to electrical feedthroughs (see figure 2.16). Quantitatively, the frequency components near f PSR, as seen in figures 4.5 and 4.6, increase from 1 µa and 0.5 µa to 1.3 µa and 1.0 µa, which is an overall amplitude increase of at least 50% from the non-integer to the integer case. Hence, nonlinear electron resonance heating is a likely candidate, responsible for enhanced heating at integer driving frequency ratios in the low pressure regime [115][116]. A comparison of discrete Fourier spectra of PSR currents for low and high pressure regime is given in section Furthermore, as verified by PROES in section 4.2.2, it is demonstrated that electron heating is additionally affected by changing the relative phase between both excitation frequencies at integer ratios [117]. Summarizing the effects of changing frequency ratio, provides three important results. First, a predicted electron density scaling law is experimentally verified to scale as the square of the highest driving frequency. One has to bear in mind though, that simply increasing frequency to gain plasma density is limited by capacitive feed-through losses that need to be determined individually for each processing tool. As a recommendation, the highest system frequency should not exceed 80 MHz, which balances plasma density considerations and rf development costs. Additionally it is recommended to use integer driving frequency ratios for plasma processing, because of two reasons. On the one hand a visible gain in plasma density

93 4.1. Variation of external parameters for VHF / MHz CCP operation 71 is achieved and on the other hand the relative phase becomes available as a further control parameter. Second, the mean electron temperature is unaffected by changing frequency, although it is believed, as shown later, to influence high energetic electron behavior (> 10 ev), which is not accessible by Langmuir probes. Finally, nonlinear electron resonance heating (NERH) as proposed by Mussenbrock and Brinkmann [1] has been experimentally verified to be an important mechanism for discharge sustainment.

94 72 4. Measurements and discussion Power ratio In addition to changing driving frequencies, a more common approach is adapting powers to meet process recipe requirements. Which is straightforward for single frequency discharges may lead to unexpected processing results for dual frequency discharges. Especially the attributed separate tunability of ion flux and ion energy need to be closely investigated. To eliminate strong coupling effects at integer frequency ratios, all further investigations are performed using f VHF = 71 MHz. Discharge pressure is held constant at 3 Pa. For the VHF power variation, P 13.56MHz was set to 50 W and for the low frequency (13.56 MHz) power variation, P VHF is held constant at 50 W. In a first approach, the dc self bias voltage as a good ion bombardment energy approximation is examined for both power variations. Results are displayed in figure 4.9. Figure 4.9: Power dependence of dc self bias voltage. Experimental conditions are 71 MHz/13.56 MHz discharge, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. It shows a very good control of ion bombardment energy through the low frequency contribution (13.56 MHz). By comparing absolute differences in dc self bias voltages for an equal change in applied power (200 W) yields a variation of 70 V for P VHF and 700 V for P 13.56MHz. Consequently, ion bombarding energy is efficiently controllable by P 13.56MHz. Although the change in dc self bias voltage is small by varying P VHF at a given P 13.56MHz, it strongly depends on the process recipe s parameter window whether such a small change is allowable, especially when additionally considering the influence on plasma density. Figure 4.10 depicts investigations into electron density n e behavior gained from Langmuir probe measurements performed at the discharge center. Conversely to the ion bombardment energy, electron density n e is strongly influenced by P VHF [31]. Nevertheless, it is also visible that above a certain threshold (here: 60 W) P 13.56MHz also influences electron density. This threshold is explainable by P VHF being the dominant source of electron density in this range. However, industrial PVD applications operate within a regime P 13.56MHz P VHF, which implies a non-negligible coupling of both frequency contributions with respect to electron

95 4.1. Variation of external parameters for VHF / MHz CCP operation 73 Figure 4.10: Power dependence of electron density n e. Varying MHz power produces a constant electron density for low power changes. Above a threshold power (here 60 W) the electron density is influenced also by the MHz. Experimental conditions are 71 MHz/13.56 MHz discharge, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. density. Hence, in such a power regime electron density is dominantly governed by P 13.56MHz. The threshold power itself is determined by P VHF and its resulting discharge voltage contribution as measurable by a VI probe. Kim et al. [118] and more recently Chung [34] propose an effective voltage concept such as V eff = V 13.56MHz + V VHF 2 3 V 13.56MHz V VHF V 13.56MHz + V VHF (4.5) in order to describe the competition of both frequency dependent voltages. The validity of equation (4.5) is assessed by considering measured VI probe values for V VHF and V 13.56MHz. They are determined to be 81 V V VHF 88 V and 110 V V 13.56MHz 360 V, indicating that in either case V 13.56MHz remains dominant. Consequently, equation (4.5) does not support the observation of constant n e at low P 13.56MHz. Simultaneously acquired VI probe current magnitudes give 5.3 A I VHF 6.8 A and 0 A I 13.56MHz 1.7 A, yielding the same behavior as above voltages. A solution to this dilemma is found in literature, where Turner and Chabert [119] follow a similar problem when discussing electron heating mechanisms in dual frequency capacitive discharges. They motivate a current amplitude rescaling on the basis of different coupling efficiencies of both frequencies. It is well known that the current scales linearly with the plasma boundary sheath capacitance. Also it is known that the sheath capacitance scales inversely with the driving frequency. Hence, the VHF current couples more easily into the discharge than the LF current. Equalizing coupling efficiencies makes both currents I VHF and I 13.56MHz comparable with respect to electron density n e. Calculating the coupling factor given as κ = f VHF f 13.56MHz = (4.6)

96 74 4. Measurements and discussion and rescaling I 13.56MHz such that Ĩ 13.56MHz = κ I 13.56MHz (4.7) with Ĩ13.56MHz as an I VHF -equivalent current, provides the necessary insight into explaining constant n e at low MHz powers. Results are plotted in figure Figure 4.11: Comparison of weighted MHz and 71 MHz current, both measured at matchbox output. Further experimental conditions are 5 sccm, 3 Pa, Argon, electrode gap 45 mm. Therein, both currents I VHF and Ĩ13.56MHz exhibit a behavior explaining a constant n e at low P 13.56MHz. If P 13.56MHz is below 60 W (as the case within this work), the highest available current magnitude is governed by I VHF. Hence, electron density is dominated by P VHF. Exceeding the threshold power of P 13.56MHz = 60 W makes Ĩ13.56MHz the highest available current magnitude. As a result P 13.56MHz starts affecting overall electron density n e. Typical power regimes for physical vapor deposition (PVD) in industrial processing tools meet the condition P 13.56MHz P VHF. Due to this fact and including aforementioned findings, the attributed decoupling from ion flux and ion energy by separately tuning P VHF and P 13.56MHz is not feasible to this regard. Although ion bombarding energy is very well controllable by P 13.56MHz, as verified above, plasma density (ion flux) is not. Moreover, it has to be regarded as a product of both operating frequency contributions. In practice it even occurs that for above given operating regime electron density usually drops when switching from single frequency VHF operation to 2f-CCP operation, due to the dominant influence of P 13.56MHz. However, it can be easily compensated by readjusting P VHF to reach the same level of electron density and even further increase it. These experimentally observed effects have been theoretically described by Kim et al. [120][121][122] and agree well. Effects in the high power PVD regime become apparent for ion distribution function measurements in section 4.3 and in more detail in section 4.4 within sputter deposition studies. Alternatively, if a narrow process control window is obligatory for e.g. advantages in tuning thin film parameters, the only option is largely increasing P VHF to stay well away from a

97 4.1. Variation of external parameters for VHF / MHz CCP operation 75 previously determined threshold power level with respect to P 13.56MHz. In that case n e remains constant and ion energy is solely tunable by P 13.56MHz. This concept would obviously limit a maximum achievable deposition rate and inevitably increase costs per wafer. Figure 4.12: Power dependence of mean electron temperature T e. Experimental conditions are 71 MHz/13.56 MHz discharge, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. Finally, the influence of varying powers on the mean electron temperature and the floating potential is studied. Figure 4.12 shows the influence of P VHF and P 13.56MHz on T e. By varying P 13.56MHz (left-hand side plot) T e exhibits a decreasing trend with increasing power. On the basis of a global model this is explainable by an enhanced discharge confinement. Interpreting the rf-corrected Child law sheath approximation from equation (3.10) with an increasing dc self bias voltage and increasing mean sheath width, provides a decrease in mean electron temperature. Similarly, the behavior of T e for varying P VHF is explained. Thereby, the dc self bias voltage as well as the mean sheath width do not significantly change. Thus, the mean electron temperature T e is found to stay constant for P VHF variations. Another relevant effect by changing P 13.56MHz is observed in the floating potential Φ float and shown in figure Therein, two regions are identifiable. In region 1 the floating potential Φ float decreases to a local minimum, whereas in region 2, Φ float rises asymptotically to a constant voltage value. This effect is explained as follows: in region 1 the observed change occurs from the transition of single-frequency to dual-frequency operation. Since Φ float can be regarded as a measure for high energetic electron contribution, the decrease in Φ float is attributed to enhanced discharge confinement. In region 2, further increasing P 13.56MHz, discharge confinement remains constant and more high energetic electrons are produced. Concluding the study of power ratio effects on dual frequency discharges, it is found that only under certain external parameter conditions a complete decoupling from ion flux and ion energy is achievable. However, these parameter sets are mostly unattractive for industrial applications, because the resulting processing speed would be too low, due to low deposition rates, and subsequently costs per wafer rise. A solution could be triple-frequency capacitive discharges where one frequency defines ion flux, another the target ion bombarding energy and a third the substrate ionic species impact energy. Although triple frequency discharges might be considered in the near future, they are beyond the scope of this work.

98 76 4. Measurements and discussion Figure 4.13: Low frequency power dependence of floating potential. Experimental conditions are 71 MHz/13.56 MHz discharge, 5 sccm, 3 Pa, Argon, electrode gap 45 mm Pressure variation As the most relevant external tuning parameters, frequency and power ratio have been studied. Changing system pressure is a further accessible control parameter studied in this section. For these investigations constant experimental conditions have been, P VHF = 100 W with f VHF = 71 MHz and P 13.56MHz = 50 W. Pressure is varied from 3 Pa up to 20 Pa. Results for the electron density n e are shown ion figure Figure 4.14: Pressure dependence of electron density n e. Experimental conditions are P 71MHz = 100 W and P 13.56MHz = 50 W, 5 sccm, Argon, electrode gap 45 mm. By increasing system pressure, electron density n e approximately rises linearly. At 20 Pa a plasma density of cm 3 is achieved. Similar observations are made for the dc self bias

