Characterization of multiple frequency driven capacitively coupled ...€¦ · Characterization of multiple frequency driven capacitively coupled plasmas for ferro-metallic thin lm

RUHR-UNIVERSITÄT BOCHUM

Characterization of multiple frequency driven

capacitively coupled plasmas for ferro-metallic thin

film sputter deposition

Dissertation

zur Erlangung des Grades einesDoktor-Ingenieurs

der Fakultat fur Elektrotechnik und Informationstechnikan der Ruhr-Universitat Bochum

Egmont Semmler

Bochum 2008

Dissertation eingereicht am: 29.05.2008Tag der mundlichen Prufung: 14.08.2008

Berichter: Prof. Dr.-Ing. Peter AwakowiczProf. Dr. rer. nat. Achim von Keudell

Contents i

Contents

Important symbols and abbreviations iii

List of figures xi

Abstract xv

1 Introduction 1

1.1 Common thin film deposition techniques . . . . . . . . . . . . . . . . . . . . 11.2 Multiple frequency driven capacitively coupled plasmas . . . . . . . . . . . . 31.3 Multiple frequency CCPs for PVD of ferro-metallic / magnetic materials . . 51.4 Thesis layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Experimental setup 7

2.1 Constructional design properties . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Electrical characterization by vector network analyzer measurements . . . . . 10

2.2.1 Evaluation of the impedance matching networks . . . . . . . . . . . . 122.2.2 Chamber characterization and equivalent circuit model for the electri-

cal feed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Plasma and thin film diagnostics 25

3.1 Voltage current (VI) probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.1.1 Plasma impedance determination in multiple frequency capacitive plas-

mas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2 Langmuir probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2.1 Compensation schemes and application in multifrequency plasmas . . 383.3 Phase resolved optical emission spectroscopy (PROES) . . . . . . . . . . . . 413.4 Self excited electron resonance spectroscopy (SEERS) / Plasma series reso-

nance (PSR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.4.1 Nonlinear electron resonance heating (NERH) . . . . . . . . . . . . . 493.4.2 Correlation of measured PSR currents to PROES . . . . . . . . . . . 503.4.3 Comparison of measured SEERS/PSR currents to model calculations 52

3.5 Retarding field energy analyzer (RFEA) . . . . . . . . . . . . . . . . . . . . 533.5.1 Ion velocity/energy distribution function measurement . . . . . . . . 56

3.6 Quartz crystal microbalance (QCM) . . . . . . . . . . . . . . . . . . . . . . . 59

4 Measurements and discussion 63

4.1 Variation of external parameters for VHF / 13.56 MHz CCP operation . . . 634.1.1 Frequency ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

ii Contents

4.1.2 Power ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.1.3 Pressure variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2 Influence of the relative phase at integer driving frequency ratios . . . . . . . 794.2.1 Langmuir probe results . . . . . . . . . . . . . . . . . . . . . . . . . . 804.2.2 PROES and SEERS/PSR measurements . . . . . . . . . . . . . . . . 83

4.3 Ion energy distribution measurements . . . . . . . . . . . . . . . . . . . . . . 874.3.1 Voltage ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.3.2 Frequency ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.4 Ferro-metallic thin film deposition study . . . . . . . . . . . . . . . . . . . . 904.4.1 Optimization of sputter deposition rate . . . . . . . . . . . . . . . . . 904.4.2 Estimation of expected deposition rates and comparison to measurements 954.4.3 Calibration of quartz-crystal microbalance and determination of film

density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.4.4 Identification of sputtered atomic species and relative densities by op-

tical emission spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . 99

5 Conclusions and outlook 101

Bibliography 105

Symbols and Abbreviations iii

Important symbols and abbreviations

Symbols

a1...2 Incident wave amplitudes

Aelectrode Area of driven electrode

aFe bcc Lattice constant of Iron (body-centered cubic)

Ai Effective decay rate of excitation level i

Aik Transition rate from excitation level i to k

AProbe Area of Langmuir probe tip

Aq Area of quartz-crystal substrate

b1...2 Outgoing wave amplitudes

BPSR Plasma series resonance bandwidth

C2M xxx Capacitive element of 2 MHz matching network

C13M xxx Capacitive element of 13.56 MHz matching network

Cacs Equivalent acoustic impedance capacitor

CContact Contact capacitance matchbox output to copper feed

Cel Capacitance of metallized quartz-crystal substrate

CFeed Capacitive coupling of vacuum feed-through

CScrews Capacitive coupling of vacuum feed screws

CSheath Plasma boundary sheath capacitance

CVHF xxx Capacitive element of VHF matching network

CVacuum Capacitance of vacuum electrodes

df Film thickness

dq Quartz-crystal substrate thickness

dQCM Film deposition rate [A/s]

~Drf(t) Electrical displacement field

ε0 Vacuum permittivity

εq Relative permittivity of quartz

εr Relative permittivity

e Electron charge

E Mean (ion/electron) energy

∆E IEDF energy spread (peak separation)

Ei(t) Excitation function

iv Symbols and Abbreviations

φ Relative phase angle

∆Φ Potential difference

Φcoil Magnetic flux in Rogowski coil

Φfloat Floating potential

Φplasma Plasma potential

f2MHz Frequency of 2 MHz

f13.56MHz Frequency of 13.56 MHz

f14MHz Frequency of 14 MHz

fcoated Coated quartz substrate oscillation frequency

fion(v) Ion velocity distribution function

fMSRF Motional series resonance frequency

fpe Electron plasma frequency

fPSR Plasma series resonance frequency

fq Quartz-crystal substrate oscillation frequency

fv,elec(E) Velocity distribution function in energy space

fVHF Variable VHF frequency (60− 90 MHz)

gik Escape factor

ΓAr+ Ion flux density of Argon ions

ΓFe Flux density of Iron atoms

γFe Sputtering yield of Iron

γloss Flux loss factor

ηall Overall electrical system efficiency

ηchamber Vacuum feed-through loss factor

ηmatching Impedance matching network electrical efficiency

ηsource Maximum amplifier efficiency

Hpower Power transmission function

Hrf(t) Magnetic field

Hvoltage Voltage transmission function

Ii Current at network port i

Iprobe Langmuir probe current

Iretard Electron retarding current

Irf(t) RF current through VI probe

Isat,elec Electron saturation current

Isat,ion Ion saturation current

Jrf(t) RF current density (VI probe)

κ Frequency ratio in 2f-CCP operation

kB Boltzmann constant

kq Collisional de-excitation coefficient

λDebye Debye-Huckel length

L Effective plasma bulk length

Symbols and Abbreviations v

L2M xxx Inductive element of 2 MHz matching network

L13M xxx Inductive element of 13.56 MHz matching network

Lacs Equivalent acoustic impedance inductor

LBulk Plasma bulk inductance

LRod Copper feed inductance at high frequencies

LScrews Inductive coupling of vacuum feed screws

LVHF xxx Inductive element of VHF matching network

µ0 Vacuum permeability

µf Shear modulus of quartz

µr Relative permeability

mAr Atomic mass of Argon

Mcoil Rogowski coil inductance

me Electron mass

mFe Atomic mass of Iron

mi Ion mass (general)

νm Effective electron-neutral collision frequency

n0 Ground state population density

Ncoil Number of coil turns (Rogowski coil)

ne Electron/Plasma density

NFe Number of Iron atoms per monolayer

nFe mono Number of Iron monolayers

ni Ion density

ni(t) Population density of excited state i

nPh,i Observed emission per volume

nq Density of all collision partners q

Nq Frequency constant for AT-cur quartz

ω2MHz Angular frequency of 2 MHz (ω2MHz = 2π f2MHz)

ω14MHz Angular frequency of 14 MHz (ω14MHz = 2π f14MHz)

ωpe Electron plasma frequency (ωpe = 2π fpe)

ωPSR Plasma series resonance frequency (ωPSR = 2π fPSR)

P13.56MHz 13.56 MHz amplifier power

PVHF Variable frequency (60− 90 MHz) amplifier power

Q(t) Time-dependent charge (sheath)

QPSR Plasma series resonance quality factor

ρA,Fe Area mass density of Iron atoms (monolayer)

ρCr Mass density of Chrome

ρf Mass density of growing film

ρFe Mass density of Iron

ρMo Mass density of Molybdenum

ρNi Mass density of Nickel

vi Symbols and Abbreviations

ρq Mass density of quartz

R13M xxx Resistive element of 13.56 MHz matching network

Racs Equivalent acoustic impedance resistor

RBulk Plasma bulk resistance

RRod Copper feed resitance at high frequencies

RVHF xxx Resistive element of VHF matching network

Rz Acoustic impedance ratio

s Mean sheath width

S Scattering parameter matrix

S11 Input reflection coefficient

S12 Reverse voltage gain

S21 Forward voltage gain

S22 Output reflection coefficient

Scirc 3-Port circulator S-Parameter matrix

Sf Sauerbrey constant

sHF Mean sheath width contribution HF

sVHF Mean sheath width contribution VHF

Te Mean electron temperature

τi Ion transit time across the sheath

τrf RF period time

U2MHz Voltage amplitude 2 MHz waveform

U14MHz Voltage amplitude 14 MHz waveform

uBohm Bohm velocity

UBulk Plasma bulk voltage

UCurrent(t) Current proportional induction voltage

Udc bias DC self bias voltage

Ui Voltage at network port i

Uphase(t) Voltage waveform

Uprobe Langmuir probe voltage

UQ Voltage source VNA

~v Velocity vector (3D)

V0 Plasma sheath voltage

Vf Volume of growing film

vq Velocity of sound for quartz

Z0 Network port wave impedance

Z1...3 Generalized matching network impedances (T-type)

Zf Acoustic impedance of growing film

Zfilm Electrical equivalent film impedance

ZL Load impedance

ZPlasma eff Effective plasma impedance

Symbols and Abbreviations vii

ZPlasma HF Plasma impedance HF contribution

ZPlasma VHF Plasma impedance VHF contribution

Zq Acoustic impedance of quartz

viii Symbols and Abbreviations

Abbreviations2f-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 Giant Magneto Resistance (Effect)

HF High Frequency band (3− 30 MHz)

HiPIMS High Power Impulse Magnetron Sputtering

HPPMS High Power Pulsed Magnetron Sputtering

ICCD Intensified Charge Coupled Device

ICP Inductively Coupled Plasma

IED Ion Energy Distribution

IDF Ion Distribution Function

LIF Laser Induced Fluorescence

MACORr Vacuum compatible and machinable glass ceramic

MBE Molecular Beam Epitaxy

MCC Monte Carlo Collisions

MEMS Micro Electro-Mechanical Machining

MF Medium Frequency band (0.3− 3 MHz)

MFC Mass Flow Controller unit

MF-CCP Multiple frequency driven capacitively coupled plasma

MO-CVD Metal-Organic Chemical Vapor Deposition

MRAM Magneto-resistive Random Access Memory

NERH Nonlinear Electron Resonance Heating

OES Optical Emission Spectroscopy

OML Orbital Motion Limited theory

PE-CVD Plasma Enhanced Chemical Vapor Deposition

PIC Particle In Cell (simulation method)

Symbols and Abbreviations ix

PROES Phase Resolved Optical Emission Spectroscopy

PSR Plasma Series Resonance

PVD Physical Vapor Deposition

QCM Quartz Crystal Microbalance

rf radio frequency

RFEA Retarding Field Energy Analyzer

RIE Reactive Ion Etching

RML Radial Motion Limited

SEERS Self-Excited Electron Resonance Spectroscopy

SEM Scanning Electron Microscopy

SNR Signal to Noise Ratio

TEM Tunneling Electron Microscopy

VHF Very High Frequency band (30− 300 MHz)

VI Voltage-Current (trace/characteristic/probe)

VNA Vector Network Analyzer

XRD X-Ray Diffraction Spectrometry

List of Figures xi

List of Figures

2.1 Gas and vacuum layout of the experimental setup . . . . . . . . . . . . . . . 8

2.2 Mechanical and electrical layout of the plasma chamber . . . . . . . . . . . . 9

2.3 Definition of voltages, currents and wave parameters for a two-port network 10

2.4 Generalized impedance network for calculating the input reflection coefficientS11 and forward voltage gain S21 . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Electrical equivalent circuit of the 2 MHz matching network including parasiticcomponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.6 Transmission function S21 for the 2 MHz impedance matching network . . . 14

2.7 Voltage transmission S21 for a matched 2 MHz impedance network using areal plasma impedance termination . . . . . . . . . . . . . . . . . . . . . . . 15

2.8 Electrical equivalent circuit of the 13.56 MHz matching network includingparasitic components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.9 Transmission function S21 for the 13.56 MHz impedance matching network . 16

2.10 Voltage transmission S21 for a matched 13.56 MHz impedance network usinga real plasma impedance termination . . . . . . . . . . . . . . . . . . . . . . 17

2.11 Electrical equivalent circuit of the VHF impedance matching network includ-ing parasitic components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.12 Transmission function S21 for the VHF impedance matching network . . . . 18

2.13 Voltage transmission S21 for a matched VHF impedance network using a realplasma impedance termination . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.14 Parasitics equivalent circuit model of the top electrode . . . . . . . . . . . . 20

2.15 Comparison of fitted voltage-current probe data to a set of reference plasmaimpedances gained from Langmuir probe measurements . . . . . . . . . . . . 22

2.16 Calculated power transmission S21 for the vacuum feedthrough equivalent circuit 24

3.1 Exemplary internal outline of a voltage-current (VI) probe sensor . . . . . . 26

3.2 Voltage transmission functions (S21) from the input port to the voltage andcurrent equivalent voltage measurement port . . . . . . . . . . . . . . . . . . 27

3.3 Raw VI probe data of a dual frequency discharge . . . . . . . . . . . . . . . 28

3.4 Plasma impedance equivalent circuit model . . . . . . . . . . . . . . . . . . . 29

3.5 Measured current equivalent induction voltage UCurrent(t) and its discrete am-plitude Fourier spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.6 Measured single frequency VI probe impedances and proposed combinationsthereof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.7 Physical explanation for the impedance splitting as performed by a VI probe 31

3.8 Comparison of magnitude and phase of an effective plasma impedance toLangmuir probe deduced plasma impedances . . . . . . . . . . . . . . . . . . 32

xii List of Figures

3.9 Characteristic Langmuir probe current-voltage (IV) curve . . . . . . . . . . . 343.10 Principal setup and measurement schematic of the APS3 Langmuir probe system 393.11 Discrete amplitude Fourier spectrum of a plasma current detected by a SEERS/PSR

current probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.12 Comparison of compensated to uncompensated probe current . . . . . . . . . 413.13 Phase resolved optical emission spectroscopy (PROES) setup for a capacitive

dual frequency discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.14 Space and time resolved excitation plot for a 2 MHz/14 MHz dual frequency

discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.15 Typical current signal acquired in a dual frequency discharge . . . . . . . . . 463.16 Measured dual frequency (13.56 MHz / 67.8 MHz) PSR current with the

according discrete Fourier spectrum . . . . . . . . . . . . . . . . . . . . . . . 463.17 Simple PSR equivalent circuit model of a capacitive rf plasma discharge . . . 473.18 Correlation of space and time dependent excitation plots from PROES to

simultaneously measured PSR currents . . . . . . . . . . . . . . . . . . . . . 513.19 Comparison of calculated to experimental PSR currents under equivalent dis-

charge conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.20 Retarding field energy analyzer (RFEA) used for ion distribution function

(IDF) measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.21 Typically used potential distribution among the grids of the applied RFEA

for ion distribution function measurements . . . . . . . . . . . . . . . . . . . 553.22 Characteristic measured current from a RFEA by sweeping the retarding po-

tential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.23 Normalized ion distribution function (IDF) calculated as the first derivative

of a measured voltage-current trace . . . . . . . . . . . . . . . . . . . . . . . 573.24 Functional schematic of a quartz-crystal microbalance . . . . . . . . . . . . . 593.25 Butterworth-van Dyke (BvD) equivalent circuit of a quartz crystal resonator 61

4.1 Frequency dependence of electron density ne by varying fVHF . . . . . . . . . 644.2 Frequency dependence of the plasma and floating potential by varying fVHF . 654.3 Frequency dependence of mean electron temperature Te by varying fVHF . . 664.4 Frequency dependence of the dc self bias voltage by varying fVHF . . . . . . 664.5 Discrete Fourier amplitude spectrum of a measured PSR current at integer

frequency ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.6 Discrete Fourier amplitude spectrum of a measured PSR current at non-

integer frequency ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.7 Comparison of both Fourier amplitude spectra from integer and non-integer

driving frequency ratio case . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.8 Signal energies calculated from acquired PSR current signals . . . . . . . . . 704.9 Power dependence of dc self bias voltage . . . . . . . . . . . . . . . . . . . . 724.10 Power dependence of electron density ne . . . . . . . . . . . . . . . . . . . . 734.11 Comparison of weighted 13.56 MHz and 71 MHz current, both measured at

matchbox output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.12 Power dependence of mean electron temperature Te . . . . . . . . . . . . . . 754.13 Low frequency power dependence of floating potential . . . . . . . . . . . . . 764.14 Pressure dependence of electron density ne . . . . . . . . . . . . . . . . . . . 764.15 Pressure dependence of mean electron temperature Te and dc self bias voltage 77

List of Figures xiii

4.16 Discrete Fourier spectra for observed PSR currents at low (3 Pa) and high(20 Pa) pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.17 PROES excitation plot for a pure 2 MHz discharge in Neon . . . . . . . . . . 794.18 Relative phase dependence of electron density ne and mean electron temper-

ature Te . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.19 Relative phase dependence of plasma impedance magnitude and phase . . . 814.20 Relative phase dependence of plasma and floating potential . . . . . . . . . . 824.21 Relative phase dependence of electron distribution function . . . . . . . . . . 824.22 Correlation of the electron excitation dynamics to SEERS/PSR currents at a

relative phase angle of -90 and +90 . . . . . . . . . . . . . . . . . . . . . . 834.23 Influence of relative phase on a simple plasma boundary sheath waveform model 844.24 Influence of relative phase on excitation behavior for PVD-like discharge con-

ditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.25 Influence of relative phase on a simple plasma boundary sheath waveform

model, resembling PVD-like conditions . . . . . . . . . . . . . . . . . . . . . 864.26 Low frequency voltage U13.56MHz influence on the ion distribution function

(IDF) on the target electrode . . . . . . . . . . . . . . . . . . . . . . . . . . 884.27 Calculated mean ion energies from measured IDFs for low frequency voltage

U13.56MHz variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.28 Dependence of the ion distribution function on the VHF driving frequency fVHF 894.29 Pressure dependence of sputter deposition rate . . . . . . . . . . . . . . . . . 914.30 Pressure dependence of dc self bias voltage . . . . . . . . . . . . . . . . . . . 924.31 Power dependence on sputter deposition rate in single frequency discharge

(13.56 MHz, 71 MHz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.32 Dependence of sputter deposition rate on single frequency 13.56 MHz and

dual frequency discharge operation (13.56/71 MHz) . . . . . . . . . . . . . . 944.33 Separate power dependence of 13.56 MHz and 71 MHz on sputter deposition

rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.34 Optical emission spectrum for determination of relative atomic species densi-

ties in single frequency VHF operation . . . . . . . . . . . . . . . . . . . . . 984.35 Optical emission spectrum for determination of relative atomic species densi-

ties in dual frequency operation . . . . . . . . . . . . . . . . . . . . . . . . . 994.36 Atomic force microscopy (AFM) picture of a 56 nm Fe-coated silicon wafer . 100

xiv List of Figures

Abstract xv

Abstract

Capacitively coupled plasmas driven at multiple frequencies have attracted industrial interestin recent years, because of their attributed advantage of separated tunability of ion flux andion impact energy. Common examples of these type of plasmas are found in new generationsof etching tools utilized in the semiconductor industry branch. The separability is usuallyachieved by using one frequency out of the VHF band (30 − 300 MHz) and another out ofthe 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 electricalcharacterization is performed, to efficiently suppress mutual amplifier interferences, ensuringstable plasma conditions. Therefore, a detailed analysis of electrical loss mechanisms dueto impedance matching networks and electrical vacuum feed-throughs is carried out. As aresult the overall electrical system efficiency can be estimated and is found to be comparableto present industrial devices. Furthermore, an electrical vacuum-feed-through descriptionallows for plasma impedance determination during discharge operation, using a standardvoltage-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, opticalemission spectroscopy (OES), phase resolved optical emission spectroscopy (PROES) andretarding field energy analyzer (RFEA). In detail, frequency ratio, power ratio, pressure andinfluence of the relative phase are studied. Anomalous heating at integer driving frequencyratios is observed and explained on the basis of theoretic considerations by Mussenbrock andBrinkmann [1] through nonlinear electron resonance heating (NERH). Furthermore, globalmodel calculations by Mussenbrock and Ziegler [2][3] can be very well matched to experi-mentally gathered PSR current signals. Thereby, a significant contribution to understandingelectron heating in capacitive discharges is achieved, which is a key parameter for dedicateddischarge 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, especiallywith respect to typical operating regimes in PVD processes, is observed. In general, the afore-mentioned desirable complete separability of ion flux from ion bombarding energy is possiblebut limited for typical plasma processing applications. However, for industrial requirements ahigh enough degree of separate tunability is achievable, as shown in deposition experiments.Investigations on changing the relative phase between driving frequencies unveil a dedicatedcontrol of the amount of high energetic electron production (discharge excitation) directly

xvi Abstract

in front of the target electrode. It is believed to be of high relevance for discharge driftcompensation and ion flux optimization, as experimental evidence supports. Furthermore,the optimization becomes electrically regulable through an observed correlation of the local-ized electron heating as measured by PROES and PSR current resonant structures. Thesefindings also agree very well to aforementioned model considerations.

Finally, deposition rate characterization on metallic targets using a quartz-crystal microbal-ance gives insight into the complex driving frequencies’ coupling behavior. Although fortypical power regimes in PVD applications, with large low frequency power and small highfrequency power contributions, most diagnostics predict a decrease in plasma density throughthe dominating influence of low frequency power, no such observation is made for depositionrate experiments. This is explained by a significant change of the ion energy dependent sput-tering yield, compensating losses in plasma density. Simultaneously raising high frequencypower verifiably boosts deposition growth rate. However, this effect only works up to a de-fined threshold power, where discharge behavior starts changing towards single-frequencyequivalent operation. Concluding, it can be said that despite an observed strong frequencycoupling, prohibiting a complete separation of ion flux and energy, an adequate level ofcontrol is achievable for industrial processing.

1

1. Introduction

Today, low pressure plasmas are a widespread tool for manufacturing micro- and nano-scaledevices. Popular examples range from semiconductor manufacturing of well-known comput-ing processors, micro-electromechanical machining (MEMS) and biomedical applications likelab-on-chip and sterilization processes, up to a large industry branch involved in specializedcoatings technology. Hereby, thin film solar cells, architectural glass coatings with optimalecological properties or layers for hardening workshop machining tools are common fields ofapplications. Several established methods for low pressure plasma processing exist and arediscussed in the following.

1.1 Common thin film deposition techniques

A number of established low pressure processes for coatings manufacturing are availabletoday. Not all of them necessarily involve the use of plasma technology. Major representativesof this area are deposition tools like chemical vapor deposition (CVD) and the atomic layerdeposition (ALD).

Chemical vapor deposition (CVD) is a deposition process, solely based on chemical reactionstaking place directly at the substrate surface through gaseous reactants. Therefore, a pre-cursor gas is injected into the processing chamber. In most cases the substrate is heated toseveral hundred degrees Celsius, in order to enable, enhance or otherwise optimize chemi-cal reactions on the substrate surface. The nitrification or carbonization of silicon wafers toproduce 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 issuethat needs to be carefully controlled. Especially if previous processing steps have broughtsensitive structures (layers) onto the substrate, they could be damaged subsequently. Duringheat-up and cool-down further temperature stress is brought upon the present and newly gen-erated layers when substrate and layer materials have largely different expansion coefficients.These temperature problems could be resolved by using a plasma to chemically activate allreactants. Thereby, the gas or gaseous precursor molecules are dissociated/fragmented intoions and can thus be deposited on the substrate surface. This method is known as plasma-enhanced CVD (PE-CVD). The plasma’s main advantage in reducing substrate heat loadresides in the different heating contributions of ions and electrons. Because the electronsare in most cases much lighter than the ions, they heat up more easily (in terms of kinetic

2 1. Introduction

energy), whereas the ions remain cold (near room temperature). Hence, chemical activationis 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 temperatureproblems. Essentially, ALD works similarly to CVD. The significant difference is, ALD allowsfor an absolutely dedicated thin film growth control down to monolayer precision. This isachieved by splitting the reactants into two half-reactions. Through purge/injection cyclesof 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 percycle. Although an absolute film growth control is possible, the numerous purge/injectioncycles are time-consuming, depending on the desired film thickness.

Two further examples for coatings manufacturing relevant to the scope of this work arerelated to physical vapor deposition (PVD). The basic working principle in all discharge casesis the production of high energetic ions. On surface impact, they are capable of removinga target atom out of its solid bond, which then diffuses towards the substrate and forminga layer. In very dense plasmas these sputtered atoms can also be ionized, allowing for acontrollable directed deposition. The latter is particularly relevant for the filling of contactholes 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 multiplefrequency driven capacitive discharges (2f-CCPs) are considered an adequate competitionwith 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 tothe target by placing strong magnets with differing orientation behind it. Through this, bulkelectrons and secondary electrons are efficiently captured in front of the target causing ahigh plasma density, hence ion flux. The combination of high ion flux and easily tunable ionacceleration voltage results in a high rate, high throughput deposition process. But there arethree weaknesses to this concept. First, for reactive deposition processes involving isolatingfilms, a committed arc management is obligatory to avoid arcing and thus substantial sub-strate damage. Second, magnetic target materials short circuit the parallel magnetic field,reducing deposition rate. As a countermeasure, specially prepared and costly targets have tobe used. Third, sputtering and deposition homogeneity is disturbed because of preferentialerosion along the magnetic field lines. Target utilization is low and frequent replacementsare needed. Recently upcoming modifications are the so-called high power impulse magnetronsputtering (HiPIMS), also known as high power pulsed magnetron sputtering (HPPMS). Oneof their advantage for PVD is through high power pulses circumventing the aforementionedproblems of arcing and deposited films tend to have good adhesion properties.

A competitive new development with respect to ferro-metallic/magnetic thin film depositionand also high aspect ratio etching are capacitively coupled plasmas (CCPs) driven at multiplefrequencies. They have the advantage of separately controlling ion flux and ion density.However the extent of separability and its dependence on external tuning parameters, likee.g. powers and pressure, are an open issue. These and related problems are the main work

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 unattrac-tive in the mid 20th century. They were first reconsidered by the appearance of single fre-quency CCPs excited at frequencies in the VHF (30 − 300 MHz) band [4][5][6]. Hereby,first applications range from PE-CVD deposition of silicon layers [7][8] to the productionof diamond-like carbon (DLC) layers [9]. A considerable potential was anticipated by usinghigher excitation frequencies, because plasma density could be increased to equivalent valuesas reported from inductively coupled plasma (ICP) sources. Detailed investigations into thedriving frequency behavior followed [10]-[15]. It was found that the elementary proportion-ality

ne ∝ f 2VHF (1.1)

holds, with ne as the plasma (electron) density and fVHF as the excitation frequency. At thesame time it was observed that the dc self bias voltage, as a good ion bombarding energyapproximation, decreases. Both effects are equally attractive in plasma processing, becausesubstrate damaging through high energetic particles is still an issue in today’s manufacturing,especially in combination with shrinking component dimensions (e. g. reduced layer thicknessor layer-to-layer separation). Although, increasing driving frequency possesses advantageousproperties a dilemma persists. Ion bombarding energy is not controllable independently fromplasma density (ion flux). One of the early experimental reports demonstrating a separatetunability was shown by Goto et al. [16]. It eventually led the way to what is now under-stood as dual frequency driven capacitive discharges. Theoretical approaches, analyzing thefunctional separation of ion flux and ion energy followed [17]-[20]. Until today, the mostwidespread field of application for 2f-CCPs is anisotropic reactive (ion) etching, documentedexperimentally [21]-[23] and theoretically [24]-[29].

