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thesis entitled

THE ELECTROMAGNETIC EVALUATION OF A COMPACT
ECR MICROWAVE PLASMA SOURCE

presented by

Mark Alan Perrin

has been accepted towards fulfillment
of the requirements for

M.S. Electrical Engineering

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msu loAnAfﬂnnatlvo Action/Equal 099M Institwon
Wan-9.1

THE ELECTROMAGNETIC EVALUATION OF A COMPACT ECR
MICROWAVE PLASMA SOURCE

By

Mark Alan Perrin

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Electrical Engineering

1 996

ABSTRACT

THE ELECTROMAGNETIC EVALUATION OF A COMPACT ECR
MICROWAVE PLASMA SOURCE

By

Mark Alan Perrin

This thesis is a preliminary study of the electromagnetic coupling behavior of a com-
pact cavity coupled ECR plasma source. The plasma source studied in this investigation
consists of: a 9.8 cm diameter microwave cavity applicator, a 70 mm diameter quartz dis-
charge chamber, and an eight pole ECR magnet array. The cavity is internally tuned by the
adjustment of: 1) a sliding short used to vary cavity length from 4 cm to 12 cm, and 2) an
adjustable end feed loop variable from 1.5 cm to 5.5 cm. This source was evaluated with
argon at pressures from 0.75 mtorr to 100 mtorr with corresponding ﬂow rates of 20 sccm
to 120 sccm. Incident power from a 2.45 GHz magnetron was held constant at 150 Watts.

Reﬂected power was measured vs. cavity length, loop length, discharge pressure, dis-
charge chamber height and magnetic ﬁeld in order to construct a parameter map of the
electromagnetic modes present in this source and to make observations on mode behavior.
Measurements of the impressed relative electric ﬁelds at the walls are made to determine
the spatial internal electric ﬁeld patterns and identify each resonant mode. Correlated mea-
surements of absorbed power, ion saturation current, and relative electric ﬁeld strength are

made to determine the relationship between absorbed power and produced charge density.

Copyright by
MARK ALAN PERRIN
1996

ACKNOWLEDGEMENTS

The author would like to thank Dr. Jes Asmussen for his direction, instruction, and
support throughout the development and execution of this research. Special thanks to Dr.
Marvin Siege] for his support and instruction during the early stages of this work. I would
also like to thank Dr. D. Reinhard and Dr. T. Grotjohn for their valuable assistance. My
colleagues Dr. A. Srivastava, P. Mak, Dr. G. King, and Dr. B. Manring deserve a great deal

of thanks for their hours of discussion and training.

. This research was supported in part by grants from International Business

Machines and the Michigan State University Research Excellence Fund.

iv

TABLE OF CONTENTS

LIST OF TABLES ------------------------------------------- ix
LIST OF FIGURES ------------------------------------------- x
Chapter 1
Wu
1.1 A Brief History of the Microwave ECR Cavity Source ----------------- 1
1.2 Motivation for Research ------------------------------------- 2
1.3 Research Goals ------------------------------------------- 3
1.4 Thesis Outline -------------------------------------------- 4
Chapter 2
E . . E l E . l S
2.1 Introduction- - - '- ------------------------------------------ 6
2.2 The Microwave Delivery System ------------------------------- 8
2.3 Gas Flow and Vacuum System --------------------------------- 10
2.4 The Microwave Plasma Source --------------------------------- 12
2.4.1 The Microwave Cavity Applicator ----------------------------- 18
2.4.2 Two Stage Base Plate and Quartz Discharge Chamber ----------- 20
2.4.3 The ECR Magnet Conﬁguration -------------------------- 22
Chapter 3
3.1 Introduction --------------------------------------------- 24
3.2 Transmission Line Load Matching ------------------------------ 25
3.3 Complex input impedance and equivalent lumped parameter circuit -------- 26
3.4 Frequency Response and Length Tuning -------------------------- 29
3.5 Transient Response and Quality Factor Q ------------------------- 29

3.6 Electromagnetic Wave Behavior ................................ 33

3.6.1 Electromagnetic Wave Propagation in Cylindrical Waveguides ------- 33
3.6.1.1 TEM propagation in coaxial waveguide sections ------------- 33
3.6.1.2 TE and TM propagation in hollow cylindrical waveguide sections - 34
3.6.2 Abrupt Waveguide Discontinuities -------------------------- 37
3.7 Standing Wave Cavities and Cavity Modes ------------------------ 40
3.8 Conclusion ---------------------------------------------- 47
Chapter 4
‘90112‘416 11-. l' 3'11V0 0.1‘U,,0\NV1" 1-11:..-
4.1 Introduction --------------------------------------------- 48
4.2 Parameter Space ------------------------------------------ 49
4.3 Experimental Setup and Start-up Procedure ------------------------ 51
4.4 Experimental Procedure for Reﬂected Power Measurements ------------ 53
4.5 Reﬂected Power Measurements -------------------------------- 61
4.5.1 Reﬂected Power vs. Ls Curves for a 5.6 cm tall Discharge
with ECR Magnets ------------------------------------- 61
4.5.2 Reﬂected Power vs. Ls Curves for a 6.9 cm tall Discharge
with ECR Magnets ------------------------------------- 62
4.5.3 Reﬂected Power vs. Ls Curves for a 5.6 cm tall Discharge
without Magnets -------------------------------------- 67
4.5.4 Reﬂected Power vs. Ls Curves for a 6.9 cm tall Discharge
without Magnets -------------------------------------- 71
4.6 Analysis of Electromagnetic Mode Behavior ---------------------- 76
4.6.1 Observations of Mode Behavior for the Four Source Geometry
Conﬁgurations ---------------------------------------- 76
4.6.2 Pressure Dependent Changes in Mode Cavity Length ------------- 79
4.6.3 Increase in Mode Cavity Length with Decrease in Loop Length ------ 81
4.6.4 Changes in Mode Cavity Length Ls vs. 5.6 cm or 6.9 cm Discharge - - - -82
4.6.5 Comparison of Plasma Behavior With and “Without Magnets -------- 88
4.6.6 Cavity Length Dependent Hysteresis for Reﬂected Power ---------- 91
4.7 Summary of Important Observations ---------------------------- 92
Chapter 5
Ono'i' V1400. pdiu OWN":-_1«. V
5.1 Introduction --------------------------------------------- 95
5.2 Parameter Space ------------------------------------------ 95
5.3 Start-up Procedure and Experimental Setup ------------------------ 97
5.4 Experimental Procedure ------------------------------------- 100
5.4.1 Relative Measurement of Electric Field ----------------------- 100

vi

5.4.2 Measurement of Absorbed Power --------------------------- 105

5.4.3 Relative Measurement of Charge Density --------------------- 106
5.5 Spatial Electric Field Patterns --------------------------------- 109
5.5.1 Description of the Experiment ----------------------------- 109
5.5.2 Identiﬁcation of the TEM Mode ---------------------------- 110
5.5.3 Spatial Field Patterns for the Low Ls Mode -------------------- 131
5.6 Correlation of Absorbed Power, Charge Density, and Internal Electric
Fields vs. Ls --------------------------------------------- 131
5.5.1 Description of the Experiment ----------------------------- 131
5.5.2 Evaluation of a 5.6 cm Discharge with ECR Magnets at l mtorr ------ 132
5.5.3 Evaluation of a 6.9 cm Discharge at 1, 10, and 50 mtorr
with ECR Magnets ------------------------------------- 133
5.7 Conclusions --------------------------------------------- 139
Chapter 6
W
6.1 Summary and Conclusions for this Investigation --------------------- 140
6.2 Transmission Line Model of a Plasma Loaded Cavity ----------------- 141
6.3 Recommendations for Future Research --------------------------- 146
LIST OF REFERENCES --------------------------------------- 148

vii

LIST OF TABLES

Table 5.1 - Summary of the Discharge Pressures Investigated in the
Evaluation of the Spatial Electric Fields of the TB” Mode ------ 110

viii

Figure 2.1 -
Figure 2.2 —
Figure 2.3 -
Figure 2.4 -
Figure 2.4 -
Figure 2.5 -
Figure 2.6 -
Figure 2.7 -
Figure 2.8 -
Figure 2.9 -

Figure 2.10 -

Figure 3.1 -

Figure 3.2 -

LIST OF FIGURES

m2
Block Diagram of The Experimental System --------------- 7
Block Diagram of Microwave Circuit -------------------- 9
Block Diagram of Gas Flow and Vacuum System ------------ 11
Cross Section of the ECR Plasma Source (# Key) ------------ 13
Cross Section of the ECR Plasma Source ------------------ 14
Assembled Microwave ECR Plasma Source ---------------- 15
Disassembled Microwave ECR Plasma Source -------------- 16
View of brass end plate, Loop antenna, and guide bolts -------- 17
Cross Section of Microwave Cavity Applicator -------------- 19
Cross Section of Base Plate and Discharge Chamber ---------- 20
ECR Magnet Conﬁguration --------------------------- 23