99 4.1. Variation of external parameters for VHF / MHz CCP operation 77 voltage. It decreases in magnitude with increasing pressure and is shown in figure 4.15(right) [115]. Figure 4.15: Pressure dependence of mean electron temperature T e (left) and dc self bias voltage (right). Experimental conditions are P 71MHz = 100 W and P 13.56MHz = 50 W, 5 sccm, Argon, electrode gap 45 mm. That is explained by the discharge becoming more symmetric at higher pressures, which effectively reduces dc self bias voltage. In the left-hand side plot of figure 4.15 the mean electron temperature is depicted. It rises for decreasing pressures which is explained by a strong increase in electron diffusion to grounded walls. Consequently, also the dc self bias voltage must move to more negative values to compensate these losses. Since the high pressure regime > 10 Pa is irrelevant for PVD processes, due to a reduced mean free path of the sputtered atomic species, optimum plasma conditions are usually found for 5 Pa and lower. The exact pressure value depends on the target substrate distance. For atomic iron the mean free path is approximately 4 mm at 3 Pa. Evaluation of simultaneously acquired PSR current signals gives an additional insight into the transition regime between nonlinear electron resonance heating (NERH), as described in section 4.1.1, and the ohmic heating regime. Observing the transition from NERH to ohmic heating As previously described, the concept of NERH as proposed by Mussenbrock and Brinkmann [1] relies on electrons being heated by plasma generated harmonics. It becomes more pronounced when going from single-frequency to dual-frequency discharges, because of additional mixing and side-band generation. A further parameter, directly influencing harmonic generation is pressure. Figure 4.16 displays the discrete Fourier spectra of acquired currents at pressures from 3 Pa (left) to 20 Pa (right). Although no direct excitation of the PSR is aimed for, exemplary calculated values, gained from simultaneous Langmuir probe data, are presented. Furthermore, the brackets in each plot indicate the anticipated PSR frequency proximity (resonance

100 78 4. Measurements and discussion Figure 4.16: Discrete Fourier spectra for observed PSR currents at low (3 Pa) and high (20 Pa) pressure. Indicated areas ( brackets) denote the anticipated PSR frequency proximity (using (3.10) as mean sheath width). The transition from NERH to ohmic heating is clearly visible through the reduction of harmonics. Further experimental conditions are P 71MHz = 100 W and P 13.56MHz = 50 W, 5 sccm, Argon, electrode gap 45 mm. bandwidth B PSR ). Hence, changes to spectral amplitudes occurring within these denoted ranges is believed to have an influence on the electron heating mechanism. It is observed that by raising system pressure from 3 Pa to 20 Pa, harmonic generation is strongly damped by at least one order of magnitude for frequencies larger than 400 MHz. Consequently also harmonic dominated electron heating is supposed to decrease, but the electron density does not. Consequently, an alternative electron heating must take place at higher pressures. By increasing pressure the electron neutral collision rate increases and thus fully compensates for the reduced electron heating through discharge harmonics. Henceforth, the transition from nonlinear electron resonance heating to collision dominated ohmic electron heating is observed. It can be summarized that for industrial PVD applications the optimum operating pressure regime is preferably given for pressures < 5 Pa. On the one hand, sputtered target atomic species have a sufficiently long mean free path and on the other hand the drop in ion flux is easily compensated by raising high frequency power P VHF. Further observations include a significant increase in harmonics generation at reduced pressures. It is deemed to be an important mechanism for discharge sustainment at low pressures and believed to present an alternative form of stochastic heating [1]. Finally, the three major external tuning options have been addressed. A further option arises by using integer excitation frequency ratios, namely the relative phase. Tuning the relative phase might become important at certain discharge operating regimes and particularly for drift compensation as presented next.

101 4.2. Influence of the relative phase at integer driving frequency ratios Influence of the relative phase at integer driving frequency ratios The advantages of choosing integer driving frequency ratios have been discussed in detail in section Appending the analysis from given frequency ratio results, the relative phase was identified as an additional tuning parameter. Since integer frequency ratios are considered as a preferred mode of discharge operation, the role of relative phase needs to be evaluated with respect to its influence on plasma parameters. As discussed in section 3.3 the proposed synchronization scheme needs to be applied in order to gain access to the relative phase. For the given experimental setup the two rf sources need to be synchronized. This is realized by feeding the clock-signal of the first signal source to the second signal generator as a reference clock. By that means, all frequencies are derived from a common master oscillator. In the presented experimental setup this method is used. Figure 4.17: PROES excitation plot for a pure 2 MHz discharge. Further experimental conditions are U 2MHz = 125 V RMS, Neon, 7 sccm, 1 Pa, electrode-wall gap 55 mm. Clearly visible is the electron beam formation (red) during sheath collapse at the driven electrode. Following this event is the extensive ( 10 cm) sheath expansion phase. Addressing relative phase in the following paragraphs is experimentally realized with respect to excitation voltages, such that U phase (t) = Û2MHz cos(ω 2MHz t) + Û14MHz cos(ω 14MHz t + ϕ) (4.8) with Û2MHz, Û14MHz as the voltage amplitudes, ω 2MHz, ω 14MHz the excitation frequencies and ϕ the relative phase. In the experiment it is varied from 180 ϕ 180 in steps of 15. Further conditions are Û2MHz = Û14MHz = V RMS, neon at 10 Pa, 7 sccm and no counter electrode installed. The effective minimum distance between the top electrode and the grounded wall is given as 55 mm. The bottom electrode had to be removed from the setup due to an observed 2 MHz related effect. During initial tests, the formation of plasma globes occurred. Estimations of the

102 80 4. Measurements and discussion mean sheath width on the basis of approximated plasma parameters yielded a significant sheath expansion of approximately 8 10 cm, which is also verified experimentally as depicted in figure As a consequence the bottom electrode needed to be removed to restore stable plasma conditions, because only a maximum gap of mm is adjustable. The choice of alternative excitation frequencies (2 MHz and 14 MHz) for the planned PROES investigations was inevitable for the following reason. Due to considerations by Gans et al. [123] the shortest lifetime of a PROES-compatible emission line is given by the Ne 2p 1 transition, with a wavelength of nm, a threshold excitation energy of 19 ev and a lifetime of 14.5 ns. Although ICCD camera properties allow for a much higher resolution in time (several hundred picoseconds), the state s transition lifetime is the limiting factor. To fully capture transient discharge behavior within the high frequency cycle (67.8 MHz / ns) implies that only one point per 67.8 MHz cycle could be resolved, which is inadequate for evaluation. Therefore, alternatively 14 MHz as the high frequency and 2 MHz as the low frequency are chosen, giving five sampling points per 14 MHz period. Before addressing electron excitation behavior, Langmuir probe measurements at dedicated phase angles have been performed Langmuir probe results Figure 4.18: Relative phase dependence of electron density n e and mean electron temperature T e. Experimental conditions are U 2MHz = U 14MHz = 125 V RMS, Neon, 7 sccm, 10 Pa, electrode-wall gap 55 mm. In order to be able to correlate changes in plasma parameters relative phase modifications and excitation behavior Langmuir probe measurements at different relative phase angles are performed. Elementary plasma parameters gained from these measurements are electron density n e and mean electron temperature T e. They are drawn in figure The influence of relative phase on electron density is clearly visible. Correlating minimum and maximum value yields a dynamic tuning range of 20%. Furthermore, a sinusoidal-like behavior can be

103 4.2. Influence of the relative phase at integer driving frequency ratios 81 anticipated. Similar observations are made for the electron temperature T e. Equivalently, the tuning range is estimated to be 20%. Also a comparable sinusoidal-like behavior is recorded. Moreover, another effect is seen in both plots of figure On the one hand, electron density n e and mean electron temperature T e reach local maxima (from ), but on the other hand no pronounced minima are observed. It appears, there exists a lower limit for n e and T e (from ), which is believed to result from phase positions where the local plasma boundary sheath expansion is near its maximum, hence only minor changes are obtained. Conversely, for phases the sheath expansion is near its minimum, hence strong electron diffusion governs electron temperature. These observations are supported by PROES measurements as is shown in the following section Additionally, correlating discussed results to simultaneous plasma impedance measurements, also exhibits a very good agreement. Figure 4.19: Relative phase dependence of plasma impedance magnitude and phase. Experimental conditions are U 2MHz = U 14MHz = 125 V RMS, Neon, 7 sccm, 10 Pa, electrode-wall gap 55 mm. Figure 4.19 shows the magnitude (left) and phase (right) of the measured plasma impedance. The phase attains values near 90 because of regarding a capacitive setup. Therein, low electron densities (< cm 3 ) correlate well to high impedance magnitudes. Local minima in the impedance magnitude also match the respective phase angle where electron density reaches a local maximum and vice versa. Furthermore, the constant behavior for phase angles of match measured plasma impedance data. A significant influence with respect to changing relative phase is noticeable in the floating potential. Figure 4.20 displays the plasma and floating potential as measured by Langmuir probe. Results exhibit a constant plasma potential, whereas the floating potential exerts a pronounced sinusoidal-like behavior. Using the picture of regarding the floating potential as an indicator for high energetic electron behavior, a significant change occurs in the production of high energetic electrons for energies larger than 7-8 ev, when scanning from 180 to 0. This interpretation is supported by PROES measurements and is discussed at a later point within this work. Since electron density and mean electron temperature exhibit a detectable influence on relative phase the electron distribution function (EDF) is analyzed in more detail. Figure 4.21

104 82 4. Measurements and discussion Figure 4.20: Relative phase dependence of plasma and floating potential. Experimental conditions are U 2MHz = U 14MHz = 125 V RMS, Neon, 7 sccm, 10 Pa, electrode-wall gap 55 mm. displays two specific relative phase positions. Figure 4.21: Relative phase dependence of electron distribution function. Experimental conditions are U 2MHz = U 14MHz = 125 V RMS, Neon, 7 sccm, 10 Pa, electrode-wall gap 55 mm. Therein, the previously discussed behaviors are visible in combination. For the phase position 90 a high mean electron temperature and electron density are found, whereas for +90 a low plasma density and mean electron temperature are noticed. Imagining a continuous tuning of the relative phase would result in an oscillation of the EDF with respect to its local maximum, ranging from 2 ev to 4.5 ev. At the same time, the peak s magnitude also performs minor fluctuations. Summarizing all results gained from Langmuir probe measurements, a significant influence

105 4.2. Influence of the relative phase at integer driving frequency ratios 83 of the phase relation between integer driving frequency ratios is found. Implications for industrial processes need further considerations, because given discharge conditions operate at equal driving voltages not suitable for PVD purposes. In the following section, the presented Langmuir probe results are supported by PROES and SEERS/PSR current measurements. Additionally, investigations under PVD-like discharge conditions are performed to verify whether findings from the equal voltage case are transferrable PROES and SEERS/PSR measurements To verify the presented Langmuir probe measurements, PROES and PSR current data have been obtained. As discussed in section it is attempted to correlate PSR current data to PROES excitation diagrams. Figure 4.22: Correlation of the electron excitation dynamics (top) to SEERS/PSR currents (bottom) at relative phase angles of -90 and +90. Experimental conditions are U 2MHz = U 14MHz = 125 V RMS, Neon, 7 sccm, 10 Pa, electrode-wall gap 55 mm. High energetic electrons have been identified to play a key role in discharge sustainment. Possibilities of accessing these electrons however are sparse. Langmuir probe diagnostics are limited to approximately 10 ev. With respect to figure 4.21 an increase might be anticipated for energies larger than 7 ev, but measurement uncertainties deny such an interpretation. On the other hand, optical diagnostics can only access energy regions in the scope of excitation or ionization energies and are therefore well suited to study high energetic