Today, dual frequency capacitively coupled plasmas are generally attributed a full separa-bility of ion flux and ion bombarding energy. However, a strong frequency coupling is ob-served when excitation frequencies are close together (fVHF/fHF < 10) [3][30]. Unfortunately,experimental evidence is sparse for dual frequency discharges in general. Although numer-ous theoretical considerations exist, detailed investigations into the frequency coupling andthe mutual dependency of other external tuning parameters on discharge characteristics isneeded. This topic is a major issue addressed within the frame of this work. Among studyingthe behavior of relevant stationary plasma parameters, such as electron density and tem-perature or floating and plasma potential, also detailed analysis into the transient electronheating (high energetic electron production / excitation mechanisms) is done by optical andelectrical diagnostics. It is anticipated that by understanding external parameter’s influenceon electron heating is the most appropriate way of discharge optimization. Therefore notonly an experimental but also a theoretical understanding of discharge heating and powerdeposition in the plasma is desired.

Several models, describing dual frequency discharges, are found in literature ranging from

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 mod-elling arise from semiconductor manufacturing needs of reported observed inhomogeneitiesin large area processing of silicon wafers. These effects have also been diagnosed in singlefrequency VHF driven CCPs [45]. Theoretical approaches [46]-[51] and [52]-[55] deal with theproblem of increasing tool and workpiece dimensions at simultaneously reduced excitationwavelengths.

Indeed, it is shown by several independent sources that with increased workpiece dimensionsin conjunction with dense plasmas (> 1017 cm−3), processing homogeneity can be seriouslycompromised through three identified effects. First, the standing wave effect is relevant whenreactor dimensions come in range of excitation wavelengths, causing an enhanced heating inthe discharge center. Second, the plasma skin effect describes the phenomenon of inducedelectric fields parallel to the electrodes causing a maximal heating at the plasma edges. Itgets more and more relevant with increasing plasma densities. Third, the well-known edgeeffects in CCPs, denoting an enhanced heating at the discharge edges due to electrostaticfield enhancements play a role. Additional edge effects with similar properties are theoret-ically reported when taking full electromagnetic calculations into account. Commonly, theabove effects occur simultaneously. As a result, there are operating regimes where eithereffect becomes dominant. One possible solution to resolve discharge inhomogeneities are spe-cially shaped electrodes [53]. Thereby, manufacturing and machining requirements are tough.These phenomena however are beyond the scope of this work and are not experimentallyaddressed, because reactor dimensions are small and densities for intended PVD experimentsare moderate.

Most commercial dual frequency plasma tools use frequencies which are an integer multipleof each other. By that, the relative phase as a further control parameter becomes availablefor discharge optimization. Since practical properties of this additional parameter have notbeen 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, specialcare has to be taken in terms of electrical discharge stability. There exist ample evidence onhow to construct single frequency CCPs. However, using two frequencies and particularlyone within the VHF band might seriously compromise discharge stability, because of mu-tual amplifier interferences. Thorough investigations into a dedicated suppression of mutualfrequency interferences are necessary. Within this work, detailed studies of the transmissioncharacteristics of the impedance matching networks are performed and methods, enhancingthe suppression of mutual interferences, are proposed.

Similar developments as presented for dc magnetron cathodes move towards magnetic en-hancement of dual frequency discharges [56][57]. Depending on magnetic field strength, thesame desired effect of boosting plasma density is achievable. By that, plasma densities of1018 m−3 can be realized. However, homogeneity decreases at the same time in favor of pref-erential heating at the discharge center. Though a further increase in plasma density isdesirable, controlling homogeneity problems might become a costly task.

1.3. Multiple frequency CCPs for PVD of ferro-metallic / magnetic materials 5

1.3 Multiple frequency CCPs for PVD of ferro-metallic /

magnetic materials

Ferro-metallic films are important especially for their impact on magneto-resistive randomaccess memory (MRAM) research. MRAMs are considered to be the successor of dynamicRAMs (DRAM), because of their advantage of non-volatility when switching off power.Because MRAM cell’s space requirements are high and manufacturing, especially of themagnetic layers, is costly, their spread is rather limited.

The development of spintronics (=spin-based electronics) is one of the key fields of appli-cation for these kind of films. Its major representative is the spin (valve) transistor basedon the giant magneto-resistive (GMR) effect. The device is manufactured by common semi-conductor processing steps (plasma deposition, etching, UV lithography) and its internalsetup 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 conduct-ing when both magnetic layers have the same magnetic field configuration. Then, electronscan tunnel through the non-conducting material by applying a voltage drop across the tran-sistor. Conversely, it possesses a high impedance when the magnetic field configuration isanti-parallel.

Two types of transistor “modes” are distinguishable. The spin valve transistor is operatedwith an open base. Switching is accomplished by an externally applied magnetic field. Thisform of the spin transistor is well-defined and controllable. Another operating mode is thespin transistor, which does not use an open base. In other words, the spin valve transistorcan be understood as a subset of the “full” spin transistor. Hereby, switching is realized byinjecting a spin-polarized current into the transistor base.

Within this work first experiments characterizing elementary deposition and thin film prop-erties of ferro-metallic layers are performed. First, sputter deposition is characterized using aquartz crystal microbalance (QCM). Results are compared to findings from Langmuir probeand retarding field energy analyzer (RFEA) data. Roughness properties and determination ofrelative sputtered atomic species densities complete the elementary characterizations. How-ever, the full development of a specific magnetic layer system lies beyond the scope of thisthesis.

1.4 Thesis layout

The presented thesis is divided into three parts. In the first part (chapter 2), the build-up phase and electrical process chamber characterization is discussed. First, constructionaldesign properties are addressed (section 2.1) and the experimental setup is described in detail.Following in section 2.2.2 is the electrical characterization of the transmission behavior ofthe applied impedance matching networks and electrical vacuum-feed-throughs, which isnecessary to ensure stable discharge conditions. Thereby, vector network analyzer (VNA)measurements are performed. For each electrical network a circuit model including parasitics

6 1. Introduction

is developed and fitted to VNA measurements, obtaining electrical component values. Specialfocus is laid on the development of an equivalent circuit model resembling electrical vacuumfeed-throughs, because they are the main reason for rf losses due to strong capacitive couplingto ground. Combining the investigations result in an accurate estimation of overall electricalsystem efficiency. More importantly, the question of how much power is deposited in theplasma with respect to applied amplifier powers is clarified.

The second part (chapter 3) primarily deals with the detailed description of used plasma di-agnostics with respect to error considerations by applying them to multiple frequency drivencapacitive discharges. Due to the nonlinear plasma boundary sheath behavior, numerous ex-citation 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, sec-tion 3.5). Investigations into uncompensated and filtered measurements gives way for thepossibility 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 developedfeed-through equivalent circuit, it is calibrated by comparison to plasma impedance data ob-tained from Langmuir probe measurements. A way is proposed on whether plasma generatedharmonics have to be considered or only measured frequency specific plasma impedances suf-fice for calculating the plasma impedance. More importantly, a method of mathematicallycombining these impedances is outlined [58].

Another set of diagnostics comprises a plasma series resonance (PSR) current sensor (section3.4) and phase resolved optical emission spectroscopy (PROES, section 3.3). They are usedto monitor the generation of harmonics and their mixing products in 2f-CCPs. The validityof a developed global model by Mussenbrock and Ziegler [3] is verified against experimentallymeasured PSR currents. Additionally, the possibility of experimental verification of nonlinearelectron resonance heating as proposed by Mussenbrock and Brinkmann [1] is discussed.Finally, industrial implications of a found correlation of local excitation phenomena observedby PROES and PSR current resonant structures is discussed.

In the third part of this thesis (chapter 4), all diagnostic results are discussed. First, Lang-muir probe, VI probe and PSR current studies on a variety of external parameters, such asfrequency ratio (section 4.1.1), power ratio (section 4.1.2) and pressure (section 4.1.3) arepresented. Thereby, phenomena related to nonlinear plasma heating are outlined. Second, therole of tuning the relative phase is investigated (section 4.2) by PROES, Langmuir probe, VIprobe and PSR current measurements. Third, the ion distribution is characterized by RFEAstudies (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 pre-viously applied diagnostics. The thesis concludes with a summary comprising all essentialresults and discusses further topics with respect to a planned scale-up version (section 5).

7

2. Experimental setup

This chapter outlines the developed experimental setup with its mechanical and electricalproperties. First, important constructional design properties with respect to capacitivelydriven discharges are discussed in section 2.1 followed by a detailed analysis of the electricalrf system.

It is a particularly important aspect for multiple frequency driven discharges, since all ap-plied rf generators need to be protected from mutual interference. Usually, this is achievedby investigating transmission behavior in conjunction with possible modifications of the re-spective impedance matching network. The detailed procedure is described in section 2.2.Especially when using excitation frequencies in the VHF band (30−300 MHz), it is inevitableto consider rf losses between an impedance matching network and the vacuum electrode. Inorder 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/radio-frequency (rf) parts is outlined in this section. To begin with, the mechanical and vacuumproperties are discussed with figure 2.1 presenting a detailed overview.

The process chamber is a modified GEC (Gaseous Electronics Conference) reference cell ina capacitive setup with an approximate volume of 30 liters. Attached is a vacuum pumpcombination consisting of a 230 l s−1 turbo-molecular pump (TMP1) and a membrane pump(3.3 m3 h−1)(FP1). System pressure is controllable by a butterfly valve (BV) assuming a con-stant gas flow, which is realized by mass flow controller units (MFC) tuned to the specificprocess gas properties. Although the MFCs are capable of shutting down the gas flow com-pletely, 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) cov-ering different ranges. PG1 is a Penning cold-cathode pressure gauge, measuring the basevacuum below 10−4 Pa and PG2 is a capacitive pressure gauge (Baratronr) monitoring theprocess pressure (0.5 - 50 Pa). Available process and diagnostic gases are N2 (nitrogen), O2

(oxygen), Ar (argon), He (helium), Ne (neon) and H2 (hydrogen).

In order to allow for sample treatment and preparation without breaking the vacuum aload-lock system is installed connecting load-lock and process chamber. Both chambers areseparated by a manual shutter (MV). Evacuation of the load-lock chamber is done by a

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 cham-ber is frequently pressurized and evacuated, a pumping bypass is installed that allows forcontinuous operation of TMP2. For secure bypass operation, it is fully automated by threeelectro-pneumatic valves (PV). A full range pressure gauge, which is a combination of a hotcathode gauge (Bayard-Alpert) and a Pirani gauge, monitors the load-lock chamber pres-sure. Sample transfer is performed by a magnetic transfer rod, taking a square silicon samplewithin a prepared holder, moving it into the process chamber and securing it into a retentionmechanism. All exhausts from both vacuum pump stations are combined and fed into a fil-tering system to prevent gas and particle leakage. This completes the general overview of thegas and vacuum layout and a more detailed introduction of the main chamber’s mechanicaland electrical properties is addressed.

Figure 2.2 shows the main chamber’s mechanical (left) and electrical (right) outline. Thepressure 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 andgas feed-throughs together with backside water-cooling. The electrode plates are made ofstainless steel and are isolated from electrical ground by a MACORr ceramic plate. Both,the stainless steel and MACORr plates are embedded in a grounded guard ring, surroundingthe capacitor stack at a distance of 1 mm. This technique focusses the discharge between theelectrodes and prevents conductive coatings of the isolating ceramics, which would eventuallylead to arcing and unstable plasma conditions. Gas is fed into the system via a circular showerhead, located above the top electrode. An even gas distribution is achieved by numerous sub-millimeter holes in the shower head.

2.1. Constructional design properties 9

aaaaaa aaaaaa

aa

aa

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 rfshielding meshes used for EMC (Electro-Magnetic Compatibility) tests need to be introducedinto the system at the indicated positions in figure 2.2 (left). Additionally, meshes are putinto the pressure gauge flanges and below the bottom electrode. They ensure an enhanceddischarge 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 anddiagnostic flanges’ parasitic volumes. One viewport for optical diagnostic access is protectedfrom the plasma by a magnetically driven shutter mechanism.

In the righthand diagram of figure 2.2, the setup’s electrical schematic is depicted. As in-dicated up to three impedance matching networks, two of which mountable onto the topelectrode, can be applied simultaneously. Their respective matching capability spans 2 MHz,13.56 MHz and 60− 90 MHz. All networks are prepared to be freely interchangeable amongboth electrodes, apart from the 2 MHz matching network. It can only be mounted to thebottom electrode, which has a long electrical feed line unfavourable for frequencies largerthan 2 MHz. Rapid matching network exchange is realized by quick connectors also provid-ing good rf contacting conditions. Both, matching network and connector are set on top of acopper rod, which is fed into the vacuum system. Figure 2.2 (right) displays the commonlyused electrical setup in this work, showing the 13.56 MHz and 60−90 MHz matching networkinstalled. Hereby, the bottom electrode is always grounded, apart from special case whichare discussed in detail later.

Every impedance matching network is connected to its according rf generator. Three differentrf generators are experimentally applicable. Two of them, 2 MHz and 13.56 MHz, are fixedfrequency rf sources at 600 W and 700 W respectively. For VHF power delivery an arbitraryfunction generator combined with a 500 W broadband amplifier (0.1 − 220 MHz) is used.


The arbitrary function generator allows for additional plasma operating options such as non-sinusoidal excitation waveforms and phase-locked dual frequency operation. Particularly thelatter 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 mutualinterference of the high power rf equipment. Otherwise, no stable plasma condition can beensured and equipment lifetime is strongly reduced. The interferences are usually suppressedby inserting absorption circuits (band-pass filters), tuned to the specific driving frequency ofthe rf generator. They can be inserted either directly at the matching network’s output, orbetween the generator and matching network connection.

Depending on the transmission behavior of each impedance matching network, the necessityof an absorption circuit needs to be determined individually. This is performed by vectornetwork analyzer (VNA) measurements. A vector network analyzer is a device, which probesa device under test (DUT) with respect to its frequency response. Prior calibration is neededto accurately eliminate systematic errors [59]. Those errors mainly include cables and con-nectors. Results are saved in the form of scattering parameters or S-parameters, which areassembled into a n × n S-parameter matrix for a n-port network. It fully describes the fre-quency 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 waveout of a given two-port network.

(b1

b2

)=(S11 S12

S21 S22

)(a1

a2

)(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 waveimpedance Z0i and are defined as depicted in figure 2.3. Defining the wave amplitudes in

2.2. Electrical characterization by vector network analyzer measurements 11

quantities of voltage and current at a port i yield

ai =Uai√Z0i

=√Z0i · Iai

(2.2)

bi =Ubi√Z0i

= −√Z0i · Ibi

. (2.3)

The connection between the wave amplitudes ai and bi to measurable values of port voltagesUi and currents Ii can be written as

Ui = Uai+ Ubi

=√Z0i (ai + bi) (2.4)

Ii = Iai+ Ibi

=1√Z0i

(ai − bi) . (2.5)

Rearranging equations (2.4) and (2.5) and solving for the wave amplitudes ai and bi yield

ai =Ui + Z0i · Ii

2√Z0i

(2.6)

bi =Ui − Z0i · Ii

2√Z0i

. (2.7)

The S-parameters can be understood by one of the following descriptions:

• S11

is the input reflection coefficient describing the ratio between a wave b1 coming out ofand a1 going into the input port of a two-port network, without a wave a2 traversingfrom the output port.

• S12

is the reverse voltage gain describing the ratio of a wave a2 traveling from the outputto the input port being detected as b1, with no incident wave a1 at the input port.

• S21

is the forward voltage gain describing the ratio of a wave a1 traveling from the inputto the output port being detected as b2, without a wave a2 traversing from the outputport.

• S22

is the output reflection coefficient describing the ratio between a wave b2 coming outof and a2 going into the output port of a two-port network, with no incident wave a1

at the input port.

Several simplifications can be applied to the S-parameter matrix if the DUT satisfies one ormore of the following conditions:

• ReciprocityA network is considered reciprocal if it is passive. Passivity of an electrical circuitis defined as only consisting of passive components such as resistors, capacitors andinductances. For the S-parameter matrix this implies the secondary diagonal elementsto be equal such that Smn = Snm with m 6= n, and for a two-port network S12 = S21.


• SymmetryWhen in addition to the reciprocity condition also the main diagonal elements Smm ofthe S-parameter matrix elements are equal, a network is considered to be symmetric.

• Loss-freeFor loss-free networks the condition SH · S = I holds, where SH is the conjugatetranspose of the S-parameter matrix and I the identity matrix. In mathematical termsthe S-parameter matrix is called unitary.

In this work, each investigated impedance matching network is reciprocal, but not symmet-ric implying S21 = S12 ∧ S11 6= S22. Since only transmission behavior is relevant for theperformed matching network investigations, only S21 is considered. All measurements areperformed using a HP8714ET vector network analyzer and the S-parameters are expressedin terms of voltages, meaning e.g. forward voltage gain and input (voltage) reflection coeffi-cient.

2.2.1 Evaluation of the impedance matching networks

In order to identify the necessity of absorption circuits, the matching network’s transmis-sion behavior is examined by measuring the forward voltage gain S21. To quantify parasiticcomponents, S21 is additionally modeled and compared to these measurements. A directcomparison of modeled and measured S-parameters becomes possible if the complete circuitincluding the VNA’s frequency tunable voltage source UQ as shown in figure 2.3 is accountedfor.

Figure 2.4: Generalized impedance network for calculating the input reflection coefficient S11 andforward voltage gain S21.

Therefore, general solutions of the input reflection coefficient S11 as well as the forwardvoltage gain S21 are derived on the basis of the circuit in figure 2.3, applied to the generalizedimpedance network in figure 2.4, with Z1...3 as freely definable impedances. These results areused in all further calculations and comparisons to VNA data.

The S-parameters S21 and S11 are defined by the wave amplitudes as

S21 =b2

a1

∣∣∣∣a2=0

and S11 =b1

a1

∣∣∣∣a2=0

. (2.8)


Substituting Z01 = Z0 (input port impedance) and Z02 = ZL (output port impedance) thewave amplitudes can be written as

a1 =U1 + Z0 · I1

2√Z0

=UQ

2√Z0

a2 = 0 (2.9)

b1 =U1 − Z0 · I1

2√Z0

=2 · U1 − UQ

2√Z0

b2 =U2√ZL

. (2.10)

Inserting the wave amplitudes from equations (2.9) and (2.10) into equation (2.8) and ex-pressing the voltage ratios as a function of the impedances Z0...3 and ZL yields

S21 =b2

a1

∣∣∣∣a2=0

= 2

√Z0

ZL

· U2

UQ

= 2

√Z0

ZL

· Z2‖(Z3 + ZL)

Z0 + Z1 + Z2‖(Z3 + ZL)· ZL

Z3 + ZL

(2.11)

S11 =b1

a1

∣∣∣∣a2=0

= 2 · U1

UQ

− 1 = 2 · Z1 + Z2‖(Z3 + ZL)

Z0 + Z1 + Z2‖(Z3 + ZL)− 1 . (2.12)

Finally, the S-parameters are successfully expressed in terms of the matching network imped-ances Z1...3, allowing for a comparison to measured VNA data. Furthermore in this work, allS-parameters are plotted in the form 20·log10(|Smn|), which always denote voltage dependentfunctions. In case the plotted S-parameters are power dependent, it is noted separately.Further references to the above representation are denoted as transmission function (S21)and reflection coefficient (S11).

Simulations are performed using equal input and output impedances Z0 = ZL = 50 Ω, rep-resenting real VNA measurement conditions. Portability to experimental plasma operationconditions however need further considerations, because the output impedance changes from50 Ω to an arbitrary complex-valued output impedance. With some constraints (see section2.2.2 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 com-ponents.

Therefore, comparisons of VNA data to simulated transmission functions with a 50Ω outputimpedance, provide a basis for matching network (stray) component determination. Repeat-ing the same simulation in a second step with a precalculated load impedance (e.g. plasmaimpedance), the transmission function valid for experimental operation is derived. Addition-ally, the impedance matching networks (2 MHz, 13.56 MHz and 60−90 MHz) are investigatedwith respect to their capability of attenuating other driving frequencies components.

For easier understanding, the electrical components of each impedance matching network arenamed according to the following defined scheme: (i) The major letter denotes the type of


electrical part (capacitor, inductor or resistor). (ii) The index’s first letters indicate to whichtype of impedance matching network the electrical part belongs (2M = 2 MHz impedancematching network). (iii) All remaining letters give information about whether this particularpart is a parasitic component (denoted as stray) or not (denoted otherwise). Hence, e.g.C2M parallel is the parallel capacitor of the 2 MHz impedance matching network.

Figure 2.6: Comparison of measured and simulated voltage transmission S21 for the 2 MHzimpedance matching network.

First, the 2 MHz impedance matching network is examined. By examining and transferringthe matching network’s topography, an equivalent circuit model is gained. The transmissionfunction is calculated according to equation (2.11) with the impedances Z1...3 chosen afterthe modeled circuitry in figure 2.5. The resulting expressions are exemplarily written downbelow. The stray inductance L2M stray = 40 nH was inserted after simulations failed toreproduce measured VNA data. The influence of a series resonance to electrical ground inthis branch cannot be neglected.

Z1 = 0 Ω

Z2 =1

ω C2M parallel

+ ω L2M stray

Z3 = ω L2M out +1

ω C2M out

Values for the electrical parts of the simulated network are found by fitting simulation tomeasurement. The results are plotted in figure 2.6. Both graphs compare well, however thefine structure as well as the rising slope for frequencies above 40 MHz are not reproducible bythe small number of components in the equivalent circuit. Nevertheless, further simulationsas well as test measurements using a voltage-current probe show the given equivalent circuitmodel to behave accurately for needed considerations in this work. As an exemplary value,the output inductance is estimated to L2M out = 23.6µH using the fit to the 2 MHz resonancematching peak (indicated in figure 2.6).

Taking the fitted component values and repeating the simulation for a changed load impedancewith ZL 6= 50 Ω produces the result shown in figure 2.7. It is noticeable, that the impedance


Figure 2.7: Voltage transmission S21 for a matched 2 MHz impedance network using a real plasmaimpedance termination. The voltage gain at 2 MHz is indicated.

matching network causes a net voltage gain for an arbitrary complex load impedance. Theexplanation is, that whenever an impedance matching network attunes itself to an opti-mum match, the reactive elements of the load impedance go into resonance with the reactivematchbox elements. A typical load impedance has a value of (2−100)Ω for a dual frequencydischarge. Due to this voltage resonance, significantly higher output voltages compared tothe 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 en-hancement is limited by resistive parasitic internal and external elements. Typically, theoutput voltage of such an impedance matching network acquires a two to three times highervalue compared to the input side when matched. For the 2 MHz matching network a 7.8 dBgain can be derived from figure 2.7, which is ≈ 2.45 times higher than on the input side ofthe network.

Furthermore, information about the network’s attenuation at the remaining driving frequen-cies of 13.56 MHz and 60 − 90 MHz are important. Referring to the measured VNA trans-mission function in figure 2.6 gives a minimum 35 dB attenuation for 13.56 MHz and a meanattenuation of 40 dB for 60 − 90 MHz. This spans a range of two orders of magnitude forbackward voltage transmission. Relating the attenuation values to corresponding measuredpeak voltages of 800 V (13.56 MHz) and 300 V (60 − 90 MHz) results in a net backwardpower of < 3 W dissipated in Z0 underlying ideal matching conditions and Z0 = 50 Ω. Thiscontribution is mainly produced by the 13.56 MHz frequency component.

For the used amplifiers this represents an uncritical value, because they are designed to oper-ate at a much larger amount of reflected power, which normally is on the order of magnitudeof their rated forward power. However, in scaled-up applications where delivered powers arelarger, considerations of integrating an additional absorption circuit for generator protectionmight become necessary. To verify simulations, VI probe measurements at the input port


Figure 2.8: Electrical equivalent circuit of the 13.56 MHz matching network including parasiticcomponents.

of the matching network have been performed and no significant voltage components weredetectable.

Figure 2.9: Comparison of measured and simulated voltage transmission S21 for the 13.56 MHzimpedance matching network.

Second, the 13.56 MHz matching network is investigated. Again the initial equivalent circuit,consisting of C13M parallel, C13M out and L13M out in figure 2.8 is gained by transferring thenetwork topography. Trying to fit this simple equivalent circuit to VNA data however isunsuccessful, 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 transmissionat 24 MHz.

Two possibilities are reasonable to this regard: (i) adding an additional inductance into theparallel capacitor C13M parallel branch or (ii) putting a parallel RC-circuit into the outputbranch of the inductance L13M out to additionally control the resonance’s bandwidth andQ-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 compo-nent values. The completed equivalent circuit model including parasitics is shown in figure2.8. R13M stray and C13M stray as additional components can be attributed to resistive lossesin the inductance’s coil and capacitive coupling between the coil turns.


Figure 2.10: Voltage transmission S21 for a matched 13.56 MHz impedance network using a realplasma impedance termination. The voltage gain at 13.56 MHz is indicated.

In a next step the effective operational transmission function is determined. Similarly acomplex-valued load impedance is assumed and the existing transmission function is re-simulated with the previously estimated component values. The result is depicted in figure2.10. As with the 2 MHz impedance matching network a net voltage gain at the outputport 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 dBand 60− 90 MHz voltages are attenuated by at least 35 dB on average. This is sufficient forexisting experimental conditions, but enhancing the 2 MHz damping must be considered ina scaled-up process.

Finally, the VHF broadband matching network is investigated. The initial electrical compo-nents derived from the matchbox topography are CVHF in, LVHF parallel and CVHF out as seenin figure 2.11.

Figure 2.11: Electrical equivalent circuit of the VHF impedance matching network including par-asitic components.

Theoretically, these elements are sufficient for obtaining an adequate match. However, tryingto fit the resulting function to measured VNA data is not possible for two reasons. On the


one hand the absorption peak at 7.4 MHz cannot be adequately modeled, because of toofew passive components. On the other hand the broad high pass behavior is similarly lackingmodel components.

To resemble the transmission minimum at 7.4 MHz additional capacitive coupling CVHF stray

to ground is inserted into the LVHF parallel branch. Furthermore, resistive losses RVHF stray

play an important role, because they limit the minimum impedance at the series resonancefrequency, which otherwise would represent a short circuit to ground. But the parasitic(LVHF 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 datato the modified circuit yields a very good agreement as seen in figure 2.12.

Figure 2.12: Comparison of measured and simulated voltage transmission S21 for the VHFimpedance matching network.

Reevaluating the simulation with a plasma impedance equivalent load, produces the effectivetransmission function plotted in figure 2.13. Hereby, the net voltage gain is 5.75 dB whichimplies a 1.94 times higher output voltage than the input voltage, which is in agreementwith VI probe measurements. As to the necessity of an absorption circuit, 2 MHz voltagesare damped by at least 70 dB and 13.56 MHz by at least 45 dB. Underlying the maximumrated output voltages of 550 V (2 MHz) and 800 V (13.56 MHz) result in a net backwardpower of < 1 W, assuming ideal matching conditions and a source resistor Z0 = 50 Ω.

Comparing the matching networks, the broadband VHF matching network is most efficientin suppressing interfering frequency components. Also the necessity of absorption circuits areeliminated for all networks. However, one remaining problem commands a protection mech-anism nevertheless. Because the plasma itself is a nonlinear medium it produces harmonicsof the excitation frequency. The amplitudes of these harmonics are negligible (sufficientlydamped) for the 2 MHz and 13.56 MHz networks, but not for the VHF network because ofits high pass characteristic.