Chapter}
Transmission line section with complex load --------------- 25

(a) Plasma loaded microwave cavity with transmission circuit,
(b)Lumped parameter equivalent circuit of the cavity for a
single resonant mode ------------------------------- 28

Figure 3.3 -

Figure 3.4 -

Figure 3.6 -

(a) power absorbed vs. driving frequency 01. (b) power
absorbed vs. cavity length LS (Variation in L8 is exaggerated

for clarity) -------------------------------------- 3O

Transient Response of a Parallel RLC Circuit --------------- 32
Figure 3.5(a)(b)(c) - Relative Wavelengths, Phase Relationships, and Field

Patterns ---------------------------------------- 35

Wave behavior at an abrupt waveguide discontinuity ---------- 39

Standing Waves and Standing Wave Cavity ---------------- 41

Figure 3.7 -
Figure 3.8 -
Figure 3.9 -

Figure 3.10-

Figure 4.1 -
Figure 4.2 -

Figure 4.3 -

Figure 4.4 -

Mode Chart for Standing Wave Cavity with 9.8 cm Diameter - - - - 43

Mode Chart for Standing Wave Cavity with 6 in. Diameter ------ 44

Field Patterns for TE] 11 and TMOH Resonant Modes

(at 90° of Cycle) ---------------------------------- 46
Cheated

Block Diagram of Experimental Variables ----------------- 50

Experimental Setup for Reﬂected Power Measurements -------- 52

a) An Example Single Reﬂected Power Curve for One Loop
Length Lp' b) An Example Set of Nine Curves Tracing Out
a Reﬂected Power Contour Surface ---------------------- 55

Loop in Contact with Discharge Chamber ----------------- 56

Figure 4.5(a)(b)(c) - Reﬂected Power vs. Cavity Length, Loop Length and

Pressure for a 5.6 cm tall discharge with ECR magnets -------- 57

Figure 4.6(a)(b)(c) - Reﬂected Power vs. Cavity Length, Loop Length and

Pressure for a 6.9 cm tall discharge with ECR magnets -------- 63

Figure 4.7(a)(b)(c) - Reﬂected Power vs. Cavity Length, Loop Length and

Pressure for a 5.6 cm tall discharge without magnets ---------- 68

Figure 4.8(a)(b)(c) - Reﬂected Power vs. Cavity Length, Loop Length and

Pressure for a 6.9 cm tall discharge without magnets ---------- 73

Figure 4.9a - Best matched positions for the 5.6 cm discharge
with ECR magnets --------------------------------- 77

Figure 4.9b - Best matched positions for the 6.9 cm discharge
with ECR magnets --------------------------------- 77

Figure 4.9c - Best matched positions for the 5.6 cm discharge
without magnets ---------------------------------- 78

Figure 4.9d ~ Best matched positions for the 6.9 cm discharge
without magnets ---------------------------------- 78

Figure 4.10 - Comparison of cavity lengths for the TB“ mode with
magnet ring vs. discharge chamber height ----------------- 84

Figure 4.11 - Comparison of cavity lengths for the TE" mode without
magnets vs. discharge chamber height -------------------- 85

Figure 4.12 — Comparison of cavity lengths for the Low Ls mode with
magnet ring vs. discharge chamber height ----------------- 87

Figure 4.13 - Plots comparing magnetized and non-magnetized

TE“ mode curves --------------------------------- 89
Figure 4.14 - Comparison of magnetized and non-magnetized

Low Ls mode curves -------------------------------- 90

Gunter;

Figure 5.1 - Block Diagram of Experimental Variables ----------------- 96
Figure 5.2 - Experimental Setup for Source Evaluation ----------------- 99
Figure 5.3 - Cross Sectional Diagram of a Microcoaxial Electric

Field Probe -------------------------------------- 100
Figure 5.4 - Measurement of Electric Field Strength ------------------- 102
Figure 5 .5 - Cross-Section of a Circumferential Ring of E—Field

Sampling Holes ----------------------------------- 103
Figure 5.6 - Reﬂected and Absorbed Power Proﬁles ------------------- 105
Figure 5.7 - Setup for Measurement of Ion Saturation Current ------------ 108

xi

Figure 5.8 -

Figure 5.9 -

Figure 5.10 -

Figure 5.11 -

Figure 5.12 -

Figure 5.13 -

Figure 5.14 -

Figure 5.15 -

Figure 5.16 -

Figure 5.17 -

Figure 5.18 -

Figure 5.19 -

Figure 5.20 -

Figure 5.21 -

Figure 5.22 -

360° Circumferential Electric Field Proﬁle for TB] 11 Mode
at l mTorr --------------------------------------- 113

Longitudinal Electric Field Proﬁle for TB] 11 Mode
at 1 mTorr --------------------------------------- 114

360° Circumferential Electric Field Proﬁle for TB} 1] Mode
at 10 mTorr -------------------------------------- 115

Longitudinal Electric Field Proﬁle for TB, 11 Mode
at 10 mTorr -------------------------------------- 116

360° Circumferential Electric Field Proﬁle for TE 1, Mode
at 50 mTorr -------------------------------------- 1 17

Longitudinal Electric Field Proﬁle for TE] 11 Mode
at 50 mTorr -------------------------------------- 118

3600 Circumferential Electric Field Proﬁle for TE 1] Mode
at 1 mTorr --------------------------------------- 121

Longitudinal Electric Field Proﬁle for TE] 11 Mode
at 1 mTorr --------------------------------------- 122

360° Circumferential Electric Field Proﬁle for TE] 11 Mode
at 10 mTorr -------------------------------------- 123

Longitudinal Electric Field Proﬁle for TE] 11 Mode
at 10 mTorr -------------------------------------- 124

3600 Circumferential Electric Field Proﬁle for TB] 1, Mode
at 50 mTorr -------------------------------------- 125

Longitudinal Electric Field Proﬁle for TE ,1 Mode
at 50 mTorr -------------------------------------- 126

360° Circumferential Electric Field Proﬁle for TE] 11 Mode
at 50 mTorr -------------------------------------- 127

Longitudinal Electric Field Proﬁle for TE, 11 Mode
at 50 mTorr -------------------------------------- 128

360° Circumferential Electric Field Proﬁle for TB] 1] Mode
at 50 mTorr -------------------------------------- 129

xii

Figure 5.23 - Longitudinal Electric Field Proﬁle for TB, 11 Mode

at 50 mTorr -------------------------------------- 130
Figure 5.24 ~ Absorbed Power, Ion Saturation Current, and Probe

Power vs. Ls ------------------------------------- 134
Figure 5.25 - Absorbed Power, Ion Saturation Current, and Probe

Power vs. Ls ------------------------------------- 135
Figure 5.26 - Absorbed Power vs. Ls for a 6.9 cm Discharge at 1 mTorr ------ 136
Figure 5.27 - Ion Saturation Current vs. Ls for a 6.9 cm Discharge

at 1 mTorr --------------------------------------- 137
Figure 5.28 - Electric Field Probe Power vs. Ls for a 6.9 cm Discharge

at 1 mTorr --------------------------------------- 138

Chm

Figure 6.1 - Four Sections of the Plasma Source and Transmission Line
Equivalent Circuit ................................. 144

xiii

Chapter 1

Introduction

1.1 A Brief History of the Microwave ECR Cavity Source:

Although the phenomenon of electron cyclotron resonance in plasmas was utilized as
early as the late 1940’s [1,2], ECR plasma sources were not widely investigated until the
mid 1970’s. Early microwave ECR plasma sources [3,4] delivered power to their dis-
charges via rectangular waveguides. A vacuum sealed quartz window separated the
waveguide from the discharge. Triple stub tuners were used to match the plasma load and
minimize reﬂected power. Large electromagnet coils were used to produce the ECR
regions necessary to couple power into the discharge.