106 84 4. Measurements and discussion electron behavior. Within investigated discharge conditions only energies larger than 19 ev are accessible. The PROES diagnostic method is chosen for its additional ability to monitor transient discharge behavior. Results of performed measurements are given in figure 4.22 (top) for two dedicated phases. In figure 4.22, the formulated assumptions of the relative phase s influence on high energetic electrons becomes apparent. Comparing excitation plots at 90 and +90 shows an increase in high energetic electron production by a factor of two. Where in the 90 case, only one electron beam is produced by incoming electrons being reflected at the plasma boundary sheath, two electron beams are produced in the +90 case. It seems to be contradicting, that despite an increased local excitation, electron density goes down (see figure 4.18). This is explained as follows: although more high energetic electrons are generated, they are produced out of the reservoir of cold electrons being accelerated by the expanding plasma boundary sheath. Hence, the number of cold electrons, measured as electron density by a Langmuir probe, reduces in favor of an increase in high energetic electrons. Additionally, a very good correlation of measured PSR currents to the traversing electron beams is observed in figure 4.22 (bottom). The resonance structures within the current signals can be perfectly matched to the points in time where electron beams are generated. Also the number of resonant occurrences and the number of electron beams fit. A physical picture describing this link between PROES and SEERS is that of electron beams traversing the discharge and hitting the grounded wall, where they are detected. Implications for industrial discharge monitoring are such that PSR current measurements provide a more cost-efficient way compared to PROES measurements. Furthermore, optical access to plasma tools is usually rather limited. Figure 4.23: Influence of relative phase on a simple plasma boundary sheath waveform model. Arrows indicate electron beam events occurring immediately after sheath collapse. The relative phase controls the number of such beam events. Simulation conditions resemble experiment in equal voltages U 2MHz = U 14MHz. To further illustrate the influence of relative phase and the concept of electron beams, exemplary waveforms, which can be understood as a very simplified plasma boundary sheath oscillation, for both phases 90 and +90 are simulated. They are shown in figure 4.23,

107 4.2. Influence of the relative phase at integer driving frequency ratios 85 where the left-hand side plot resembles 90 and the right-hand side plot resembles +90. Inserted arrows within both plots indicate the position in time, responsible for the electron beam generation due to the (hard wall) sheath expansion. In detail it is understood as follows: When the plasma boundary sheath reaches its minimum expansion, numerous bulk electrons move towards the sheath because its potential barrier is easily bridged. These incoming electrons, encounter the expanding 14 MHz sheath oscillation and are reflected back into the discharge, gaining energy. Subsequently, those electrons are detected as electron beams in PROES and resonant structures in SEERS/PSR currents. An alternative explanation can be found by considering total sheath collapse. Reanalyzing figure 4.23 motivates the formulation of a simple time-dependent generalized sheath capacitance as C Sheath (t) = ε 0 A electrode s(t) (4.9) with s(t) = s + s 2MHz cos(ω 2MHz t + ϕ 2MHz ) + s 14MHz cos(ω 14MHz t + ϕ 14MHz ). (4.10) Figure 4.24: Influence of relative phase on excitation behavior for PVD-like discharge conditions. Experimental conditions are U 2MHz = 125 V RMS U 14MHz = 25 V RMS, Neon, 7 sccm, 1 Pa, electrode-wall gap 55 mm. Plots taken from [43]. The influence of changing relative phase is less pronounced than in figure 4.22(top), but sufficient for industrial applications. Thereby, s is the mean sheath width and s 2MHz and s 14MHz the respective sheath amplitude contributions with corresponding phases and frequencies. By evaluating equation 4.10 the boundary sheath collapses at a certain point in time (s(t) 0). Depending on the relative phase, this event can occur more than once as presented in figure 4.23 (right). At the time of sheath collapse, equation 4.9 yields a near infinite sheath capacitance, which in other words denotes a short circuit. During this time interval when the sheath is bridged, the full rf current passes into the discharge. These events are detectable as electron beams. The following subsequent sheath expansion additionally accelerates these electrons away from the electrode into the plasma bulk, producing high energetic electrons.

108 86 4. Measurements and discussion Relating the presented physical ideas to observed electron production, there is only one occurrence for the left-hand side plot in figure 4.23, whereas by adjusting the phase, two such occurrences can be produced, visible in the right-hand side plot. This is in good agreement with experimental observations. However, these findings have been obtained for equal excitation voltages, which is not the case for PVD applications. Hence, measurements are retaken for given discharge conditions. Because plasma densities are too low in 2 MHz dominant plasmas only PROES is applicable as a diagnostic tool. The results of these measurements are shown in figure Here, discharge conditions are chosen to be 1 Pa, Neon, 7 sccm and Û2MHz = V RMS Û14MHz = 2 25 V RMS. As expected, the mean sheath width becomes large. However, the same observations as with the previously presented case (equal voltages and high pressure) are made. For a phase of 90 only one beam of high energetic electrons is observed and for a phase of +90 two beams are noticeable. Exemplarily, simulated waveforms for Û2MHz Û14MHz are given in figure 4.25, expressing the same behavior as shown in figure In spite of only minor 14 MHz oscillations being visible, the same physical concepts apply for this case of discharge operating regime, which means the relative phase is an important tuning parameter for dual frequency discharges. Figure 4.25: Influence of relative phase on a simple plasma boundary sheath waveform model, resembling PVD-like conditions. Arrows indicate electron beam events occurring immediately after sheath collapse. The relative phase controls the number of such beam events. Simulation conditions resemble experiment regarding voltages U 2MHz U 14MHz. Concluding this section, the relative phase between driving frequencies at integer ratios is studied. A reproducibly detectable influence of phase on the production of high energetic electrons is observed. These electrons are a key mechanism for discharge sustainment in capacitive plasmas. For industrial applications, adjusting the phase exerts a direct influence on the plasma boundary sheath expansion and collapse, hence modifying local heating directly in front of the sputtering target. Furthermore, stationary plasma parameters such as electron density n e and mean electron temperature T e vary within 5 20%, depending on the mode of operation. However, this tuning range is small compared to using other available external tuning parameters.

109 4.3. Ion energy distribution measurements 87 But phase tuning might become useful for compensation of process drifts or optimizing adjustments in ion bombarding energy. Additionally considering figure 4.20, total charging contributions onto the substrate become controllable through floating potential optimization, hence arc management control especially in reactive (isolating) PVD processes is a possible field of application requiring further attention. Nevertheless, these investigations are beyond the scope of this work. With respect to magnetically enhanced discharges phase tuning is an interesting prospect of enhancing electron production by maximizing high energetic electron emission. A major drawback however, are inhomogeneity problems due to preferential sputtering along the magnetic field lines. Those considerations are being incorporated in follow-up works on this project. Prior to analyzing elementary thin film deposition, the ion energy distribution on the electrically driven electrode is investigated in the following section. 4.3 Ion energy distribution measurements In this section, ion distribution function (IDF) measurements using a retarding field energy analyzer (RFEA) are performed on the electrically driven electrode. From determined ion distribution functions (IDF), the ion flux onto the target and the mean ion energy is derived. These investigations are relevant, because ion impact behavior on the target materials is characterized and compared to previous findings from Langmuir probe parameter studies. Especially the behavior of ion flux with increasing P 13.56MHz and verification of frequency ratio behavior with respect to increased electron density are investigated. Thus, the parameter variations are derived from presented Langmuir probe studies. Hereby, voltage ratio and frequency ratio are investigated. Measurement conditions are 3.5 Pa at 10 sccm in argon. The voltage is set to a constant value of 70 V, with the other voltage varying respectively. Applied frequencies are f VHF = 67.8 MHz and f 13.56MHz Voltage ratio As deduced from Langmuir probe results, the voltage ratio (power ratio) plays an important role in adjusting plasma density and ion bombarding energy. It was discovered, that ion bombarding energy is mainly regulated by the low frequency power P 13.56MHz. In contrast, plasma density cannot be properly regulated independently by P VHF, especially in PVD power regimes where P 13.56MHz P VHF. In this case, the low frequency power contribution P 13.56MHz also significantly influences plasma density. To verify these findings a retarding field energy analyzer is mounted on the driven electrode. Results for the voltage variation, where the low frequency voltage U 13.56MHz is swept from 0 70 V with a constant high frequency voltage U VHF = 70 V are shown in figure The first and most significant result is, that by changing the discharge from a single frequency 67.8 MHz into a dual frequency mode (adding MHz), ion flux reduces and ion energy increases simultaneously. It underlines the discussed fact of strong frequency coupling also

110 88 4. Measurements and discussion Figure 4.26: Low frequency voltage U 13.56MHz influence on the ion distribution function (IDF) on the target electrode. Experimental conditions are U 67.8MHz = 70 V RMS, 3.5 Pa, 10 sccm, Argon. predicted theoretically [28]. An immediate implication for industrial PVD is, that VHF power has to be increased to compensate for the losses in ion flux. By studying directly the sputter deposition rate in section 4.4, those effects are outlined in more detail. Second, a transition from a single peak to a two-peaked structure in the IDF is observed. This effect is directly related to equation (3.59), correlating the energy spread (peak separation) E to the dc self bias voltage U dc bias and the rf sheath voltage U rf. Consequently, since U dc bias significantly increases by raising U 13.56MHz, the energy spread E has to increase because the mean sheath width grows. Figure 4.27: Calculated mean ion energies from measured IDFs for low frequency voltage U 13.56MHz variation. Experimental conditions are U 67.8MHz = 70 V RMS, 3.5 Pa, 10 sccm, Argon. Taking these IDFs and calculating each mean ion bombarding energy, gives the plot in figure

111 4.3. Ion energy distribution measurements By linearly raising U 13.56MHz, the mean ion energy is verified to similarly rise linearly. Expressed in values, a rise by 40 V in U MHz approximately yields a rise of 40 ev in mean ion energy. This result supports findings from Langmuir probes, where ion energy is found to be well solely tunable by P 13.56MHz Frequency ratio To investigate the effect of frequency ratio on ion distribution function, the same discharge conditions apply. The voltage values are U VHF = 70 V to ensure a dominant high frequency, and U 13.56MHz = 35 V. Exemplarily, four distinct frequencies have been analyzed. Results are shown in figure As discovered within Langmuir probe data, the influence of frequency on dc self bias and hence mean ion bombarding energy is low. In figure 4.28 a slow decrease of mean ion energy is found. This is visible by the total IDF shifting to lower energy values without changing shape. Additionally, the energy spread E stays constant as U 13.56MHz stays constant, indicating a negligible influence the VHF frequency on ion bombarding energy. Figure 4.28: Dependence of the ion distribution function on the VHF driving frequency f VHF. Experimental conditions are U VHF = 70 V RMS, U 13.56MHz = 35 V RMS, 3.5 Pa, 10 sccm, Argon. Summarizing, RFEA measurements with varying voltage and frequency ratio have been performed. Results show a decrease in ion flux and increase in ion energy by raising the low frequency voltage U 13.56MHz. For PVD applications this implies an increase in high frequency power P VHF to compensate for plasma density losses. It was shown, that ion bombarding energy is very well controllable through low frequency power P 13.56MHz yielding a linear relationship. From frequency ratio variations a negligible influence with respect to mean ion energy is detected. This concludes the detailed section on plasma characterization. Various parameter sets relevant for sputter deposition purposes have been thoroughly investigated. These findings are brought to application in the following section for the study of elementary thin film deposition

112 90 4. Measurements and discussion properties. 4.4 Ferro-metallic thin film deposition study Ferro-metallic films became important in recent times especially for their impact on magnetoresistive random access memory (MRAM) research. MRAMs are considered to be the successor of dynamic RAMs (DRAM), because of their advantage of non-volatility. But because MRAM cell s space requirements are high and manufacturing of the magnetic layers is costly their spreading is rather limited. The development of spintronics (short for spin-based electronics) is one of the key fields of application for these kind of films. Its major representative is the spin (valve) transistor based on the giant magneto-resistive (GMR) effect. In microelectronics it is manufactured by common semiconductor processing steps (plasma deposition, etching, lithography) and its internal build-up resembles that of a silicon transistor. The difference lies within applied materials, where in this case thin ferro-metallic films are used. They are separated by an aluminium oxide spacer layer. Electrically, the transistor becomes conducting when both magnetic layers exhibit the same field configuration. Conversely a high impedance is available when the both field configurations are anti-parallel. In the conducting case, electrons can tunnel through the non-conducting material by applying a voltage drop across the transistor stack. Hereby, two transistor modes are distinguished. The spin valve transistor is operated with an open base and switching is accomplished by external magnetic fields. This variant of the spin transistor is well controllable and forms the basis for MRAMs. Another mode is the spin transistor without an open base. In this case switching is realized by injecting a spin-polarized current into the transistor base, which is a current research topic. Within this work experiments characterizing elementary deposition and thin film properties are performed. First, sputter deposition is characterized using a quartz crystal microbalance (QCM). Results are compared to findings from Langmuir probe and retarding field energy analyzer (RFEA) data. Discovered discrepancies between thin deposited layer thicknesses on silicon wafers and QCM readings are investigated by verifying deposited thin film density. Roughness properties and the determination of relative atomic species densities conclude the elementary characterizations Optimization of sputter deposition rate Prior to beginning with thin film analysis, the sputter deposition rate needs to be characterized and optimized first. Therefore the quartz-crystal microbalance is positioned 20 mm underneath the target. Since for initial experiments on maximizing the sputter deposition rate no costly pure iron target is wasted a fully equivalent material is chosen. High-grade steel with an iron content of at least 70% is considered to be an adequate replacement.