An inspection of figure 2.13 reveals a constant gain above 100 MHz of 0 dB. Estimatingthe amplitude of the first harmonic to be 30% of the basic frequency, allows generator


Figure 2.13: Voltage transmission S21 for a matched VHF impedance network using a real plasmaimpedance termination. The voltage gain at 67.8 MHz is indicated.

loading with more than 120 W of harmonic power at a maximum generator forward powerof 500 W assuming an ideal match. This is important, because this amount of backwardharmonic power, coming solely from the VHF excitation, can seriously influence plasmaprocess stability and amplifier lifetime. A solution is inserting an rf broadband circulatorinto the power line between the generator and impedance matching network. It is complexto 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 possiblein a fixed port order from e.g. “PORT 1⇒ PORT 2⇒ PORT 3⇒ PORT 1”. By terminatingport 3 with a 50 Ω load, which is practically realized by a 40 dB (1 kW maximum powerrating) attenuator and a 5 W load, the circulator is transformed into an rf isolator. Termi-nating PORT 3 prohibits any power transfer to PORT 1 by full power consumption intothe 50Ω load. The ideal S-parameter matrix of such a three-port circulator without crosstalkand insertion losses is represented by

Scirc =

(0 0 11 0 00 1 0

)(2.13)

From (2.13) it follows that a circulator is a non-reciprocal rf component. Its internal struc-ture consists of a Faraday-rotator relying on the non-reciprocal Faraday-effect. This effectdescribes the polarization plane change of an electromagnetic (EM) wave under the influenceof an applied magnetic field. Practically it allows the directed guidance of an EM wave fromone port to another by constructive interference and disallows the direct return path bydestructive interference.

Concluding, all impedance matching networks have been investigated for the option of anabsorption circuit. Results show that no modifications on the standard components need to


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, becauseindividual matching network behavior and exact amplifier power specifications need to beconsidered in conjunction. Furthermore, not only impedance matching networks need to becharacterized, but also the behavior of the plasma chamber itself especially with respectto rf losses. Regarding backward harmonic power and an equivalent circuit model for theelectrical feed, a circulator might become irrelevant, because of the additionally consideredtransmission function.

2.2.2 Chamber characterization and equivalent circuit model for theelectrical feed

The overall electrical efficiency of any type of rf driven discharge crucially depends on lossfactors 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 2.2.1 andnetwork efficiency is determined by the respective measured transmission function. Regardingrf contacts, only losses at the network outputs are relevant. Other contacts are realizedby available low-loss coaxial connectors and cables, where no significant losses could beexperimentally identified. Finally, the vacuum feed-throughs are considered in conjunctionwith rf contacts, since both effects are closely linked and can also be recorded simultaneouslyby 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 modelis developed on the basis of common methods. In literature, similar equivalent circuits existand are well established [61]-[65]. Among those, the equivalent circuit proposed by Sobolewski[61] is most adequate for given experimental conditions. He thoroughly characterized strayparasitic effects by voltage and current measurement on a GEC reference cell. Based on


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 mechanicalproperties between an impedance matching network and the vacuum electrode plate. Figure2.14 shows all components that could be derived from mechanical properties. The validityof each component is verified by fitting VNA and real plasma impedance data to measuredinput impedance data. Each component is explained by one of the following descriptions:

• RRod represents ohmic losses on the electrical line (copper rod) between the matchingnetwork and the vacuum feed-through connector. Due to the skin depth at higherfrequencies this component rapidly grows in magnitude.

• LRod represents an equivalent coaxial inductance calculated from geometric data.

• CContact represents the stray capacitance of the connector between a matching networkand the electrical line (copper rod).

• LScrews and CScrews represent twelve individual screws holding the vacuum stack of theelectrode and MACORr ceramic plate together. Additionally they are responsible fortightening the vacuum seals.

• CFeed represents the coaxial capacitance of the vacuum feed-through.

A crucial task is to gain related values for above listed components. Some components likeLRod, CFeed and CScrews can be adequately estimated from geometric data and later refinediteratively. The most important calculated values are

LRod ≈ 60 nH

CScrews ≈ 140 pF

CFeed ≈ 130 pF

The contact capacitance CContact and vacuum screws inductance LScrews are evaluated sep-arately in the fitting process with respect to feasibility. Initially, they are introduced forcompleteness 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 parametersare determined by iteratively adapting measured voltage-current (VI) probe data to knownplasma impedances. These plasma impedances are derived from Langmuir probe measure-ments on the basis of a plasma impedance model, which incorporates relevant plasma pa-rameters, such as electron density and mean electron temperature [60].

Both impedance magnitudes are depicted in figure 2.15. The VI probe is located betweenthe 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 vacuumelectrode. The Langmuir probe derived plasma impedances are calculated from plasma pa-rameters by applying an appropriate equivalent circuit model by Lieberman and Lichtenberg[60]. A more detailed outline is found in section 3.1.1 ([58]).


Figure 2.15: Comparison of fitted voltage-current probe data to a set of reference plasmaimpedances 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 foundto be

RRod = 1.03 Ω

LRod = 51.22 nH

CContact = 12.837 nF

CFeed = 97.92 pF

LScrews = 373.14 pH

CScrews = 103.79 pF

Comparing these results to previous approximations, they show a good agreement. LRod,CFeed + CScrews and RRod have reasonable values with respect to mechanical considerations.However, the component values for LScrews and CContact need to be validated.

During the fitting process CContact was found to adopt a comparably high value of 12.837 nFgiving way for two implications. On the one hand CContact is in series to the output capacitorof a matchbox, which typically ranges from several pF to a few hundred pF. The combinationof both produces an even lower capacitance than from the matchbox alone. On the otherhand such a high value indicates a very good contacting condition, which in an ideal casewould be CContact →∞. Testing these assumptions by eliminating CContact and reevaluatingthe simulation delivers no detectable deviation in the calculated complex impedances.

Similar considerations apply for LScrews. Calculating the resonance frequency for LScrews

and CScrews gives fres Screws = 808.74 MHz which is one order of magnitude larger thanthe driving frequencies in question. Even the resonance frequency for CFeed + CScrews givesfres Screws = 562.29 MHz, which still is significantly larger. Similarly, the simulation isrepeated with LScrews left out and no change was observable. Essentially, the developed


and verified equivalent circuit model consists of three relevant component RRod, LRod andCFeed +CScrews, which is in good agreement with Sobolewski’s findings [61]. Using this refinedequivalent circuit model allows for accurate interpretation of voltage and current measure-ments and ensures stable, reproducible plasma conditions. Furthermore the possibility isgiven to predict the overall electrical efficiency of a plasma setup, by considering the trans-mission functions from the impedance matching networks and equivalent circuit model. Thismeans, deposited power within the plasma can be directly correlated to VI probe measure-ments at the matching network output.

It is also stated by Sobolewski [61] that implications for commercial use of this diagnosticmethod for plasma impedance monitoring are delicate. A significant drawback is the deter-mination of exact stray component values, which needs to be performed for each plasmachamber individually. Above calculations have unveiled the derived plasma impedance mag-nitude to be very sensitive to small stray component value deviations (≈10%). Additionally,depending on mechanical chamber properties, the validity of the equivalent circuit modelneeds to be verified and modified if applicable. Both arguments prevent a wider use of thisdiagnostic method. The availability of cheaper and more efficient plasma monitoring toolssupersedes impedance measurements (see next chapter).

Estimation of electrical system efficiency

For an accurate estimation of the overall electrical system efficiency, all loss mechanisms needto be known. Major losses have been identified in the impedance matching networks, rf con-tacts and feed-throughs (see equivalent circuit model). Voltage transmission functions havebeen determined for all networks. They are transferable into equivalent power transmissionfunctions under the following conditions: (i) the impedance matching network is terminatedwith a 50Ω load during measurement or simulation and (ii) the DUT is reciprocal. Both con-ditions are met in this work, so that power transmission functions are derived from voltagetransmission functions by

Hpower = 10 · log10(|S21|) =1

2·Hvoltage =

1

2(20 · log10(|S21|)) . (2.14)

On this basis, also the power transmission function of the electrode equivalent circuit modelis calculated. The result is shown in figure 2.16.

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, powertransmission is reduced by approximately 5 dB. Exemplarily considering the measured VHFbroadband matching network transmission in figure 2.12 at 71 MHz gives an approximatevoltage reduction of 3 dB or ∼= 1.5 dB in power. To calculate the overall electrical efficiencythe power source’s efficiency needs to be known. From the maximum power transfer theoremthis is derived to be ηsource = 1

2. Combining all sub-efficiencies yields the overall electrical

efficiency ηall to be

ηall = ηsource · ηmatching · ηchamber =1

2· 10

−1.510 · 10

−510 ≈ 11.194% . (2.15)


Figure 2.16: Calculated power transmission S21 for the vacuum feedthrough equivalent circuit.

Nonetheless, overall system efficiency is very low at 11.2%. Depending on the given matchingnetworks an efficiency range is calculated to 5% ≤ ηall ≤ 13%. These calculations clearlyindicate the generator power readout to be an unsuitable external tuning parameter forplasma processes. Only the impedance matching network’s output voltage is an adequatecontrolling parameter, because it represents the discharge voltage to a very good extent.For asymmetric capacitively coupled plasmas exist an easy approximation in the dc selfbias voltage. In stationary state it acquires a value, which results from balancing ion andelectron current at the grounded walls. Thus it is dependent on the electrode to groundratio, used gases and grounding conditions (e.g. non-conducting liners for enhanced dischargeconfinement). Usually, every type of impedance matching network measures the dc self biasvoltage by acquiring the dc voltage drop between the blocking capacitor and electrical ground.

This concludes the electrical characterization of the applied impedance matching networksand the plasma chamber. It was found, that the measured transmission functions are accurateand applicable to further calculations of the overall electrical efficiency. Furthermore nomodifications in the prototype system are necessary to prevent mutual generator interference.However, harmonic power was discovered to be a potential source of process instabilityif left unfiltered. Hence, a broadband circulator was inserted into the power line betweenamplifier and matching network. An equivalent circuit model for the electrode was developedconsidering different loss mechanisms. Results are in good agreement with literature. Despitea favorable transmission function of the electrical feed with respect to plasma generatorbackward harmonic power, a circulator is used to ensure stable amplifier operation. Finally,the results are combined to estimate the electrical system efficiency to be ηall = 11.2%, whichmeans only a small amount of amplifier power is deposited in the plasma.

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. Afurther such diagnostic is a vector network analyzer applied without plasma operation. TheVI probe’s working principle including transmission behavior and theory of calibration willbe 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 spectroscopycurrent sensor and a retarding field energy analyzer. Each diagnostic covers a range of mea-surable 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 con-trast, not applied are absorption methods like laser induced fluorescence (LIF) or cavity ringdown spectroscopy (CRDS). The focus of this section concentrates on phase resolved opticalemission spectroscopy (PROES). Compared to simple optical emission spectroscopy (OES),PROES gives insight into transient plasma processes, whereas OES as a time-averaged tech-nique gives information about stationary plasma processes. Therefore, PROES is used tostudy discharge heating mechanisms with respect to external parameter variations. On theother hand, OES is applied for investigating atomic species (relative densities) in sputterdeposition experiments.

Finally, thin film deposition diagnostics are briefly addressed by using a quartz crystal mi-crobalance (QCM). The theory of operation is discussed and possible problems with respectto metallic film deposition are considered. Furthermore, the microbalance is classified andcompared to equivalent thin film diagnostics as e.g. ellipsometry.

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 ameans of passive discharge diagnostic. Usually, a VI probe is therefore installed between theimpedance matching network output and vacuum feed-through connector. At this position,the discharge voltage is accurately measurable and the discharge current is not. Hence, re-producible plasma conditions are achievable by tuning to this voltage value. As presented insection 2.2.2, an adequate description of electrode loss mechanisms in the form of an equiv-alent circuit model is needed to convert measured VI probe currents into realistic dischargecurrents. Such a model also allows for the plasma impedance determination. In the experi-ment a standard available VI probe (MKS/ENI VI Prober 4100) with a specified frequencyrange of 0.6 - 100 MHz is used. The calibration procedure is explained theoretically andverified 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 volt-age 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 significantrf current. On the other hand, the voltage has to be reduced down to low amplitude levelsfor easier post-processing by the evaluation electronics.

Current measurement is more complex, since only a current equivalent induction voltageUCurrent is measurable. Similarly, the induction voltage measurement has to be realized highlyresistive, because counter-induction would otherwise introduce significant measurement er-rors. A correlation from the rf current to the induction voltage is derived next. Generally, therf current Irf(t) is correlated to the time-dependent magnetic field ~Hrf(t) through Ampere’slaw ∮

~Hrf(t) d~s =

∫A

~Jrf(t) d ~A︸︷︷︸conduction current

+

∫A

∂

∂t~Drf(t) d ~A︸︷︷︸

displacement current

(3.1)

3.1. Voltage current (VI) probe 27

where ~Jrf(t) is the current density, ~Drf(t) the electric displacement field, d~s the line elementof 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 rHrf(r, t) = Irf(t) . (3.2)

Multiplying both sides with the permeability µ0µr and reforming equation (3.2) to the mag-netic flux density Brf(r, t) yields

Brf(r, t) =µ0 µr

2π r· Irf(t) . (3.3)

Assuming the Rogowski coil to be ideal (neglecting magnetic stray fluxes) and only consid-ering field contributions at a constant radius r, the expression 2πr equals the coil’s meanlength lcoil. Furthermore, multiplying equation (3.3) with the turn’s cross sectional area Acoil

gives the total magnetic flux Φcoil(t) in the inner coil to be

Φcoil(t) =µ0 µrAcoil

lcoil

· Irf(t) . (3.4)

Finally, the measurable induction voltage UCurrent(t) is described by Lenz’s law

UCurrent(t) = −Ncoil ·dΦcoil(t)

dt= − µ0 µrAcoil Ncoil

lcoil︸︷︷︸coil inductance Mcoil

·dIrf(t)

dt. (3.5)

Since no magnetic materials are used within the Rogowski coil, the relative permeability isµr = 1 in above equations. The coil inductance has been determined experimentally in acalibration measurement to Mcoil = 138.5885± 9.9 nH.

Figure 3.2: Voltage transmission functions (S21) from the input port to the voltage and currentequivalent voltage measurement port.


A crucial task is to calibrate the transmission characteristics from the rf current input con-nector to the voltage and current measurement ports. Figure 3.2 displays the voltage andcurrent transmission function measured by a vector network analyzer. Although the workingprinciple is comparably easy, calibration is not. Because voltage and current transmission arestrongly frequency dependent due to nonlinear coupling and stray elements, the calibrationneeds 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 fromfigure 3.2 are needed if the commercial evaluation electronics, wherein calibration results areintegrated, is not used and direct oscilloscope measurements are performed. In this case, alltime-domain signals have to be transferred into frequency space, corrected, and transferredback to time-domain in order to obtain realistic current and voltage amplitudes.

3.1.1 Plasma impedance determination in multiple frequency capaci-

tive 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 suitablemethod correlating measured impedances to true plasma impedances has been presentedin section 2.2.2. This procedure is further explained in detail in the following paragraphs.Additionally, investigations into the plasma impedance determination for multiple frequencydriven plasmas are presented.

Figure 3.3: Raw VI probe data of a dual frequency discharge operated at fHF = 13.56 MHzand a variable frequency fVHF = 67 − 83 MHz. Left: absolute impedance magnitudes. Right:corresponding phase information.

Figure 3.3 shows raw VI probe data of a dual frequency discharge operated at fHF =13.56 MHz and a variable frequency fVHF = 67 − 83 MHz. On the left-hand side, abso-lute impedance magnitudes of ZVIProbe HF and ZVIProbe VHF are drawn. On the right-handside, corresponding phase information is found. Since these data are gained from a capaci-tive discharge where the plasma boundary sheath capacitance always dominates the plasmaimpedance, a phase angle near −90 is expected. This holds for ZVIProbe HF resulting fromfHF = 13.56 MHz but not for ZVIProbe VHF resulting from fVHF = 67 − 83 MHz. The VHF


impedance clearly expresses an inductive behavior which does not fit considerations for acapacitive discharge.

This problem is solved by comparing given VI probe impedances to realistic plasma impedancevalues. By that, all component values of an equivalent circuit model can be determined. Theseplasma impedances are obtained from simultaneously performed Langmuir probe measure-ments, which are described in chapter 4 in more detail. From those measurements, theelectron density ne and mean electron temperature Te are derived. In turn, both parametersne and Te are used to calculate true plasma impedances by the following set of equationsfrom Lieberman and Lichtenberg [60]

CVacuum =ε0 Aelectrode

L− s(3.6)

LBulk =1

ω2pe CVacuum

(3.7)

RBulk = νm LBulk (3.8)

CSheath =ε0 Aelectrode

s(3.9)

in conjunction with the plasma impedance equivalent circuit in figure 3.4.

Figure 3.4: Plasma impedance equivalent circuit model from Lieberman and Lichtenberg [60].

In above equations, the electrode radius relectrode, electrode separation L and electron-neutralcollision rate νm are experimentally given as relectrode = 70 mm, L = 45 mm and νm =10−8 s−1. The electrode area is defined as Aelectrode = π r2

electrode. Electron-neutral collisionrate is assumed to be constant for all calculations. Additionally, definitions for the meansheath expansion s and the electron-plasma frequency ωpe are given as

s =

√50

27·√

2

3· λDebye ·

(2 e V0

kB Te

) 34

(3.10)

λDebye =

√ε0 kB Te

e2 ne

(3.11)

ωpe =

√e2 ne

ε0 me

(3.12)

where λDebye is the Debye-Huckel length, V0 the voltage drop across the plasma boundarysheath, kB the Boltzmann constant, ε0 the vacuum permittivity, e the electron charge andme the electron mass [60].

One problem of directly comparing Langmuir probe derived impedances to VI probe data isan indeterminate frequency reference. On the one hand, a Langmuir probe as an electrostaticplasma diagnostic determines time-averaged frequency-insensitive (dc) plasma parameters.


On the other hand, VI probe impedances and their respective plasma impedances can onlybe gained with respect to a dedicated frequency. Moreover, they are usually determined forthe 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 dischargeharmonic contributions have to be included in VI probe measurements. And second, if andin which way all frequency-discrete plasma impedances are to be combined to an effectiveplasma impedance.

Addressing the role of harmonics for VI probe measurements, it is found by considering figure2.16 that most generated discharge harmonics larger than 50 MHz are not accessible by aVI probe because they are significantly damped by the vacuum feed-through. An exemplar-ily acquired current-equivalent induction voltage signal UCurrent(t) and its discrete Fourierspectrum are shown in figure 3.5.

Figure 3.5: Measured current equivalent induction voltage UCurrent(t) (left) for a 13.56 MHz and71 MHz discharge with its according discrete amplitude Fourier spectrum (right).

Clearly visible are the two main excitation frequencies of 71 MHz and 13.56 MHz and only twoadditional harmonic components at 142 MHz (= 2·71 MHz) and 213 MHz (= 3·71 MHz) canbe detected. Other frequency components have too low amplitudes to be useful for impedancecalculations. Hence, because driving frequency harmonics are strongly attenuated by the feed-through’s transmission function they are not available for plasma impedance calculations andonly the excitation driving frequencies are used further.

Eventually, the question of combining all frequency-discrete plasma impedances remains andwhether realistic results can be obtained. Therefore, an empirical approach is used. Twosimple possibilities of generating an effective frequency-independent plasma impedance area series or a parallel combination according to

ZPlasma eff1 = ZPlasma VHF + ZPlasma HF (3.13)

1

ZPlasma eff2

=1

ZPlasma VHF

+1

ZPlasma HF

. (3.14)

Applying above equations to measured VI probe impedances produces figure 3.6 showing theresulting impedance magnitudes.


Figure 3.6: Measured single frequency VI probe impedances of 13.56 MHz (•) and 67-83 MHz(•) and proposed combinations in series () and parallel (♦) compared to the Langmuir probededuced plasma impedance (×).

Additionally, the pre-calculated Langmuir probe plasma impedances are plotted for compara-bility. A significant deviation is observed for adding up each plasma impedance contributionaccording to equation (3.13). This is explainable by the significantly differing impedancemagnitudes of |ZPlasma VHF| and |ZPlasma HF|. Summing over all components yields an evenlarger value as seen in figure 3.6. Building the effective plasma impedance out of a parallelcombination of the frequency contributions, according to equation (3.14) shows a very goodagreement to pre-calculated impedance values gained out of Langmuir probe measurementparameters.

Figure 3.7: Physical explanation for the impedance splitting as performed by a VI probe. Arrowsin the electrical line indicate the corresponding rf current direction. The voltage drop across thedischarge is considered as UPlasma.

Physically, this is explained as follows. Consider multiple power sources at different operatingfrequencies connected to the input port of a VI probe, assuming each current passing throughthe VI probe and the plasma. Thereby, it is unimportant how they are connected (in seriesor parallel), because the frequency-specific current contributions add up according to Shan-non et al. [20], implying a parallel circuitry. Consequently only one dedicated voltage drop


UPlasma is found across the plasma. Figure 3.7 resembles the experimental situation for easierunderstanding. Practically, a VI probe is capable of detecting frequency-specific impedancesZPlasma(ω). In case of multiple frequency components, each single impedance is recorded.Relating this to plasma impedance determination in multiple frequency driven plasmas, allmeasured frequency-specific VI probe impedances have to be combined in parallel in order togain the plasma impedance as derived from Langmuir probe determined plasma parameters.

Figure 3.8: Comparison of magnitude and phase of an effective plasma impedance (•) afterequation (3.14) to Langmuir probe deduced plasma impedances (×). From the effective plasmaimpedance the mean sheath (♦) width is deducible using equation (3.18) and a fit to the meansheath 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 ne [64][73] and ion current[64]. Exemplarily, the mean sheath thickness s is derived and compared to simulations fromliterature [10][19]. In a dual frequency capacitive discharge, the total mean sheath thicknesscan be expressed by

s = sVHF + sHF (3.15)

with sVHF and sHF representing the mean sheath thickness for each frequency component[20]. Since only fVHF is varied in this particular measurement series, the contribution of sHF

is constant. Accordingly, equation (3.15) is rewritten to

s(ωVHF) = sVHF(ωVHF) + sHF . (3.16)

Consequently, also the plasma impedance magnitude can be written as

|ZPlasma eff| =1

ωVHF CSheath(s(ωVHF)). (3.17)

Rearranging equation (3.17), substituting ωVHF = 2 π fVHF and solving for s(ωVHF) yields

s(ωVHF) = 2 π |ZPlasma eff| · Aelectrode · fVHF · ε0 . (3.18)

Plotting equation (3.18) by using the previously derived plasma impedances |ZPlasma eff| re-sults in figure 3.8. For completion, ZPlasma eff and the pre-calculated Langmuir probe plasma

3.2. Langmuir probe 33

impedance magnitudes and phases are incorporated, both agreeing well. Also, the respectivephases agree well underlining the equivalent circuit model validity. Furthermore, a fit to themean sheath thickness on the basis of simulation predictions [10] is performed. Results ex-hibit a proportionality of s ∝ f−0.8

VHF which is in very good agreement to findings of Vahediet al. [10]. They predict a scaling of the mean sheath width with frequency of s ∝ f−1.

3.2 Langmuir probe

Langmuir probes belong to the category of invasive plasma diagnostics and the measurementprinciple works as follows. A thin wire electrode, typically several µm in diameter, is broughtinto the plasma. Then, voltage is applied between the wire and a grounded electrode. Thisvoltage 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 parameterssuch as plasma- and floating potential, mean electron temperature, electron density andelectron distribution function are gained. Despite the method’s simplicity several evaluationdifficulties 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 distributionfunction (EDF ).

• Filtering of discharge harmonics and excitation frequency components in the VHFband.

To quantify the above statements a more detailed description is needed. Therefore figure 3.9depicts a measured typical IV-trace, described in the following.

The shown IV trace is formally dividable into three distinct regions with different physicalmeanings. However, in reality the transition between each region cannot be pinpointed ex-actly to the indicated positions. At large negative voltages only ions and very fast electronscan traverse the probe electrode’s sheath. This part of the IV curve is denoted as ion satu-ration current. Because the number of very fast electrons is small compared to the numberof ions, the resulting current is assumed to be carried by ions only. The second region isdenoted electron retarding current. Here, a significant number of electrons begin to traversethe sheath, but still have to overcome the probe sheath potential. It describes the transi-tion from ion current to a mixed ion/electron current. At the point where the total currentbecomes zero, the probe voltage UProbe equals the floating potential Φfloat with respect toelectrical ground. Every isolated (electrically floating) object in a plasma acquires that po-tential, because ion and electron current have to balance. The plasma potential Φplasma isderived from the curve’s inflection point, where the ion current is assumed to be zero andelectrons are no longer repelled. Increasing the applied voltage further, only the electronsaturation current remains. However, the term “saturation” only applies for planar probe


Figure 3.9: Characteristic Langmuir probe current-voltage (IV) curve. Three regions are identi-fiable: 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 cylindri-cal 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 isexplainable by additionally considering angular momentum and a different sheath expan-sion for cylindrical geometries. By further assuming a collisionless sheath all currents canbe defined by the orbital motion limited (OML) theory. Within this work only cylindricalelectrodes 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 thistheory are mathematical descriptions for all currents, from which the plasma parameterselectron temperature Te, electron density ne and the electron distribution function (EDF)can be calculated. An elementary equation describes the relation between electron retardingcurrent and a measured IV trace. It was described by Druyvesteyn [76] and is known asDruyvesteyn’s relation.

fv,elec(E) =

√8meE

AProbe e3· d2Iretard

dU2Probe

and E = −eUProbe (3.19)

Thereby, e represents the electron charge, me the electron mass, E the equivalent probeenergy, UProbe the applied probe voltage, Iretard the electron retarding current and AProbe =2πRwire lwire the probe tip’s surface area with Rwire as the tip radius and lwire the tip length.

Interpreting equation (3.19) directly correlates the electron distribution function (EDF) tomeasured current-voltage characteristics. This is very important, because no additional as-sumptions on the distribution’s mathematical form are made. Therefore, an arbitrary EDFis the result of applying equation (3.19). Calculating all plasma parameters directly froman EDF resulting from Druyvesteyn’s relation is the most accurate way, because otherformulas explicitly or implicitly underly a Maxwellian distribution. Within this work all IV


trace evaluations are performed using equation (3.19). To give a complete overview the pos-sible methods are explained in the following. To begin with, the three regions of a probecharacteristic need to be described.

Assuming an isotropic Maxwellian distribution of the form

f(~v ) = ne

(me

2π kB Te

)3/2

exp

[− me ~v

2

2 kB Te

](3.20)

where, ne is the electron density, Te the mean electron temperature and ~v the velocity vector,the electron retarding current Iretard can be written as

Iretard(UProbe) = eAProbe ne

√kB Te

2 πme

exp

[eUProbe

kB Te

](3.21)

and describes the behavior of electrons capable of traversing the potential barrier larger thanUProbe [77]. Similarly the electron saturation current Isat with

Isat,elec(UProbe) = eAProbe ne

√kB Te

2 πme

2√π

√1 +

eUProbe

kB Te

(3.22)

is derivable. Equation (3.22) holds under the following constraints: (i) the probe radius rProbe

needs to be small against the surrounding sheath radius rSheath, so that rProbe rSheath.(ii) Only for sufficiently high values of UProbe >

(ΦPlasma + 2 · kB Te

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 byintroducing the Bohm velocity, which gives

Isat,ion(UProbe) = −eAProbe ni uBohm2√π

√1− e UProbe

kB Te

(3.23)

with

uBohm =

√kB Te

mi

(3.24)

where ni and mi represent the ion density and mass. As with the electron saturation currentthe applicability begins for sufficiently low values of UProbe < (Φfloat − 2 · kB Te

e). The Bohm

velocity uBohm is the minimum ion velocity when entering the plasma sheath region. Comingfrom the plasma bulk, they are accelerated to the Bohm speed within the so-called pre-sheathregion. If they would not attain this speed, energy conservation within the space chargesheath would be violated. As a countermeasure the pre-sheath would extend accordingly toachieve 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 howto derive the plasma parameters mean electron temperature Te, electron density ne andelectron distribution function (EDF). Beginning with the mean electron temperature Te


which is obtained by taking the natural logarithm of the electron retarding current Iretard

provides

ln(Iretard(UProbe)) = ln

(eAProbe ne

√kB Te

2 πme

)+

e

kB Te

· UProbe

= C1 +m1 · UProbe

(3.25)

which is a linear relation. Hence, the mean electron temperature Te is calculable by determin-ing the slope of the logarithmic of the electron retarding current Iretard yielding the electrontemperature to be

d ln(Iretard(UProbe))

dUProbe

= m1 =e

kB Te

(3.26)

⇒ Te =e

kB

· dUProbe

d ln(Iretard). (3.27)

Instead of taking Iretard, using d2IretarddU2

Probeyields exactly the same equation as (3.27), only re-

placing Iretard with d2IretarddU2

Probe. However the original electron retarding current (3.21) is gained,

based on the assumption of a Maxwellian distribution, which might not be the case for anytype of discharge.