In the early 1980’s an ECR plasma source design was developed (by Asmussen, et al.)
at Michigan State University [5,6,7,8]. This source, designated as the Microwave Plasma
Disk Reactor (MPDR), contained numerous innovations [9,10,1 1,12,13,14,]5] that
improved the performance and versatility of the ECR plasma source. Rectangular wave
guide, triple stub tuned, microwave excitation was replaced by a resonant cylindrical cav-
ity, tunable with sliding short and coupling probe antenna. This reduced tuning complex-
ity, improved coupling efﬁciency, and allowed more control over the electromagnetic
ﬁelds exciting the plasma. The quartz window was replaced by a vacuum ﬁtted quartz

dome placed at the bottom of the cylindrical cavity. This quartz dome contained the

plasma and improved the coupling of microwave power into the plasma volume. Rare
earth permanent magnets were introduced to generate the ECR zone and conﬁne the
plasma. This eliminated the need for large, heavy, and power intensive electromagnet
coils. What resulted from these innovations was a very efﬁcient, light weight, and control-
lable ECR source concept that was also versatile in its scaleability and applicability.

Since the mid 1980’s the MPDR ECR plasma source has evolved to ﬁt the varied
requirements of several speciﬁc applications. A few examples are: large diameter wafer
etching [16,17], low pressure thin ﬁlm deposition, molecular beam epitaxy [18], experi-
mental spacecraft propulsion [19], ion sources for low energy materials processing [20],

ion implantation, and high energy accelerator physics [21].

1.2 Motivation for Research:

Despite all the applications and uses described above there are still things that are not
fully understood about these plasma sources, such as electromagnetic mode behavior and
power coupling vs. the experimental variables of tuning, pressure, and input power. The
overall motivation for this research is to work toward the answers to some of these ques-
tions.

In any careful scientiﬁc investigation it is usually best to begin by observing the input/
output behavior of the simplest systems possible. The cavity used in this research was
designed to excite only the TB“ or TMm electromagnetic modes, thus reducing the con-

fusing interactions between many modes that may exist in larger cavities. Knowledge of

small diameter source behavior can eventually lead to a greater understanding of the elec-

tromagnetics of large diameter microwave discharges.

1.3 Research Goals:

The primary objective of this thesis and the research presented herein is to record and
analyze the internal and output behavior of a compact microwave ECR plasma source vs.

the many experimental inputs. Input variables varied in these experiments were:

1. Cavity Length, Ls

2. Loop Antenna Length, Lp

3. Discharge Pressure (coupled to Flow Rate), P/ i-
4. Input Power (held constant at 150 W), Pine

5. Discharge Chamber Height, h

6. Magnetic Field (presence or absence of Multipole Magnet Ring)

Internal and Output variables investigated and recorded were:

1. Reﬂected Power, Pref
2. Spatial Variation of Electric Field Strength
3. Relative Electric Field Strength (measured vs. Ls), EM

4. Ion Saturation Current (used to measure Relative Plasma Density), Isalt

One goal in this research was to ﬁnd the location of the resonant modes vs. the input
variables. To this end reﬂected power was recorded as the experimental input parameters
were varied. From this reﬂected power data a map of the locations of resonant modes was
constructed and hence mode behavior vs. the variation of input parameters could be stud-
ied. A second goal was to use electric ﬁeld probe measurements to identify the spatial
variation of the impressed electric ﬁeld and then use electromagnetic theory to identify the
resonant modes. The ﬁnal goal was to investigate the relationship between power absorbed
by the plasma source and output charge density produced by the discharge. Overall, the
experiments performed in this thesis were intended to contribute to the wider goal com-
mon to all those investigating MPDR sources at Michigan State University: a better under-
standing of the physical mechanisms responsible for the operation of microwave plasma

sources and to develop an improved model of source behavior.

1.4 Thesis Outline:

The main parts of this thesis include: a description of the experimental system, a basic
dreary of operation, a presentation of experimental data, and the conclusions drawn from
this research. In Chapter 2 the description of the experimental system is given. This
includes a description of the microwave network, the vacuum system, and the plasma
source. In Chapter 3 the theoretical background necessary in understanding the basic oper-
ation of the plasma source is outlined. Presentation of experimental results begins with

Chapter 4 where electromagnetic matching behavior is investigated vs. cavity length, short

length, discharge pressure, discharge chamber height, and magnetic ﬁeld. This data is then
used to map the parameter location of matched resonant modes and study their behavior as
each of the inputs are varied. In Chapter 5 electric ﬁeld patterns are measured and used to
identify, wherever possible, each of the resonant modes found in Chapter 4. Chapter 5 also
includes experimental measurements that relate the power absorbed by the plasma source
to relative measurements of plasma charge density and internal electric ﬁeld strength. In
Chapter 6 the conclusions drawn from the experimental data are summarized and sugges-

tions for future research are presented.

Chapter 2

Description of the Experimental System

2.1 Introduction:

The plasma source described in this work is considered a compact plasma source of
the type speciﬁcally designed for ion beam generation or molecular beam epitaxy applica-
tions. It has a 9.8 cm diameter cavity and 7 cm diameter discharge.

This thesis is a continuation of work done in part by L. Mahoney [20] in characterizing
the performance of a small ECR plasma source. This design differs from that used by
Mahoney in that the cavity is excited by an end feed loop antenna instead of a side feed
probe. The microwave cavity end feed component of this source was originally designed
by L. Mahoney while he was employed at IBM Watson Research Center. It was then
donated to MSU for this research by Dr. S. .1 . Whitehair from IBM Watson Research Cen-
ter. The other working components including ECR magnets and baseplate were designed
and built by the author combining the best features of existing base plate designs.

The experimental system (see Figure 2.1) used in this research is described in the sec-
tions below. First in sections 2.2 and 2.3 the support systems including the microwave
delivery system (1) and the gas/vacuum system (2) are described. Then the ECR micro-

wave plasma source (3) and its components are described in detail in section 2.4.

 

 

 

 

 

1) Microwave Delivery System
2) GasNacuum System
3) ECR Microwave Plasma Source

Figure 2.1 - Block Diagram of The Experimental System

2.2 The Microwave Delivery System:

The microwave power supply for this system is a 2.45 GHz magnetron source (see
Figure 2.2) made by MicroNow, Inc. (1) with a maximum CW power output of 300 Watts.
Attached to the power supply is a coaxial microwave circuit that is used to: deliver power
to the plasma source, allow power measurement, and to protect the MicroNow source
from power reﬂected back into the magnetron.

Forward traveling microwave power is guided from the magnetron source through
ports A and B of the circulator (2) and on through a 30 dB directional coupler (3) that sam-
ples forward power for measurement. Power is then guided through a coaxial cable (4) to
the cavity applicator (5). The cavity applicator applies microwave power to the plasma
load. When the cavity applicator is perfectly matched to the transmission circuit all for-
ward power is absorbed in the cavity and plasma. If the cavity applicator is not matched.
some microwave power is reﬂected back through the coaxial cable and directional coupler
to the circulator. Reﬂected power will then ﬂow from port B to C of the circulator and on
through a 20 dB directional coupler (6) that samples reﬂected power. Power then travels
through a second coaxial cable (7) and is dissipated in a matched 50 Q, 500 Watt dummy-
1oad (8). Since the dummy load is matched to the transmission system only a small and
harmless amount of power is reﬂected back through ports C to A of the circulator and back

into the power source.

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1) 2.45 GHz Microwave Power Supply 7) 50 Q Coaxial Cable

2) Three Port Circulator 8) 500 Watt Dummy Load

3) 30 dB Directional Coupler 9) 20 dB Attenuator

4) 50 Q Coaxial Cable 10) HP Power Meter (Forward Power)
5) Cavity Applicator 11) HP Power Meter (Reﬂected Power)
6) 20 dB Directional Coupler 12) Therrnistor Power Detectors

Figure 2.2 - Block Diagram of Microwave Circuit

10

Each directional coupler is ﬁtted with a 20 dB attenuator (9) giving a total attenuation
of 50 dB for sampled forward power (30 dB directional coupler + 20 dB attenuator) and a
40 dB attenuation for sampled reﬂected power. Forward and reﬂected power measure-
ments are made by two analog Hewlett-Packard power meters (10 & ll) ﬁtted with ther-

mi star power detectors(12).

2.3 Gas Flow and Vacuum System:

Argon gas used in the vacuum system (Figure 2.3) ﬂows from a pressurized tank (1)
through a polyvinyl tube (2) to an MKS digital ﬂow controller (3). This controller regu-
lates the ﬂow of Argon and has a maximum ﬂow rate of 120 sccm. Argon ﬂows from here
through a stainless steel tube (4) to the baseplate of the plasma source (5). There it ﬂows
into an annular channel and escapes into the discharge zone through eight 1/ ” diameter
gas inlets that are equally spaced around the circular opening at the bottom of the base-
plate.

The plasma source sits on top of a 100 liter stainless steel vacuum chamber (6). Pres-
sures in the chamber are measured by three different pressure gauges: a thermocouple
gauge (7) which measures pressures above 100 mtorr, an MKS 1 Torr rated baratron gauge
(8) which measures pressures from 0.1 mtorr to 100 mtorr, and an ion gauge (9) which
measures pressures from 0.001 mtorr to 1 mtorr.