113 4.4. Ferro-metallic thin film deposition study 91 The remaining steel contents such as nickel (13%) and chromium (12%) have a similar mass density as iron and the sputtering yields also exhibit similar behaviors. Hence, performed QCM measurements are safely transferrable to experiments using a pure iron target. The full optimization process regarding sputter deposition rates is found in literature and only the most important excerpts are presented in this section [124]. Figure 4.29: Pressure dependence of sputter deposition rate and determination of optimum deposition pressure. Experimental conditions are P 13.56MHz = 400 W single frequency operation, Argon, 10 sccm, target-qcm gap 20 mm. The target to substrate distance is a key parameter in PVD processes, because it defines in conjunction with system pressure the optimum for the sputter deposition rate. System pressure itself directly governs the argon ion mean free path. Therefore, an initial pressure variation study to determine the optimum pressure for a given distance is performed. Discharge conditions were P 13.56MHz = 400 W, P VHF = 0 W and argon at 10 sccm gas flow. To ensure only pressure effects being studied, the plasma is operated in single frequency MHz mode. From Langmuir probe measurements it is known that enough density is produced, but sputtering with MHz is almost completely realized by changing the energy dependent sputtering yield. Figure 4.29 displays the pressure variation study. Therein, the expected behavior of deposition rate versus system pressure is observed. Essentially, the plot can be divided into two regions (left and right of the local maximum). For pressures below the curve s maximum plasma density is too low, respectively ion flux, so deposition rate diminishes in this direction. On the other hand, raising system pressure beyond the curve s maximum results in a decreasing deposition rate due to more collisions (decreasing mean free path for iron atoms) of sputtered atomic species with the argon background gas. To accurately determine the optimum operating pressure a polynomial fit through the measured data is calculated. The first derivative s root yields the exact local maximum position and is found to be 2.5 Pa. In figure 4.30 also the dc self bias voltage behavior as a measure for ion bombarding energy is seen. Thereby, two slopes are identifiable. From very low pressures up to approximately 4 Pa

114 92 4. Measurements and discussion Figure 4.30: Pressure dependence of dc self bias voltage. Experimental conditions are P 13.56MHz = 400 W single frequency operation, Argon, 10 sccm, target-qcm gap 20 mm. the ion bombarding energy rises more rapidly than for pressures larger than 4 Pa. For low pressures this is explainable by an increase in electron temperature, due to rising diffusion. In turn it implies steeper electric field gradients to the grounded wall. Consequently, the dc self bias voltage has to rise in magnitude to compensate for growing losses. For further measurements, system pressure is set to the previously determined optimum at 2.5 Pa. Continuing the characterization of iron deposition rate, the power dependence is investigated in the following. Therefore, each power P 13.56MHz and P VHF is varied individually. The high frequency f VHF is chosen as 71 MHz to intentionally leave out resonant effects at integer frequency ratios. Also 71 MHz is chosen, because of a comparable plasma density with respect to 67.8 MHz (see figure 4.1) such that ion fluxes do not differ significantly. Remaining discharge conditions stay the same as mentioned earlier. Figure 4.31 depicts the obtained QCM deposition data. Hereby, the separate influence of each single frequency contributions becomes apparent. Both detected deposition rates show a linear relationship to the varied respective powers. However, one has to keep in mind the different causes of an increase in sputter rate. Concerning low frequency power P 13.56MHz, deposition rate grows due to growing mean ion bombarding energy, acquiring values of up to 1125 ev at P 13.56MHz = 600 W. Conversely, deposition rate increases with 71 MHz power P 71MHz due to a significant boost in ion flux (plasma density) as shown by Langmuir probe measurements. Additionally a moderate increase in ion bombarding energy up to 174 ev at P 71MHz = 400 W contributes to increasing sputter rates. On the one hand these results support the predicted lemma of a strong frequency coupling, essentially not allowing a complete separable control of ion bombarding energy and ion flux. On the other hand, frequency-specific individual influences can be clearly identified. Thereby, a single frequency 71 MHz discharge is found to be inefficient for PVD because of low ion bombarding energies. In turn, a single frequency MHz discharge cannot provide

115 4.4. Ferro-metallic thin film deposition study 93 Figure 4.31: Power dependence on sputter deposition rate in single frequency discharge (13.56 MHz, 71 MHz). Discharge conditions are Argon, 2.5 Pa, 10 sccm, target-qcm gap 20 mm. sufficient plasma density. Expressed in values the slopes are found to be 0.2 Å/s per 100 W change in P 71MHz and 0.4 Å/s per 100 W change in P 13.56MHz. The transition from single frequency to dual frequency operation well illustrates the potential of 2f-CCPs for physical vapor deposition (PVD). Figure 4.32 depicts these investigations for the transition from MHz single frequency to 71/13.56 MHz dual frequency mode. Thereby, P 71MHz = 100 W remains constant and P 13.56MHz is varied in both cases. Comparing both slopes yields an increase of 62.5% from the single frequency MHz case to the 71/13.56 MHz dual frequency case at the previously determined optimum pressure of 2.5 Pa. Finally moving the focus to comparing dual frequency operation with varying powers for 71 MHz and MHz individually, unveils a further phenomenon. Hereby, plasma conditions in pressure and gas flow rate stay constant. For varying P 71MHz, MHz power is held constant at 400 W and for varying P 13.56MHz, 71 MHz power is held constant at 100 W. Figure 4.33 presents the obtained QCM data. The power variation of MHz under constant P 71MHz has been discussed previously in figure 4.32 and is introduced for reference. A more interesting observation is made for constant MHz power under varying P 71MHz conditions. Thereby, the sputter deposition rate is not linearly increasing for the complete range, but does so in two anticipated linear slopes. As a direct consequence for PVD processing, simply increasing 71 MHz power to raise deposition rate through raising ion flux is possible within certain constraints. As can be seen from figure 4.33, passing a certain threshold results in a reduced slope and deposition rate increases much slower. Hence, the gain in deposition rate by increasing P 71MHz diminishes. By significantly increasing P 71MHz, an intersection point with the P 13.56MHz variation can be extrapolated. That means, exceeding a second threshold for P 71MHz under constant MHz power conditions, would result in a lower deposition rate than achievable by changing MHz power.

116 94 4. Measurements and discussion Figure 4.32: Dependence of sputter deposition rate on single frequency MHz and dual frequency discharge operation (13.56/71 MHz). Discharge conditions are Argon, 2.5 Pa, 10 sccm, target-qcm gap 20 mm and P 71MHz = 100 W. A reasonable explanation for the first change in slope was given in section for Langmuir power variation measurements. Hereby, the intersection point is defined by the different current contributions of MHz and 71 MHz. In this case for large enough P 71MHz, the 71 MHz current becomes large compared to the MHz current, hence discharge characteristics are dominated by 71 MHz behavior. This is strongly supported by the single frequency power variation shown in figure Comparing the single frequency 71 MHz slope from figure 4.31 with the given dual frequency P 71MHz slope from figure 4.33 yields a good agreement. This means deposition rate behavior eventually changes to a much reduced slope magnitude resulting from single frequency contributions only. Conversely, this effect is not observable for the P 13.56MHz variation. This is explained by the low frequency power s significant control over ion bombarding energy. By increasing ion energy the energy-dependent sputter yield ensures an increase in deposition rate up to energy levels where bombarding ions are implanted. In this case deposition rate will reduce again. Summarizing, different parameter variations for power and pressure have been performed to optimize the sputter deposition rate. It was found that each single frequency contribution is less efficient than even a non-optimized dual frequency discharge. Furthermore, analysis of dual frequency power variations unveiled a significant change in deposition rate behavior for varying P 71MHz, which is explained by the discharge adapting single frequency behavior. However, this effect cannot be transferred to varying P 13.56MHz since the dominant increase in ion bombarding energy compensates for losses in ion flux, due to an increase in sputtering yield [125]. For considerations on a scale-up version of the given experimental setup, an estimation of expected deposition rates is given on the basis of extrapolating parameters from gathered Langmuir probe and quartz-crystal microbalance data in the following section. Furthermore, recorded deposition rates are correlated to Langmuir probe and RFEA measurements.

117 4.4. Ferro-metallic thin film deposition study 95 Figure 4.33: Separate power dependence of MHz and 71 MHz on sputter deposition rate. Discharge conditions MHz variation are P 71MHz = 100 W, Argon, 2.5 Pa, 10 sccm, target- QCM gap 20 mm. Discharge conditions 71 MHz variation are P 13.56MHz = 400 W, Argon, 2.5 Pa, 10 sccm, target-qcm gap 20 mm Estimation of expected deposition rates and comparison to measurements In order to get an adequate estimation for measured deposition rates, several assumptions have to be made, which are discussed in the following. First, the ion flux density onto the target material needs to be calculated. It is determined by the Bohm velocity and a mean averaged plasma density. To simplify calculations only singly charged argon ions Ar + are considered, such that the number of available ions equals the number of free electrons. The ion flux density is then formulated as Γ Ar + = n e u Bohm = n e kb T e m i (4.11) with n e as the plasma density, k B as the Boltzmann constant, T e the mean electron temperature and m i the ion mass. Because argon ion and neutral atomic masses are nearly equal, the approximation m i = m Ar + m Ar is used. The argon ion flux density and the resulting iron neutral atom flux density Γ Fe are correlated through the sputter yield γ Fe. It defines the number of sputtered target iron atoms per incident argon ion. Additionally, this quantity depends on the impact ion energy. For the performed calculations the ion bombarding energy is determined to be approximately 1000 ev for given process conditions, which gives a sputter yield for iron to γ Fe = 1.3 as found in Matsunami et al. [125]. Γ Fe = Γ Ar + γ Fe (4.12) The given yield γ Fe holds for pure iron targets, however the applied stainless steel and most of its containing metallic alloys, such as chromium and nickel, have a similar sputter yield.