The most general way of determining the mean electron temperature, is using Druyvesteyn’srelation (3.19) to obtain the electron distribution function (EDF). Since no assumptions aremade on the gained distribution, the term “mean temperature” needs to be reconsidered.The mean electron temperature Te correlates to the mean electron energy by

E =3

2kB Te . (3.28)

From the calculated EDF fv,elec(E) the mean energy of an arbitrary distribution is

E =

∫∞0E · fv,elec(E) dE∫∞

0fv,elec(E) dE

. (3.29)

In the following sense the term “mean temperature” is defined as the equivalent Maxwelliantemperature found by inserting equation (3.29) into equation (3.28) and solving for Te. Solelythis method is applied within this work to obtain the mean electron temperature Te, unlessstated otherwise.

Te =2

3 kB

E (3.30)

Summing up, there basically exist two important ways of finding the mean electron temper-ature. Both methods focus on the electron retarding region of an IV trace. One techniqueuses the slope of the semi-logarithmic IV-trace representation and the other applies a generalapproach by using the EDF gained from Druyvesteyn’s relation, which is proportional tothe current’s second derivative.

Besides electron temperature, electron density is an important plasma parameter. Essentiallythere exist three methods for calculating the electron density out of measured IV traces. Two


of them implicitly assume a Maxwell distribution, whereas the third follows a general ap-proach. First, one way of gaining the electron density ne is looking at the electron saturationcurrent Isat,elec. Squaring equation (3.22)

Isat,elec(UProbe)2 = e2A2

Probe n2e

kB Te

2πme

4

π

(1 +

eUProbe

kB Te

)(3.31)

and building the first derivative with respect to UProbe

dI2sat,elec(UProbe)

dUProbe

= e3A2Probe n

2e

2

π2me

(3.32)

produces an estimation for the electron density

ne =

√π2me

2 e3A2Probe

·dI2

sat,elec

dUProbe

. (3.33)

In short, the electron density ne can be obtained from the slope of the squared saturationcurrent. However, it is important to keep the prerequisites of using the saturation current inmind. Therefore only values of Isat,elec(UProbe ΦPlasma) are applicable.

A second method involves the exact current value of Iretard(UProbe = ΦPlasma) at the plasmapotential ΦPlasma. Thereby, ΦPlasma needs to be determined by finding the root of

d2Iretard(UProbe)

dU2Probe

= 0 (3.34)

which is the curve’s inflection point. Solving equation (3.21) for ne and using the currentIretard at the plasma potential ΦPlasma gives

ne =1

eAProbe

√2 πme

kB Te

· Iretard(UProbe = ΦPlasma) . (3.35)

Hereby, the accuracy of ne crucially depends on the accuracy of the plasma potential estima-tion (3.34). When using the second derivative of Iretard for plasma potential determinationnumerical instabilities occur. Measured data always include statistical uncertainties, whichworsen when applying derivatives. Thus, using the second derivative on Iretard can lead tolarge errors in the plasma potential. This is circumvented by applying a statistical methoddeveloped 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 ateach data point ~p = (UProbe, IProbe). Therefore, a number of points, defined by the smoothingfunction’s bandwidth, around ~p are included to calculate the desired polynomial approxi-mation. Depending on the mathematical distance to ~p, all additional points are weighedand included. By supporting adaptive bandwidths the different slopes of a Langmuir probecharacteristic can be described separately. Resulting is a smoothed curve with significantlyreduced measurement noise that can be differentiated twice. This algorithm ensures a sta-ble and reproducible estimation of the plasma potential and is solely used in this work. Adetailed description of this algorithm and its requirements is found in the works of Schulzeand Wenig [78][74].


Finally, the most general way of calculating the electron density ne is presented. Both pre-viously discussed methods rely on the assumption of a Maxwellian distribution, whereas thefollowing does not. It is based on the prior calculation of the electron energy distributionfunction (EDF) from Druyvesteyn’s relation (3.19) and correlates to the electron density as

ne =

∫ ∞0

fv,elec(E) dE . (3.36)

Because of its general applicability only this method is used in this work for electron densitydetermination.

Returning to the difficulties of Langmuir probe measurements mentioned earlier in the in-troduction, the first three arguments have been addressed. Regarding the plasma potentialdetermination and the IV trace’s second derivative, a newly developed algorithm by Schulzeand Wenig [78][74] is applied in the evaluations of Langmuir probe current-voltage character-istics. From the smoothed curve the EDF is calculated and the electron density ne and meanelectron temperature Te are derived. To qualify the influence and necessity of ion currentcorrection on plasma parameter determination, investigations performed by Wenig [74] arereferenced. He unveiled in simulations, also supported by measurements, that ion currentcorrection is only possible in IV traces with nearly ideal properties (without noise). He alsoexemplarily performed ion current correction on measured IV traces, showing that even innear ideal measurements, the noise level is high enough to disallow useful ion current correc-tion. Because noise reduction to the required extent is not feasible, ion current correction isnot applied within this work. Finally, the filtering of discharge harmonics in the VHF bandremains to be discussed, which is done in the following section.

3.2.1 Compensation schemes and application in multifrequency plas-

mas

As discussed in the previous section, a Langmuir probe is a useful diagnostic for obtainingseveral relevant plasma parameters. In practice, taking measurements in rf driven dischargesis made difficult by the oscillating plasma and floating potential, which is detected as anaveraging effect for the IV trace. In turn, particularly the mean electron temperature isoverestimated by above equations. As a consequence, the probe tip needs to follow the rfoscillation, which is achieved by capacitive coupling of the probe tip to a large floatingelectrode.

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 resultingLangmuir probe characteristic will be obtained. However, filters are needed to protect themeasuring electronics. For the floating voltage measurements this is realized by a low-passfilter, and in the probe tip branch by a passive filter concept. Further details of the APS3Langmuir probe system are found in literature [79][74][78].

When discussing rf filtering, a frequency (range) needs to be specified to work efficientlyin a band-stop array. For the case within this work the fundamental frequency 13.56 MHz


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 frequencyVHF driven capacitive plasmas produce more high frequency components with additionalside-bands depending on the used frequencies.

These high frequency components can have two origins. On the one hand, they are gener-ated 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 dif-fering in strength for individual frequencies. A more detailed explanation of this is foundin section 3.4. On the other hand, the investigated VHF dual frequency discharge appliescritical frequencies directly as the plasma’s excitation frequency. Hence, their amplitude islarge compared to amplitudes resulting from plasma generated harmonics. Additionally, allfundamentals and harmonics of each excitation frequency produce mixing frequencies leadingto numerous components in frequency space as shown in figure 3.11.

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 filterscannot be used because of their strong capacitive coupling to electrical ground. In thatway a significant amount of current does not reach the evaluation electronics. A furtherpossibility is active filtering using operational amplifiers, however these sensitive componentscannot be incorporated into the probe head mechanics, because of size and temperaturespecifications. The last option involves putting an inductance into the probe head, but theneeded magnitude and the permeability’s strong frequency dependence at VHF frequenciesare not realizable. This only leaves the option using band-stop filters of the most significantfrequency components. Those have been built into the applied filter array.


Figure 3.11: Discrete amplitude Fourier spectrum of a plasma current (excitation with f =13.56 MHz and 5 · f = 67.8 MHz) detected by a SEERS/PSR current probe. The strongestharmonic content is found at 12 · f = 162.72 MHz with a three times larger amplitude than thebase frequency f .

Consequently, not all frequency components are filtered and the remaining oscillation of theLangmuir IV trace needs to be characterized. Therefore two IV traces are compared in figure3.12. The compensated IV trace results from a 81.36 MHz/13.56 MHz discharge, whereasthe uncompensated is measured in a 83 MHz/13.56 MHz discharge. Considering the realizedpassive filtering concept, it becomes clear that the compensated case is effectively filtered inthe fundamental VHF frequency, whereas the uncompensated case is not. In that way theinfluence of filtering the strong VHF excitation component is determined.

Analyzing figure 3.12 (left) only a minor change is observable between compensated anduncompensated 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) deliverthe mean electron temperature from equation (3.27). Results for both cases are an equalmean temperature. Reanalyzing the IV traces with the new algorithm by Schulze and Wenigdelivers a deviation of 5% between both cases. The result is in good agreement with findingsof Oksuz et al. [80]. They investigated and compared fully uncompensated to compensatedLangmuir probe measurements in rf driven discharges. Since in this work at least a partialcompensation is always achieved, the results show less errors.

Summarizing, in multiple frequency driven capacitive plasmas only a partial rf compensationcan be achieved. However, a comparison of compensated to uncompensated measurementsshow minor differences using the improved algorithm by Schulze and Wenig. Consequently,Langmuir probe measurements can be performed without producing errors attributed tocompensation problems. With respect to the presented different methods of determiningplasma 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.

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 toelectrical ground. Right: Semi-logarithmic plot with fits to the electron retarding current formean electron temperature determination.

3.3 Phase resolved optical emission spectroscopy (PROES)

The Langmuir probe as an invasive diagnostic was presented in the previous section. Withinthis section a non-invasive optical diagnostic is addressed. Phase resolved optical emissionspectroscopy (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 dynam-ics. Both play an important role for capacitive discharges, because they are a key mechanismfor discharge sustainment and control. As seen later, also an alternative diagnostic methodexists capable of capturing the same transient excitation and ionization behavior, althoughspacial information is lost in this particular case. Prior to going into more details on theevaluation 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 PicoStarr) 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 2p1 state atλNeon = 585.2 nm with an excitation energy level of 19.0 eV. Within this work PROESmeasurements are only performed on neon discharges. The wavelength selection is achievedby an electrically tunable wavelength filter (CRI VariSpecr). Its transmission behavior iscalibrated prior to measurements to avoid optical artefacts, minimizing distortions.

Since PROES is a time-resolved plasma diagnostic the camera needs to be synchronizedwith the plasma excitation. In dual frequency discharges this is usually the lowest availablefrequency. Hereby, the complete discharge behavior can be captured. However, when scanningthe low frequency cycle, the step width has to be sufficiently small to allow for an adequateresolution of the high frequency cycle. Furthermore, the two applied frequencies need to bean 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


Figure 3.13: Phase resolved optical emission spectroscopy (PROES) setup for a capacitive dualfrequency discharge.

diagnostics as seen in figure 3.13. Practically, source synchronization is difficult becauseboth frequency signal sources are different with respect to signal generation. The 2 MHzsource uses an internal generator with a combined amplifier and the 14 MHz source consistsof a signal generator and a broadband power amplifier.

Synchronization is achieved by feeding the 2 MHz clock signal into the 14 MHz signal gener-ator. Although the signal generator produces discrete programmable frequencies internally,also an external clock reference signal can be supplied. Consequently, the signal generatorderives the 14 MHz frequency from the 2 MHz clock reference signal, such that there is onlyone master oscillator from which all signals are derived. The according signal path is shownin figure 3.13. Additionally the clock reference signal is fed into a trigger delay unit, whichallows for scanning the 2 MHz signal at different phases by adjusting the delay between inputand output signal. The unit’s output signal triggers the ICCD camera. With this conceptthe 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 MHzcycle 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 needsto be shorter than a 14 MHz period (71.43 ns), otherwise temporal resolution is lost. For thechosen Ne 2p1 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 phaseposition 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 entireset of discrete time snapshots is gained. Nevertheless, one has to keep in mind, that those datado not represent the excitation or ionization directly. They have to be deconvoluted with thetemporal behavior of the chosen Ne 2p1 transition. Therefore an appropriate model describingthe (de-)excitation needs to be developed. The presented model has been developed by Ganset al. and will be presented comprehensively. Full details can be found in literature [82].

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 rateequations. In its simplified case used within this work only electron impact excitation out ofthe ground state and de-excitation by spontaneous emission are taken into account. Becauseother (de-)excitation processes like inelastic collisions, cascades, excitation out of metastablestates or reabsorption of radiation might also be of importance, possible sources of errorsquickly become apparent. However, the used Ne 2p1 emission line was chosen for severalreasons. First, an exact knowledge of electron impact excitation cross sections and opticaltransition rates are available from literature and databases. Second, the expected influence ofcascading processes and collisional de-excitation is generally low, which has been investigatedand verified in detail by Gans et al. [82]. Third, the chosen transition exhibits enough intensityfor diagnostic purposes and has no superposition with other possible emission lines. Mostimportantly, the chosen neon line relaxes fast enough for a high temporal resolution andfurthermore, due to its excitation energy level of 19 eV gives access to the strongly rf-modulated high energetic tail of the EDF. Finally the time-dependency is incorporated byusing rate equations as an adequate description of the transient excitation behavior.

Because the diagnostic interest lies in determining the transient excitation one has to corre-late it to the observed emission. This can be written as

nPh,i(t) = Aik · ni(t) (3.37)

where nPh,i(t) is the observed emission per volume and time from level i, Aik the transitionrate of the observed emission and ni(t) the population density of an excited level i. Next,the time-dependent (de-)population of the used Ne 2p1 transition needs to be described bya rate equation. Therefore only excitation from ground state and spontaneous emission areconsidered, yielding the relation

dni(t)

d t= n0Ei(t)− Ai ni(t) (3.38)

where n0 is the ground state density, Ei(t) the excitation function with Ei(t) = ne ·X0i andX0i as a rate coefficient. Furthermore Ai is defined as an effective decay rate by

Ai =∑k

Aik gik +∑q

kq nq (3.39)

with∑

k Aik gik describing the radiation by spontaneous emission and∑

q kq nq describingradiation-less de-excitation by inelastic collisional processes. Hereby, gik is the so-called es-cape factor, kq the collisional de-excitation coefficient and nq the density of all collisionpartners q. For more details on the determination of kq please refer to Gans et al. [83]. In-serting equation (3.37) into (3.38) and solving for Ei(t) correlates the excitation directly tothe observed emission.

Ei(t) =1

n0Aik·(

d nPh,i(t)

d t+ Ai nPh,i(t)

)(3.40)

Because, de-excitation by inelastic collisions is found to be low for the chosen Ne 2p1 tran-sition the term

∑q kq nq becomes negligible in equation (3.39).


Figure 3.14: Space and time resolved excitation plot for a 2 MHz/14 MHz dual frequency dis-charge. 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 3.14. This plot in-corporates a full set of time-discrete images recorded at dedicated phases, such that a onedimensional spatial and temporal resolution is achieved. Figure 3.14 depicts the distancefrom 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 secondhalf (250− 500 ns) no such electrons are detectable. This group of hot electrons are furtherdenoted as electron beams [84]. The electron beam concept, with respect to electron heat-ing in rf driven capacitive discharges, was investigated experimentally and theoretically bySchulze, Heil et al. [84].

The production of high energetic electron beams is explainable by electrons being reflectedat the expanding plasma boundary sheath gaining additional energy, which in a low pressureregime (≤ 10 Pa) is recognized as a form of stochastic heating. Since the discharge is operatedin such a pressure regime, stochastic heating is considered the main mechanism of electronheating and thus discharge sustainment. By reducing pressure the intensity of the highenergetic electron beams becomes more pronounced, indicating the electron beams acquirean 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 anear symmetric industrial dual frequency capacitive setup, Schulze et al. found the electronbeams being reflected at the opposite electrode’s sheath performing additional heating asthey traverse the plasma bulk several times [85]. The discussed phenomenon of electronbeams is more easily detectable by electrical means, which is of relevance for industrialprocess monitoring as seen later in section 3.4.

Normally, in a single frequency rf discharge only one beam of high energetic electrons isproduced each frequency cycle. However in a dual frequency discharge the plasma boundary

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 producedas seen in figure 3.14. Theoretically, for the given discharge conditions (2 MHz/14 MHz), amaximum 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 influenceon the number of produced beams, which is explained in more detail later on in section4.2. Generally it can be stated, that the observed high energetic electron beams are notonly the key mechanism for discharge sustainment, but also a directly accessible dischargeoptimization parameter.

Summing up, PROES as a plasma diagnostic is used for the time-resolved determination ofexcitation mechanisms. With respect to capacitively coupled dual frequency discharges thisdiagnostic method is important for determining effects resulting from changing the relativephase between excitation frequencies. Therefore a phase-locked synchronization has to beensured. Practically, this is achieved by supplying the 2 MHz source’s reference clock signalinto the 14 MHz rf source. In that way, only one dedicated clock signal exists and the relativephase becomes adjustable. Additionally synchronizing the camera system with the 2 MHzcycle through a trigger delay generator enables the acquisition of time-discrete dischargesnapshots 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 exhibitthe generation of high energetic beams of electrons by reflection at the expanding plasmasheath edge. The role of relative phase change between the excitation frequencies is furtherinvestigated in section 4.2. Since optical diagnostics of the discussed scale are unsuited forindustrial plasma processing another possibility of investigating discharge excitation mecha-nisms 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 resolvedoptical emission spectroscopy (PROES) was discussed. In industrial plasma processes how-ever, where realtime process monitoring is desired, PROES is expensive and unmanageableto be applied on numerous processing tools. As mentioned previously, an alternative wayof detecting those electron beams can be used. By introducing a metallic sensor plate iso-lated from electrical ground, a part of the total rf current to the wall can be recorded. Itis measured by a current equivalent voltage drop across a 50 Ω resistor. An exemplary ac-quired current signal is seen in figure 3.15 (right). Additionally, the scaled purely sinusoidalexcitation voltage waveform is plotted (figure 3.15 (left)). Both waveforms were not sampledsynchronized, such that their relative phase relation is arbitrary.

What becomes apparent is, despite the excitation voltage consisting only of sinusoidal wave-forms, the measured plasma current obviously contains more frequency components. This isexplained by the generation of harmonics and their mixing frequencies due to the nonlinearnature of the plasma boundary sheath in front of the driven electrode. But especially high-lighted is the appearance of resonant structures at each 13.56 MHz period, as illustrated in


Figure 3.15: Typical current signal acquired in a dual frequency discharge (right). Additionally thearbitrarily scaled (purely sinusoidal) excitation voltage waveform is plotted for comparison (left).Discharge conditions are 67.8 and 13.56 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 3.15with 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 the-oretical explanation for the exhibited resonance is needed. Mussenbrock et al. developed asimple nonlinear global model and a sophisticated analytic model capable of addressing thismissing 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 ofa capacitive discharge [60], with the difference of introducing nonlinear capacitors for therespective sheaths in front of the grounded and conducting electrode as shown in figure 3.17.

For the case of a dual frequency driven plasma two voltage sources URF1(t) and URF2(t) areused. Mussenbrock’s et al. model separates the mathematical description of plasma bulk andplasma boundary sheath, because in capacitive discharges the Debye-Huckel length λDebye asdefined by equation (3.11) is typically much smaller than the electrode separation. In thiscase, the plasma bulk can be described by the concentrated electrical components LBulk and


Figure 3.17: Simple PSR equivalent circuit model of a capacitive rf plasma discharge.

RBulk. They represent electron inertia and ohmic power dissipation in the plasma. Withinthe bulk, quasi-neutrality holds (ne = ni) and the current is carried solely by conduction.Hence, the resulting total current through the plasma bulk can be written in time-domainrepresentation as

UBulk =me L

e2 neAelectrode

·(

d I

d t+ νm I

)(3.41)

where νm is the electron-neutral collision frequency, ne the average plasma density in thebulk, Aelectrode the area of the driven electrode, L the effective bulk length (electrode gapminus both sheath extensions) and UBulk the voltage drop across the plasma bulk [87]. Byregrouping above equation values for the electrical components LBulk andRBulk can be derivedas

LBulk =me L

e2 neAelectrode

(3.42)

RBulk = LBulk · νm . (3.43)

Thereby, the description of the plasma bulk is complete and the plasma boundary sheathsare described next. For the sheath description a matrix sheath is assumed. A matrix sheathdescribes the divergence of electron and ion density in the sheath region as a hard wall(non-continuous) concept. That means, the electron density ne drops to zero at the sheathedge. Overall, it is the simplest concept of formulating the charge density divergence. Analternative possibility involves the Child law sheath assumption, which uses a uniformlycontinuous function for ne and ni. For the given model description by Mussenbrock et al. noelectrons are present within the sheath region. Hence, the total discharge current is carriedsolely by displacement.

Figure 3.17 includes both plasma sheath regions in front of the driven electrode CSheath electrode

and the grounded wall CSheath ground. Additionally, a dc current blocking capacitor CBlock isintroduced into the system. The voltage drop across this component is the plasma’s dcself bias voltage. The standard case for capacitive discharges, which also holds for theexperiment within this work, assumes a strongly asymmetric operation (ASheath ground ASheath electrode), which makes CSheath ground large compared to CSheath electrode such that the


voltages are USheath electrode USheath ground. Because both capacitors are in series, the totalcapacitance in the circuit is expressed as CSheath total ≈ CSheath electrode. In the following step,expressions for the voltage drops across both capacitors need to be determined. As mentionedearlier the main cause for harmonics generation lies with the nonlinear nature of the sheathcapacitances. Hence, no linear formulation, such as e.g. IC(t) = C · dUC

d tis allowed. On the

basis of a self-consistent simulation, Mussenbrock et al. propose a voltage-charge relation forthe nonlinear plasma sheath region in front of the driven electrode as follows

USheath electrode(Q(t)) = USheath electrode +s

ε0Aelectrode

Q+1

2 ε0 e ni,Sheath A2electrode

Q2 . (3.44)

It has been shown, that even for large sheath modulations the quadratic-order voltage-chargeapproximation remains reasonable [88]. For the sheath in front of the grounded electrode asimple description is found, because the voltage drop remains constant as

USheath ground(Q) = USheath ground . (3.45)

Additionally the dc components within both voltage equations are recognized to be the dcself bias voltage

Udc bias = USheath electrode − USheath ground = UBlock ≈ USheath electrode . (3.46)

Using the fundamental relation

dQ

d t= −I (3.47)

to couple bulk and sheath model and further applying Kirchhoff’s law on the completeequivalent circuit from figure 3.17 yields a differential equation with respect to dischargecurrent

URF1(t) + URF2(t) = URF1 cos(ωRF1 t) + URF2 cos(ωRF2 t) =

LBulk ·(

d I

d t+ νm I

)︸︷︷︸

UBulk

−(

s

ε0Aelectrode

Q+1

2 ε0 e ni,Sheath A2electrode

Q2

)︸︷︷︸

USheath electrode

. (3.48)

Finally, equation (3.48) represents the desired nonlinear global model for a dual frequencydriven capacitive discharge, capable of describing the generation of harmonics by the nonlin-ear 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 arecomparable to a very good extent as outlined in more detail in section 3.4.3. Obviously, bytaking a closer look, the given equivalent circuitry is determined to be a series resonance cir-cuit, which is the main reason for the naming of plasma series resonance (PSR). By solvingthe differential equation (3.48), a characteristic geometric resonance frequency ωPSR, oftenreferred to as “self-excited electron resonance spectroscopy”, is found. It is formulated as

ωPSR =

√e2 ne s

ε0me L= ωpe ·

√s

L. (3.49)

Using a characteristic set of plasma parameters for the presented dual frequency setup withne = 2 · 1016 m−3, Te = 3.0 eV, L = 35 mm and V0 = 500 V yields a plasma series resonance


frequency of fPSR = 458.15 MHz. Hereby, equation (3.10) was used to calculate an accuratemean sheath extension of s = 4.556 mm. At the same time the Debye-Huckel length λDebye =91.05µm and the electron plasma frequency fpe = 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 anapproximation of the PSR only. Hence, all calculated PSR frequencies within this work areintended to be reasonable approximations.

Before returning to the original question of correlating the dynamic electron excitationrecorded by PROES measurements with the harmonic loaded plasma rf currents, another in-teresting mechanism for heating a plasma discharge is discussed. Since a capacitive dischargecan be understood in a simplified sense to be a series resonance circuit with a resonance fre-quency ωPSR, the question of heating the plasma directly at this frequency arises. Godyaket al. [89] and Qiu et al. [90] closely investigated the possibility of heating a capacitive dis-charge at the plasma series resonance frequency. They found it to be a highly efficient wayof heating the plasma. However, a further possibility can be thought of which is presentedin detail in the following section.

3.4.1 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 theoreticalconsiderations of Mussenbrock and Brinkmann [1]. They propose a further explanation forlow pressure ohmic heating. It works as an indirect plasma series resonance heating, termednonlinear electron resonance heating (NERH). The indirect heating is achieved by the factthat the nonlinear plasma boundary sheath generates numerous harmonics of various ampli-tudes 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 canbe excited by a set of harmonic frequency components, within a certain vicinity. Furtherworks, 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. Fromelectrical engineering the concepts of Q-factor or quality-factor and bandwidth of a resonanceare well established. Thereby the Q-factor QPSR denotes the maximum rise of magnitude atthe exact resonance frequency, and the bandwidth BPSR the resonance broadening (width).Generally, they are defined as follows

QPSR =ωPSR LBulk

RBulk

(3.50)

BPSR =fPSR

QPSR

. (3.51)

By above equations, the “vicinity” is now adequately described through the bandwidth BPSR.Inserting equation (3.50) into (3.51) and simplifying for relevant plasma parameters yields

BPSR =νm

2 π(3.52)


and also for the Q-factor

QPSR =ωPSR

νm

. (3.53)

It is a remarkable result, because the PSR bandwidth only depends on the electron-neutralcollision rate νm. Exemplarily calculating BPSR for typical experimental values of νm, with108 s−1 ≤ νm ≤ 109 s−1, yields 15.915 MHz ≤ BPSR ≤ 159.15 MHz. Similarly a range for theQ-factor is given by 28.786 ≥ QPSR ≥ 2.879. This result strongly emphasizes the possibilityof an indirect heating at the plasma series resonance (NERH), because even for low electron-neutral collision rates νm all mixing/harmonic frequency components satisfying

(fPSR −BPSR

2) ≤ fharmonic ≤ (fPSR +

BPSR

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 ωPSR by harmonics is pro-vided at a small bandwidth but with a steep magnitude rise or at a broad bandwidth with amuch reduced magnitude rise. This finding is also the self-limiting factor of additional har-monic heating, because the more efficient a plasma is heated (resulting in increased ohmicpower dissipation, thus increasing also νm), the more reduced QPSR will get. Hence, the mag-nitude rise is reduced, which in the extreme case becomes QPSR = 1, which in turn impliesthe bandwidth becomes equal to the resonance frequency. In this special case, no additionalresonance heating is possible. Later in section 4.1.1 an experimental example of nonlinearelectron resonance heating (NERH) is presented.

3.4.2 Correlation of measured PSR currents to PROES

Continuing the discourse on process monitoring, this section will discuss implications ofcorrelating SEERS to PROES measurements.

Figure 3.18 (top) displays the same PROES plot as shown in figure 3.14. Again the spatio-temporal structures of the electron beam concept are visible. Recapitulating, the two electronbeams around t = 100 ns are formed by electrons being reflected at the expanding plasmaboundary sheath. Because of the lack of a true counter electrode, in this case the groundedwall acts as the counter electrode, no reflected beams are observed within the second 2 MHzhalf-period.

Correlating a synchronously measured PSR current 3.18 (bottom) to the PROES excitationplot, provides a strong similarity. Although the PSR signal neglects spacial resolution, com-parable structures are recognizable in the current signal. More exactly, each resonant peakin 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 thesignal magnitude, which correlates with the recorded amount of emission. Also the second2 MHz half-cycle as measured by PROES can be compared well with the current signalstructure, exhibiting no resonances where PROES accordingly shows no excitation.

Since the SEERS diagnostic method [95][96] is in wide-spread commercial use, this additionalinformation provide a deeper insight into fine-tuning plasma processes, so as to optimize ex-


Figure 3.18: Correlation of time and space dependent excitation plots from PROES to simulta-neously measured PSR currents. Discharge conditions are 2/14 MHz, Neon, 10 Pa, 7 sccm, nocounter electrode (electrode=grounded wall) installed.

citation behavior within certain limits. These limits are set e.g. by a needed plasma chemistryrecipe spanning a certain parameter space. An illustrative example for the fine-tuning con-trollability by PSR current monitoring is provided within this work in section 4.2. Therebythe relative phase between the excitation frequencies is varied and both, PROES as well asPSR measurements unveil a noticeable and tunable effect.