Gas is removed from the system by a 10 inch diameter diffusion pump (10) with a rat-
ing of 2500 Us. The diffusion pump is aided by a 33 m3/hr roughing pump (11). Both the

roughing pump and the diffusion pump are water cooled.

ll

 

 

 

 

 

 

 

 

 

 

 

 

 

1) Argon Tank 8) Baratron Guage

2) Polyvinyl Tube 9) Ion Guage

3) MKS Digital Flow Controller 10) Diffusion Pump

4) Stainless Steel Tubing 11) Roughing Pump

5) Plasma Source 12) Pneumatic Shutter Valve
6) Stainless Steel Vacuum Chamber 13) Manual Flow Valve

7) Thermocouple Guage

Figure 2.3 - Block Diagram of Gas Flow and Vacuum System

12

A high vacuum pneumatic shutter valve (12) is installed over the diffusion pump. This
valve is closed when the system is exposed to pressures above 100 mtorr. A manual ﬂow
valve (13) is located between the roughing pump and the chamber. This valve is open
while the roughing pump is the primary pump evacuating the chamber from pressures of 1
atmosphere to 50 mtorr, and then it is closed while the diffusion pump is in operation.

When the system is initially evacuated the roughing pump is used to pump the system
down to 50 mtorr. At that pressure the manual ﬂow valve (13) is closed and the pneumatic
gate valve (12) is Opened to allow the diffusion pump to evacuate gas from the chamber.
The diffusion pump then takes the system down to a base pressure of 10'6 Torr. Experi-
mental pressures in the system range from 10’4 to 10'1 Torr. This corresponds to argon gas
ﬂow rates of 27.5 seem to 120 sccm. Since there is no throttle valve in this system the

pressure and ﬂow rates are interdependent.

2.4 The Microwave Plasma Source:

The plasma source consists of: a microwave cavity applicator, a discharge chamber, a
base plate, and a set of ECR permanent magnets. A complete diagram of the assembled
source is shown in Figure 2.4. Photographs of the assembled source and disassembled
source are shown in Figures 2.5, 2.6, and 2.7. Sections 2.4.1, 2.4.2, and 2.4.3 describe the
components of the source in detail.

There are certain features shown in the photographs that must be identiﬁed here. In
Figure 2.5 the curved tube attached to the stainless steel base plate is the input inlet for the

discharge gas. The curved brass tube attached to the brass cooling stage is one of the inlets

13

for compressed air. The other air inlet can be partially seen on the other side of the brass
stage near the ruler. The barbed inlet and outlet tubes for cooling water are seen near the
curved air inlet tube on the brass cooling stage. Note the holes machined vertically and
horizontally on the stainless steel cavity for electric ﬁeld measurement. A disassembled
view of the source is shown in Figure 2.6 including: stainless steel base plate, cavity,
quartz discharge chamber, and brass cooling stage. In Figure 2.7 the brass end plate is
shown along with a bottom view of the cavity exposing the loop antenna. A view of the

stainless steel base plate showing guide bolts and discharge chamber is also seen. i

1) Stainless Steel Cylindrical Shell 15) ECR Magnet Ring

2) Sliding Short 16) Air Channel

3) Contact Fingers 17) Air Cooling Holes

4) Brass End Plate 18) Stainless Steel Base Plate
5) End Feed Loop Antenna 19) 8cm Vitan O-Ring

6) Coaxial Cable 20) 20cm Vitan O-Ring

7) Outer Coaxial Conductor 21) Discharge Gas Channel

8) Outer Coaxial Contact Fingers 22) Gas Inlet Holes

9) Coaxial Center Conductor 23) Quartz Discharge Chamber
10) Plate to Antenna Contact Fingers 24) Plasma Discharge

11) Screened Window 25) ECR Zone (shown in ﬁg. 2.10)
12) E-Field Measurement Holes 26) Outer Soft Iron Keeper

13) Brass Water/Air Cooling Stage 27) Bottom Soft Iron Keeper
14) Water Channel

Figure 2.4 - Cross-Section of the ECR Plasma Source (# Key)

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Le
L = 0 plane

 

 

20 19 21
Figure 2.4 - Cross-Section of the ECR Plasma Source

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18

2.4.1 The Microwave Cavity Applicator:

The microwave applicator (Figure 2.8) consists of a stainless steel cylindrical shell (1)
9.8 cm in diameter. It is bounded at the top by a sliding short (2) with ﬂexible contact ﬁn-
gers (3) that maintain constant electrical contact with the cavity wall. At the bottom it is
bounded by a stationary brass end plate (4) with contact ﬁngers. The bottom end plate has
a 3 inch diameter hole in it’s center where the quartz bell jar (23) extends up into the cav-
ity (see Figure 2.4). The length, Ls, of the cylindrical cavity can be varied from 5 cm to 13
cm by adjusting the movable sliding short (2).

Power is delivered to the cavity with an adjustable length end feed loop antenna (5)
that extends through the sliding short. The loop is adjustable, in that, the height of the loop
antenna (LP) can be varied from 1.5 cm to 5.5 cm. The loop is made from 3/16 inch copper
rod bent to form a loop with a 0.5 inch radius. Electromagnetic power is delivered to the
antenna through a coaxial cable (6). The outer coaxial conductor (7) maintains electrical
contact with the sliding short through a set of contact ﬁngers (8), and the center conductor
(9) extends out into the cavity and loops back to make contact with the sliding short
through another set of contact ﬁngers (10), thus forming the loop antenna (5).

An adjustable sliding short and a moveable loop provide two degrees of freedom to
tune the cavity to a speciﬁc resonant mode and minimize reﬂected power.

The cylindrical shell has a one square inch screened window (11) near the bottom of
the cavity for viewing of the plasma and to allow for ventilation of the compressed air that
cools the quartz bell jar. There are 148 holes each 3mm in diameter (12) drilled into the

wall of the cavity in a grid like pattern to allow measurement of the internal electric ﬁelds.

l9

o'o2e2e2o2e2o2o‘o

    
  

120.029.020.02. \
‘..0.0 \ 6
O O x
O O.
0 v
“0‘
9.0.

 

"-""""'-I'---"'--"‘

—
. a
—

 

 

 

 

 

 

 

 

A
L5

1) Stainless Steel Cylindrical Shell 7) Outer Coaxial Conductor
2) Sliding Short 8) Outer Coaxial Contact Fingers
3) Contact Fingers 9) Center Conductor
4) Stationary Brass End Plate 10) Plate to Antenna Contact Fingers
5) End Feed Loop Antenna 11) Screened Window
6) Coaxial Cable 12) E—Field Sampling Holes

Figure 2.8 - Cross Section of Microwave Cavity Applicator

20

It is important to note that neither the screened window nor the holes permit microwaves
to leak from the cavity, primarily because their dimension is much smaller than the 12.24

cm wavelength of the 2.45 GHz radiation.

2.4.2 Two Stage Base Plate and Quartz Discharge Chamber:

The microwave cavity sits on top of a 6.5” diameter 1.25” tall brass stage (Figure 2.9)
(13) responsible for air and water cooling. This stage also contains the ECR magnets(15).
Cold water circulates through an annular ring channel (14) and conducts away heat

generated by the discharge. The water channel surrounds the compartment that contains

 

 

 

 

 

/

      

20 19 21
13) Brass Water/Air Cooling Stage 19) 8cm Vitan O-Ring
14) Water Channel 20) 20cm Vitan O-Ring
15) ECR Magnet Ring 21) Discharge Gas Channel
16) Air Channel 22) Gas Inlet Holes
17) Air Cooling Holes 23) Quartz Discharge Chamber
18) Stainless Steel Base Plate 24) Plasma Discharge

Figure 2.9 - Cross Section of Base Plate and Discharge Chamber

21

the ECR magnets (15). It is necessary to keep excessive heat from the magnets which must
not be exposed to temperatures above 100 degrees C.

Compressed air is delivered through two brass pipes on opposite sides of the stage
(See Figure 2.5, air pipe is shown below and in the center of two water barbs). Air ﬂows
through two radial channels to an annular ring channel (16) near the bottom of the brass
stage. Air is forced across the outer surface of the bell jar through eight l/64” diameter
holes (17) that are evenly spaced at 45 degree angles around the inner wall of the brass
stage. This compressed air cools the bell jar by convection and is then forced out of the
system through the screen window of the microwave cavity (1 1).