118 96 4. Measurements and discussion In a following step, the iron atom flux density Γ Fe needs to be correlated to actually measured deposition rates. Therefore, the growing film s crystalline structure needs to be known. From literature [106], iron is known to adopt a body-centered cubic (bcc) crystal structure. Only for temperatures above 1185 K its crystal structure changes to face-centered cubic (fcc). This property of changing crystal structure is called allotropy. Using the information on iron crystal structure, the lattice constant a Fe bcc is given by a Fe bcc = 4 3 r Fe = pm (4.13) with r Fe being the iron atomic (Van-der-Waals) radius. The lattice constant is important, because it defines the distance from one monolayer of atoms to an adjacent monolayer. A connection between the lattice constant and deposition rate is provided by the number of monolayers being deposited/etched per second, which in turn has to be expressed by the number of iron atoms arriving at the quartz-crystal microbalance (QCM). The number of monolayers being deposited per second on the QCM s crystal substrate is defined by with ρ A,Fe being the area density of iron atoms as ṅ Fe mono = Γ Fe ρ A,Fe (4.14) ρ A,Fe = N Fe A electrode (4.15) with N Fe as the number of iron atoms per monolayer and A electrode as the total area of the electrically driven electrode. The number of iron atoms per monolayer is found by calculating the mass of a monolayer and dividing it by the iron s atomic mass, such that N Fe = A electrode a Fe bcc ρ Fe m Fe (4.16) where ρ Fe is the iron mass density as g cm 3. Inserting and simplifying equation (4.16) into (4.15) yields expression (4.17) without the electrode area dependence. ρ A,Fe = a Fe bcc ρ Fe m Fe (4.17) Finally, the QCM deposition rate in Angstrom per second (Å/s) is found by multiplying the number of deposited monolayers with the lattice constant. d QCM = ṅ Fe mono a Fe bcc = m Fe ρ Fe Γ Fe (4.18) Now it is possible to calculate backwards to the electron density n e which is necessary to achieve the detected deposition rates. This is done by substituting and reordering equation (4.18) to n e = d QCM ρ Fe m Fe γ Fe u Bohm. (4.19) To quantify the electron density, the maximum detected deposition rate value is inserted, yielding a value of n e = cm 3, which is approximately six times lower than measured

119 4.4. Ferro-metallic thin film deposition study 97 Langmuir probe densities, expected to be cm 3. In order to account for the discrepancy, the mean free path of an iron atom at 2.5 Pa is calculated to be approximately 4 mm, which implies statistically five collisions with neutral gas atoms on its way to the quartz-crystal microbalance. Although most collisions are considered to exert a small change to the iron atom s flight direction, a higher number of collisions significantly increases the angular distribution. Furthermore, ions coming from the plasma bulk towards the target electrode encounter the grounded QCM first, where they are neutralized. These ions are no longer available for sputtering. Therefore an estimation of this loss mechanism is performed on the basis of considering the area ratio of the target and the QCM. It is determined to be 50%. Correcting the iron atom flux density by inserting the determined loss yield γ loss = 0.5 into equation (4.19) gives a revised expression for the electron density. n e = d QCM ρ Fe 0.61 m Fe γ Fe γ loss u Bohm (4.20) Reevaluating equation (4.20) with the same maximum deposition rate value gives n e = cm 3, which still is too low by a factor of three. Additionally considering the difference in electron density between the plasma bulk and the electrode on the basis of a cosine profile would incorporate a factor (0.61) 1 = 1.64, which in turn yields n e = cm 3. Thus, another mechanism is deemed possible to be responsible for such a low plasma density estimation. A likely possibility is that thin film density is significantly deviating from the set density of pure iron within the QCM electronics. Verifying and evaluating this possibility is performed in the following section. Performing additional estimations on the minimum expected deposition rates for a planned scale-up version of the dual frequency PVD setup yields the following results. Assuming a minimum realizable plasma density of n e = cm 3 under similar process conditions gives an approximate deposition rate of at least 17 Å/s. Furthermore, also the power input per area can be calculated by assuming a voltage drop across the sheath on the order of the plasma s dc self bias voltage ( 1000 V). Using the same parameter set gives a power input of 3.5 W/cm Calibration of quartz-crystal microbalance and determination of film density Simultaneous experiments using small silicon wafers attached to the QCM shutter mechanism, provide a reproducible thin film layer thickness of about twice the size of obtained QCM measurements. Indicated values of the QCM were 7.7 µm versus measured 14.4 µm on the silicon wafer samples. A possible explanation for this discrepancy could be a significant change in film mass density, compared to elementary iron. This would happen, e.g. due to a large increase in porosity of the resulting layer. In order to verify the density of deposited films several silicon wafer samples are coated to average out statistical errors. Thin film density is determined by the following procedure: (i) the raw silicon wafer samples are weighed without film, (ii) a thick film of several microns is deposited onto the wafer samples to produce a detectable mass change and (iii) the prepared

120 98 4. Measurements and discussion samples are weighed again to determine the mass difference. For mass density determination the thin film s volume is additionally required. Since the samples have a very well defined area, only the deposited film thickness needs to be determined. This is done by using a contacting profilometer (Veeco Dektak 6M stylus). Figure 4.34: Optical emission spectrum for determination of relative atomic species densities in single frequency VHF operation. Discharge conditions are: Argon, 2.5 Pa, 10 sccm and P 71MHz = 200 W. Left: Full spectrum. Right: Zoomed spectrum. Arrows in both cases indicate either intervals of attributed lines or specific single emission lines. A contacting profilometer uses a probe tip which is brought onto the surface. By scanning the substrate and by passing over the film border, the detected change in height gives the film thickness. Therefore, it is necessary to produce a sharp film border by previously covering a defined area during the deposition process. Having determined the film thickness, the total film volume can be calculated. From the change in mass and volume one is able to calculate the film density using the elementary relation ρ film = V film /m film, yielding ρ film = g cm 3. Comparing this result to ρ Fe gives a deviation of 11% with respect to iron density. This deviation results from neglecting components within the stainless steel target such as chromium (ρ Cr = 7.19 g cm 3 ), nickel (ρ Ni = g cm 3 ), and molybdenum (ρ Mo = g cm 3 ). On the other hand, the found deviation of 11% also lies within the measurement accuracy of the micro-scales, such that the film density is found to very well resemble the mass density of pure iron. Further evidence of additionally sputtered elements is given in section Depending on their respective sputtering yields, the resulting film assembly will consist of different mass ratios than the original steel target, leading to a systematic deviation of the film s mass density. Due to the fact, that measured film thickness is about twice as high as detected by the QCM and film density does not significantly differ from programmed QCM values, the iron atom flux has to be at least twice as large. Simultaneously also plasma density has to increase by a factor of two. Recalculating the electron density on this basis yields an approximated plasma density of cm 3, which agrees to measured Langmuir probe data and lies within measurement accuracy.

121 4.4. Ferro-metallic thin film deposition study Identification of sputtered atomic species and relative densities by optical emission spectroscopy In the previous section, possible issues using a QCM have been identified. One of which addressed the topic of additional chemical elements being incorporated into the film, originating from the stainless steel reference target. Evidence of this is supplied by simultaneous optical emission spectroscopic measurements. Figure 4.35: Optical emission spectrum for determination of relative atomic species densities in dual frequency operation. Discharge conditions are: Argon, 2.5 Pa, 10 sccm, P 13.56MHz = 400 W and P 71MHz = 200 W. Figures 4.34 and 4.35 compare the two modes of single frequency to dual frequency discharge operation at indicated conditions. Thereby, two observations are made. First, the relative argon density decreases (indicated spectral range from 700 nm to 950 nm) and second, simultaneously atomic lines of iron and chromium appear (indicated by according markers) in the visible spectral range. For a quantitative analysis the van Regemorter formula is used to evaluate relative atomic species densities. It correlates the observed intensity of an emission line with the true relative number density of the according species as I rel = η vσ ik n e [F e ] (4.21) where I rel is the observed relative intensity, n e the corresponding electron density, [F e ] the relative number density of the observed species (here: atomic iron) and vσ ik considering related collision cross sections found in literature. Additionally, the electron density ratio is optically evaluated by an admixture of nitrogen. Both evaluations yield the following results. First, the relative electron density ratio is found to reduce by a factor of two from single frequency 71 MHz to dual frequency discharge operation. Relating this to Langmuir probe power variation studies, yields a good agreement and strongly supports the observation of low frequency current exerting a significant influence on total plasma density in PVD operation. Second, the relative atomic density of iron is found to rise by a factor of four for

122 Measurements and discussion Figure 4.36: Atomic force microscopy (AFM) picture of a 56 nm Fe-coated silicon wafer. Roughness is less than 0.54 nm, compared to 0.01 nm of the uncoated silicon wafer. a similar change in discharge operation. This is also in very good agreement to observations by quartz-crystal microbalance measurements. Finally, the roughness of a 56 nm thin film layer is investigated by atomic force microscopy (AFM). The scanned image is presented in figure A roughness of less than 1% of the thickness is achieved, which is within specifications of typical MRAM fabrication. Summarizing the investigations of ferro-metallic thin film deposition: first, the sputter deposition rate has been maximized with respect to given experimental capabilities. Thereby, linear dependencies of each power contribution in single frequency discharge operation were found. Moving to dual frequency discharge mode, the increase in low frequency power did not show an expected dip in deposition rate as gathered by retarding field energy analyzer and optical measurements. However it even further increased. This is explained by the dominant increase in ion bombarding energy, which sufficiently compensates for plasma density (ion flux) losses. This compensation is achieved due to an increase in the energy dependent sputter yield. For iron and with respect to given changes in bombarding energy, the sputter yield changes by one order of magnitude from 0.2 to 2.0 (from Matsunami et al. [125]). Furthermore, a high frequency power variation study unveiled a complex dependence of deposition rate on P 71MHz. By comparing the two-slope curve to single frequency VHF deposition rates, an apparent change in discharge behavior in favor of VHF discharge operation is discovered, if P 71MHz power becomes too high. Finally, elementary thin film parameters have been investigated and a simple model describing the deposition rate and loss mechanisms was developed. All QCM measurements show a good correlation to results gained from previously applied plasma diagnostics, completing the picture of dual frequency capacitive discharges.

Coating Technology: Evaporation Vs Sputtering

Coating Technology: Evaporation Vs Sputtering Satisloh Italy S.r.l. Coating Technology: Evaporation Vs Sputtering Gianni Monaco, PhD R&D project manager, Satisloh Italy 04.04.2016 V1 The aim of this document is to provide basic technical information

More information

A Remote Plasma Sputter Process for High Rate Web Coating of Low Temperature Plastic Film with High Quality Thin Film Metals and Insulators

A Remote Plasma Sputter Process for High Rate Web Coating of Low Temperature Plastic Film with High Quality Thin Film Metals and Insulators A Remote Plasma Sputter Process for High Rate Web Coating of Low Temperature Plastic Film with High Quality Thin Film Metals and Insulators Dr Peter Hockley and Professor Mike Thwaites, Plasma Quest Limited

More information

Vacuum Evaporation Recap

Vacuum Evaporation Recap Sputtering Vacuum Evaporation Recap Use high temperatures at high vacuum to evaporate (eject) atoms or molecules off a material surface. Use ballistic flow to transport them to a substrate and deposit.