The commercially available system is produced by the German company Plasmetrex GmbH,in the form of Herculesr PMX. In its standard version it provides real-time access to theeffective electron-neutral collision rate νm and volume-averaged plasma density ne. Theseparameters are found by a real-time capable method of either determining the equivalentcircuit elements RBulk and LBulk or frequency-space analysis, determining ωPSR and BPSR.

The following final section verifies the validity of the previously presented global model byMussenbrock et al. [3] by comparing measured PSR currents to calculated current signals.For the calculations realistic experimental input parameters are used.


3.4.3 Comparison of measured SEERS/PSR currents to model calcu-

lations

In this section the applicability for dual frequency discharges of the presented model byMussenbrock et al. [3] is verified by comparing measured PSR currents to simulated currentsignals. Therefore the model needs to reproduce the measured PSR currents by setting offwith realistic experimental discharge conditions. Those have been 67.8/13.56 MHz with anelectrode separation of 35 mm, Argon at 5.4 Pa and 10 sccm. The PSR current samplingis realized by an integrated wall sensor with a diameter of 5 mm, isolated from electricalground and connected to a digitizer card. Sampling conditions are at a sampling frequencyof 2 GHz and a bandwidth of 1 GHz.

Most of the above listed external discharge parameters can be directly integrated into themodel. However, the model equation (3.48) takes voltages as input parameters and notgenerator powers. Experimentally, the power ratio has been set to P67.8 MHz : P13.56 MHz =2 : 1. As input parameters for model calculations the equivalent voltage ratio results toU67.8 MHz : U13.56 MHz =

√2 : 1. Consequently using all given external discharge parameters

and calculating the expected PSR current signal yields figure 3.19.

All plots on the left-hand side denote measured PSR currents and on the right-hand siderepresent calculated PSR currents. What becomes apparent first is a very good agreementof both time-domain signals. They exhibit the same resonance structures and also individualpeak behavior matches well. A close inspection by performing a discrete Fourier transfor-mation on both current signals provides insight into the differences between model andmeasurement. As seen in figure 3.19 (bottom), the first ten harmonics of 13.56 MHz comparereasonably well. Harmonics larger than ten times 13.56 MHz are different. This is explainedby using simplified initial model assumptions. It is assumed from the beginning, that only oneoverall plasma series resonance exists. However, a more realistic consideration would involvea multitude of these so-called resonant modes. Including these additional modes would leadto very good agreement also for harmonics larger than the tenth harmonic of 13.56 MHz [2].This is subject to a current research topic of Ziegler and Mussenbrock [2]. Nevertheless, inspite of the model’s simplicity, the results compare remarkably well. For further explanationsand a detailed outline of above presented calculations please refer to [2].

Summarizing, a direct connection between excitation plots recorded by PROES measure-ments and electrical PSR current measurements can be established. On the basis of a globalmodel developed by Mussenbrock, Ziegler et al. it becomes possible to reach a very goodcomparability between measured and simulated PSR current signals [3][98]. Essentially, thismodel 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 phenomenonobserved in low-pressure discharge operation, namely through nonlinear electron resonanceheating (NERH). In section 4.1.1 the experimentally observed effects of NERH are discussed.

The previously discussed diagnostics address the topic of electron heating in capacitive dis-charges and their correlated plasma parameters. For the following two applied diagnostics thefocus moves to ions and neutral species behavior, which is directly relevant for surface modi-fications and sputter deposition characterization. Therefore a retarding field energy analyzer

3.5. Retarding field energy analyzer (RFEA) 53

Figure 3.19: Comparison of calculated to experimental PSR currents under equivalent dischargeconditions. Simulation input parameters correspond to experimental tuning parameters. Plotsshowing simulation results on the righthand-side are taken from [97]. An even better agreementis 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) distri-bution function. In general, its working principle is also transferrable to the determinationof electron distributions by changing the direction of the retarding potential. It can be seena mass-integrated ion energy analyzer. The theory of operation is explained by consideringfigure 3.20.

Physically, an RFEA works as an electrostatic probe. This means negative dc voltages are ap-plied to attract ions and repel electrons. Sweeping the dc voltage produces different detectablecurrent magnitudes. Evaluating the acquired (ion)current/voltage characteristic yields theion distribution function (IDF). In principal, one sweeping voltage should be sufficient. How-


aaaaaaaaaaaaaaa 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 electronemission within the analyzer and the ion’s angle of acceptance.

Figure 3.20 depicts the electrical and mechanical setup of an RFEA. The mechanical layoutconsists of an entrance orifice, three grids and a collector area. Schematically only one en-trance orifice is plotted, however the applied commercial system by Impedans Ltd. consistsof multiple 800µm holes evenly distributed across an area of 1 cm2, ensuring a sufficientamount of collected ion current. “Grids 1-3” are made out of nickel, each having 18µm holes.Furthermore, they are electrically separated against each other by insulators (quartz, ce-ramic etc.). More detailed information about the sensor’s internal build-up are described inliterature [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 angulardistribution. The only objective of “Grid 1” is narrowing the effective angle of acceptance foreither charged species. All ions and electrons having passed the entrance orifices and “Grid1” encounter the negative (with respect to floating potential) potential U1 of “Grid 2”. Itspurpose is to filter out the incoming plasma generated electrons, which is particularly relevantat the time of sheath collapse in capacitive discharges, when a large amount of electrons canenter 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−kB Te) to effectively filter most of the incoming electrons.

Traversing the gap between “Grid 2” towards “Grid 3”, ions are discriminated by the variablevoltage U2. Usually, the potential range for U2 is scanned between the dc potential of “Grid1” (retarding potential of 0 V) to 10− 20 V above the plasma potential. Thereby, one has tokeep 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


e (ΦPlasma + 2 |Udc bias|). This makes an increase in the scanning range for U2 necessary. Inthat way all possible ion energies are covered. Eventually, ions with sufficient energy passing“Grid 3” are attracted by a small negative potential U3 towards the collector plate where theresulting ion current is detected. An important condition for the attracting potential U3 isto not bias it too negatively, so as to largely accelerate the ions. In this case the ions wouldgain sufficient kinetic energy, bridging the collector material’s work function (typically onlyseveral 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 tothe collector potential. This restrains secondary electrons to the volume between“Grid 4”andthe collector, not disturbing the sensitive ion current measurement. For the measurementswithin 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 nodistortions of the kind measured by Bohm and Perrin [100], who thoroughly investigated sec-ondary electron emission in RFEAs. Figure 3.21 depicts an exemplary potential distributionwithin the used RFEA with three grids.

Figure 3.21: Typically used potential distribution among the grids of the applied RFEA for iondistribution function measurements.

The presented RFEA is used for ion energy measurements on the electrically rf driven elec-trode, which on the one hand enforces additional considerations of suppressing rf influenceon the electrostatic probe parameters. On the other hand a synchronous modulation of “Grid2” and “Grid 3” need to be realized to suppress distortions of the voltage-current trace. Sim-ilar to the presented Langmuir probe compensation scheme in section 3.2.1 a passive filterconcept is incorporated into the commercial solution. Low-pass filters are inserted betweenthe electrical circuit of “Grid 2”, “Grid 3” and the collector to ensure that all grids and thecollector maintain electrode rf potential. They also prevent rf voltages from building withinthe RFEA measurement electronics. A detailed analysis of the applied filter concept is foundin literature [99]. In the following section the derivation of the ion velocity distribution outof measured voltage-current traces is discussed.


3.5.1 Ion velocity/energy distribution function measurement

With the given RFEA measurements on the rf driven electrode are performed . An exemplarymeasured and post-processed (smoothed) voltage-current trace is depicted in figure 3.22. Assmoothing algorithm a Savitzky-Golay scheme with a third order polynomial and a fixedbandwidth 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 poten-tial in a dual frequency discharge at 67.8/13.56 MHz. Experimental conditions are U13.56MHz =35 VRMS and U67.8MHz = 70 VRMS, Argon, 3.5 Pa, 10 sccm.

Increasing the retarding potential to positive values, repels more and more ions. Consequentlythe measured current amplitude reduces from 630 nA down to zero. A two-slope-like behaviorof the curve is observable. From the obtained voltage-current curve the ion velocity/energydistribution is directly calculable. A detailed derivation by Bohm and Perrin is presented ina comprehensive form to illustrate the scheme [100].

Assuming a one-dimensional velocity distribution function evolving in the ion flight pathinto the analyzer, the total ion density ni is set to

ni =

∫ ∞0

fion(v) dv . (3.55)

The conversion from velocity to energy distribution is achieved by substituting the velocitywith E = 1

2mi v

2 and hence also dE = mi v dv, withmi as the ion mass, v the one-dimensionalion velocity (only the ion’s preferential direction is considered), ni the ion density and E theion energy.

The total ion current density at the analyzer entrance is defined by

I = −e∫vf(v) dv = − e

mi

∫f

(√2E

mi

)dE (3.56)


with the additional transformation of the ion velocity distribution into the ion energy distri-bution function [100]. Deriving expression (3.56) with respect to energy E, the ion distribu-tion function is gained

f

(√2E

mi

)= −mi

e·(

dI(E)

dE

). (3.57)

Expression (3.57) shows the ion distribution function to be directly proportional to the firstderivative of the voltage-current characteristic. It can further be rewritten by replacing theenergy E with the retarding potential φret given as E = e φret.

f

(√2 e φret

mi

)= −mi

e2·(

dI(e φret)

dφret

)(3.58)

Finally, applying equation (3.58) to the sample voltage-current trace shown in figure 3.22provides the ion distribution function depicted in figure 3.23.

Figure 3.23: Normalized ion distribution function (IDF) calculated as the first derivative of thevoltage-current trace shown in figure 3.22.

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 includethe bimodal structure in general and the peak separation ∆E. The reason for the two peaksbecomes apparent by considering an ion’s incident energy on the electrode. Its energy stronglydepends 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, moreions corresponding to those energies are collected, resulting in the characteristic bimodalstructure.

A further parameter is the time an ion needs to pass the sheath region, denoted as the iontransit time τi. Relating the ion transit time and the rf period τrf gives rise to two separateregimes. First, if τi τrf the ions are able to cross the sheath in less time than an rf period,


hence they are able to follow the instantaneous sheath modulation. As a result, a broad IDFis 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 energyions 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 plasmapotential.

Second, if τi τrf 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 themaximum gainable ion energy is solely governed by the dc self bias voltage (in asymmetriccapacitive discharges). Consequently, the IDF narrows, leaving the energy gap ∆E at smallervalues. 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 analyticexpression for the energy spread ∆E in this regime was derived by Benoit-Cattin and Bernard[101] and shows

∆E =4

π

τrf

τi

· eUrf (3.59)

where Urf is the rf sheath voltage and τrf = 2πωrf

the rf period time. τi is the ion transit timedefined as

τi = 3 s

√mi

2 eUdc bias

(3.60)

with s as the mean sheath width defined by equation (3.10), mi the ion mass and Udc bias

as the dc self bias voltage. It can be seen that the energy spread ∆E is proportional tothe ion mass with m

−1/2i . 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 ∆Eof both peaks. Since the presented dual frequency setup is constructed for thin film sputterdeposition, only argon IDFs are investigated in section 4.3. A more detailed theoreticalapproach for calculating ion distribution functions in dual frequency discharges is derivedby Wu et al. [102]. Further recent investigations involve the excitation by arbitrary (non-sinusoidal) waveforms for dedicated manipulation of IDFs [103]. Considerations on ion energydistribution control are outlined by Lee et al. [104] and Georgieva et al. [105].

3.6. Quartz crystal microbalance (QCM) 59

3.6 Quartz crystal microbalance (QCM)

A typical field of application for quartz-crystal microbalances (QCM) is film thickness mon-itoring in various kinds of deposition processes, by detecting the change of mass under theassumption of a known film density.

Figure 3.24: Functional schematic of a quartz-crystal microbalance. Arrows indicate the elec-trode contacts (black) and the deposited thin film (gray). Furthermore the thickness shear modeoscillation direction (dashed line) is included.

The measurement principle is based on piezoelectricity and illustrated in figure 3.24. 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 from4 − 6 MHz for common applications. Therefore, usually gold-plated contacts are broughtonto the crystal substrate from both sides. By applying an alternating voltage betweenboth contacts, the crystal starts oscillating due to the piezoelectric effect. Depending onthe crystal structure a predefined resonance mode, in this case the so-called thickness shearmode, is excited. It solely produces a lateral displacement as indicated in figure ??. Becausethe resonance is strongly temperature dependent, a special crystal cut, the so-called AT-cut, is used to optimize temperature stability. Thereby, a quartz crystal block is cut undera certain angle to the crystallographic axis. An alternative type of crystal cut is able tocompensate mechanical stress (SC-cut). Further details on crystal cuts, piezoelectricity andrelated 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 (usingthe fundamental relation Q = fres

B, also see equation (3.51)). Realistic Q-factor values can be

as high as 106, denoting a very sharp resonance. This condition provides a stable resonanceand 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 tothe thickness. By loading the crystal with a material, two changes are observable. First, theresonance shifts to lower frequencies and second the resonance magnitude is damped. Dueto the aforementioned resonance’s nature the frequency shift from the “unloaded case” tothe “loaded case” can be precisely determined and directly correlated to the change of totalmass. This relation was formulated by Sauerbrey [107] and is given as

∆f = −2f 2

q

Zq

∆m

Aq

(3.61)

where fq is the uncoated quartz resonance frequency, Aq the electrode area and Zq the quartzacoustic impedance defined by

Zq =√ρq µq = ρq vq (3.62)


with ρq as the quartz mass density, µq as the quartz shear modulus and vq the velocityof sound. The fraction Sf = 2f 2

q/Zq is purely material specific and commonly denoted asSauerbrey constant.

If the mass density of the growing film ρf is known, equation (3.61) can be expressed interms of thin film thickness df or more exactly by its change ∆df using the elementaryrelation expressing mass in terms of mass density and volume m = ρ · V

∆f = −Sfρf ∆Vf

Aq

= −Sf ρf ∆df . (3.63)

Regrouping equation (3.63) to ∆df yields the film thickness change to be

∆df = − ∆f

Sf ρf

=fq − fcoated

2f 2q

ρq vq

ρf

. (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 mustbe rigid and (iii) the frequency change (fq − fcoated)/fq must be smaller than < 5%. Forvacuum coating processes conditions, assumptions (i) and (ii) are easily met. But dependingon the atomic weight of the deposited material, condition (iii) is usually not met. As a resulta more sophisticated load approximation was derived by Lu and Lewis [108] to

∆df =Nq ρq

ρf fcoated

1

π Rz

arctan

[Rz tan

(πfq − fcoated

fq

)](3.65)

where Nq is the frequency constant for AT-cut quartz crystals and Rz the acoustic impedanceratio given by

Rz =Zq

Zf

=

√ρq µq

ρf µf

(3.66)

with the respective mass densities and shear moduli of the quartz and film material. Thisfinal equation (3.65) is the standard method applied in available QCM equipment.

To quantitatively correlate electrical to physical properties of quartz and film a mathematicaldescription is needed. It is given by the Butterworth-van Dyke equivalent circuit model of aquartz-crystal resonator as shown in figure 3.25 [109].

Therein, two impedance categories can be identified. First, the electrical and the acousticimpedance branch and second, the perturbed and unperturbed case. Beginning with therepresentation for the unperturbed crystal, the electrical capacitance Cel originates from thecontact electrodes and is calculated by

Cel =ε0 εqAq

dq

(3.67)

with εq and dq as the permittivity and the quartz crystal substrate thickness. Describing theseries resonance circuit of the acoustic branch in the unperturbed case, a linear differentialequation of second order is used

md2x

dt2+ α

dx

dt+ k x = 0 (3.68)

3.6. Quartz crystal microbalance (QCM) 61

Figure 3.25: Butterworth-van Dyke (BvD) equivalent circuit of a quartz crystal resonator. Theacoustic branch parts represent the electrically equivalent behavior of the piezoelectro-mechanicalcrystal behavior expressed in equations 3.69-3.71. The acoustic film impedance ZFilm also consistsof an inductance LFilm and a resistor RFilm.

with m as the oscillating mass, k the spring constant and α the attenuation constant. Adirect connection to electrical equivalent series resonators is given by replacing the mechanicaldisplacement x with the chargeQ. Consequently, the electrical components Racs, Lacs and Cacs

can be written in terms of mechanical variables. All of them depend on the real electricalcapacitor Cel as found by Bechmann [110]. The validity of these findings was verified bySauerbrey [111]. They are defined as

Cacs =8K2

0 Cel

(nπ)2(3.69)

Lacs =1

ω2q Cacs

(3.70)

Racs =ηq

cqCacs

(ω

ωq

)2

(3.71)

where K0 is the piezoelectric coupling factor, n the excitation frequency harmonic order, ηq

the dynamic viscosity and cq the quartz constant for AT-cut crystal substrates (incorporatingthe speed of sound) . Initially only the contribution of the unperturbed crystal exists andno load impedance ZFilm is present. By depositing a material onto the crystal substrate,a load impedance of the form ZFilm = RFilm + ω LFilm is added to the system as shownin figure 3.25. Hereby, the resistive component RFilm describes the resonance amplitude’sattenuation 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 itsdisturbing nature regarding plasma homogeneity. In that case, alternatively an ellipsometeras a non-invasive film monitoring diagnostic is available. With respect to the planned metallicfilm deposition however, several problems arise by using ellipsometry. First, thin metallicfilms usually exhibit a low roughness when deposited onto silicon wafers. Simultaneously thereflectivity 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 resultinglayers significantly increase, the probing polarized light is depolarized, caused by scatteringeffects on the rough surface. Experiments with thin metallic films deposited onto silicon


wafers show ellipsometry to be difficult in application for these specific materials. Althoughunder certain conditions, such as e.g. only a few monolayers thick films, ellipsometry isapplicable for investigations.

This finalizes the discussion on the experimentally applied plasma and thin film diagnosticswithin the frame of this work. The following chapter 4 is concerned with the applicationof the aforementioned diagnostics to different relevant plasma and thin film tasks. Mostrelevant investigations for this work involve the optimization and characterization of dis-charge parameters with respect to frequency coupling and observations in electron heatingmechanisms.

63

4. Measurements and discussion

This chapter discusses investigations into various parameter studies on the introduced dualfrequency driven capacitively coupled plasma. Thereby, three dedicated fields of interest withtechnological relevance to commercial plasma processes are subject to research. As motivatedin the introduction, 2f-CCPs are particularly interesting for their attributed property ofseparated 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 separabilityof ion flux and energy by tuning respective frequencies and powers.

Therefore, the frequency ratio is characterized in detail by Langmuir probe, PROES andPSR measurements. However, not only the frequency ratio is of interest, but also the tun-ability of the relative phase between both excitation frequencies is examined. Additionallythe theoretical investigations of Mussenbrock and Brinkmann [1] concerning nonlinear elec-tron resonance heating are addressed. The correlation between measured PSR currents andPROES excitation plots is outlined in further detail.

Furthermore, in a second parameter study, the behavior of ions impinging on the sputtertarget electrode are investigated using a retarding field analyzer (RFEA) capable of beingmounted onto the electrically driven electrode. To this regard, especially the power varia-tion/ratio of both excitation frequencies is most important, because the frequency ratio’seffect on the expected ion energy is low. This is also experimentally verified.

Finally, detailed investigations and findings from the aforementioned plasma diagnostics isbrought to application by performing physical vapor deposition (PVD) experiments withmetallic materials. Because of their increasing relevance for memory applications in the formof magneto-resistive random access memories (MRAM), they pose a new industrially relevantfield of application for 2f-CCPs. Thus, for initial studies of the sputter deposition rate anddeposition homogeneity ferro-magnetic equivalent materials are used.

4.1 Variation of external parameters for VHF / 13.56 MHz

CCP operation

Within this section three parameter studies are performed, which include the variation offrequency ratio, power ratio and system pressure. As plasma diagnostics, Langmuir probeand a PSR current sensor are applied to the experiment. The Langmuir probe tip position

64 4. Measurements and discussion

for all measurements is situated in the discharge center, symmetrically placed between bothelectrodes. Measurement conditions holding for all investigations within this section are aconstant gas flow rate of 5 sccm argon and an electrode separation of 45 mm. The twoexcitation frequencies are 13.56 MHz denoted as f13.56MHz and one discrete frequency outof the range 63 − 85 MHz denoted as fVHF. Both excitation frequencies are fed to the topelectrode in the way described in section 2.1. All further applicable discharge parametersare mentioned individually for each parameter study. To begin with, the frequency ratio ispresented.

4.1.1 Frequency ratio

In this section the frequency ratio is studied by varying the high frequency component fVHF

in the range of 63− 85 MHz, while leaving the low frequency component f13.56MHz constant.The given range for fVHF 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 arefixed to P13.56MHz = 50 W and PVHF = 100 W. The condition PVHF > P13.56MHz ensures theplasma 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 ne by varying fVHF. Experimental conditionsare P13.56MHz = 50 W, PVHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm. The nonlinearfit validates the quadratic scaling of ne with fVHF.

Figure 4.1 displays the dependence of electron density ne on fVHF and a non-linearly increas-ing electron density is observed. It is well known from theoretical approaches by Surendraand Graves [5], Vahedi et al. [10] and Meyyappan and Colgan [6] that the electron densityapproximately scales with the square of the driving frequency in the system. To verify thiselementary scaling law for 2f-CCPs, a parametric estimator of the form ne ∝ fβVHF is fit tothe measured data in the least-squares sense. The exponent β is estimated to β = 2.111.

4.1. Variation of external parameters for VHF / 13.56 MHz CCP operation 65

This result agrees well with findings from [5][6][10], who predict the exponent β to lie be-tween 1.5 and 2.2, depending on whether radially averaged or peak electron densities fromthe discharge center are regarded.

Figure 4.2: Frequency dependence of the plasma and floating potential by varying fVHF. Exper-imental conditions are P13.56MHz = 50 W, PVHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap45 mm.

Also resulting from Langmuir probe measurements are the floating potential Φfloat and plasmapotential Φplasma. Both are shown in figure 4.2. As discussed in section 3.2, Φfloat is found atthe current zero-crossing and Φplasma is gained from the inflection point of the Langmuir probecurrent-voltage characteristic. Interpreting the results in figure 4.2 gives an approximatelylinear increase in the plasma potential by increasing fVHF. The floating potential exhibitsa similar behavior, but at a much larger variance. A rough approximation of the meanelectron temperature, adapted to argon in the following case, is known to be Te ∝ ∆Φ with∆Φ = (Φplasma − Φfloat) and

Te ≈[

1

2ln

(mAr

2 πme

)]−1

·∆Φ =∆Φ

4.679(4.1)

giving Te directly in Volts [60]. By applying above information to the approximated linearbehavior of Φplasma and Φfloat in figure 4.2 an estimation of the mean electron temperatureis gained. Since the potential difference ∆Φ remains approximately constant at 12.5 V, it inturn implies a constant mean electron temperature of Te = 2.7 eV.

For verification purposes, above estimation is compared to evaluations of Te from measuredLangmuir probe characteristics. Thereby, equation (3.30) is used and the outcome is displayedin figure 4.3. It becomes apparent, that the determination of Te on the measured probecharacteristics using equation (3.30) yields a large variance (≤ 0.8 eV) of the mean electrontemperature. This fact is clearly visible in figure 4.3. Nevertheless, combining aforementionedrough approximation and shown results for Te leads to the conclusion, that changing theexcitation frequency ratio has a negligible influence on the mean electron temperature. This is


Figure 4.3: Frequency dependence of mean electron temperature Te by varying fVHF. Experimentalconditions are P13.56MHz = 50 W, PVHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm.

in accordance with global model considerations, because discharge confinement (mean sheathextension) is only weakly affected and hence no significant changes in electron temperatureare expected. Further analyzing floating potential behavior on the basis of a global modelcan be understood such that the amount of high energetic electrons > 10 eV increases. Theseassumptions are experimentally verified later by optical measurements in section 4.2.2.

Returning to figure 4.1, local maxima in the electron density are observed. They reproduciblyappear at integer driving frequency ratios for 67.8/13.56 MHz and 81.36/13.56 MHz and evenmore 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 fVHF. Experimentalconditions are P13.56MHz = 50 W, PVHF = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm.


Hereby, the dc self bias voltage drops strongly in magnitude to an amount of approximately10%. To describe this phenomenon two possible explanations are deemed adequate. On theone hand, it has been discovered in recent experiments, that this effect becomes much lesspronounced if both excitation frequencies are mounted onto separate electrodes. Mountingboth rf sources onto one electrode always produces a stronger mutual coupling than havingthe plasma impedance separating both frequencies. Also, the effect only occurring at inte-ger frequency ratios is physically reasonable, because available power from fVHF is directlydeposited into available harmonics of f13.56MHz, generated by the plasma itself.

Conversely, in the case of non-integer frequency ratios the generation of side-bands andmixing products is caused, leaving the delivered powers of fVHF and f13.56MHz spectrally moredistributed. This last explanation gives way for the discussion in section 3.4.1, describing thepossibility of electron heating by plasma generated harmonics through nonlinear electronresonance 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 drivingfrequency ratio fVHF/f13.56MHz = 67.8 MHz/13.56 MHz. The PSR frequency is calculated to befPSR = 454.99 MHz using equation (3.49) with the Child-Langmuir sheath (3.10). Experimentalconditions are P13.56MHz = 50 W, P67.8MHz = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm.

When discussing the observed phenomenon of local electron density maxima occurring at in-teger frequency ratios, nonlinear electron resonance heating (NERH) has been deemed one ofthe possible explanations. Besides other electron heating effects commonly accumulated un-der the term “stochastic heating”, NERH proposes an alternative approach to efficient powerdissipation in the low pressure regime (< 10 Pa) due to discharge harmonics [113]. Experi-mental conditions within the frequency ratio investigations meet this pressure prerequisite.Nonlinear electron resonance heating, as explained in detail in section 3.4.1, describes anindirect excitation of the plasma series resonance (PSR) through plasma generated harmon-


Figure 4.6: Discrete Fourier amplitude spectrum of a measured PSR current at non-integerfrequency ratio fVHF/f13.56MHz = 63 MHz/13.56 MHz. The PSR frequency is calculated to befPSR = 431.37 MHz using equation (3.49) with the Child-Langmuir sheath (3.10). Experimentalconditions are P13.56MHz = 50 W, P63MHz = 100 W, 5 sccm, 3 Pa, Argon, electrode gap 45 mm.

ics laying close to the PSR. Therefore, the PSR’s “proximity” was mathematically describedby the resonance bandwidth BPSR and calculations for the predicted bandwidth have beendetermined to be at least ≈ 16 MHz at given experimental conditions.

To quantify and correlate the indirect PSR heating to local electron density maxima, dis-charge currents have been recorded for a non-integer and integer frequency ratio. The accord-ing 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 thespectrum 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 frequencieshave been additionally inserted.

For calculating PSR frequencies the rf-corrected Child-Langmuir mean sheath width approx-imation according to equation (3.10) is used, although other sheath width approximationsexist. Depending on the used approximation, considerable differences may arise in the cal-culated PSR frequencies. Using for example the simpler matrix sheath approximation givenas

s = λDebye

√2 e V0

kB Te

(4.2)

would result in PSR frequencies ranging from 200 MHz to 300 MHz. In comparison to thevalues given in figures 4.5 and 4.6 a non-negligible difference becomes apparent. As to thequestion of which is the correct calculation method, the Child law approximation yieldsexperimentally 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 derivethe PSR frequency expression (3.49). Hence, the limits of this easy resonance frequencyconcept quickly become apparent. To cope with this, more sophisticated multi-mode PSR


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 drivingfrequency ratio case. Amplitudes (arrows indicated) for the 67.8/13.56 MHz dual frequency oper-ation 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 approxi-mations. Experimental conditions are P13.56MHz = 50 W, P63MHz = 100 W, 5 sccm, 3 Pa, Argon,electrode gap 45 mm.