Below the brass air/water cooling stage sits a stainless steel base plate (18) that sup-
ports the quartz bell jar (23). Eight 1/4” bolts are attached to, and extend up from the base
plate (See Figure 2.7). These bolts serve as guideposts for the microwave cavity and brass
cooling stage, allowing the system to be assembled or disassembled quickly. The base
plate contains two vacuum sealing groves that contain o-rings. The ﬁrst grove surrounds
the bell jar ﬂange where an 8 cm diameter Vitan o-ring (19) is wedged between the diago-
nal grove and the outer diameter of the ﬂange. The second grove is on the bottom of the
plate and contains a 19 cm diameter Vitan o-ring (20) that forms a seal between the base
plate and the processing chamber.

Argon gas is delivered through a radial channel to an annular ring (21) near the bottom
of the base plate and then escapes into the discharge through eight 1/64” diameter holes
(22). These holes are angled so that the incoming gas is directed toward the center of the
bell jar.

A quartz bell jar (23), that contains the plasma discharge (24), is attached to the center

22

of the base plate. The bell jar sits above a 2.5 inch diameter hole in the center of base plate
(18) that allows the plasma to diffuse into the processing chamber below. Two bell jars of
different height 2.2 inch (5.6 cm) and 2.7 inch (6.9 cm), were used in the experimental
evaluation of this system. The distance denoted by LC in Figure 2.4 is the distance the bell
jar extends into the microwave cavity above the L8 = 0 plane. The 5.6 cm quartz bell jar
has Le = 1.4 cm, and the 6.9 cm bell jar has an Le = 2.7 cm. The distance between the bell

jar and the loop antenna can be calculated by subtracting LC and LI) from L8.
2.4.3 The ECR Magnet Conﬁguration:

Powerful rare earth permanent magnets (Figure 2.10) (15) are placed around the dis-
charge to facilitate electron cyclotron resonance in the plasma. Eight alternating pole arc-
magnets are assembled in a solid ring around the midsection of the discharge chamber
(23). The magnets are made of a Neodymium-Iron-Boron alloy and exhibit a magnetic
energy product of 42 Mega Gauss-Oersted. Measured with a Gaussmeter the pole face
strength of these magnets is 4 KiloGauss (when placed in the soft iron keeper) and the 875
Gauss ECR zone (25) lies approximately 1 cm away from the face of the magnets. The
magnets are glued together with metal bonding epoxy (loctite 324) and also glued to a soft
iron keeper (26) that surrounds the ring magnet structure. The soft iron keeper conﬁnes the
stray magnetic ﬁelds on the outside of the arc-magnet ring. This serves to increase the ﬁeld
strength and pushes the ECR zone farther away from the quartz walls and into the dis-
charge. The magnets also sit on a second soft iron keeper (27) that prevents excessive

magnetic ﬂux from extending into to processing chamber below the discharge.

15

 

23

 

 

 

 

 

 

 

 

 

 

 

 

 

23
Top View
25
26
23
15
\m f “(a
26 . ‘ ‘ t. f ’ ’ . Side View
_ ‘ a . Cross Section
.. . \ / 1:]
25
27 / I
15) ECR Magnet Ring
23) Quartz Discharge Chamber
25) ECR Zone
26) Outer Soft Iron Keeper
27) Bottom Soft Iron Keeper

Figure 2.10 - ECR Magnet Conﬁguration

Chapter 3

Theog of Operation For A Microwave Excited Cavity Plasma Source

3.1 Introduction:

The use of a single mode resonant microwave cavity to focus microwaves into a

plasma discharge has many advantages.

1) The input impedance of the plasma cavity system can be matched to the micro-
wave delivery circuit by tuning the cavity. When the cavity is matched all power
incident to the cavity is absorbed and no power is reﬂected back into the delivery
circuit.

2) The tuning of a resonant cavity with a movable sliding short and cou-
pling probe or loop requires the optimization of only two variables. Other
methods such as triple stub tuning require the optimization of three vari-
ables.

3) Coaxial loop or probe coupling allows the use of coaxial transmission
line as a method of power delivery reducing the system size and cost and
increasing ﬂexibility of placement.

4) In other methods of load matching tuning elements may be many half
wavelengths away from the plasma load. In contrast, the resonant mode

. ﬁeld structure in a microwave cavity is usually only one half wavelength
long: reducing wall losses, concentrating stored energy, and reducing the
size of the reactor.

5) The quality factor Q of a microwave cavity can be very high, making
possible very large internal ﬁeld magnitudes capable of maintaining high
density plasmas at very low discharge pressures even though the input
power may be modest.

24

25

6) The use of single-mode excitation instead of multi-mode excitation
allows spatial control of the electric ﬁelds exciting a plasma load.

7) It is possible to create cavities with a variety of tunable resonant modes

each having different spatial ﬁeld structures.
This Chapter includes a theoretical development of: transmission line load matching, elec-
tromagnetic propagation in waveguides, eigenlengths and ﬁeld structures of standing wave

cavity modes.

3.2 'Ii‘ansmission Line Load Matching:

A transmission line section with length I and characteristic impedance 20, shown in
Figure 3.1, is terminated by a complex load impedance Zin = R + jX. This load impedance
can be representative of any lumped circuit of complex impedance, a microwave cavity, or

the characteristic impedance of another attached transmission line section of inﬁnite

I Transmission Line I

 

Figure 3.1 - Transmission line section with complex load

26

length. The time average power delivered to the this complex load is given by:

P P 2" __2z,.n E 31
t— (Z; Zin+zo) q. '

where Pt is the power transmitted to the load, Pi is the power incident on the z = 0 plane
interface, Zia is the input impedance at z = 0, and 20 is the characteristic impedance of the

transmission line. Similarly, the time average reﬂected power is given by:

 

P = P.(Zin-ZO)2
r . Z». +20 Eq.3.2

where Pr is power reﬂected from the z = 0 plane interface. It can be seen that if Zin = Z0
then Pt = P, and Pr = 0. Therefore, if the cavity applicator shown in Figure 3.2(a) has an
input impedance Zin that is matched to the transmission line characteristic impedance 20
all power incident on this interface will be absorbed by the cavity and no power will be

reﬂected back through the transmission line toward the microwave generator.
3.3 Complex input impedance and equivalent lumped parameter circuit:

The complex input impedance of the plasma loaded cavity system can be given as:

P, + j20)( Wm — We)

1 2
§IIOI

 

= Rin + inn Eq. 3.3

in

where Pt is total time average power coupled into the cavity, 0) is the radian microwave

excitation frequency, Wm and We are time average stored magnetic and electric energy,

27

and IIOI is the magnitude of the current on the coupling loop. Since Zin is complex it can be
resolved into a real resistive part Rin and an imaginary reactive part inn. The complex
impedance of the plasma cavity system can be varied by the movement of the sliding short
or coupling loop, both shown in Figure 3.2(a). Generally, movement of the sliding short
will change the imaginary or reactive part of the complex impedance and moving the cou-
pling loop will change the real or resistive value. Under resonant conditions Wm and We
will be equal, making Xi“ = 0. Yet, the cavity will not be matched unless the value of Io,
controlled by the position of the coupling loop, is such that it produces an Rin equal to 20.

Another way to understand the concept of cavity matching is by physical analogy with
a parallel RLC circuit. If only one resonant cavity mode is considered it is then possible to
model the plasma cavity system as a parallel RLC circuit shown in Figure 3.2(b). All ele-
ments drawn with a diagonal arrow indicate that they are variable. The complex phasor

impedance of this circuit is given in terms of it’s lumped component values as:

1

joiL +ijc+Gc+jBP+Gp Eq. 3'4
C

 

z," = zom2 jX+

 

where Z0 is the characteristic impedance of input transmission line, m is the number of
turns on the generator side of the ideal transformer, jX is the equivalent reactance of the
coupling loop, LC and Cc are the equivalent inductance and capacitance of the microwave
cavity, GC is an equivalent conductance arising from ohmic losses in the metallic cavity
walls,ij is the equivalent admittance of the plasma load, and GP is an equivalent conduc-

tance arising from losses in the plasma load.

28

Microwave Transmission Plasma Source
Generator Line

I I
a) I l

 

Cavity Applicator

 

    

 

 

Plasma Load

8

 

 

 

 

 

jX

 

 

 

 

 

 

 

 

 

 

 

I
|
l
i
|
I
l
l
l
l
!

 

 

 

;_1
Lc cc G ij Gp
Cavity Applicator I Equivalent
Equivalent Circuit I Plasma Load
' Impedance

Yg - Microwave Generator Source Admittance

Z0 - Intrinsic impedance of the transmission line

Zin - Input impedance to the microwave cavity at the 2:0 plane
jX - Reactance of coupling element (loop antenna or transformer)
LC, Cc, Gc - Lumped parameter elements of the microwave cavity

ij, Gp - Lumped parameter elements of the plasma load

Figure 3.2 - (a) Plasma loaded microwave cavity with transmission circuit,
(b)Lumped parameter equivalent circuit of the cavity for a single resonant mode.