More information

Reactive Sputtering Using a Dual-Anode Magnetron System

Reactive Sputtering Using a Dual-Anode Magnetron System Reactive Sputtering Using a Dual-Anode Magnetron System A. Belkind and Z. Zhao, Stevens Institute of Technology, Hoboken, NJ; and D. Carter, G. McDonough, G. Roche, and R. Scholl, Advanced Energy Industries,

More information

Active noise control in practice: transformer station

Active noise control in practice: transformer station Active noise control in practice: transformer station Edwin Buikema 1 ; Fokke D. van der Ploeg 2 ; Jan H. Granneman 3 1, 2, 3 Peutz bv, Netherlands ABSTRACT Based on literature and extensive measurements

More information

How To Make A Plasma Control System

How To Make A Plasma Control System XXII. Erfahrungsaustausch Mühlleiten 2015 Plasmaanalyse und Prozessoptimierung mittels spektroskopischem Plasmamonitoring in industriellen Anwendungen Swen Marke,, Lichtenau Thomas Schütte, Plasus GmbH,

More information

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

More information

High Rate Oxide Deposition onto Web by Reactive Sputtering from Rotatable Magnetrons

High Rate Oxide Deposition onto Web by Reactive Sputtering from Rotatable Magnetrons High Rate Oxide Deposition onto Web by Reactive Sputtering from Rotatable Magnetrons D.Monaghan, V. Bellido-Gonzalez, M. Audronis. B. Daniel Gencoa, Physics Rd, Liverpool, L24 9HP, UK. www.gencoa.com,

More information

Cathode Ray Tube. Introduction. Functional principle

Cathode Ray Tube. Introduction. Functional principle Introduction The Cathode Ray Tube or Braun s Tube was invented by the German physicist Karl Ferdinand Braun in 897 and is today used in computer monitors, TV sets and oscilloscope tubes. The path of the

More information

Impedance Matching and Matching Networks. Valentin Todorow, December, 2009

Impedance Matching and Matching Networks. Valentin Todorow, December, 2009 Impedance Matching and Matching Networks Valentin Todorow, December, 2009 RF for Plasma Processing - Definition of RF What is RF? The IEEE Standard Dictionary of Electrical and Electronics Terms defines

More information

E. K. A. ADVANCED PHYSICS LABORATORY PHYSICS 3081, 4051 NUCLEAR MAGNETIC RESONANCE

E. K. A. ADVANCED PHYSICS LABORATORY PHYSICS 3081, 4051 NUCLEAR MAGNETIC RESONANCE E. K. A. ADVANCED PHYSICS LABORATORY PHYSICS 3081, 4051 NUCLEAR MAGNETIC RESONANCE References for Nuclear Magnetic Resonance 1. Slichter, Principles of Magnetic Resonance, Harper and Row, 1963. chapter

More information

PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS

PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS 1. Photons 2. Photoelectric Effect 3. Experimental Set-up to study Photoelectric Effect 4. Effect of Intensity, Frequency, Potential on P.E.

More information

Chemical Sputtering. von Kohlenstoff durch Wasserstoff. W. Jacob

Chemical Sputtering. von Kohlenstoff durch Wasserstoff. W. Jacob Chemical Sputtering von Kohlenstoff durch Wasserstoff W. Jacob Centre for Interdisciplinary Plasma Science Max-Planck-Institut für Plasmaphysik, 85748 Garching Content: Definitions: Chemical erosion, physical

More information

Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies

Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies Soonwook Hong, Ph. D. Michael Zuercher Martinson Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies 1. Introduction PV inverters use semiconductor devices to transform the

More information

An equivalent circuit of a loop antenna.

An equivalent circuit of a loop antenna. 3.2.1. Circuit Modeling: Loop Impedance A loop antenna can be represented by a lumped circuit when its dimension is small with respect to a wavelength. In this representation, the circuit parameters (generally

More information

2. Deposition process

2. Deposition process Properties of optical thin films produced by reactive low voltage ion plating (RLVIP) Antje Hallbauer Thin Film Technology Institute of Ion Physics & Applied Physics University of Innsbruck Investigations

More information

A wave lab inside a coaxial cable

A wave lab inside a coaxial cable INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S0143-0807(04)76273-X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera

More information

MEASUREMENT SET-UP FOR TRAPS

MEASUREMENT SET-UP FOR TRAPS Completed on 26th of June, 2012 MEASUREMENT SET-UP FOR TRAPS AUTHOR: IW2FND Attolini Lucio Via XXV Aprile, 52/B 26037 San Giovanni in Croce (CR) - Italy iw2fnd@gmail.com Trappole_01_EN 1 1 DESCRIPTION...3

More information

Neuere Entwicklungen zur Herstellung optischer Schichten durch reaktive. Wolfgang Hentsch, Dr. Reinhard Fendler. FHR Anlagenbau GmbH

Neuere Entwicklungen zur Herstellung optischer Schichten durch reaktive. Wolfgang Hentsch, Dr. Reinhard Fendler. FHR Anlagenbau GmbH Neuere Entwicklungen zur Herstellung optischer Schichten durch reaktive Sputtertechnologien Wolfgang Hentsch, Dr. Reinhard Fendler FHR Anlagenbau GmbH Germany Contents: 1. FHR Anlagenbau GmbH in Brief

More information

X2Y Solution for Decoupling Printed Circuit Boards

X2Y Solution for Decoupling Printed Circuit Boards Summary As printed circuit board s (PCB) power distribution systems (PDS) gain in complexity (i.e. multiple voltages and lower voltages levels) the sensitivity to transients and noise voltage is becoming

More information

Lecture 12. Physical Vapor Deposition: Evaporation and Sputtering Reading: Chapter 12. ECE 6450 - Dr. Alan Doolittle

Lecture 12. Physical Vapor Deposition: Evaporation and Sputtering Reading: Chapter 12. ECE 6450 - Dr. Alan Doolittle Lecture 12 Physical Vapor Deposition: Evaporation and Sputtering Reading: Chapter 12 Evaporation and Sputtering (Metalization) Evaporation For all devices, there is a need to go from semiconductor to metal.

More information

AS COMPETITION PAPER 2008

AS COMPETITION PAPER 2008 AS COMPETITION PAPER 28 Name School Town & County Total Mark/5 Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question

More information

h e l p s y o u C O N T R O L

h e l p s y o u C O N T R O L contamination analysis for compound semiconductors ANALYTICAL SERVICES B u r i e d d e f e c t s, E v a n s A n a l y t i c a l g r o u p h e l p s y o u C O N T R O L C O N T A M I N A T I O N Contamination

More information

ELECTRON SPIN RESONANCE Last Revised: July 2007

ELECTRON SPIN RESONANCE Last Revised: July 2007 QUESTION TO BE INVESTIGATED ELECTRON SPIN RESONANCE Last Revised: July 2007 How can we measure the Landé g factor for the free electron in DPPH as predicted by quantum mechanics? INTRODUCTION Electron

More information

SALES SPECIFICATION. SC7640 Auto/Manual High Resolution Sputter Coater

SALES SPECIFICATION. SC7640 Auto/Manual High Resolution Sputter Coater SALES SPECIFICATION SC7640 Auto/Manual High Resolution Sputter Coater Document Number SS-SC7640 Issue 1 (01/02) Disclaimer The components and packages described in this document are mutually compatible

More information

Development of New Inkjet Head Applying MEMS Technology and Thin Film Actuator

Development of New Inkjet Head Applying MEMS Technology and Thin Film Actuator Development of New Inkjet Head Applying MEMS Technology and Thin Film Actuator Kenji MAWATARI, Koich SAMESHIMA, Mitsuyoshi MIYAI, Shinya MATSUDA Abstract We developed a new inkjet head by applying MEMS

More information

Understanding Power Impedance Supply for Optimum Decoupling

Understanding Power Impedance Supply for Optimum Decoupling Introduction Noise in power supplies is not only caused by the power supply itself, but also the load s interaction with the power supply (i.e. dynamic loads, switching, etc.). To lower load induced noise,

More information

bulk 5. Surface Analysis Why surface Analysis? Introduction Methods: XPS, AES, RBS

bulk 5. Surface Analysis Why surface Analysis? Introduction Methods: XPS, AES, RBS 5. Surface Analysis Introduction Methods: XPS, AES, RBS Autumn 2011 Experimental Methods in Physics Marco Cantoni Why surface Analysis? Bulk: structural function Electrical/thermal conduction Volume increases

More information

Troubleshooting accelerometer installations

Troubleshooting accelerometer installations Troubleshooting accelerometer installations Accelerometer based monitoring systems can be tested to verify proper installation and operation. Testing ensures data integrity and can identify most problems.

More information

Grounding Demystified

Grounding Demystified Grounding Demystified 3-1 Importance Of Grounding Techniques 45 40 35 30 25 20 15 10 5 0 Grounding 42% Case 22% Cable 18% Percent Used Filter 12% PCB 6% Grounding 42% Case Shield 22% Cable Shielding 18%

More information

For Touch Panel and LCD Sputtering/PECVD/ Wet Processing

For Touch Panel and LCD Sputtering/PECVD/ Wet Processing production Systems For Touch Panel and LCD Sputtering/PECVD/ Wet Processing Pilot and Production Systems Process Solutions with over 20 Years of Know-how Process Technology at a Glance for Touch Panel,

More information

SECTION 13. Multipliers. Outline of Multiplier Design Process:

SECTION 13. Multipliers. Outline of Multiplier Design Process: SECTION 13 Multipliers VMI manufactures many high voltage multipliers, most of which are custom designed for specific requirements. The following information provides general information and basic guidance

More information

Electron Beam and Sputter Deposition Choosing Process Parameters

Electron Beam and Sputter Deposition Choosing Process Parameters Electron Beam and Sputter Deposition Choosing Process Parameters General Introduction The choice of process parameters for any process is determined not only by the physics and/or chemistry of the process,

More information

Micro Power Generators. Sung Park Kelvin Yuk ECS 203

Micro Power Generators. Sung Park Kelvin Yuk ECS 203 Micro Power Generators Sung Park Kelvin Yuk ECS 203 Overview Why Micro Power Generators are becoming important Types of Micro Power Generators Power Generators Reviewed Ambient Vibrational energy Radiant

More information

PHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator.

PHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator. PHYS 222 Spring 2012 Final Exam Closed books, notes, etc. No electronic device except a calculator. NAME: (all questions with equal weight) 1. If the distance between two point charges is tripled, the

More information

Preface Light Microscopy X-ray Diffraction Methods

Preface Light Microscopy X-ray Diffraction Methods Preface xi 1 Light Microscopy 1 1.1 Optical Principles 1 1.1.1 Image Formation 1 1.1.2 Resolution 3 1.1.3 Depth of Field 5 1.1.4 Aberrations 6 1.2 Instrumentation 8 1.2.1 Illumination System 9 1.2.2 Objective

More information

ION ENERGY DISTRIBUTION FUNCTION MEASURED BY RETARDING FIELD ENERGY ANALYZERS

ION ENERGY DISTRIBUTION FUNCTION MEASURED BY RETARDING FIELD ENERGY ANALYZERS ION ENERGY DISTRIBUTION FUNCTION MEASURED BY RETARDING FIELD ENERGY ANALYZERS Laboratoire de Physique des Plasmas Ane Aanesland CNRS Ecole Polytechnique France Overview 1. Principle and requirements for

More information

Chapter 7-1. Definition of ALD

Chapter 7-1. Definition of ALD Chapter 7-1 Atomic Layer Deposition (ALD) Definition of ALD Brief history of ALD ALD process and equipments ALD applications 1 Definition of ALD ALD is a method of applying thin films to various substrates

More information

State of the art in reactive magnetron sputtering

State of the art in reactive magnetron sputtering State of the art in reactive magnetron sputtering T. Nyberg, O. Kappertz, T. Kubart and S. Berg Solid State Electronics, The Ångström Laboratory, Uppsala University, Box 534, S-751 21 Uppsala, Sweden D.

