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ERNST-MORITZ-ARNDT-UNIVERSITAT
GREIFSWALD
Detailed Investigations of the Sheath Dynamics and
Elementary Processes in Capacitively Coupled RF Plasmas
I n a u g u r a l d i s s e r t a t i o n
zur
Erlangung des akademischen Grades
doctor rerum naturalium (Dr. rer. nat.)
an der Mathematisch-Naturwissenschaftlichen Fakult at
der
Ernst-Moritz-Arndt-Universit at Greifswald
vorgelegt von: Kristian Dittmann
geboren am 18. September 1980
in Prenzlau
Greifswald, 25. Juni 2009Dekan: Prof. Dr. K. Fesser
1. Gutachter: Prof. Dr. J. Meichsner
2. Gutachter: Prof. Dr. W. Graham
Tag des Promotionskolloquiums: 12. Oktober 2009"Let us now assume that the plane electrode be charged to a negative
potential of 100 volts. Electrons will therefore be prevent from
approaching close to the electrode, whereas positive ions will be drawn
towards it. There will therefore be a layer of gas near the electrode
where there are positive ions but no electrons, and in this region there
will therefore be a positive ion space charge. The outer edge of this
sheath of ions will have a potential of -1 and the positive ions pass
through this outer edge with a velocity corresponding to 2 volts."
Langmuir (1923) [1]
"Except near the electrodes, where there are sheaths containing very
few electrons, the ionized gas contains ions and electrons in about equal
numbers so that the resultant space charge is very small. We shall use
the name plasma to describe this region containing balanced charges
of ions and electrons."
Langmuir (1928) [2]Contents
List of Symbols iii
Abbreviations vii
1 Introduction 1
2 Basics 3
2.1 Asymmetric Capacitively Coupled RF-Discharges . . . . . . . . . . . . . . . . 4
2.1.1 The Simpli ed Linear ’Electrical Engineering’ Model . . . . . . . . . . 7
2.2 Oxygen RF-Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Optical Emission Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 The Corona-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 Actinometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Experimental Setup and Implementation of Diagnostics 17
3.1 Vacuum Chamber and RF Discharge . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Phase Resolved Optical Emission Spectroscopy on Capacitively Coupled RF-
Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Laser Absorption Spectroscopy in Argon RF-Plasma . . . . . . . . . . . . . . 25
4 Particle-In-Cell Simulation of Capacitive RF Discharges { Main Features 31
4.1 Particle-In-Cell Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Extrapolation of Particle Charge Density . . . . . . . . . . . . . . . . . . . . 33
4.4 Calculation of a Self-Consistent Electric Field . . . . . . . . . . . . . . . . . . 34
4.5 Coulomb Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.6 Electron-Neutral and Ion-Neutral Collisions . . . . . . . . . . . . . . . . . . . 35
4.7 PIC-MCC Simulation of Oxygen RF Plasmas . . . . . . . . . . . . . . . . . . 37
5 Preliminary Investigations 47
5.1 Oxygen RF-Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1.1 Applicability of Actinometry on Atomic Oxygen . . . . . . . . . . . . 48
5.2 Hydrogen RF-Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3 Argon RF-Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.1 Metastable Excited Argon Atoms in Argon RF-Plasma . . . . . . . . . 56
iContents
6 Spatial and Phase Resolved Optical Excitation Patterns in CCPs 61
6.1 Excitation Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2 I - Sheath Expansion Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.1 Excitation Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.2 Sheath Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.3 II - Full Sheath Expansion, Secondary Electrons . . . . . . . . . . . . . . . . 73
6.3.1 Excitation Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.3.2 Transition from - to -Mode { Pseudo--Mode . . . . . . . . . . . . 75
6.4 III - Sheath Collapse Phase, Field Reversal . . . . . . . . . . . . . . . . . . . 77
7 IV - Heavy Particle Impact Excitation in the RF-Sheath 81
7.1 Excitation Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2 Simple Analytic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.3 Pressure and Mass Dependence of the Temporal Modulation . . . . . . . . . . 87
7.4 Energetic Oxygen Ions in the RF-Sheath { A PIC Simulation . . . . . . . . . 88
7.5 The Role of Metastables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8 Summary 97
A Appendix 101
A.1 Interference Phenomenon at ICCD-Cameras . . . . . . . . . . . . . . . . . . . 101
A.2 ’Ghost Lines’ in Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
A.3 Numerical Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.3.1 Calculation of the Mean Gas Residence Time . . . . . . . . . . . . . . 103
A.3.2 Additional Averaging of Measured Emission Intensities . . . . . . . . . 103
A.3.3 Calculation of the Time Derivative of Measured Emission Intensities . 103
A.4 List of Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
A.5 Spectroscopical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A.6 Overview of Phase Resolved Optical Emission Intensity Pro les . . . . . . . . 110
A.7 Additional Phase Resolved Excitation Rate Pro les . . . . . . . . . . . . . . . 118
List of Figures 123
List of Tables 128
Bibliography 130
iiList of Symbols
All quantities are in International System (SI).
absorption coe cient
A rate
A(p; q) transition probability of one particle in the state p
in the lower level q
A area of the grounded electrodeground
A area of the powered electrodeRF
A Einstein coe cient of spontaneous emission of a transitionki
from an excited (upper) state k into a lower state i, transition probability
~B magnetic eld
b impact parameter
c light speed
C capacity at the powered, grounded electrode1;2
C capacitor
C coupling capacitorcouple
d thickness of the plasma sheath boundarys
19e elementary charge ( 1:602 10 C)
12 1 1" permittivity of free space ( 8:854 10 A s V m )0
" emission coe cient
E energy level of the lower state at transitionsi
E energy level of the upper state atk
E ionization energyion
~E electric eld
E eld in the plasma sheath boundarys
E energy thresholdth
f oscillator strength of the transition from level i to kik
g lower level statistical weight (g = 2J + 1)i i i
g upper level weight (g = 2J + 1)k k k
ux of negative charge carriers
+ ux of positive charge
I emission intensity
i(t) current
J total electronic angular momentum of the lower leveli
J totaltum of the upper levelk
23 1k Boltzmann constant ( 1:381 10 J K )B
iiiList of Symbols
k rate coe cient
k quenching rate of the species qq
degree of ionization; e ective absorption coe cient
L absorption length, distance between electrodes
L spectral radiance density
mean free path length; wavelength
electron Debye lengthDe
center wavelength0
M molecular weight
m mass
31m electron mass ( 9:109 10 kg)e
m ion massi
n number density
n electron densitye
n ion densityi
n number density of neutral particlesn
frequency
vibration quantum number of the lower statei
quantum number of the upper statek
frequency of discharge applied voltageRF
Doppler widthD
! plasma frequencyp
! electron plasma frequencype
! ion plasma frequencypi
! angular of discharge applied voltageRF
electrical potential
p pressure
P power, probabiliy
q charge
Q gas ow rate
charge density
1 1R gas constant ( 8:315 J K mol )
S area of the of absorption line pro le
cross section
t time
t collision time-stepcol
t mean gas residence timeg
t rise timerise
lifetime; optical depth
e ective lifetimee
naturaln
T temperature; transmission
iv

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