29

3.4 Frequency Response and Length 'lhning:

RLC circuits and microwave cavities are examples of resonant systems analogous to
spring-mass oscillators. All resonant systems have: a natural oscillatory frequency or fre-
quencies, the ability to absorb and _store energy, an energy damping mechanism, and a
quality factor Q. When excited by a driving force that oscillates near it’s resonant fre-
quency, a resonant system absorbs energy. A curve plotting power transferred to the reso-
nant system as a function of driving frequency is shown in ﬁgure 3.3(a). Note that when
the resonant system is driven at exactly the resonant frequency (00 the power transferred to
the system is equal to Pmc the total incident power. All power in the driving force is then
absorbed by the resonant system. This corresponds to the situation where a microwave
cavity is matched to its transmission system. Altemately, if the driving frequency is held
constant and the parameters of the system are varied, i.e. short length for a microwave cav-
ity or LC for an RLC circuit, there is an optimum parameter point (short length) where the

power transferred to the system is equal to Pine: This is shown in Figure 3.3(b).

3.5 Transient Response and Quality Factor Q:

Even when the power delivered by the driving force is small, if the driving force is at
or near the resonant frequency, a very large amount of energy can accumulate in the reso-
nant system until a steady state equilibrium is reached with the damping mechanism. This
can be shown in the transient response of a parallel RLC circuit, shown in Figure 3.4. At

time to the sinusoidal current source with magnitude IO begins delivering power to the

30

Power Transferred
Power Transferred

 

 

 

 

 

 

 

 

 

 

r-

Variable driving frequency a) Fixed driving frequency (0
Fixed Length Ls Variable Length Ls
a) b)

Figure 3.3 - (a) power absorbed vs. driving frequency a), (b) power absorbed vs.
cavity length Ls (Variation in L8 is exaggerated for clarity)

31

RLC circuit. Between time to and t1 energy is absorbed by the inductor capacitor system
and the amplitude of current ﬂowing in the LC subcircuit increases, shown as IL in Figure
3.4. As time progresses the magnitude of current oscillating in the LC subcircuit
approaches a steady state equilibrium where the power dissipated in the resistor equals the
time average power delivered to the circuit by the current source. The magnitude of the
steady state current in the inductor is a factor Q times the magnitude of current from the
current source 10. Therefore if the quality factor Q of the circuit is large then the magni-
tude of inductor current and stored energy will also be large. (In a microwave cavity this
high stored energy translates to large internal electric and magnetic ﬁelds.) If at time t2 the
current source is shut off then no further power is delivered to the circuit. The stored
energy is then dissipated in the resistor and exponentially decays to zero. The transient
response of a microwave cavity or any resonant system is physically analogous to the tran-
sient response of the parallel RLC circuit just described. The plasma cavity differs from a
spring-mass oscillator or an RLC circuit in that it has many degrees of freedom and there-
fore many possible resonances.

Note that the rise time and decay time of stored energy in the circuit, a microwave cav-
ity, or any resonant system is also related to the quality factor Q. A time constant for the

decay of stored energy can be given as:

T = gag Eq.3.5

where (no is the resonant frequency of the resonant system. Two important relations deﬁn-

ing the quality factor of a resonant system are given as:

32

 

 

 

:u

n

JI

||

6‘"
<——

r

 

 

 

 

IS
A
Ioh—-rA7\7IITK—A7\7'IKIVI\7\7IKICA7I7\NI———- >
VVVVVVVVVVVVVVVV t
IL
I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I, = Iocos((oor) for tOSt<t2

 

 

I L = QIO(1 - exp(—%m0Qt))sin((ot) for ‘0 S t < t1 where t1 » (0:Q

I L = Qloexp(—%moQt)sin(cot) for :2 S. t < oo

 

Q = ER—L where Q is the quality factor of the RLC circuit
0

 

 

Figure 3.4 - Transient Response of a Parallel RLC Circuit

Q = (DOWS _ (00 Eq. 3.6

P103! A60

 

where Ws is the time-average energy stored in the resonator at resonance, Pk,St is the time-

average power loss, and Ad) is the half power bandwidth of the resonant system.

3.6 Electromagnetic Wave Behavior:

3.6.1 Electromagnetic Wave Propagation in Cylindrical Waveguides:

Electromagnetic waves propagate within enclosed conducting waveguide structures
with one of three mechanisms: 1) transverse electromagnetic, 2) transverse electric, and 3)

transverse magnetic.

3.6.1.1 TEM propagation in coaxial waveguide sections:

Enclosed cylindrical waveguides with a coaxial center conductor, like regions I and II
of the plasma source, support transverse electromagnetic (TEM) waves as their fundamen-
tal mode of propagation. TEM waves are so named because both the electric and magnetic
ﬁelds are both transverse to the direction of propagation. TEM waves propagate along air
ﬁlled coaxial waveguides with the same wavelength and velocity as free space TEM plane

waves. Therefore, the wavelength of radiation in coaxial waveguide sections is determined

34

by the simple relation: 1 = u/ f where u is the speed of light in the dielectric medium ﬁlling
the waveguide and f is the frequency of the propagated wave. Given the 2.45 GHz excita-
tion frequency of the plasma source the wavelength of TEM propagation in each coaxial
section is 12.24 cm. The phase relationship and ﬁeld pattern of a coaxial TEM wave is
shown for a general coaxial waveguide in Figure 3.5a.

Transverse electric (TE) and transverse magnetic (TM) modes of propagation, dis-
cussed in the next section, may also exist in a coaxial waveguide, but only if the distance
between the center and outer conductor is greater than the order of one half wavelength
[22]. If this distance is less than one half wavelength the TB and TM modes are non-prop-
agating or evanescent. TEM waves do not propagate in cylindrical waveguide sections

without a center conductor.

3.6.1.2 TE and TM propagation in hollow cylindrical waveguide sections:

In waveguides without a center conductor, such as section III of the plasma source, the
only electromagnetic modes of propagation are Transverse Electric (TE) or Transverse
Magnetic (TM). TE waves have no electric ﬁeld components in the direction of propaga-
tion (i.e. electric ﬁelds are conﬁned to the transverse plane) while TM waves have no mag-
netic ﬁeld components in the direction of propagation.

Propagation of a TB or TM wave mode in a waveguide is only possible if the fre-
quency of electromagnetic excitation exceeds the cutoff frequency associated with that
mode at the given waveguide radius. The cutoff frequencies [23] for given TM and TE

modes in a waveguide with radius a are given:

35

 

 

270° Direction of propagation—p
"— Electric Field Direction of propagation
— Magnetic Field for ﬁeld diagrams is
out of the page.

Eimaxm

TEM;

<
>

 

90° 2700

 

 

90° 2700

Figure 3.5(a)(b)(c) - Relative Wavelengths, Phase Relationships, and Field Patterns

36

 

 

For TMum modes:
x
f = "m E . 3.7
C mm. q
For TE“m modes:
f = x’nm 8
c aznﬁ Eq. 3.

where u and e are the permeability and permittivity of free space, x“m is the mth root of
the Bessel function In, and x’nm is the mth root of the derivative of the Bessel function J ’n .

Some values of the Bessel function are given below:

Table 3.1 - Selected roots of the Bessel Funciton

 

 

Roots of Jn(x) Roots of J’n(x)
x01 = 2.405 x’m = 3.832
x02 = 5.520 x’02 = 7.016
3‘11 = 3.832 x’ll = 1.814
x12 = 7.016 x’lz = 5.331

The waveguide in section III of the plasma source had a radius a of 4.9 cm and the fre-
quency of excitation was 2.45 GHz. Therefore, the only modes that may propagate in this
waveguide are the TB“ with a cutoff frequency of 1.794 GHz and the TM01 with a cutoff

frequency of 2.343 GHz. All other roots of the Bessel function except x01 and x’11 give

37

cutoff frequencies that exceed 2.45 GHz and hence do not propagate in this waveguide.

The guide wavelength kg is given as:

Eq. 3.9

where fc is the cutoff frequency of the TB or TM waveguide mode, f is the excitation fre-
quency, and c is the free space velocity of light. Note that the guided wavelength for any
excitation frequency is longer than the free space wavelength at that frequency.

For the TE“ mode in section III of the plasma source the guided wavelength is 17.98
cm. Similarly, the guided wavelength for a TMOI mode is 41.89 cm. The ﬁeld patterns and
relative wavelengths of the TB” and mm guided modes for a general waveguide of

radius of 4.9 cm and 2.45 GHz excitation are shown in Figure 3.5(b) and (c).