More information

RF Network Analyzer Basics

RF Network Analyzer Basics RF Network Analyzer Basics A tutorial, information and overview about the basics of the RF Network Analyzer. What is a Network Analyzer and how to use them, to include the Scalar Network Analyzer (SNA),

More information

A NEAR FIELD INJECTION MODEL FOR SUSCEPTIBILITY PREDICTION IN INTEGRATED CIRCUITS

A NEAR FIELD INJECTION MODEL FOR SUSCEPTIBILITY PREDICTION IN INTEGRATED CIRCUITS ICONIC 2007 St. Louis, MO, USA June 27-29, 2007 A NEAR FIELD INJECTION MODEL FOR SUSCEPTIBILITY PREDICTION IN INTEGRATED CIRCUITS Ali Alaeldine 12, Alexandre Boyer 3, Richard Perdriau 1, Sonia Ben Dhia

More information

It has long been a goal to achieve higher spatial resolution in optical imaging and

It has long been a goal to achieve higher spatial resolution in optical imaging and Nano-optical Imaging using Scattering Scanning Near-field Optical Microscopy Fehmi Yasin, Advisor: Dr. Markus Raschke, Post-doc: Dr. Gregory Andreev, Graduate Student: Benjamin Pollard Department of Physics,

More information

Issues and Solutions for Dealing With a Highly Capacitive Transmission Cable

Issues and Solutions for Dealing With a Highly Capacitive Transmission Cable Issues and Solutions for Dealing With a Highly Capacitive Transmission Cable F.N. Morgan and K.C. Cameron, Advanced Energy Industries, Inc., Fort Collins, CO ABSTRACT For glass coaters, the transmission

More information

Sputtered AlN Thin Films on Si and Electrodes for MEMS Resonators: Relationship Between Surface Quality Microstructure and Film Properties

Sputtered AlN Thin Films on Si and Electrodes for MEMS Resonators: Relationship Between Surface Quality Microstructure and Film Properties Sputtered AlN Thin Films on and Electrodes for MEMS Resonators: Relationship Between Surface Quality Microstructure and Film Properties S. Mishin, D. R. Marx and B. Sylvia, Advanced Modular Sputtering,

More information

MEASUREMENT UNCERTAINTY IN VECTOR NETWORK ANALYZER

MEASUREMENT UNCERTAINTY IN VECTOR NETWORK ANALYZER MEASUREMENT UNCERTAINTY IN VECTOR NETWORK ANALYZER W. Li, J. Vandewege Department of Information Technology (INTEC) University of Gent, St.Pietersnieuwstaat 41, B-9000, Gent, Belgium Abstract: Precision

More information

Iron Powder Cores for Switchmode Power Supply Inductors. by: Jim Cox

Iron Powder Cores for Switchmode Power Supply Inductors. by: Jim Cox HOME APPLICATION NOTES Iron Powder Cores for Switchmode Power Supply Inductors by: Jim Cox Purpose: The purpose of this application note is to cover the properties of iron powder as a magnetic core material

More information

Evaluating AC Current Sensor Options for Power Delivery Systems

Evaluating AC Current Sensor Options for Power Delivery Systems Evaluating AC Current Sensor Options for Power Delivery Systems State-of-the-art isolated ac current sensors based on CMOS technology can increase efficiency, performance and reliability compared to legacy

More information

Spectroscopy. Biogeochemical Methods OCN 633. Rebecca Briggs

Spectroscopy. Biogeochemical Methods OCN 633. Rebecca Briggs Spectroscopy Biogeochemical Methods OCN 633 Rebecca Briggs Definitions of Spectrometry Defined by the method used to prepare the sample 1. Optical spectrometry Elements are converted to gaseous atoms or

More information

Chapter 8. Low energy ion scattering study of Fe 4 N on Cu(100)

Chapter 8. Low energy ion scattering study of Fe 4 N on Cu(100) Low energy ion scattering study of 4 on Cu(1) Chapter 8. Low energy ion scattering study of 4 on Cu(1) 8.1. Introduction For a better understanding of the reconstructed 4 surfaces one would like to know

More information

Experimental results for the focal waveform and beam width in the focusing lens with a 100 ps filter

Experimental results for the focal waveform and beam width in the focusing lens with a 100 ps filter EM Implosion Memos Memo 51 July, 2010 Experimental results for the focal waveform and beam width in the focusing lens with a 100 ps filter Prashanth Kumar, Carl E. Baum, Serhat Altunc, Christos G. Christodoulou

More information

Scanning Near Field Optical Microscopy: Principle, Instrumentation and Applications

Scanning Near Field Optical Microscopy: Principle, Instrumentation and Applications Scanning Near Field Optical Microscopy: Principle, Instrumentation and Applications Saulius Marcinkevičius Optics, ICT, KTH 1 Outline Optical near field. Principle of scanning near field optical microscope

More information

Module 11: Conducted Emissions

Module 11: Conducted Emissions Module 11: Conducted Emissions 11.1 Overview The term conducted emissions refers to the mechanism that enables electromagnetic energy to be created in an electronic device and coupled to its AC power cord.

More information

Silicon-On-Glass MEMS. Design. Handbook

Silicon-On-Glass MEMS. Design. Handbook Silicon-On-Glass MEMS Design Handbook A Process Module for a Multi-User Service Program A Michigan Nanofabrication Facility process at the University of Michigan March 2007 TABLE OF CONTENTS Chapter 1...

More information

PHYSICS PAPER 1 (THEORY)

PHYSICS PAPER 1 (THEORY) PHYSICS PAPER 1 (THEORY) (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) ---------------------------------------------------------------------------------------------------------------------

More information

Relationship between large subject matter areas

Relationship between large subject matter areas H02M APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER;

More information

Ion Beam Sputtering: Practical Applications to Electron Microscopy

Ion Beam Sputtering: Practical Applications to Electron Microscopy Ion Beam Sputtering: Practical Applications to Electron Microscopy Applications Laboratory Report Introduction Electron microscope specimens, both scanning (SEM) and transmission (TEM), often require a

More information

Dry Etching and Reactive Ion Etching (RIE)

Dry Etching and Reactive Ion Etching (RIE) Dry Etching and Reactive Ion Etching (RIE) MEMS 5611 Feb 19 th 2013 Shengkui Gao Contents refer slides from UC Berkeley, Georgia Tech., KU, etc. (see reference) 1 Contents Etching and its terminologies

More information

- particle with kinetic energy E strikes a barrier with height U 0 > E and width L. - classically the particle cannot overcome the barrier

- particle with kinetic energy E strikes a barrier with height U 0 > E and width L. - classically the particle cannot overcome the barrier Tunnel Effect: - particle with kinetic energy E strikes a barrier with height U 0 > E and width L - classically the particle cannot overcome the barrier - quantum mechanically the particle can penetrated

More information

By Randy Heckman, Gregory Roche, James R. Usher of Advanced Energy Industries, Inc.

By Randy Heckman, Gregory Roche, James R. Usher of Advanced Energy Industries, Inc. WHITEPAPER By Randy Heckman, Gregory Roche, James R. Usher of Advanced Energy Industries, Inc. THE EVOLUTION OF RF POWER DELIVERY IN Radio frequency (RF) technology has been around since the beginnings

More information

Candidate Number. General Certificate of Education Advanced Level Examination June 2014

Candidate Number. General Certificate of Education Advanced Level Examination June 2014 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 214 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Wednesday

More information

Application Note, Rev.1.0, September 2008 TLE8366. Application Information. Automotive Power

Application Note, Rev.1.0, September 2008 TLE8366. Application Information. Automotive Power Application Note, Rev.1.0, September 2008 TLE8366 Automotive Power Table of Contents 1 Abstract...3 2 Introduction...3 3 Dimensioning the Output and Input Filter...4 3.1 Theory...4 3.2 Output Filter Capacitor(s)

More information

Implementation Of High-k/Metal Gates In High-Volume Manufacturing

Implementation Of High-k/Metal Gates In High-Volume Manufacturing White Paper Implementation Of High-k/Metal Gates In High-Volume Manufacturing INTRODUCTION There have been significant breakthroughs in IC technology in the past decade. The upper interconnect layers of

More information

Quantum Computing for Beginners: Building Qubits

Quantum Computing for Beginners: Building Qubits Quantum Computing for Beginners: Building Qubits Suzanne Gildert Condensed Matter Physics Research (Quantum Devices Group) University of Birmingham 28/03/2007 Overview of this presentation What is a Qubit?

More information

Cumbria Designs T-1. SSB/CW Filter kit (4.9152MHz) User Manual

Cumbria Designs T-1. SSB/CW Filter kit (4.9152MHz) User Manual Cumbria Designs T-1 SSB/CW Filter kit (4.9152MHz) User Manual CONTENTS 1 INTRODUCTION 2 2 CIRCUIT DESCRIPTION 2 3 ASSEMBLY 2 4 TESTING 4 The Steading Stainton PENRITH Cumbria CA11 0ES UK 1 Introduction

More information

for Communication Systems Protection EMI CD-ROM INCLUDED

for Communication Systems Protection EMI CD-ROM INCLUDED Krešimir Malarić EMI Protection for Communication Systems CD-ROM INCLUDED Contents Preface xiii CHAPTER 1 Communications Systems 1 1.1 Components of Communications Systems 1 1.2 Transmitter Systems 2 1.2.1

More information

Process Diagnostics of Industrial Plasma Systems

Process Diagnostics of Industrial Plasma Systems Process Diagnostics of Industrial Plasma Systems A thesis for the degree of PHILOSOPHIAE DOCTOR Presented to Dublin City University By Niall Mac Gearailt B.Eng. Faculty of Engineering and Computing Dublin

More information

When designing. Inductors at UHF: EM Simulation Guides Vector Network Analyzer. measurement. EM SIMULATION. There are times when it is

When designing. Inductors at UHF: EM Simulation Guides Vector Network Analyzer. measurement. EM SIMULATION. There are times when it is Inductors at UHF: EM Simulation Guides Vector Network Analyzer Measurements John B. Call Thales Communications Inc., USA When designing There are times when it is circuits for necessary to measure a operation

More information

High Voltage Power Supplies for Analytical Instrumentation

High Voltage Power Supplies for Analytical Instrumentation ABSTRACT High Voltage Power Supplies for Analytical Instrumentation by Cliff Scapellati Power supply requirements for Analytical Instrumentation are as varied as the applications themselves. Power supply

More information

Department of Aerospace Engineering Indian Institute of Science Bangalore

Department of Aerospace Engineering Indian Institute of Science Bangalore Department of Aerospace Engineering Indian Institute of Science Bangalore Brief Outline of Department The department of Aerospace Engineering is one of the oldest departments in the country encompassing