Returning to and interpreting the discrete Fourier spectra for both cases draws attention tothe difference in the amount and magnitudes of generated harmonics. In the integer ratiocase only dedicated harmonics of 13.56 MHz are produced, whereas in the non-integer casenumerous more are generated due to nonlinear frequency mixing. A comparison of both spec-tra is shown in figure 4.7. Focussing on the proximity of the pre-calculated PSR frequenciesshows an amplitude increase per frequency component for the integer ratio case. This alsoholds for the remaining frequency components. Hence, the transition from non-integer tointeger ratio goes together with a reduced number of frequency components at detectablyincreased amplitudes. As a consequence, less but stronger frequency components are foundwithin the resonance bandwidth contributing to the plasma series resonance and leading tothe increased local electron density maxima. The mathematical concept is a “redistribution”of the available signal energy among the number of present frequency components. Consid-ering e.g. a constant amount of signal energy and distributing it among only a few frequencycomponents leaves more “amplitude” per frequency component (integer ratio case) than bydistributing the same amount among numerous frequency components (non-integer case).

The term signal energy in literature is often misleading since usually, depending on the typeof signal, it is not expressed in units of energy. It only becomes a true energy in physicalterms 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

Nn),

which in this case is the sampled PSR current, by

Esig =N∑n=1

x2

(T

N· n)

(4.3)

where N is the total number of sampled points and T being the length in time of thecontinuous analytic signal. A true physical energy is gained by correlating equation (4.3)


with the oscilloscope’s internal resistor to

Esig = Esig · 50.0 Ω . (4.4)

Above equation is applied for calculations shown in figure 4.8. Further considerations onsignal 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 P13.56MHz = 50 W, PVHF = 100 W, 5 sccm, 3 Pa, Argon, electrodegap 45 mm.

Figure 4.8 illustrates the calculated signal energy for each frequency fVHF. It can be seenthat up to 75 MHz the signal energy can be considered constant. For frequencies above75 MHz it rapidly reduces, which is explained by increasing losses due to electrical feed-throughs (see figure 2.16). Quantitatively, the frequency components near fPSR, as seen infigures 4.5 and 4.6, increase from 1µA and 0.5µA to 1.3µA and 1.0µA, which is an overallamplitude increase of at least 50% from the non-integer to the integer case. Hence, nonlinearelectron resonance heating is a likely candidate, responsible for enhanced heating at integerdriving frequency ratios in the low pressure regime [115][116]. A comparison of discreteFourier spectra of PSR currents for low and high pressure regime is given in section 4.1.3.Furthermore, as verified by PROES in section 4.2.2, it is demonstrated that electron heatingis additionally affected by changing the relative phase between both excitation frequenciesat 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 squareof the highest driving frequency. One has to bear in mind though, that simply increasingfrequency to gain plasma density is limited by capacitive feed-through losses that need to bedetermined individually for each processing tool. As a recommendation, the highest systemfrequency should not exceed 80 MHz, which balances plasma density considerations and rfdevelopment costs. Additionally it is recommended to use integer driving frequency ratios forplasma processing, because of two reasons. On the one hand a visible gain in plasma density


is achieved and on the other hand the relative phase becomes available as a further controlparameter. 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 verifiedto be an important mechanism for discharge sustainment.


4.1.2 Power ratio

In addition to changing driving frequencies, a more common approach is adapting powers tomeet process recipe requirements. Which is straightforward for single frequency dischargesmay lead to unexpected processing results for dual frequency discharges. Especially theattributed 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 areperformed using fVHF = 71 MHz. Discharge pressure is held constant at 3 Pa. For the VHFpower variation, P13.56MHz was set to 50 W and for the low frequency (13.56 MHz) powervariation, PVHF is held constant at 50 W.

In a first approach, the dc self bias voltage as a good ion bombardment energy approximationis examined for both power variations. Results are displayed in figure 4.9.

Figure 4.9: Power dependence of dc self bias voltage. Experimental conditions are71 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 contri-bution (13.56 MHz). By comparing absolute differences in dc self bias voltages for an equalchange in applied power (200 W) yields a variation of 70 V for PVHF and 700 V for P13.56MHz.Consequently, ion bombarding energy is efficiently controllable by P13.56MHz. Although thechange in dc self bias voltage is small by varying PVHF at a given P13.56MHz, it strongly de-pends 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 ne behavior gained from Langmuirprobe measurements performed at the discharge center. Conversely to the ion bombardmentenergy, electron density ne is strongly influenced by PVHF [31]. Nevertheless, it is also visiblethat above a certain threshold (here: 60 W) P13.56MHz also influences electron density . Thisthreshold is explainable by PVHF being the dominant source of electron density in this range.However, industrial PVD applications operate within a regime P13.56MHz PVHF, whichimplies a non-negligible coupling of both frequency contributions with respect to electron


Figure 4.10: Power dependence of electron density ne. Varying 13.56 MHz power produces aconstant electron density for low power changes. Above a threshold power (here 60 W) the electrondensity is influenced also by the 13.56 MHz. Experimental conditions are 71 MHz/13.56 MHzdischarge, 5 sccm, 3 Pa, Argon, electrode gap 45 mm.

density. Hence, in such a power regime electron density is dominantly governed by P13.56MHz.The threshold power itself is determined by PVHF and its resulting discharge voltage contri-bution as measurable by a VI probe.

Kim et al. [118] and more recently Chung [34] propose an effective voltage concept such as

Veff = V13.56MHz + VVHF −2

3

V13.56MHz VVHF

V13.56MHz + VVHF

(4.5)

in order to describe the competition of both frequency dependent voltages. The validity ofequation (4.5) is assessed by considering measured VI probe values for VVHF and V13.56MHz.They are determined to be 81 V ≤ VVHF ≤ 88 V and 110 V ≤ V13.56MHz ≤ 360 V, indicatingthat in either case V13.56MHz remains dominant. Consequently, equation (4.5) does not supportthe observation of constant ne at low P13.56MHz.

Simultaneously acquired VI probe current magnitudes give 5.3 A ≤ IVHF ≤ 6.8 A and 0 A ≤I13.56MHz ≤ 1.7 A, yielding the same behavior as above voltages. A solution to this dilemma isfound in literature, where Turner and Chabert [119] follow a similar problem when discussingelectron heating mechanisms in dual frequency capacitive discharges. They motivate a currentamplitude rescaling on the basis of different coupling efficiencies of both frequencies. It is wellknown that the current scales linearly with the plasma boundary sheath capacitance. Alsoit 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. Equalizingcoupling efficiencies makes both currents IVHF and I13.56MHz comparable with respect toelectron density ne. Calculating the coupling factor given as

κ =fVHF

f13.56MHz

= 5.236 (4.6)


and rescaling I13.56MHz such that

I13.56MHz = κ · I13.56MHz (4.7)

with I13.56MHz as an IVHF-equivalent current, provides the necessary insight into explainingconstant ne at low 13.56 MHz powers. Results are plotted in figure 4.11.

Figure 4.11: Comparison of weighted 13.56 MHz and 71 MHz current, both measured at matchboxoutput. Further experimental conditions are 5 sccm, 3 Pa, Argon, electrode gap 45 mm.

Therein, both currents IVHF and I13.56MHz exhibit a behavior explaining a constant ne atlow P13.56MHz. If P13.56MHz is below 60 W (as the case within this work), the highest avail-able current magnitude is governed by IVHF. Hence, electron density is dominated by PVHF.Exceeding the “threshold power” of P13.56MHz = 60 W makes I13.56MHz the highest availablecurrent magnitude. As a result P13.56MHz starts affecting overall electron density ne.

Typical power regimes for physical vapor deposition (PVD) in industrial processing toolsmeet the condition P13.56MHz PVHF. Due to this fact and including aforementioned find-ings, the attributed decoupling from ion flux and ion energy by separately tuning PVHF andP13.56MHz is not feasible to this regard. Although ion bombarding energy is very well con-trollable by P13.56MHz, as verified above, plasma density (ion flux) is not. Moreover, it hasto be regarded as a product of both operating frequency contributions. In practice it evenoccurs that for above given operating regime electron density usually drops when switchingfrom single frequency VHF operation to 2f-CCP operation, due to the dominant influence ofP13.56MHz. However, it can be easily compensated by readjusting PVHF to reach the same levelof electron density and even further increase it. These experimentally observed effects havebeen theoretically described by Kim et al. [120][121][122] and agree well. Effects in the highpower PVD regime become apparent for ion distribution function measurements in section4.3 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 tuningthin film parameters, the only option is largely increasing PVHF to stay well away from a


previously determined threshold power level with respect to P13.56MHz. In that case ne remainsconstant and ion energy is solely tunable by P13.56MHz. This concept would obviously limit amaximum achievable deposition rate and inevitably increase costs per wafer.

Figure 4.12: Power dependence of mean electron temperature Te. Experimental conditions are71 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 floatingpotential is studied. Figure 4.12 shows the influence of PVHF and P13.56MHz on Te. By varyingP13.56MHz (left-hand side plot) Te exhibits a decreasing trend with increasing power. On thebasis of a global model this is explainable by an enhanced discharge confinement. Interpretingthe rf-corrected Child law sheath approximation from equation (3.10) with an increasing dcself bias voltage and increasing mean sheath width, provides a decrease in mean electrontemperature. Similarly, the behavior of Te for varying PVHF is explained. Thereby, the dc selfbias voltage as well as the mean sheath width do not significantly change. Thus, the meanelectron temperature Te is found to stay constant for PVHF variations.

Another relevant effect by changing P13.56MHz is observed in the floating potential Φfloat andshown in figure 4.13. Therein, two regions are identifiable. In region 1 the floating potentialΦfloat decreases to a local minimum, whereas in region 2, Φfloat rises asymptotically to aconstant voltage value. This effect is explained as follows: in region 1 the observed changeoccurs from the transition of single-frequency to dual-frequency operation. Since Φfloat canbe regarded as a measure for high energetic electron contribution, the decrease in Φfloat

is attributed to enhanced discharge confinement. In region 2, further increasing P13.56MHz,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 thatonly under certain external parameter conditions a complete decoupling from ion flux andion energy is achievable. However, these parameter sets are mostly unattractive for industrialapplications, because the resulting processing speed would be too low, due to low depositionrates, and subsequently costs per wafer rise. A solution could be triple-frequency capacitivedischarges where one frequency defines ion flux, another the target ion bombarding energyand a third the substrate ionic species impact energy. Although triple frequency dischargesmight be considered in the near future, they are beyond the scope of this work.


Figure 4.13: Low frequency power dependence of floating potential. Experimental conditions are71 MHz/13.56 MHz discharge, 5 sccm, 3 Pa, Argon, electrode gap 45 mm.

4.1.3 Pressure variation

As the most relevant external tuning parameters, frequency and power ratio have beenstudied. Changing system pressure is a further accessible control parameter studied in thissection. For these investigations constant experimental conditions have been, PVHF = 100 Wwith fVHF = 71 MHz and P13.56MHz = 50 W. Pressure is varied from 3 Pa up to 20 Pa. Resultsfor the electron density ne are shown ion figure 4.14.

Figure 4.14: Pressure dependence of electron density ne. Experimental conditions are P71MHz =100 W and P13.56MHz = 50 W, 5 sccm, Argon, electrode gap 45 mm.

By increasing system pressure, electron density ne approximately rises linearly. At 20 Pa aplasma density of ≈ 1011 cm−3 is achieved. Similar observations are made for the dc self bias


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 Te (left) and dc self bias voltage(right). Experimental conditions are P71MHz = 100 W and P13.56MHz = 50 W, 5 sccm, Argon,electrode gap 45 mm.

That is explained by the discharge becoming more symmetric at higher pressures, whicheffectively reduces dc self bias voltage. In the left-hand side plot of figure 4.15 the meanelectron temperature is depicted. It rises for decreasing pressures which is explained by astrong increase in electron diffusion to grounded walls. Consequently, also the dc self biasvoltage 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 reducedmean free path of the sputtered atomic species, optimum plasma conditions are usually foundfor 5 Pa and lower. The exact pressure value depends on the target substrate distance. Foratomic iron the mean free path is approximately 4 mm at 3 Pa. Evaluation of simultaneouslyacquired PSR current signals gives an additional insight into the transition regime betweennonlinear electron resonance heating (NERH), as described in section 4.1.1, and the ohmicheating 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 pro-nounced when going from single-frequency to dual-frequency discharges, because of addi-tional mixing and side-band generation. A further parameter, directly influencing harmonicgeneration 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, exemplarycalculated values, gained from simultaneous Langmuir probe data, are presented. Further-more, the brackets in each plot indicate the anticipated PSR frequency proximity (resonance


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 visiblethrough the reduction of harmonics. Further experimental conditions are P71MHz = 100 W andP13.56MHz = 50 W, 5 sccm, Argon, electrode gap 45 mm.

bandwidth BPSR). Hence, changes to spectral amplitudes occurring within these denotedranges 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 isstrongly 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 theelectron density does not. Consequently, an alternative electron heating must take placeat higher pressures. By increasing pressure the electron neutral collision rate increases andthus fully compensates for the reduced electron heating through discharge harmonics. Hence-forth, the transition from nonlinear electron resonance heating to collision dominated ohmicelectron heating is observed.

It can be summarized that for industrial PVD applications the optimum operating pressureregime is preferably given for pressures < 5 Pa. On the one hand, sputtered target atomicspecies have a sufficiently long mean free path and on the other hand the drop in ion fluxis easily compensated by raising high frequency power PVHF. Further observations includea significant increase in harmonics generation at reduced pressures. It is deemed to be animportant mechanism for discharge sustainment at low pressures and believed to present analternative form of stochastic heating [1].

Finally, the three major external tuning options have been addressed. A further option arisesby using integer excitation frequency ratios, namely the relative phase. Tuning the relativephase might become important at certain discharge operating regimes and particularly fordrift compensation as presented next.

4.2. Influence of the relative phase at integer driving frequency ratios 79

4.2 Influence of the relative phase at integer driving fre-

quency ratios

The advantages of choosing integer driving frequency ratios have been discussed in detail insection 4.1.1. Appending the analysis from given frequency ratio results, the relative phasewas identified as an additional tuning parameter. Since integer frequency ratios are consideredas a preferred mode of discharge operation, the role of relative phase needs to be evaluatedwith respect to its influence on plasma parameters.

As discussed in section 3.3 the proposed synchronization scheme needs to be applied in orderto gain access to the relative phase. For the given experimental setup the two rf sources needto be synchronized. This is realized by feeding the clock-signal of the first signal source tothe second signal generator as a reference clock. By that means, all frequencies are derivedfrom 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 conditionsare U2MHz = 125 VRMS, Neon, 7 sccm, 1 Pa, electrode-wall gap 55 mm. Clearly visible is theelectron beam formation (red) during sheath collapse at the driven electrode. Following thisevent is the extensive (≈ 10 cm) sheath expansion phase.

Addressing relative phase in the following paragraphs is experimentally realized with respectto excitation voltages, such that

Uphase(t) = U2MHz cos(ω2MHz t) + U14MHz cos(ω14MHz t+ ϕ) (4.8)

with U2MHz, U14MHz as the voltage amplitudes, ω2MHz, ω14MHz the excitation frequencies andϕ the relative phase. In the experiment it is varied from −180 ≤ ϕ ≤ 180 in steps of 15.Further conditions are U2MHz = U14MHz =

√2 · 125 VRMS, neon at 10 Pa, 7 sccm and no

counter electrode installed. The effective minimum distance between the top electrode andthe grounded wall is given as 55 mm.

The bottom electrode had to be removed from the setup due to an observed 2 MHz relatedeffect. During initial tests, the formation of “plasma globes” occurred. Estimations of the


mean sheath width on the basis of approximated plasma parameters yielded a significantsheath expansion of approximately ≈ 8 − 10 cm, which is also verified experimentally asdepicted in figure 4.17. As a consequence the bottom electrode needed to be removed torestore stable plasma conditions, because only a maximum gap of 40− 45 mm is adjustable.

The choice of alternative excitation frequencies (2 MHz and 14 MHz) for the plannedPROES investigations was inevitable for the following reason. Due to considerations byGans et al. [123] the shortest lifetime of a PROES-compatible emission line is given by theNe 2p1 transition, with a wavelength of 585.2 nm, a threshold excitation energy of 19 eV anda lifetime of 14.5 ns. Although ICCD camera properties allow for a much higher resolutionin 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 /14.75 ns) implies that only one point per 67.8 MHz cycle could be resolved, which is inade-quate for evaluation. Therefore, alternatively 14 MHz as the high frequency and 2 MHz as thelow frequency are chosen, giving five sampling points per 14 MHz period. Before addressingelectron excitation behavior, Langmuir probe measurements at dedicated phase angles havebeen performed.

4.2.1 Langmuir probe results

Figure 4.18: Relative phase dependence of electron density ne and mean electron temperature Te.Experimental conditions are U2MHz = U14MHz = 125 VRMS, Neon, 7 sccm, 10 Pa, electrode-wallgap 55 mm.

In order to be able to correlate changes in plasma parameters relative phase modificationsand excitation behavior Langmuir probe measurements at different relative phase anglesare performed. Elementary plasma parameters gained from these measurements are electrondensity ne and mean electron temperature Te. They are drawn in figure 4.18. The influenceof relative phase on electron density is clearly visible. Correlating minimum and maximumvalue yields a dynamic tuning range of 20%. Furthermore, a sinusoidal-like behavior can be


anticipated.

Similar observations are made for the electron temperature Te. Equivalently, the tuningrange is estimated to be ≈ 20%. Also a comparable sinusoidal-like behavior is recorded.Moreover, another effect is seen in both plots of figure 4.18. On the one hand, electrondensity ne and mean electron temperature Te reach local maxima (from −180− 0), but onthe other hand no pronounced minima are observed. It appears, there exists a lower limitfor ne and Te (from 0 − 180), which is believed to result from phase positions where thelocal plasma boundary sheath expansion is near its maximum, hence only minor changes areobtained. Conversely, for phases −180−0 the sheath expansion is near its minimum, hencestrong electron diffusion governs electron temperature. These observations are supported byPROES measurements as is shown in the following section 4.2.2. Additionally, correlatingdiscussed results to simultaneous plasma impedance measurements, also exhibits a very goodagreement.

Figure 4.19: Relative phase dependence of plasma impedance magnitude and phase. Experimentalconditions are U2MHz = U14MHz = 125 VRMS, 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, lowelectron densities (< 1010 cm−3) correlate well to high impedance magnitudes. Local minimain the impedance magnitude also match the respective phase angle where electron densityreaches a local maximum and vice versa. Furthermore, the constant behavior for phase anglesof 0 − 180 match measured plasma impedance data.

A significant influence with respect to changing relative phase is noticeable in the floatingpotential. Figure 4.20 displays the plasma and floating potential as measured by Langmuirprobe. Results exhibit a constant plasma potential, whereas the floating potential exerts apronounced sinusoidal-like behavior. Using the picture of regarding the floating potential asan indicator for high energetic electron behavior, a significant change occurs in the productionof 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 pointwithin this work.

Since electron density and mean electron temperature exhibit a detectable influence on rel-ative phase the electron distribution function (EDF) is analyzed in more detail. Figure 4.21


Figure 4.20: Relative phase dependence of plasma and floating potential. Experimental conditionsare U2MHz = U14MHz = 125 VRMS, 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 conditionsare U2MHz = U14MHz = 125 VRMS, 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 continuoustuning of the relative phase would result in an oscillation of the EDF with respect to itslocal maximum, ranging from 2 eV to 4.5 eV. At the same time, the peak’s magnitude alsoperforms minor fluctuations.

Summarizing all results gained from Langmuir probe measurements, a significant influence


of the phase relation between integer driving frequency ratios is found. Implications for in-dustrial processes need further considerations, because given discharge conditions operate atequal driving voltages not suitable for PVD purposes. In the following section, the presentedLangmuir probe results are supported by PROES and SEERS/PSR current measurements.Additionally, investigations under PVD-like discharge conditions are performed to verifywhether findings from the equal voltage case are transferrable.

4.2.2 PROES and SEERS/PSR measurements

To verify the presented Langmuir probe measurements, PROES and PSR current data havebeen obtained. As discussed in section 3.4.2 it is attempted to correlate PSR current datato PROES excitation diagrams.

Figure 4.22: Correlation of the electron excitation dynamics (top) to SEERS/PSR currents (bot-tom) at relative phase angles of -90 and +90. Experimental conditions are U2MHz = U14MHz =125 VRMS, 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 diagnosticsare limited to approximately ≈ 10 eV. With respect to figure 4.21 an increase might beanticipated for energies larger than 7 eV, but measurement uncertainties deny such an in-terpretation. On the other hand, optical diagnostics can only access energy regions in thescope of excitation or ionization energies and are therefore well suited to study high energetic


electron behavior. Within investigated discharge conditions only energies larger than 19 eVare accessible. The PROES diagnostic method is chosen for its additional ability to monitortransient 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 energeticelectrons becomes apparent. Comparing excitation plots at −90 and +90 shows an increasein high energetic electron production by a factor of two. Where in the −90 case, only oneelectron beam is produced by incoming electrons being reflected at the plasma boundarysheath, two electron beams are produced in the +90 case. It seems to be contradicting, thatdespite an increased local excitation, electron density goes down (see figure 4.18). This isexplained as follows: although more high energetic electrons are generated, they are producedout of the reservoir of cold electrons being accelerated by the expanding plasma boundarysheath. Hence, the number of cold electrons, measured as “electron density” by a Langmuirprobe, reduces in favor of an increase in high energetic electrons.

Additionally, a very good correlation of measured PSR currents to the traversing electronbeams is observed in figure 4.22 (bottom). The resonance structures within the current signalscan be perfectly matched to the points in time where electron beams are generated. Also thenumber of resonant occurrences and the number of electron beams fit. A physical picturedescribing this link between PROES and SEERS is that of electron beams traversing thedischarge and hitting the grounded wall, where they are detected. Implications for industrialdischarge monitoring are such that PSR current measurements provide a more cost-efficientway compared to PROES measurements. Furthermore, optical access to plasma tools isusually 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 relativephase controls the number of such beam events. Simulation conditions resemble experiment inequal voltages U2MHz = U14MHz.

To further illustrate the influence of relative phase and the concept of electron beams, ex-emplary waveforms, which can be understood as a very simplified plasma boundary sheathoscillation, for both phases −90 and +90 are simulated. They are shown in figure 4.23,


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 electronbeam 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 electronsmove towards the sheath because its potential barrier is easily bridged. These incomingelectrons, encounter the expanding 14 MHz sheath oscillation and are reflected back into thedischarge, gaining energy. Subsequently, those electrons are detected as electron beams inPROES and resonant structures in SEERS/PSR currents.

An alternative explanation can be found by considering total sheath collapse. Reanalyzingfigure 4.23 motivates the formulation of a simple time-dependent generalized sheath capaci-tance as

CSheath(t) =ε0Aelectrode

s(t)(4.9)

with

s(t) = s+ s2MHz cos(ω2MHz t+ ϕ2MHz) + s14MHz cos(ω14MHz t+ ϕ14MHz) . (4.10)

Figure 4.24: Influence of relative phase on excitation behavior for PVD-like discharge conditions.Experimental conditions are U2MHz = 125 VRMS U14MHz = 25 VRMS, Neon, 7 sccm, 1 Pa,electrode-wall gap 55 mm. Plots taken from [43]. The influence of changing relative phase is lesspronounced than in figure 4.22(top), but sufficient for industrial applications.

Thereby, s is the mean sheath width and s2MHz and s14MHz the respective sheath amplitudecontributions with corresponding phases and frequencies. By evaluating equation 4.10 theboundary sheath collapses at a certain point in time (s(t) ≈ 0). Depending on the relativephase, this event can occur more than once as presented in figure 4.23 (right). At the timeof sheath collapse, equation 4.9 yields a near infinite sheath capacitance, which in otherwords denotes a short circuit. During this time interval when the sheath is bridged, thefull rf current passes into the discharge. These events are detectable as electron beams. Thefollowing subsequent sheath expansion additionally accelerates these electrons away from theelectrode into the plasma bulk, producing high energetic electrons.


Relating the presented physical ideas to observed electron production, there is only one oc-currence for the left-hand side plot in figure 4.23, whereas by adjusting the phase, two suchoccurrences can be produced, visible in the right-hand side plot. This is in good agreementwith experimental observations. However, these findings have been obtained for equal excita-tion voltages, which is not the case for PVD applications. Hence, measurements are retakenfor given discharge conditions. Because plasma densities are too low in 2 MHz dominantplasmas only PROES is applicable as a diagnostic tool.

The results of these measurements are shown in figure 4.24. Here, discharge conditions arechosen to be 1 Pa, Neon, 7 sccm and U2MHz =

√2 · 125 VRMS U14MHz =

√2 · 25 VRMS.

As expected, the mean sheath width becomes large. However, the same observations as withthe 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 twobeams are noticeable. Exemplarily, simulated waveforms for U2MHz U14MHz are given infigure 4.25, expressing the same behavior as shown in figure 4.23. In spite of only minor14 MHz oscillations being visible, the same physical concepts apply for this case of dischargeoperating regime, which means the relative phase is an important tuning parameter for dualfrequency 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 immediatelyafter sheath collapse. The relative phase controls the number of such beam events. Simulationconditions resemble experiment regarding voltages U2MHz U14MHz.

Concluding this section, the relative phase between driving frequencies at integer ratios isstudied. A reproducibly detectable influence of phase on the production of high energeticelectrons is observed. These electrons are a key mechanism for discharge sustainment in ca-pacitive plasmas. For industrial applications, adjusting the phase exerts a direct influence onthe plasma boundary sheath expansion and collapse, hence modifying local heating directlyin front of the sputtering target.

Furthermore, stationary plasma parameters such as electron density ne and mean electrontemperature Te vary within ≈ 5 − 20%, depending on the mode of operation. However,this tuning range is small compared to using other available external tuning parameters.

4.3. Ion energy distribution measurements 87

But phase tuning might become useful for compensation of process drifts or optimizingadjustments in ion bombarding energy. Additionally considering figure 4.20, total chargingcontributions onto the substrate become controllable through floating potential optimization,hence arc management control especially in reactive (isolating) PVD processes is a possiblefield of application requiring further attention. Nevertheless, these investigations are beyondthe scope of this work.

With respect to magnetically enhanced discharges phase tuning is an interesting prospectof enhancing electron production by maximizing high energetic electron emission. A majordrawback however, are inhomogeneity problems due to preferential sputtering along themagnetic field lines. Those considerations are being incorporated in follow-up works on thisproject. Prior to analyzing elementary thin film deposition, the ion energy distribution onthe 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 energyanalyzer (RFEA) are performed on the electrically driven electrode. From determined iondistribution 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 ischaracterized and compared to previous findings from Langmuir probe parameter studies.Especially the behavior of ion flux with increasing P13.56MHz and verification of frequency ratiobehavior with respect to increased electron density are investigated. Thus, the parametervariations are derived from presented Langmuir probe studies. Hereby, voltage ratio andfrequency 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 fVHF = 67.8 MHz and f13.56MHz.

4.3.1 Voltage ratio

As deduced from Langmuir probe results, the voltage ratio (power ratio) plays an importantrole in adjusting plasma density and ion bombarding energy. It was discovered, that ionbombarding energy is mainly regulated by the low frequency power P13.56MHz. In contrast,plasma density cannot be properly regulated independently by PVHF, especially in PVDpower regimes where P13.56MHz PVHF. In this case, the low frequency power contributionP13.56MHz also significantly influences plasma density. To verify these findings a retarding fieldenergy analyzer is mounted on the driven electrode. Results for the voltage variation, wherethe low frequency voltage U13.56MHz is swept from 0 − 70 V with a constant high frequencyvoltage UVHF = 70 V are shown in figure 4.26.

The first and most significant result is, that by changing the discharge from a single frequency67.8 MHz into a dual frequency mode (adding 13.56 MHz), ion flux reduces and ion energyincreases simultaneously. It underlines the discussed fact of strong frequency coupling also


Figure 4.26: Low frequency voltage U13.56MHz influence on the ion distribution function (IDF) onthe target electrode. Experimental conditions are U67.8MHz = 70 VRMS, 3.5 Pa, 10 sccm, Argon.

predicted theoretically [28]. An immediate implication for industrial PVD is, that VHF powerhas to be increased to compensate for the losses in ion flux. By studying directly the sputterdeposition 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. Thiseffect is directly related to equation (3.59), correlating the energy spread (peak separation)∆E to the dc self bias voltage Udc bias and the rf sheath voltage Urf. Consequently, sinceUdc bias significantly increases by raising U13.56MHz, the energy spread ∆E has to increasebecause the mean sheath width grows.