3.6.2 Abrupt Waveguide Discontinuities:

It is important to consider abrupt discontinuities in transmission systems, because they
have a signiﬁcant effect on wave propagation where they occur. Wave propagation across a
discontinuity may result in: 1) the wave being split into forward and reﬂected components,
2) the generation of higher order propagating modes that may be reﬂected and transmitted
from the discontinuity, 3) the generation of higher order evanescent modes that reactively
store energy in the vicinity of the discontinuity, or 4) the change in mode of waveguide
propagation (i.e. from TEM to TB or TM).

In such a case where the geometry of the waveguide has changed, but the dielectric

38

medium ﬁlling both waveguides is the same, we can assume that there is a change in the
geometry of the electric and magnetic ﬁelds from one section of waveguide to the next.
However, the ﬁeld magnitudes must not change abruptly (discontinuously) at a point in
space, so even though there may be an abrupt discontinuity in the geometry of the
waveguide the total modal ﬁeld geometry must make a smooth transition from one
waveguide section to the next. This is made possible by the Fourier summation of higher
order evanescent (non-propagating) modes in the vicinity of the discontinuity.

Therefore, the electric ﬁeld in the region of waveguide just before the discontinuity
arises from the summation of ﬁelds from: 1) the propagating forward wave(s), 2) propa-
gating reﬂected waves, and 3) reﬂected evanescent modes.

Similarly, the electric ﬁeld in the region of waveguide just following the discontinuity
arises from the summation of: 1) propagating transmitted waves, and 2) transmitted eva-
nescent modes. The generation of, reﬂected or transmitted, propagating or evanescent,
modes is determined by the geometry of the discontinuity. The magnitudes of these gener-
ated modes are determined by the boundary conditions at the discontinuity.

A diagram illustrating a waveguide discontinuity is shown in Figure 3.6. In the coaxial
waveguide section the mode of propagation is assumed to be TEM with all coaxial TE or
TM modes assumed to be in cutoff. In the hollow waveguide section TE“ and TMOI
modes are assumed to propagate while all higher order TE and TM modes are assumed to
be in cutoff. Figure 3.6(a) depicts propagating wave modes while Figure 3.6(b) depicts the
spatially decaying evanescent modes in the vicinity of the discontinuity. Physically eva-

nescent modes act as reactive energy storage elements such as capacitors or inductors.

39

 

E m a, Reﬂected TEM Wave I Transmitted TMOl wave
/ i /
— \ L' . L ......... - . —-—
a) m+\\ /! \ \‘ N.-. ’1 / >
/ \ \ __ ~ %
I V_ I . ~ ..........
/ /

Incident TEM Wave Transmitted TE“ Wave

    
 
 

Transmitted Evanescent
/ TE and TM modes

5 Reﬂected Evanescent
“m TE and TM modes

1

 

w JL

 

Coaxial Waveguide | Hollow Waveguide

d) Z01 ]— Zoz and Zo3

Transmission Line Equivalent Circuit

 

 

 

Z01 - characteristic impedance of TEM propagation in the coaxial waveguide
202 - characteristic impedance of TE” propagation in the hollow waveguide

Z03 - characteristic impedance of TMOI propagation in the hollow waveguide

Figure 3.6 - Wave behavior at an abrupt waveguide discontinuity

40

Thus, a transmission line equivalent circuit, shown in Figure 3.6(d), can be deﬁned for this

waveguide system, where the capacitor represents the effect of evanescent modes.

3.7 Standing Wave Cavities and Cavity Modes:

With the information provided in the previous section it is now possible to introduce
the concept of a standing wave cavity. If one end of the waveguide is covered with a con-
ducting end plate then the incident wave, shown traveling to the right in Figure 3.7, is
reﬂected producing a reﬂected wave that travels in the opposite direction. A standing wave
is produced in front of the conducting end plate by the interference of incident and
reﬂected waves. If both ends of the waveguide are covered with a conducting end plate and
he length of the waveguide is some integer multiple of 33/2, where 18 is the guide wave-
length, then a standing wave can be maintained in this section of waveguide as shown in
ﬁgure 3.7. This is commonly called a standing wave cavity.

To obtain a set of vector equations describing the time harmonic electric and magnetic
ﬁelds inside the cavity volume it is standard procedure to use the Helmholtz equation and
solve the boundary value problem for the boundary conditions. For a perfectly conducting
cylindrical cavity with radius a, length Ls the parallel component of the electric ﬁeld must
be zero at the boundary. From the separation constant equations for TM and TE modes we

can determine the resonant frequency for any mode given any cavity length Ls.

For TMnm. modes:

 

 

_ 1 2 lrt_a_
(f)nml " ZﬂaJ—lﬁﬂlxnm + ( Ls )2 Eq. 3.10

41

ll

Traveling Waves

Reﬂected Wave Electric Field
\\ Intensity

Incident Wave

 

 

 

 

   

 

/ \ / / ' \ .
/ \ / \
\ \ / I \ \ Reﬂecting
\ / \ Boundary
\ \ I /
Standing Wave 11<t2<t3<t4
. — ’ ' ‘ ~ . Electric Field
V .' t2 Intensrty
\\ / \ z ’ — _ ‘ \ \ / \
‘ Q. / \ ,I, , \ \\ / \
/ ff \ , ’7 \ / T“ \ t3 , 17' Reﬂecting
\“~__/’,’ \ / ‘.‘x-_/’,' Boundary
+ 14
Conducting
End Plate
Standing Wave Cavity .\ ,,
Conductin CondUCIing
g End Plate

End Plate

\ /

 

Figure 3.7 Standing Waves and Standing Wave Cavity

42

For TEnml modes:

 

 

_ l , 2 [rt—a
(f)nml _ 21taJlT€J<xnnJ +(Ls)2 Eq..311

where a is the radius of the circular waveguide, L8 is the cavity length, xnm, and x’nm are
the roots of the Bessel function (see Table 3.1).

These frequency vs. cavity length curves are plotted, in Figure 3.8, for a cavity diame-
ter of 9.8 cm. For a cavity excited at a ﬁxed frequency there are speciﬁc cavity lengths that
correspond to speciﬁc TE and TM resonant modes. If a cavity with a movable or sliding
end plate is used then all modes within the maximum length of the end plate can be
accessed. For a ﬁxed excitation frequency of 2.45 GHz. this corresponds to moving along
the horizontal constant frequency line shown in Figure 3.8. When the cavity length of the
empty cavity is tuned to 8.99 cm the T131” mode can be accessed, correspondingly at a
length of 20.95 cm the TMon mode can be accessed. Note however that, the maximum of
length for the cavity applicator of the plasma source is 14 cm, so the TMon resonant mode
is not accessible.

Waveguides with larger diameter can propagate many more than two modes at a fre-
quency of 2.45 GHz and therefore a larger diameter cavity can support a larger number of
resonant modes. A mode chart for a cavity with 6 in. diameter is shown in ﬁgure 3.9. Dif-
ferent modes can be accessed with a constant cavity length if the frequency is changed, as
shown on the vertical constant length line (10 cm) in Figure 3.9. In order to use this type

of mode selection a variable frequency microwave source must be used.

43

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From the solution of the Helmholtz equation the phasor magnitudes for ﬁelds in the
cylindrical cavity can be given:

TEM“ Field Solutions for a Cylindrical Cavity:

 

 

 

 

 

 

 

E - '(uuA[2]J (x’nmr)sin(n0)sin(lltz) E 312
' - J r " a L5 q' '
E —'xc1111A[""‘]J’(x"’"r)cos(ne)s1n(ll‘z) E 313
9 _ J a a L ‘1‘ '
um , xnm 11!
Hr = A[L—1:l[xa J ]n( a r)cos(n0)cos(l:z) Eq. 3.14
x nm . In
”0 = (—A)[f1:l[-] J [:l"( a r)srn(n0)cos(l:z) Eq. 3.15
11: x nm 11!
Hz = A k [2-(L-.1")2]J( a r)cos(n0)sin(fz) Eq. 3.16

TMnml Field Solutions for a Cylindrical Cavity:

E = (—B)[lL-1—:][-—]Lm]l’nigﬂ(r)cos(n0)sin(%tz) Eq. 3.17

S

E, = B[L-1-:][—]HJ(-"—"’r)sin(n0)sinG—nz) Eq. 3.18

S

Ez = B k l:2-(l—1:)Z]Jn (x—r)cos(n0)cos(%tz) Eq. 3.19
S
. n xnm . In
H, = —](D€B[-]J (—r)s1n(n0)cos(—z) Eq. 3.20
r n a Ls
H — — ‘x—(oeBI: ""‘]J’ (ﬁr)cos(ne)cos(-’l‘z) Eq 3 21
9 — J a ,1 a L ° '

3

where A and B are constants, r is the distance from the central axis, 2 is longitudinal dis-
tance, and k is the wavenumber. The spacial pattern of ﬁelds for the 'I'Em and TMon
modes are illustrated in Figure 3.10 (a) and (b).