More information

Modification of Pd-H 2 and Pd-D 2 thin films processed by He-Ne laser

Modification of Pd-H 2 and Pd-D 2 thin films processed by He-Ne laser Modification of Pd-H 2 and Pd-D 2 thin films processed by He-Ne laser V.Nassisi #, G.Caretto #, A. Lorusso #, D.Manno %, L.Famà %, G.Buccolieri %, A.Buccolieri %, U.Mastromatteo* # Laboratory of Applied

More information

3 - Atomic Absorption Spectroscopy

3 - Atomic Absorption Spectroscopy 3 - Atomic Absorption Spectroscopy Introduction Atomic-absorption (AA) spectroscopy uses the absorption of light to measure the concentration of gas-phase atoms. Since samples are usually liquids or solids,

More information

Robert G. Hunsperger. Integrated Optics. Theory and Technology. Fourth Edition. With 195 Figures and 17 Tables. Springer

Robert G. Hunsperger. Integrated Optics. Theory and Technology. Fourth Edition. With 195 Figures and 17 Tables. Springer Robert G. Hunsperger Integrated Optics Theory and Technology Fourth Edition With 195 Figures and 17 Tables Springer Contents 1. Introduction 1 1.1 Advantages of Integrated Optics 2 1.1.1 Comparison of

More information

AVX EMI SOLUTIONS Ron Demcko, Fellow of AVX Corporation Chris Mello, Principal Engineer, AVX Corporation Brian Ward, Business Manager, AVX Corporation

AVX EMI SOLUTIONS Ron Demcko, Fellow of AVX Corporation Chris Mello, Principal Engineer, AVX Corporation Brian Ward, Business Manager, AVX Corporation AVX EMI SOLUTIONS Ron Demcko, Fellow of AVX Corporation Chris Mello, Principal Engineer, AVX Corporation Brian Ward, Business Manager, AVX Corporation Abstract EMC compatibility is becoming a key design

More information

S-Band Low Noise Amplifier Using the ATF-10136. Application Note G004

S-Band Low Noise Amplifier Using the ATF-10136. Application Note G004 S-Band Low Noise Amplifier Using the ATF-10136 Application Note G004 Introduction This application note documents the results of using the ATF-10136 in low noise amplifier applications at S band. The ATF-10136

More information

Welding of Plastics. Amit Mukund Joshi. (B.E Mechanical, A.M.I.Prod.E)

Welding of Plastics. Amit Mukund Joshi. (B.E Mechanical, A.M.I.Prod.E) Welding of Plastics Amit Mukund Joshi (B.E Mechanical, A.M.I.Prod.E) Introduction Mechanical fasteners, adhesives, and welding processes can all be employed to form joints between engineering plastics.

More information

Scanning Probe Microscopy

Scanning Probe Microscopy Ernst Meyer Hans Josef Hug Roland Bennewitz Scanning Probe Microscopy The Lab on a Tip With 117 Figures Mß Springer Contents 1 Introduction to Scanning Probe Microscopy f f.1 Overview 2 f.2 Basic Concepts

More information

Simulation and Design of Printed Circuit Boards Utilizing Novel Embedded Capacitance Material

Simulation and Design of Printed Circuit Boards Utilizing Novel Embedded Capacitance Material Simulation and Design of Printed Circuit Boards Utilizing Novel Embedded Capacitance Material Yu Xuequan, Yan Hang, Zhang Gezi, Wang Haisan Huawei Technologies Co., Ltd Lujiazui Subpark, Pudong Software

More information

This paper describes Digital Equipment Corporation Semiconductor Division s

This paper describes Digital Equipment Corporation Semiconductor Division s WHITEPAPER By Edd Hanson and Heather Benson-Woodward of Digital Semiconductor Michael Bonner of Advanced Energy Industries, Inc. This paper describes Digital Equipment Corporation Semiconductor Division

More information

Transistor Characteristics and Single Transistor Amplifier Sept. 8, 1997

Transistor Characteristics and Single Transistor Amplifier Sept. 8, 1997 Physics 623 Transistor Characteristics and Single Transistor Amplifier Sept. 8, 1997 1 Purpose To measure and understand the common emitter transistor characteristic curves. To use the base current gain

More information

Current Probes, More Useful Than You Think

Current Probes, More Useful Than You Think Current Probes, More Useful Than You Think Training and design help in most areas of Electrical Engineering Copyright 1998 Institute of Electrical and Electronics Engineers. Reprinted from the IEEE 1998

More information

Module 7 Wet and Dry Etching. Class Notes

Module 7 Wet and Dry Etching. Class Notes Module 7 Wet and Dry Etching Class Notes 1. Introduction Etching techniques are commonly used in the fabrication processes of semiconductor devices to remove selected layers for the purposes of pattern

More information

Critical thin-film processes such as deposition and etching take place in a vacuum

Critical thin-film processes such as deposition and etching take place in a vacuum WHITEPAPER INTRODUCING POWER SUPPLIES AND PLASMA Critical thin-film processes such as deposition and etching take place in a vacuum SYSTEMS chamber in the presence of a plasma. A plasma is an electrically

More information

Overview. also give you an idea of ANSYS capabilities. In this chapter, we will define Finite Element Analysis and. Topics covered: B.

Overview. also give you an idea of ANSYS capabilities. In this chapter, we will define Finite Element Analysis and. Topics covered: B. 2. FEA and ANSYS FEA and ANSYS Overview In this chapter, we will define Finite Element Analysis and also give you an idea of ANSYS capabilities. Topics covered: A. What is FEA? B. About ANSYS FEA and ANSYS

More information

APPLICATION NOTE ULTRASONIC CERAMIC TRANSDUCERS

APPLICATION NOTE ULTRASONIC CERAMIC TRANSDUCERS APPLICATION NOTE ULTRASONIC CERAMIC TRANSDUCERS Selection and use of Ultrasonic Ceramic Transducers The purpose of this application note is to aid the user in the selection and application of the Ultrasonic

More information

Power Electronics. Prof. K. Gopakumar. Centre for Electronics Design and Technology. Indian Institute of Science, Bangalore.

Power Electronics. Prof. K. Gopakumar. Centre for Electronics Design and Technology. Indian Institute of Science, Bangalore. Power Electronics Prof. K. Gopakumar Centre for Electronics Design and Technology Indian Institute of Science, Bangalore Lecture - 1 Electric Drive Today, we will start with the topic on industrial drive

More information

UNIT I: INTRFERENCE & DIFFRACTION Div. B Div. D Div. F INTRFERENCE

UNIT I: INTRFERENCE & DIFFRACTION Div. B Div. D Div. F INTRFERENCE 107002: EngineeringPhysics Teaching Scheme: Lectures: 4 Hrs/week Practicals-2 Hrs./week T.W.-25 marks Examination Scheme: Paper-50 marks (2 hrs) Online -50marks Prerequisite: Basics till 12 th Standard

More information

Physics 441/2: Transmission Electron Microscope

Physics 441/2: Transmission Electron Microscope Physics 441/2: Transmission Electron Microscope Introduction In this experiment we will explore the use of transmission electron microscopy (TEM) to take us into the world of ultrasmall structures. This

More information

Coating Thickness and Composition Analysis by Micro-EDXRF

Coating Thickness and Composition Analysis by Micro-EDXRF Application Note: XRF Coating Thickness and Composition Analysis by Micro-EDXRF www.edax.com Coating Thickness and Composition Analysis by Micro-EDXRF Introduction: The use of coatings in the modern manufacturing

More information

Candidate Number. General Certificate of Education Advanced Level Examination June 2010

Candidate Number. General Certificate of Education Advanced Level Examination June 2010 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 1 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Friday 18

More information

Active Vibration Isolation of an Unbalanced Machine Spindle

Active Vibration Isolation of an Unbalanced Machine Spindle UCRL-CONF-206108 Active Vibration Isolation of an Unbalanced Machine Spindle D. J. Hopkins, P. Geraghty August 18, 2004 American Society of Precision Engineering Annual Conference Orlando, FL, United States

More information

Paper No. 4071 APPLICATION OF EQCM TO THE STUDY OF CO2 CORROSION

Paper No. 4071 APPLICATION OF EQCM TO THE STUDY OF CO2 CORROSION Paper No. 471 APPLICATION OF EQCM TO THE STUDY OF CO2 CORROSION Yang Yang, Bruce Brown and Srdjan Nešić Institute for Corrosion and Multiphase Technology, Department of Chemical and Biomolecular Engineering

More information

Acousto-optic modulator

Acousto-optic modulator 1 of 3 Acousto-optic modulator F An acousto-optic modulator (AOM), also called a Bragg cell, uses the acousto-optic effect to diffract and shift the frequency of light using sound waves (usually at radio-frequency).

More information

TOF FUNDAMENTALS TUTORIAL

TOF FUNDAMENTALS TUTORIAL TOF FUNDAMENTALS TUTORIAL Presented By: JORDAN TOF PRODUCTS, INC. 990 Golden Gate Terrace Grass Valley, CA 95945 530-272-4580 / 530-272-2955 [fax] www.rmjordan.com [web] info@rmjordan.com [e-mail] This

More information

Oscillators. 2.0 RF Sine Wave Oscillators. www.learnabout-electronics.org. Module. RF Oscillators

Oscillators. 2.0 RF Sine Wave Oscillators. www.learnabout-electronics.org. Module. RF Oscillators Module 2 www.learnabout-electronics.org Oscillators 2.0 RF Sine Wave Oscillators What you ll Learn in Module 2 Section 2.0 High Frequency Sine Wave Oscillators. Frequency Control in RF Oscillators. LC

More information

Physics 30 Worksheet # 14: Michelson Experiment

Physics 30 Worksheet # 14: Michelson Experiment Physics 30 Worksheet # 14: Michelson Experiment 1. The speed of light found by a Michelson experiment was found to be 2.90 x 10 8 m/s. If the two hills were 20.0 km apart, what was the frequency of the

More information

View of ΣIGMA TM (Ref. 1)

View of ΣIGMA TM (Ref. 1) Overview of the FESEM system 1. Electron optical column 2. Specimen chamber 3. EDS detector [Electron Dispersive Spectroscopy] 4. Monitors 5. BSD (Back scatter detector) 6. Personal Computer 7. ON/STANDBY/OFF

More information

Candidate Number. General Certificate of Education Advanced Level Examination June 2012

Candidate Number. General Certificate of Education Advanced Level Examination June 2012 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 212 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Monday

More information

Indiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance.

Indiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance. .1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations

More information

Diagnostics. Electric probes. Instituto de Plasmas e Fusão Nuclear Instituto Superior Técnico Lisbon, Portugal http://www.ipfn.ist.utl.

Diagnostics. Electric probes. Instituto de Plasmas e Fusão Nuclear Instituto Superior Técnico Lisbon, Portugal http://www.ipfn.ist.utl. Diagnostics Electric probes Instituto de Plasmas e Fusão Nuclear Instituto Superior Técnico Lisbon, Portugal http://www.ipfn.ist.utl.pt Langmuir probes Simplest diagnostic (1920) conductor immerse into

More information

Understanding the p-n Junction by Dr. Alistair Sproul Senior Lecturer in Photovoltaics The Key Centre for Photovoltaic Engineering, UNSW

Understanding the p-n Junction by Dr. Alistair Sproul Senior Lecturer in Photovoltaics The Key Centre for Photovoltaic Engineering, UNSW Understanding the p-n Junction by Dr. Alistair Sproul Senior Lecturer in Photovoltaics The Key Centre for Photovoltaic Engineering, UNSW The p-n junction is the fundamental building block of the electronic

More information