Figure 4.27: Calculated mean ion energies from measured IDFs for low frequency voltage U13.56MHz

variation. Experimental conditions are U67.8MHz = 70 VRMS, 3.5 Pa, 10 sccm, Argon.

Taking these IDFs and calculating each mean ion bombarding energy, gives the plot in figure

4.3. Ion energy distribution measurements 89

4.27. By linearly raising U13.56MHz, the mean ion energy is verified to similarly rise linearly.Expressed in values, a rise by 40 V in U13.56 MHz approximately yields a rise of 40 eV in meanion energy. This result supports findings from Langmuir probes, where ion energy is foundto be well solely tunable by P13.56MHz.

4.3.2 Frequency ratio

To investigate the effect of frequency ratio on ion distribution function, the same dischargeconditions apply. The voltage values are UVHF = 70 V to ensure a dominant high frequency,and U13.56MHz = 35 V. Exemplarily, four distinct frequencies have been analyzed. Results areshown in figure 4.28. As discovered within Langmuir probe data, the influence of frequencyon dc self bias and hence mean ion bombarding energy is low. In figure 4.28 a slow decreaseof mean ion energy is found. This is visible by the total IDF shifting to lower energy valueswithout changing shape. Additionally, the energy spread ∆E stays constant as U13.56MHz staysconstant, 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 fVHF.Experimental conditions are UVHF = 70 VRMS, U13.56MHz = 35 VRMS, 3.5 Pa, 10 sccm, Argon.

Summarizing, RFEA measurements with varying voltage and frequency ratio have beenperformed. Results show a decrease in ion flux and increase in ion energy by raising the lowfrequency voltage U13.56MHz. For PVD applications this implies an increase in high frequencypower PVHF to compensate for plasma density losses. It was shown, that ion bombardingenergy is very well controllable through low frequency power P13.56MHz yielding a linearrelationship. From frequency ratio variations a negligible influence with respect to mean ionenergy is detected.

This concludes the detailed section on plasma characterization. Various parameter sets rel-evant for sputter deposition purposes have been thoroughly investigated. These findings arebrought to application in the following section for the study of elementary thin film deposition


properties.

4.4 Ferro-metallic thin film deposition study

Ferro-metallic films became important in recent times especially for their impact on magneto-resistive random access memory (MRAM) research. MRAMs are considered to be the suc-cessor of dynamic RAMs (DRAM), because of their advantage of non-volatility. But becauseMRAM cell’s space requirements are high and manufacturing of the magnetic layers is costlytheir spreading is rather limited.

The development of spintronics (short for spin-based electronics) is one of the key fieldsof application for these kind of films. Its major representative is the spin (valve) transistorbased on the giant magneto-resistive (GMR) effect. In microelectronics it is manufacturedby common semiconductor processing steps (plasma deposition, etching, lithography) andits internal build-up resembles that of a silicon transistor. The difference lies within appliedmaterials, where in this case thin ferro-metallic films are used. They are separated by analuminium oxide spacer layer. Electrically, the transistor becomes conducting when bothmagnetic layers exhibit the same field configuration. Conversely a high impedance is availablewhen the both field configurations are anti-parallel. In the conducting case, electrons cantunnel through the non-conducting material by applying a voltage drop across the transistorstack.

Hereby, two transistor “modes” are distinguished. The spin valve transistor is operated withan open base and switching is accomplished by external magnetic fields. This variant ofthe spin transistor is well controllable and forms the basis for MRAMs. Another mode isthe spin transistor without an open base. In this case switching is realized by injecting aspin-polarized current into the transistor base, which is a current research topic.

Within this work experiments characterizing elementary deposition and thin film propertiesare performed. First, sputter deposition is characterized using a quartz crystal microbalance(QCM). Results are compared to findings from Langmuir probe and retarding field energyanalyzer (RFEA) data. Discovered discrepancies between thin deposited layer thicknesses onsilicon wafers and QCM readings are investigated by verifying deposited thin film density.Roughness properties and the determination of relative atomic species densities conclude theelementary characterizations.

4.4.1 Optimization of sputter deposition rate

Prior to beginning with thin film analysis, the sputter deposition rate needs to be charac-terized and optimized first. Therefore the quartz-crystal microbalance is positioned 20 mmunderneath the target. Since for initial experiments on maximizing the sputter depositionrate no costly pure iron target is wasted a fully equivalent material is chosen. High-gradesteel with an iron content of at least 70% is considered to be an adequate replacement.

4.4. Ferro-metallic thin film deposition study 91

The remaining steel contents such as nickel (13%) and chromium (12%) have a similar massdensity as iron and the sputtering yields also exhibit similar behaviors. Hence, performedQCM measurements are safely transferrable to experiments using a pure iron target. Thefull optimization process regarding sputter deposition rates is found in literature and onlythe most important excerpts are presented in this section [124].

Figure 4.29: Pressure dependence of sputter deposition rate and determination of optimum de-position pressure. Experimental conditions are P13.56MHz = 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 definesin conjunction with system pressure the optimum for the sputter deposition rate. Systempressure itself directly governs the argon ion mean free path. Therefore, an initial pressurevariation study to determine the optimum pressure for a given distance is performed. Dis-charge conditions were P13.56MHz = 400 W, PVHF = 0 W and argon at 10 sccm gas flow.To ensure only pressure effects being studied, the plasma is operated in single frequency13.56 MHz mode. From Langmuir probe measurements it is known that enough density isproduced, but sputtering with 13.56 MHz is almost completely realized by changing theenergy dependent sputtering yield.

Figure 4.29 displays the pressure variation study. Therein, the expected behavior of depo-sition rate versus system pressure is observed. Essentially, the plot can be divided into tworegions (left and right of the local maximum). For pressures below the curve’s maximumplasma density is too low, respectively ion flux, so deposition rate diminishes in this direc-tion. On the other hand, raising system pressure beyond the curve’s maximum results in adecreasing 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 theoptimum operating pressure a polynomial fit through the measured data is calculated. Thefirst 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 isseen. Thereby, two slopes are identifiable. From very low pressures up to approximately 4 Pa


Figure 4.30: Pressure dependence of dc self bias voltage. Experimental conditions are P13.56MHz =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 lowpressures 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, thedc self bias voltage has to rise in magnitude to compensate for growing losses. For furthermeasurements, system pressure is set to the previously determined optimum at 2.5 Pa.

Continuing the characterization of iron deposition rate, the power dependence is investigatedin the following. Therefore, each power P13.56MHz and PVHF is varied individually. The highfrequency fVHF is chosen as 71 MHz to intentionally leave out resonant effects at integerfrequency ratios. Also 71 MHz is chosen, because of a comparable plasma density withrespect to 67.8 MHz (see figure 4.1) such that ion fluxes do not differ significantly. Remainingdischarge conditions stay the same as mentioned earlier. Figure 4.31 depicts the obtainedQCM deposition data.

Hereby, the separate influence of each single frequency contributions becomes apparent. Bothdetected 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. Concerninglow frequency power P13.56MHz, deposition rate grows due to growing mean ion bombardingenergy, acquiring values of up to 1125 eV at P13.56MHz = 600 W. Conversely, depositionrate increases with 71 MHz power P71MHz due to a significant boost in ion flux (plasmadensity) as shown by Langmuir probe measurements. Additionally a moderate increase inion bombarding energy up to 174 eV at P71MHz = 400 W contributes to increasing sputterrates.

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 ionflux. 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 oflow ion bombarding energies. In turn, a single frequency 13.56 MHz discharge cannot provide


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 A/s per 100 Wchange in P71MHz and 0.4 A/s per 100 W change in P13.56MHz.

The transition from single frequency to dual frequency operation well illustrates the potentialof 2f-CCPs for physical vapor deposition (PVD). Figure 4.32 depicts these investigations forthe transition from 13.56 MHz single frequency to 71/13.56 MHz dual frequency mode.Thereby, P71MHz = 100 W remains constant and P13.56MHz is varied in both cases. Comparingboth slopes yields an increase of 62.5% from the single frequency 13.56 MHz case to the71/13.56 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 for71 MHz and 13.56 MHz individually, unveils a further phenomenon. Hereby, plasma condi-tions in pressure and gas flow rate stay constant. For varying P71MHz, 13.56 MHz power isheld constant at 400 W and for varying P13.56MHz, 71 MHz power is held constant at 100 W.Figure 4.33 presents the obtained QCM data. The power variation of 13.56 MHz under con-stant P71MHz has been discussed previously in figure 4.32 and is introduced for reference. Amore interesting observation is made for constant 13.56 MHz power under varying P71MHz

conditions. Thereby, the sputter deposition rate is not linearly increasing for the completerange, but does so in two anticipated linear slopes.

As a direct consequence for PVD processing, simply increasing 71 MHz power to raise depo-sition rate through raising ion flux is possible within certain constraints. As can be seen fromfigure 4.33, passing a certain threshold results in a reduced slope and deposition rate increasesmuch slower. Hence, the gain in deposition rate by increasing P71MHz diminishes. By signifi-cantly increasing P71MHz, an intersection point with the P13.56MHz variation can be extrapo-lated. That means, exceeding a second threshold for P71MHz under constant 13.56 MHz powerconditions, would result in a lower deposition rate than achievable by changing 13.56 MHzpower.


Figure 4.32: Dependence of sputter deposition rate on single frequency 13.56 MHz and dualfrequency discharge operation (13.56/71 MHz). Discharge conditions are Argon, 2.5 Pa, 10 sccm,target-QCM gap 20 mm and P71MHz = 100 W.

A reasonable explanation for the first change in slope was given in section 4.1.2 for Lang-muir power variation measurements. Hereby, the intersection point is defined by the differentcurrent contributions of 13.56 MHz and 71 MHz. In this case for large enough P71MHz, the71 MHz current becomes large compared to the 13.56 MHz current, hence discharge char-acteristics are dominated by 71 MHz behavior. This is strongly supported by the singlefrequency power variation shown in figure 4.31. Comparing the single frequency 71 MHzslope from figure 4.31 with the given dual frequency P71MHz slope from figure 4.33 yields agood agreement. This means deposition rate behavior eventually changes to a much reducedslope magnitude resulting from single frequency contributions only. Conversely, this effect isnot observable for the P13.56MHz variation. This is explained by the low frequency power’s sig-nificant control over ion bombarding energy. By increasing ion energy the energy-dependentsputter yield ensures an increase in deposition rate up to energy levels where bombardingions are implanted. In this case deposition rate will reduce again.

Summarizing, different parameter variations for power and pressure have been performed tooptimize the sputter deposition rate. It was found that each single frequency contributionis less efficient than even a non-optimized dual frequency discharge. Furthermore, analysisof dual frequency power variations unveiled a significant change in deposition rate behaviorfor varying P71MHz, which is explained by the discharge adapting single frequency behavior.However, this effect cannot be transferred to varying P13.56MHz since the dominant increasein ion bombarding energy compensates for losses in ion flux, due to an increase in sputteringyield [125].

For considerations on a scale-up version of the given experimental setup, an estimation ofexpected deposition rates is given on the basis of extrapolating parameters from gatheredLangmuir probe and quartz-crystal microbalance data in the following section. Furthermore,recorded deposition rates are correlated to Langmuir probe and RFEA measurements.


Figure 4.33: Separate power dependence of 13.56 MHz and 71 MHz on sputter deposition rate.Discharge conditions 13.56 MHz variation are P71MHz = 100 W, Argon, 2.5 Pa, 10 sccm, target-QCM gap 20 mm. Discharge conditions 71 MHz variation are P13.56MHz = 400 W, Argon, 2.5 Pa,10 sccm, target-QCM gap 20 mm.

4.4.2 Estimation of expected deposition rates and comparison to mea-surements

In order to get an adequate estimation for measured deposition rates, several assumptionshave to be made, which are discussed in the following. First, the ion flux density onto thetarget material needs to be calculated. It is determined by the Bohm velocity and a meanaveraged plasma density. To simplify calculations only singly charged argon ions Ar+ areconsidered, such that the number of available ions equals the number of free electrons. Theion flux density is then formulated as

ΓAr+ = ne · uBohm = ne ·√kB Te

mi

(4.11)

with ne as the plasma density, kB as the Boltzmann constant, Te the mean electron temper-ature and mi the ion mass. Because argon ion and neutral atomic masses are nearly equal,the approximation mi = mAr+ ≈ mAr is used. The argon ion flux density and the resultingiron neutral atom flux density ΓFe are correlated through the sputter yield γFe. It defines thenumber of sputtered target iron atoms per incident argon ion. Additionally, this quantitydepends on the impact ion energy. For the performed calculations the ion bombarding en-ergy is determined to be approximately 1000 eV for given process conditions, which gives asputter yield for iron to γFe = 1.3 as found in Matsunami et al. [125].

ΓFe = ΓAr+ · γFe (4.12)

The given yield γFe holds for pure iron targets, however the applied stainless steel and mostof its containing metallic alloys, such as chromium and nickel, have a similar sputter yield.


In a following step, the iron atom flux density ΓFe needs to be correlated to actually measureddeposition rates. Therefore, the growing film’s crystalline structure needs to be known. Fromliterature [106], iron is known to adopt a body-centered cubic (bcc) crystal structure. Onlyfor 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 ironcrystal structure, the lattice constant aFe bcc is given by

aFe bcc =4√3· rFe = 286.65 pm (4.13)

with rFe 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. Aconnection between the lattice constant and deposition rate is provided by the number ofmonolayers being deposited/etched per second, which in turn has to be expressed by thenumber of iron atoms arriving at the quartz-crystal microbalance (QCM). The number ofmonolayers being deposited per second on the QCM’s crystal substrate is defined by

nFe mono =ΓFe

ρA,Fe

(4.14)

with ρA,Fe being the area density of iron atoms as

ρA,Fe =NFe

Aelectrode

(4.15)

with NFe as the number of iron atoms per monolayer and Aelectrode as the total area of theelectrically driven electrode. The number of iron atoms per monolayer is found by calculatingthe mass of a monolayer and dividing it by the iron’s atomic mass, such that

NFe =Aelectrode aFe bcc ρFe

mFe

(4.16)

where ρFe is the iron mass density as 7.874 g cm−3. Inserting and simplifying equation (4.16)into (4.15) yields expression (4.17) without the electrode area dependence.

ρA,Fe =aFe bcc ρFe

mFe

(4.17)

Finally, the QCM deposition rate in Angstrom per second (A/s) is found by multiplying thenumber of deposited monolayers with the lattice constant.

dQCM = nFe mono · aFe bcc =mFe

ρFe

· ΓFe (4.18)

Now it is possible to calculate backwards to the electron density ne which is necessary toachieve the detected deposition rates. This is done by substituting and reordering equation(4.18) to

ne =dQCM ρFe

mFe γFe uBohm

. (4.19)

To quantify the electron density, the maximum detected deposition rate value is inserted,yielding a value of ne = 1.31·1010 cm−3, which is approximately six times lower than measured


Langmuir probe densities, expected to be 6 − 7 · 1010 cm−3. In order to account for thediscrepancy, the mean free path of an iron atom at 2.5 Pa is calculated to be approximately4 mm, which implies statistically five collisions with neutral gas atoms on its way to thequartz-crystal microbalance. Although most collisions are considered to exert a small changeto the iron atom’s flight direction, a higher number of collisions significantly increases theangular distribution. Furthermore, ions coming from the plasma bulk towards the targetelectrode encounter the grounded QCM first, where they are neutralized. These ions are nolonger available for sputtering. Therefore an estimation of this loss mechanism is performedon the basis of considering the area ratio of the target and the QCM. It is determined to be50%. Correcting the iron atom flux density by inserting the determined loss yield γloss = 0.5into equation (4.19) gives a revised expression for the electron density.

ne =dQCM ρFe

0.61 ·mFe γFe γloss uBohm

(4.20)

Reevaluating equation (4.20) with the same maximum deposition rate value gives ne = 2.62 ·1010 cm−3, which still is too low by a factor of three. Additionally considering the differencein electron density between the plasma bulk and the electrode on the basis of a cosine profilewould incorporate a factor (0.61)−1 = 1.64, which in turn yields ne = 4.30 · 1010 cm−3.Thus, another mechanism is deemed possible to be responsible for such a low plasma densityestimation. A likely possibility is that thin film density is significantly deviating from the setdensity of pure iron within the QCM electronics. Verifying and evaluating this possibility isperformed in the following section.

Performing additional estimations on the minimum expected deposition rates for a plannedscale-up version of the dual frequency PVD setup yields the following results. Assuming aminimum realizable plasma density of ne = 1 · 1011 cm−3 under similar process conditionsgives an approximate deposition rate of at least ≈ 17 A/s. Furthermore, also the power inputper area can be calculated by assuming a voltage drop across the sheath on the order of theplasma’s dc self bias voltage (≈ 1000 V). Using the same parameter set gives a power inputof 3.5 W/cm2.

4.4.3 Calibration of quartz-crystal microbalance and determination of

film density

Simultaneous experiments using small silicon wafers attached to the QCM shutter mecha-nism, provide a reproducible thin film layer thickness of about twice the size of obtainedQCM measurements. Indicated values of the QCM were 7.7µm versus measured 14.4µm onthe silicon wafer samples. A possible explanation for this discrepancy could be a significantchange in film mass density, compared to elementary iron. This would happen, e.g. due to alarge increase in porosity of the resulting layer.

In order to verify the density of deposited films several silicon wafer samples are coated toaverage 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 isdeposited onto the wafer samples to produce a detectable mass change and (iii) the prepared


samples are weighed again to determine the mass difference. For mass density determinationthe thin film’s volume is additionally required. Since the samples have a very well definedarea, only the deposited film thickness needs to be determined. This is done by using acontacting profilometer (Veeco Dektak 6M stylus).

Figure 4.34: Optical emission spectrum for determination of relative atomic species densitiesin single frequency VHF operation. Discharge conditions are: Argon, 2.5 Pa, 10 sccm andP71MHz = 200 W. Left: Full spectrum. Right: Zoomed spectrum. Arrows in both cases indicateeither intervals of attributed lines or specific single emission lines.

A contacting profilometer uses a probe tip which is brought onto the surface. By scan-ning the substrate and by passing over the film border, the detected change in height givesthe film thickness. Therefore, it is necessary to produce a sharp film border by previouslycovering a defined area during the deposition process. Having determined the film thick-ness, the total film volume can be calculated. From the change in mass and volume one isable to calculate the film density using the elementary relation ρfilm = Vfilm/mfilm, yieldingρfilm = 8.7315 g cm−3. Comparing this result to ρFe gives a deviation of 11% with respectto iron density. This deviation results from neglecting components within the stainless steeltarget such as chromium (ρCr = 7.19 g cm−3), nickel (ρNi = 8.908 g cm−3), and molybdenum(ρMo = 10.28 g cm−3). On the other hand, the found deviation of 11% also lies within themeasurement accuracy of the micro-scales, such that the film density is found to very wellresemble the mass density of pure iron. Further evidence of additionally sputtered elementsis given in section 4.4.4. Depending on their respective sputtering yields, the resulting filmassembly will consist of different mass ratios than the original steel target, leading to asystematic deviation of the film’s mass density.

Due to the fact, that measured film thickness is about twice as high as detected by the QCMand film density does not significantly differ from programmed QCM values, the iron atomflux has to be at least twice as large. Simultaneously also plasma density has to increaseby a factor of two. Recalculating the electron density on this basis yields an approximatedplasma density of 5.3 · 1010 cm−3, which agrees to measured Langmuir probe data and lieswithin measurement accuracy.


4.4.4 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 whichaddressed the topic of additional chemical elements being incorporated into the film, origi-nating from the stainless steel reference target. Evidence of this is supplied by simultaneousoptical emission spectroscopic measurements.

Figure 4.35: Optical emission spectrum for determination of relative atomic species densities indual frequency operation. Discharge conditions are: Argon, 2.5 Pa, 10 sccm, P13.56MHz = 400 Wand P71MHz = 200 W.

Figures 4.34 and 4.35 compare the two modes of single frequency to dual frequency dischargeoperation at indicated conditions. Thereby, two observations are made. First, the relativeargon 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 isused to evaluate relative atomic species densities. It correlates the observed intensity of anemission line with the true relative number density of the according species as

Irel = η · 〈vσik〉 · ne · [Fe] (4.21)

where Irel is the observed relative intensity, ne the corresponding electron density, [Fe] therelative number density of the observed species (here: atomic iron) and 〈vσik〉 consideringrelated collision cross sections found in literature. Additionally, the electron density ratio isoptically 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 singlefrequency 71 MHz to dual frequency discharge operation. Relating this to Langmuir probepower variation studies, yields a good agreement and strongly supports the observationof low frequency current exerting a significant influence on total plasma density in PVDoperation. Second, the relative atomic density of iron is found to rise by a factor of four for


Figure 4.36: Atomic force microscopy (AFM) picture of a 56 nm Fe-coated silicon wafer. Rough-ness 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 observationsby 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 4.36. A roughness of less than 1% of thethickness is achieved, which is within specifications of typical MRAM fabrication.

Summarizing the investigations of ferro-metallic thin film deposition: first, the sputter de-position rate has been maximized with respect to given experimental capabilities. Thereby,linear dependencies of each power contribution in single frequency discharge operation werefound. Moving to dual frequency discharge mode, the increase in low frequency power didnot show an expected dip in deposition rate as gathered by retarding field energy analyzerand optical measurements. However it even further increased. This is explained by the dom-inant 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 dependentsputter yield. For iron and with respect to given changes in bombarding energy, the sputteryield 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 depo-sition rate on P71MHz. By comparing the two-slope curve to single frequency VHF depositionrates, an apparent change in discharge behavior in favor of VHF discharge operation is dis-covered, if P71MHz power becomes too high. Finally, elementary thin film parameters havebeen investigated and a simple model describing the deposition rate and loss mechanisms wasdeveloped. All QCM measurements show a good correlation to results gained from previouslyapplied plasma diagnostics, completing the picture of dual frequency capacitive discharges.

101

5. Conclusions and outlook

In this work a capacitively coupled plasma driven at multiple frequencies (MFCCP) has beendesigned and constructed for physical vapor deposition (PVD) experiments of ferro-metallicthin films. These films with dedicated magnetic properties are important material systems fora broad range of applications. Popular examples are anti-theft foils, miniature Rheed-sensorsor magneto-resistive based devices. Thereof, most well-known examples include computerhard disks and magneto-resistive random access memories (MRAM). Especially the latter isthe topic of recent scientific research efforts for its advantages over common dynamic RAMs(DRAM).

In the first stage of this work, a prototype process chamber has been developed and setup. Therefore, thorough investigations into the electrical stability of the plasma excitationby two frequencies, simultaneously fed onto one electrode, were needed. Investigations by anetwork analyzer give important insight into the transmission behavior of applied impedancematching networks and vacuum feed-throughs. Those properties are relevant to suppressmutual interferences of the power amplifiers, otherwise leading to unstable plasma conditions.It has been determined, that the chosen impedance matching networks exhibit a sufficientattenuation within the desired frequency bands. Only the VHF frequency matching networkneeded to be extended by introducing an rf isolator into the electrical line. In a secondstep, an equivalent circuit model for the rf vacuum feed-throughs has been developed andsuccessfully verified by measurements. They compare well to results gained from Langmuirprobe measurements. Finally, the overall electrical efficiency of the system was evaluated andit was found, that the vacuum-feed throughs are a major cause for losses within the entiresystem, leaving total efficiency between 5− 13%.

In the second stage of this work, complete discharge characterization by multiple plasma diag-nostics is performed. Thereby, frequency ratio, power ratio, pressure variation and influenceof the relative phase have been studied with Langmuir probe, VI probe, self excited electronresonance spectroscopy (SEERS), (phase resolved) optical emission spectroscopy (PROES)and retarding field energy analyzer (RFEA) measurements. Elementary scaling laws couldbe experimentally verified. An anomalous heating was observed for integer driving frequencyratios and could be explained by a theoretically developed concept of Mussenbrock andBrinkmann [1], termed nonlinear electron resonance heating (NERH). Hereby, plasma gener-ated harmonics cause a resonant enhancement due to excitation at approximately the plasmaseries resonance frequency (PSR). Furthermore, global model calculations by Mussenbrockand Ziegler [98][3] using realistic discharge parameters as input values show an excellentagreement to measured PSR currents. Thereby, a significant contribution to understandingelectron heating in low pressure regimes in capacitive discharges has been achieved.

102 5. Conclusions and outlook

Power ratio investigations exhibit a very strong frequency coupling. As predicted, high fre-quency power dominantly controls plasma density and exerts a negligible influence on ionbombarding energy. Conversely, low frequency power P13.56MHz significantly controls ion bom-barding energy as is generally attributed. However, it was shown to significantly influenceplasma density at the same time, even leading to a decrease in plasma density, as verifiedby RFEA and optical measurements. Relating the given results to typical PVD parametersets, leaves a possible but limited decoupling of ion flux and ion energy. However, as it isshown later in deposition experiments, a sufficient separate tunability remains. During pres-sure variation studies, the transition of NERH dominated heating to ohmic heating couldbe observed in discrete Fourier spectra of acquired PSR current signals, exhibiting a largelyreduced harmonic excitation within the PSR proximity.

A second investigation series addressed the role of relative phase at integer driving frequencyratios, which are mostly used in industry. Hereby, PROES as a time-resolved optical diag-nostic, Langmuir probe, VI probe and the PSR current sensor are experimentally applied.An important result of this work is that by tuning the relative phase, a significant influenceon the production of high energetic electrons immediately in front of the target material isachievable. Consequently, local plasma density increases, hence optimizing ion flux. Anotherimportant result of this work is a documented correlation of electron heating occurrencesto PSR current resonant structures. These findings also fit well with aforementioned modelconsiderations. Hence, phase tuning essentially allows for an optimization of ion flux withrespect to process drift compensation. The described effects of changing relative phase be-come less pronounced at largely different coupled power contributions, but nonetheless thediscussed optimization potential was shown to persist.

In the third stage of this work, the sputter deposition rate on a ferro-metallic target wasinvestigated and optimized. Beforehand, retarding field energy analyzer (RFEA) measure-ments have been performed to characterize ion impact behavior onto the target electrode.For typical power ratios in PVD systems (P13.56MHz PVHF) a decrease in ion flux wasobserved under constant VHF power conditions. Although this can be easily compensatedby adapting VHF power, it is an important result for industrial applications showing a non-negligible coupling of both excitation frequencies. Nevertheless, later deposition rate studiesusing a quartz-crystal microbalance (QCM) showed no detectable influence of increasing lowfrequency power on deposition rate. This is explained by high discharge asymmetry leadingto a rapid increase in ion bombarding energy. In turn, the energy dependent iron sputteryield changes significantly from 0.2 at low P13.56MHz powers up to nearly 2.0 at standardPVD operating powers. Considering these changes on the order of one magnitude for theiron sputter yield, the simultaneous loss of ion flux, which is much less than one order ofmagnitude due to different discharge heating, is fully compensated. Moreover, further rais-ing VHF power boosts deposition rates significantly. Additionally, a limiting phenomenon ofPVHF has been determined. Exceeding a threshold power for PVHF, deposition growth ratereduces close to single frequency VHF discharge operation. It is an important result, becauseit effectively defines an upper limit for coupled PVHF power dependent on P13.56MHz power[126].

Summarizing, a multiple frequency driven capacitively coupled processing setup has beendeveloped and thoroughly characterized electrically. Overall electrical efficiency was found

103

to be comparable to commercial system. A developed transmission model allows for dischargemonitoring through plasma impedance measurements using a VI probe. Important dischargeproperties have been investigated by performing various parameter studies in frequency,power, pressure and relative phase. It can be concluded, that a complete decoupling of ionflux and ion energy through PVHF and P13.56MHz is possible but limited with regard to PVD.However, a sufficient degree of decoupling is achievable as film deposition experiments show.Tuning the relative phase was identified as an important additional optimization parameterfor 2f-CCPs, exerting a direct influence on heating properties close to the target electrode.Deposition rate optimization has unveiled a complex dependence of high frequency powerPVHF on deposition growth rate behavior, where the discharge changes from an efficient dualfrequency operation to a less efficient single-frequency-like mode.

The built discharge vessel is intended as a prototype reactor system (electrode diameter140 mm) to allow for identifying effects related to the plasma as well as the deposition. Theyneed to be considered for a planned scale-up version with an intended electrode diameter of500 mm. In particular electromagnetic effects like the standing wave and skin effect need to betaken into account to ensure discharge homogeneity across the entire processing area. Thoseeffects have been experimentally and theoretically considered and found to be important athigh plasma densities in large area processing with VHF driving frequencies [52][53][45][55].With the detailed parameter studies performed in thin work, its results can be directlyapplied and validated for the future use in deposition experiments.

104 5. Conclusions and outlook

Bibliography 105

Bibliography

[1] T. Mussenbrock and R. P. Brinkmann. Nonlinear electron resonance heating in capac-itive radio frequency discharges. Appl. Phys. Lett., 88(15):151503, 2006.

[2] D. Ziegler, T. Mussenbrock, and R. P. Brinkmann. Temporal structure of electronheating in single-frequency and dual-frequency capacitive discharges. Phys. Plasmas,2008. submitted.

[3] T. Mussenbrock, D. Ziegler, and R. P. Brinkmann. A nonlinear global model of a dualfrequency capacitive discharge. Phys. Plasmas, 13(8):083501, 2006.

[4] B. N. Chapman. Glow discharge processes. John Wiley & Sons, 1980.

[5] M. Surendra and D. B. Graves. Capacitively coupled glow discharges at frequenciesabove 13.56 mhz. Appl. Phys. Lett., 59(17):2091–2093, 1991.

[6] M. Meyyappan and M. J. Colgan. Very high frequency capacitively coupled dischargesfor large area processing. J. Vac. Sci. Technol. A, 14(5):2790–2794, 1996.

[7] H. Keppner, U. Kroll, P. Torres, J. Meier, D. Fischer, M. Goetz, R. Tscharner, andA. Shah. Scope of VHF plasma deposition for thin-film silicon solar cells. In IEEEConference Record of the 25th PVSC, pages 669–672, Washington DC., USA, May 1996.

[8] Y. Mori, H. Kakiuchi, K. Yoshii, K. Yasutake, and H. Ohmi. Characterization ofhydrogenated amorphous Si1−xCx films prepared at extremely high rates using veryhigh frequency plasma at atmospheric pressure. J. Phys. D: Appl. Phys., 36(23):3057–3063, 2003.

[9] S. Kumar, P. N. Dixit, D. Sarangi, and R. Bhattacharyya. Diamond-like carbon filmsgrown by very high frequency (100 MHz) plasma enhanced chemical vapour depositiontechnique. Appl. Phys. Lett., 69(1):49–51, 1996.

[10] V. Vahedi, C. K. Birdsall, M. A. Lieberman, G. DiPeso, and T. D. Rognlien. Veri-fication of frequency scaling laws for capacitive radio-frequency discharges using twodimensional simulations. Phys. Fluids B, 5(7):2719–2729, 1993.

[11] S. Oda. Frequency effects in processing plasmas of the VHF band. Plasma SourcesSci. Technol., 2(1):26–29, 1993.

[12] N. Nakano and T. Makabe. Influence of driving frequency on narrow gap reactive ionetching in SF6. J. Phys. D: Appl. Phys., 28:31–39, 1995.

106 Bibliography

[13] M. Klick, L. Eichhorn, W. Rehak, M. Kammeyer, and H. Mischke. Influence of exci-tation frequency on plasma parameters and etching characteristics of radio-frequencydischarges. Surf. Coat. Technol., 116-119:468–471, 1999.

[14] M. Yan and W. J. Goedheer. A PIC-MC simulation of the effect of frequency on thecharacteristics of VHF SiH4/H2 discharges. Plasma Sources Sci. Technol., 8(3):349–354, 1999.

[15] E. Amanatides and D. Mataras. Frequency variation under constant power conditionsin hydrogen radio frequency discharges. J. Appl. Phys., 89(3):1556–1566, 2001.

[16] H. H. Goto, H.-D. Lowe, and T. Ohmi. Dual excitation reactive ion etcher for lowenergy plasma processing. J. Vac. Sci. Technol. A, 10(5):3048–3054, 1992.

[17] T. Kitajima, Y. Takeo, Z. Lj. Petrovic, and T. Makabe. Functional separation ofbiasing and sustaining voltages in two-frequency capacitively coupled plasma. Appl.Phys. Lett., 77(4):489–491, 2000.

[18] P. C. Boyle, A. R. Ellingboe, and M. M. Turner. Independent control of ion currentand ion impact energy onto electrodes in dual frequency plasma devices. J. Phys. D:Appl. Phys., 37(5):697–701, 2004.

[19] J. K. Lee, N. Yu Babaeva, H. C. Kim, O. V. Manuilenko, and J. W. Shon. Simulationof capacitively coupled single- and dual frequency rf discharges. IEEE Trans. PlasmaSci., 32(1):47–53, 2004.

[20] S. Shannon, D. Hoffman, J.-G. Yang, A. Paterson, and J. Holland. The impact offrequency mixing on sheath properties: Ion energy distribution and VDC/Vrf interaction.J. Appl. Phys., 97(10):103304, 2005.

[21] T. Fujita and T. Makabe. Diagnostics of a wafer interface of a pulsed two-frequencycapacitively coupled plasma for oxide etching by emission selected computerized to-mography. Plasma Sources Sci. Technol., 11(2):142–145, 2002.

[22] K. Maeshige, G. Washio, T. Yagisawa, and T. Makabe. Functional design of a pulsedtwo-frequency capacitively coupled plasma in CF4/Ar for SiO2 etching. J. Appl. Phys.,91(12):9494–9501, 2002.

[23] T. Ohmori, T. K. Goto, T. Kitajima, and T. Makabe. Negative charge injection toa positively charged SiO2 hole exposed to plasma etching in a pulsed two-frequencycapacitively coupled plasma in CF4/Ar. Appl. Phys. Lett., 83(22):4637–4639, 2003.

[24] J.-P. Booth. Diagnostics of etching plasmas. Pure Appl. Chem., 74(3):397–400, 2002.

[25] V. Georgieva, A. Bogaerts, and R. Gijbels. Numerical study of Ar/CF4/N2 dischargesin single- and dual-frequency capacitively coupled plasma reactors. J. Appl. Phys.,94(6):3748–3756, 2003.

[26] V. Georgieva and A. Bogaerts. Numerical simulation of dual frequency etching reactors:Influence of the external process parameters on the plasma characteristics. J. Appl.Phys., 98(2):023308, 2005.

Bibliography 107

[27] J.-P. Booth, C. S. Corr, G. A. Curley, J. Jolly, and J. Guillon. Fluorine negativeion density measurement in a dual frequency capacitive plasma etch reactor by cavityring-down spectroscopy. Appl. Phys. Lett., 88(15):151502, 2006.

[28] L. Z. Tong and K. Nanbu. Numerical study of dual-frequency capacitively-coupleddischarges in electronegative SF6. Europhys. Lett., 75(1):63–69, 2006.

[29] V. Georgieva and A. Bogaerts. Negative ion behaviour in single- and dual-frequencyplasma etching reactors: Particle-in-cell/Monte Carlo collision study. Phys. Rev. E,73(3):036402, 2006.

[30] T. Gans, J. Schulze, D. O’Connell, U. Czarnetzki, R. Faulkner, A. R. Ellingboe, andM. M. Turner. Frequency coupling in dual frequency capacitively coupled radio fre-quency plasmas. Appl. Phys. Lett., 89(26):261502, 2006.

[31] S. Rauf and M. Kushner. Nonlinear dynamics of radio frequency plasma processingreactors powered by multifrequency sources. IEEE Trans. Plasma Sci., 27(5):1329–1338, 1999.

[32] F. A. Haas. A simple model of an asymmetric capacitive plasma with dual frequency.J. Phys. D: Appl. Phys., 37(22):3117–3120, 2004.

[33] P. C. Boyle, A. R. Ellingboe, and M. M. Turner. Electrostatic modelling of dualfrequency rf plasma discharges. Plasma Sources Sci. Technol., 13(3):493–503, 2004.

[34] T. H. Chung. Scaling laws for dual radio-frequency capacitively coupled discharges.Phys. Plasmas, 12(10):104503, 2005.

[35] V. Lisovskiy, J.-P. Booth, K. Landry, D. Douai, V. Cassagne, and V. Yegorenkov. Low-pressure gas breakdown in dual-frequency rf electric fields in nitrogen. Europhys. Lett.,80(2):25001, 2007.

[36] V. Georgieva and A. Bogaerts. Plasma characteristics of an Ar/CF4/N2 discharge inan asymmetric dual frequency reactor: numerical investigation by a PIC/MC model.Plasma Sources Sci. Technol., 15(3):368–377, 2006.

[37] G. Wakayama and K. Nanbu. Study on the dual frequency capacitively coupled plasmasby the Particle-In-Cell/Monte Carlo Method. IEEE Trans. Plasma Sci., 31(4):638–644, 2003.

[38] M. M. Turner and P. Chabert. Collisionless heating in capacitive discharges enhancedby dual-frequency excitation. Phys. Rev. Lett., 96:205001, 2006.

[39] D. O’Connell. Investigations of high voltage plasma boundary sheaths in radio-frequencydischarges operated with multiple frequencies. Phd thesis, School of Physical Sciences,Dublin City University, July 2004.

[40] W. Jiang, M. Mao, and Y.-N. Wang. A time-dependent analytical sheath model fordual-frequency capacitively coupled plasma. Phys. Plasmas, 13(11):113502, 2006.

[41] J. Robiche, P. C. Boyle, M. M. Turner, and A. R. Ellingboe. Analytical model of adual frequency capacitive sheath. J. Phys. D: Appl. Phys., 36(15):1810–1816, 2003.

108 Bibliography

[42] R. N. Franklin. The dual frequency radio-frequency sheath revisited. J. Phys. D: Appl.Phys., 36(21):2660–2661, 2003.

[43] D. O’Connell, T. Gans, E. Semmler, P. Awakowicz, A. R. Ellingboe, and M. M. Turner.Ionisation dynamics and frequency coupling in dual frequency capacitively coupledplasmas. 60thGaseousElectronicsConference, Arlington, V A, USA, October 2007.

[44] Z.-Q. Guan, Z.-L. Dai, and Y.-N. Wang. Simulations of dual rf-biased sheathsand ion energy distributions arriving at a dual rf-biased electrode. Phys. Plasmas,12(12):123502, 2005.

[45] P. A. Miller, E. V. Barnat, G. A. Hebner, A. M. Paterson, and J. P. Holland. Spatialand frequency dependence of plasma currents in a 300 mm capacitively coupled plasmareactor. Plasma Sources Sci. Technol., 15(4):889–899, 2006.

[46] A. Perret, P. Chabert, J. Jolly, J.-P. Booth, J. Guillon, and P. Auvray. Ion fluxuniformity in large area high frequency capacitive discharges. In Proceedings of the26th International Conference on Phenomena in Ionized Gases (ICPIG), Greifswald,Germany, July 2003.

[47] A. A. Howling, L. Sansonnens, J. Ballutaud, and Ch. Hollenstein. Nonuniform radio-frequency plasma potential due to edge asymmetry in large-area radio-frequency reac-tors. J. Appl. Phys., 96(10):5429–5440, 2004.

[48] K. Satake, H. Yamakoshi, and M. Noda. Experimental and numerical studies on voltagedistribution in capacitively coupled very high-frequency plasmas. Plasma Sources Sci.Technol., 13(3):436–445, 2004.

[49] A. Perret, P. Chabert, J. Jolly, and J.-P. Booth. Ion energy uniformity in high-frequencycapacitive discharges. Appl. Phys. Lett., 86(2):021501, 2005.

[50] P. Chabert, J.-L. Raimbault, P. Levif, J.-M. Rax, and M. A. Lieberman. Inductiveheating and E to H transitions in high frequency capacitive discharges. Plasma SourcesSci. Technol., 15(2):S130–S136, 2006.

[51] P. Chabert. Electromagnetic effects in high-frequency capacitive discharges used forplasma processing. J. Phys. D: Appl. Phys., 40(3):R63–R73, 2007.

[52] M. A. Lieberman, J.-P. Booth, P. Chabert, J. M. Rax, and M. M. Turner. Stand-ing wave and skin effects in large-area, high-frequency capacitive discharges. PlasmaSources Sci. Technol., 11(3):283–293, 2002.

[53] P. Chabert, J.-L. Raimbault, J.-M. Rax, and A. Perret. Suppression of the standingwave effect in high frequency capacitive discharges using a shaped electrode and adielectric lens: Self-consistent approach. Phys. Plasmas, 11(8):4081–4087, 2004.

[54] P. Chabert, J.-L. Raimbault, J.-M. Rax, and M. A. Lieberman. Self-consistent nonlin-ear transmission line model of standing wave effects in a capacitive discharge. Phys.Plasmas, 11(5):1775–1785, 2004.

Bibliography 109

[55] T. Mussenbrock, T. Hemke, D. Ziegler, R. P. Brinkmann, and M. Klick. Skin effectin a small symmetrically driven capacitive discharge. Plasma Sources Sci. Technol.,17(2):025018, 2008.

[56] D. H. Kim and C.-H. Ryu. Particle simulation of a magnetically enhanced dual-frequency capacitively coupled plasma. J. Phys. D: Appl. Phys., 41(1):015207, 2008.

[57] S. Wickramanayaka, Y. Nakagawa, Y. Sago, and Y. Numasawa. Optimization of plasmadensity and radial uniformity of a point-cusp magnetic field applied capacitive plasma.J. Vac. Sci. Technol. A, 18(3):823–829, 2000.

[58] E. Semmler, P. Awakowicz, and A. von Keudell. Plasma impedance determination invery high frequency (vhf) driven dual frequency capacitively coupled plasmas. PlasmaSources Sci. Technol, 2008. submitted.

[59] B. Schiek. Grundlagen der Hochfrequenz-Messtechnik. Springer Verlag Berlin, 1999.

[60] M. A. Lieberman and A. J. Lichtenberg. Principles of Plasma Discharges and MaterialsProcessing. John Wiley & Sons Inc., 2nd edition, 2005.

[61] M. A. Sobolewski. Electrical characterization of radio-frequency discharges in theGaseous Electronics Conference Reference Cell. J. Vac. Sci. Technol. A, 10(6):3550–3562, 1992.

[62] S. Dine, J. Jolly, and J. Guillon. Coupled power and plasma impedance measure-ments in a VHF capacitive discharge in hydrogen. In Proceedings of the 5th FLTPDConference, Specchia, Italy, April 2003.

[63] J. S. Logan, N. M. Mazza, and P. D. Davidse. Electrical characterization of radio-frequency sputtering gas discharge. J. Vac. Sci. Technol., 6(1):120–123, 1969.

[64] B. Andries, G. Ravel, and L. Peccoud. Electrical characterization of radio-frequencyparallel-plate capacitively coupled discharges. J. Vac. Sci. Technol. A, 7(4):2774–2783,1989.

[65] P. Bletzinger and M. J. Flemming. Impedance characteristics of an rf parallel platedischarge and the validity of a simple circuit model. J. Appl. Phys., 62(12):4688–4695,1987.

[66] W. E. Mlynko and D. W. Hess. Electrical characterization of rf glow discharges usingan operating impedance bridge. J. Vac. Sci. Technol. A, 3(3):499–503, 1985.

[67] A. J. Miranda and C. J. Spanos. Impedance modeling of a Cl2/He plasma dischargefor very large scale integrated circuit production monitoring. J. Vac. Sci. Technol. A,14(3):1888–1893, 1996.

[68] N. Spiliopoulos, D. Mataras, and D. E. Rapakoulias. Power dissipation and impedancemeasurements in radio-frequency discharges. J. Vac. Sci. Technol. A, 14(5):2757–2765,1996.

110 Bibliography

[69] J. G. Langan, S. W. Rynders, B. S. Felker, and S. E. Beck. Electrical impedanceanalysis and etch rate maximization in NF3/Ar discharges. J. Vac. Sci. Technol. A,16(4):2108–2114, 1998.

[70] L. P. Bakker, G. M. W. Kroesen, and F. J. de Hoog. Rf discharge impedance measure-ments using a new method to determine the stray impedances. IEEE Trans. PlasmaSci., 27(3):759–765, 1999.

[71] D. Teuner, C. Lucking, and J. Mentel. Electrical characterization of capacitive RFdischarges. In Proceedings of the 24th ICPIG Conference, volume 1, pages 45–46,Warsaw, Poland, July 1999.

[72] K. Bera, C.-A. Chen, and P. Vitello. Plasma impedance in a narrow gap capacitivelycoupled rf discharge. IEEE Trans. Plasma Sci., 30(1):144–145, 2002.

[73] J. W. Butterbaugh, L. D. Baston, and H. H. Sawin. Measurement and analysis of radiofrequency glow discharge electrical impedance and network power loss. J. Vac. Sci.Technol. A, 8(2):916–923, 1990.

[74] G. Wenig. Modellierung und Diagnostik nachleuchtender Niederdruckplasmen. Disser-tation, Ruhr-Universitat Bochum, November 2006.

[75] P. Awakowicz. Niederdruckplasmen: Modelle, Diagnostikmethoden und Anwendungen.Habilitation, Technische Universitat Munchen, 1998.

[76] M. Druyvesteyn. Der Niedervoltbogen. Zeitschrift fur Physik, 64(11-12):781–798, 1930.

[77] J. D. Swift and M. J. R. Schwar. Electrical Probes for Plasma Diagnostics. Iliffe BooksLondon Ltd., 1970.

[78] M. Schulze. Diagnostik von Niederdruckplasmen zur kontrollierten Synthese vonKohlenwasserstoff-Nanoteilchen. PhD thesis, Ruhr-Universitat Bochum, August 2007.

[79] P. Scheubert, U. Fantz, P. Awakowicz, and H. Paulin. Experimental and theoreticalcharacterization of an inductively coupled plasma source. J. Appl. Phys., 90(2):587–598, 2001.

[80] L. Oksuz, F. Soberon, and A. R. Ellingboe. Analysis of uncompensated langmuir probecharacteristics in radio-frequency discharges revisited. J. Appl. Phys., 99(1):013304,2006.

[81] National Institute for Standard and Technology (NIST). NIST Atomic SpectraDatabase (ASD), http://physics.nist.gov/PhysRefData/ASD/index.html.

[82] T. Gans, V. Schulz von der Gathen, and H. F. Dobele. Spectroscopic measurements ofphase resolved electron energy distribution functions in rf-excited discharges. Europhys.Lett., 66(2):232–238, 2004.

[83] T. Gans, Chun C. Lin, V. Schulz von der Gathen, and H. F. Dobele. Phase-resolvedemission spectroscopy of a hydrogen rf discharge for the determination of quenchingcoefficients. Phys. Rev. A, 67(1):012707, 2003.

http://physics.nist.gov/PhysRefData/ASD/index.html

Bibliography 111

[84] J. Schulze, B. G. Heil, D. Luggenholscher, T. Mussenbrock, R. P. Brinkmann, andU. Czarnetzki. Electron beams in asymmetric capacitively coupled radio frequencydischarges at low pressures. J. Phys. D: Appl. Phys., 41(4):042003, 2008.

[85] J. Schulze, T. Gans, D. O’Connell, U. Czarnetzki, A. R. Ellingboe, and M. M. Turner.Space and phase resolved plasma parameters in an industrial dual-frequency capaci-tively coupled radio-frequency discharge. J. Phys. D: Appl. Phys., 40(22):7008–7018,2007.

[86] U. Czarnetzki, T. Mussenbrock, and R. P. Brinkmann. Self-excitation of the plasma se-ries resonance in radio-frequency discharges: An analytical description. Phys. Plasmas,13(12):123503, 2006.

[87] T. Mussenbrock. Zur Theorie auf selbsterregter Elektronenresonanz basierender Di-agnostikmethoden fur kapazitiv gekoppelte Niederdruckplasmen. Dissertation, Ruhr-Universitat Bochum, June 2004.

[88] T. Mussenbrock and R. P. Brinkmann. Nonlinear plasma dynamics in capacitive radiofrequency discharges. Plasma Sources Sci. Technol., 16(2):377–385, 2007.

[89] V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich. Electrical characteristics ofparallel-plate rf discharges in argon. IEEE Trans. Plasma Sci., 19(4):660–681, 1991.

[90] W. D. Qiu, K. J. Bowers, and C. K. Birdsall. Electron series resonant discharges: com-parison between simulation and experiment. Plasma Sources Sci. Technol., 12(1):57–68, 2003.

[91] G. Franz and M. Klick. Excitation mechanisms in low pressure capacitively coupleddischarges. In Oral presentation 51st AVS International Symposium, Anaheim (CA),USA, November 2004.

[92] G. Franz and M. Klick. Electron heating in capacitively coupled discharges and reactivegases. J. Vac. Sci. Technol. A, 23(4):917–921, 2005.

[93] E. Kawamura, M. A. Lieberman, and A. J. Lichtenberg. Stochastic heating in singleand dual frequency capacitive discharges. Phys. Plasmas, 13(5):053506, 2006.

[94] P. Chabert, P. Levif, J.-L. Raimbault, J.-M. Rax, M. M. Turner, and M. A. Lieberman.Electron heating in multiple-frequency capacitive discharges. Plasma Phys. Control.Fusion, 48(12B):B231–B237, 2006.

[95] M. Klick, W. Rehak, and M. Kammeyer. Plasma diagnostics in rf discharges usingnonlinear and resonance effects. Jpn. J. Appl. Phys., 36(7B):4625–4631, 1997.

[96] M. Klick, M. Kammeyer, W. Rehak, G. Franz, W. Kasper, and P. Awakowicz. Inno-vative plasma diagnostics and control of process in reactive low-temperature plasmas.Surf. Coat. Technol., 98(1-3):1395–1399, 1998.

[97] D. Ziegler. private communication. 2008.

112 Bibliography

[98] D. Ziegler, T. Mussenbrock, and R. P. Brinkmann. Nonlinear dynamics of dual fre-quency capacitive discharges: a global model matched to an experiment. PlasmaSources Sci. Technol., 17(4):045011, 2008.

[99] D. Gahan, B. Dolinaj, and M. B. Hopkins. Retarding field analyzer for ion energydistribution measurements at a radio-frequency biased electrode. Rev. Sci. Instrum.,79(3):033502, 2008.

[100] C. Bohm and J. Perrin. Retarding-field analyzer for measurements of ion energy dis-tributions and secondary electron emission coefficients in low-pressure radio frequencydischarges. Rev. Sci. Instrum., 64(1):31–44, 1993.

[101] P. Benoit-Cattin and L. C. Bernard. Anomalies of the energy of positive ions extractedfrom high-frequency ion sources. a theoretical study. J. Appl. Phys., 39(12):5723–5726,1968.

[102] A. C. F. Wu, M. A. Lieberman, and J. P. Verboncoeur. A method for comput-ing ion energy distributions for multifrequency capacitve discharges. J. Appl. Phys.,101(5):056105, 2007.

[103] M. M. Patterson, H.-Y. Chu, and A. E. Wendt. Arbitrary substrate voltage wave formsfor manipulating energy distribution of bombarding ions during plasma processing.Plasma Sources Sci. Technol., 16(2):257–264, 2007.

[104] J. K. Lee, O. V. Manuilenko, N. Yu Babaeva, H. C. Kim, and J. W. Shon. Ion energydistribution control in single and dual frequency capacitive plasma sources. PlasmaSources Sci. Technol., 14(1):89–97, 2005.

[105] V. Georgieva, A. Bogaerts, and R. Gijbels. Numerical investigation of ion-energy-distribution functions in single and dual frequency capacitively coupled plasma reac-tors. Phys. Rev. E, 69(2):026406, 2004.

[106] J. F. Shackelford. Werkstofftechnologie fur Ingenieure. Pearson Education DeutschlandGmbH, Munchen, 6th revised edition, 2007.

[107] G. Sauerbrey. Verwendung von Schwingquarzen zur Mikrowagung. Z. Phys., 155:206–222, 1959.

[108] C. Lu and O. Lewis. Investigation of film-thickness determination by oscillating quartzresonators with large mass load. J. Appl. Phys., 43:4385, 1972.

[109] A. Arnau, T. Sogorb, and Y. Jimenez. Circuit for continuous motional series resonantfrequency and motional resistance monitoring of quartz crystal resonators by parallelcapacitance compensation. Rev. Sci. Instrum., 73(7):2724–2737, 2002.

[110] R. Bechmann. Dickenscherschwingungen piezoelektrisch erregter Kristallplatten.Hochfrequenztechnik und Elektroakustik, 56:17–21, 1950.

[111] G. Sauerbrey. Amplitudenverteilung und elektrische Ersatzdaten von Schwingquarz-platten (AT-Schnitt). Mitteilungen aus dem 1. Physikalischen Institut der TU BerlinAEO, 18:624–628, 1961.

Bibliography 113

[112] M. Liebau. Resonante Quarzsensoren zum Nachweis von Wechselwirkungensupramolekularer Systeme. PhD thesis, Martin-Luther-Universitat Halle-Wittenberg,1998.

[113] D. Ziegler, T. Mussenbrock, and R. P. Brinkmann. Phys. Plasmas, 2008. in preparation.

[114] A. V. Oppenheim, R. W. Schafer, and J. R. Buck. Discrete-Time Signal Processing.Pearson Education Inc., 2nd edition, 2004.

[115] E. Semmler, P. Awakowicz, and A. von Keudell. Heating of a dual frequency capaci-tively coupled plasma via the plasma series resonance. Plasma Sources Sci. Technol.,16:839–848, 2007.

[116] E. Semmler, P. Awakowicz, D. Ziegler, T. Mussenbrock, and R. P. Brinkmann. Highfrequency behaviour of dual frequency capacitively coupled plasmas. In Proceedings ofthe 28th ICPIG Conference, pages 2158–2159, Prague, Czech Republic, July 2007.

[117] E. Semmler, D. O’Connell, T. Gans, P. Awakowicz, and A. von Keudell. Electronheating and ionization mechanisms in capacitively coupled dual frequency plasmas.Arlington (VA), USA, October 2007. American Physical Society.

[118] H. C. Kim, J. K. Lee, and J. W. Shon. Analytic model for a dual frequency capacitivedischarge. Phys. Plasmas, 10(11):4545–4551, 2003.

[119] M. M. Turner and P. Chabert. Electron heating mechanisms in dual-frequency capac-itive discharges. Plasma Sources Sci. Technol., 16(2):364–371, 2007.

[120] H. C. Kim and J. K. Lee. Mode transition induced by low-frequency current in dual-frequency capacitive discharges. Phys. Rev. Lett., 93(8):085003, 2004.

[121] H. C. Kim and J. K. Lee. Dual-frequency capacitive discharges: Effect of low-frequencycurrent on electron distribution function. Phys. Plasmas, 12(5):053501, 2005.

[122] H. C. Kim and J. K. Lee. Dual radio-frequency discharges: Effective frequency conceptand effective frequency transition. J. Vac. Sci. Technol. A, 23(4):651–657, 2005.

[123] T. Gans, V. Schulz von der Gathen, and H. F. Dobele. Prospects of Phase ResolvedOptical Emission Spectroscopy as a Powerful Diagnostic Tool for RF-Discharges. InProceedings of the 26th ICPIG Conference, Greifswald, Germany, July 2003.

[124] A. Yuece. Optimierung des Sputterabscheideprozesses metallischer Schichten in ka-pazitiv gekoppelten Multifrequenzplasmen. Diplomarbeit, Ruhr-Universitat Bochum,May 2008.

[125] N. Matsunami, Y. Yamamura, Y. Itikawa, N. Itoh, Y. Kazumata, S. Miyagawa,K. Morita, R. Shimizu, and H. Tawara. Atomic Data Nuclear Data Tables, 31:1,1984.

[126] E. Semmler, D. O’Connell, T. Gans, A. Yuece, P. Awakowicz, and A. von Keudell.Plasma and thin film growth control in dual frequency driven capacitive discharges.Garmisch-Partenkirchen, Germany, 2008. Plasma Surface Engineering 2008.

Documents

Characterization of multiple frequency driven capacitively coupled ...€¦ · Characterization of multiple frequency driven capacitively coupled plasmas for ferro-metallic thin lm