 

 

‘\
/

a 6

\l

1’
\'

 

 

 

 

 

 

 

 

 

 

  

Electric Fields —->
Magnetic Fields ——

 

13)
TMOI 1

Figure 3.10 - Field Patterns for TB, 11 and TMml Resonant Modes (at 90° of Cycle)

47

3.9 Conclusion:

The main advantages of cavity coupled plasma sources are that they are: 1) easily
matched to the microwave network, 2) capable of concentrating stored energy and main-
taining high internal ﬁelds, 3) capable of minimizing wall losses, and 4) tunable to a vari-
ety of different resonant modes with different spatial ﬁeld characteristics. At the beginning
of this chapter the importance of matching the complex load of the plasma source to the
microwave network was explained. Then the frequency response, quality factor, and tran-
sient response of resonant systems was illustrated. Finally, the electromagnetic wave
behavior of cylindrical waveguides and standing wave cavities was explained in detail in
order to provide an understanding of internal electromagnetic behavior of the plasma

source and to lay the ground work for a transmission line model that will be presented in

Chapter 6.

 

Chapter 4

Electromagnetic Matching Behavior of the Microwave Plasma Source

4.1 Introduction:

The experimental investigation presented in this Chapter has two purposes: 1) provide
an operational guide or parameter map that shows where to tune the source for best micro-
wave match given parameters such as discharge gas, pressure, and forward input power,
and 2) to develop a physical understanding of the plasma cavity system by correlating
observed source behavior with electromagnetic and plasma theory.

In order to investigate the electromagnetic tuning behavior of the plasma source and
determine the best cavity length and loop antenna positions for matched operation the ﬁrst
experimental investigation performed was a survey of microwave matching. A general
overview of matching behavior was obtained by recording power reﬂected from the
plasma cavity system as a function of cavity length, Ls, and coupling antenna length, 111'
for ﬁxed input power and discharge pressure. The numerical value of reﬂected power
verses these two independent variables was plotted as a set of curves. Regions of low
reﬂected power were then identiﬁed and investigated.

Absorbed power vs. sliding short position and coupling antenna length has been plot-
ted by other investigators: for empty and dielectric loaded cavities by M. Siege] [24], and

for large diameter plasma loaded cavities by P. Malt [25].

48

49

4.2. Parameter Space:

Experimental variables inﬂuencing the plasma source were classiﬁed as: macroscopic
controllable input variables U1, reactor geometry variables U2, process variables U3,inter-
nal variables X, and output variables Y. A block diagram of the experimental variables is
shown in Fig. 4.1.

The macroscopic controllable variables were: 1) discharge pressure/ﬂow rate, 2) loop
antenna length, 3) cavity length, and 4) incident power. This system did not have a throttle
valve, thus discharge pressure, p, and ﬂow rate, 1", were interdependent and thus were con-
sidered a single variable, p/f'. Discharge pressures investigated were 0.75, 40, 70, and
100 mtorr and the corresponding argon ﬂow rates were 20, 80, 100, and 120 sccrn, respec-
tively. The loop length, [1” was varied in half centimeter intervals from 1.5 cm to 5.5 cm.
The cavity length, Ls, was varied from 4.5 cm to 13.35 cm. Input power, Pine, in all exper-
iments described in this thesis was held constant at 150 Watts.

The reactor geometry variables were: 1) discharge height, h, and 2) magnet geometry.
Two 7 cm diameter quartz discharge chambers, one 5.6 cm tall and another 6.9 cm tall,
were used to vary discharge height. Note that the 5.6 cm discharge extends a distance of
1.4 cm into the microwave cavity and the 6.9 cm discharge extends a distance of 2.7 cm. A
multipolar ECR magnet ring (see Section 2.4.3) was used to provide a magnetic ﬁeld

when needed. The plasma source behavior was investigated with both discharge chambers

50

Reactor Geometry Variables, U2

 

1) h - '
5.6 cm or 6.9 cm

3W

Magnets Present or Not Present

 

 

 

Macroscopic Controllable
Input Variables, U1 Output Variables, Y

 

 

 

 

1) p/r' - Pressure/ﬂaw
0.75, 40, 70, 100 mtorr

 

2) Lp ' 14952111208111 Internal Variables, X
1.5 - 5.5 cm None
1) P Measured
3) L - W m” ’
43 - 13.35 cm 010 150 w

 

 

 

4) Pine ' MW
Constant at 150 Watts

 

 

 

 

 

 

Process Variables, U3

 

None Measured

 

 

 

Figure 4.1 - Block diagram of experimental variables

51

and both with and without the ECR magnets. Thus the four discharge geometry conﬁgura-

tions investigated are:

1.) a 5.6 cm tall discharge chamber with multipolar ECR magnet ring
2.) a 6.9 cm tall discharge chamber with multipolar ECR magnet ring
3.) a 5.6 cm tall discharge chamber without magnets

4.) a 6.9 cm tall discharge chamber without magnets

The only internal variable measured in this experiment was reﬂected power, Pref.
Reﬂected power ranged from less than one Watt to complete reﬂection of 150 Watts. Pro-

cess variables and output variables were not measured in this experimental investigation.

4.3 Experimental Setup and Start-up Procedure:

The plasma source was mounted on the vacuum chamber (1) and connected via a
coaxial cable (2) to the microwave network as shown in Figure 4.2. The reﬂected power
was measured from a Hewlet Packard analog power meter (3) and the forward power was
measured similarly (4).

In preparation for each set of experiments the appropriate discharge chamber (5) was
installed and the magnet array (6) was installed or removed. The vacuum chamber (1) was
then pumped down to approximately 50 to 100 mtorr with the mechanical pump (7). The
diffusion pump (8) was allowed to warm up with the pneumatic gate valve (9) closed.

After approximately 1 hour the gate valve (9) was opened and the system was allowed to

52

 

\
Q
a
b
4
P
I
I

.v’

 

 

 

11

   

  
 

     

   

10

.V‘v‘vA-‘v‘vAv‘v...
\

      
   
 
 

Q

      
 
 

Q
Q

   

I
v
\

   

   
      

:-
1'..-‘
P
O\

 

 

 

 

   
 
 

 

U

 

7

 

 

 

 

 

 

   

Figure 4.2 - Experimental setup for reﬂected power measurements

53

pump down to 10'5 Torr. The Argon ﬂow rate was initiated and set with the ﬂow rate con-
troller (10) to a value consistent with the requirements of the experiment. In order to strike
the discharge the pneumatic gate valve (9) was closed and pressure was allowed to rise to
100 mTorr or more. The sliding short (11) was set at L8 = 13.35 cm with loop antenna (12)
position l..p = 3.5 cm. Note that L5 = 13.35 cm is the highest experimental cavity length.
Then microwave power was switched on and increased usually to about 100 to 200 Watts
forward power until a discharge glow was seen through the screened window. Forward
power was then set to 150 Watts and the gate valve (9) opened. As the pressure of the sys-
tem was allowed to stabilize the plasma cavity was tuned to minimize reﬂected power. The
pressure was then ﬁne tuned by changing the argon ﬂow rate to the pressure required by
the experiment. Approximate ﬂow rates of 20, 80, 100, 120 sccm generated pressures of

0.75, 40, 70 and 100 mtorr, respectively.

4.4 Experimental Procedure for Reﬂected Power Measurements:

In order to record and plot reﬂected power as a function of short length, Ls, and loop
length, LP, a set of nine reﬂected power curves were recorded for each ﬁxed discharge
pressure and input power. Each reﬂected power vs. Ls curve was taken by measuring the
reﬂected power level from the power meter (item 3 in Figure 4.2) as the sliding short of the
cavity was varied from its highest position, Ls max, to it’s lowest position, I.s min., or vice
versa. The loop length was kept constant for each curve and an independent curve was
taken for nine separate Lp values at 0.5 cm intervals from 1..p = 1.5 cm to Lp = 5.5 cm. For-

ward power and discharge pressure were kept constant as each set of nine curves were

54

taken. These nine curves can be thought of as tracing the reﬂected power contour surface
over the Lst plane. An example of such a set of reﬂected power contour surfaces is
shown in Figure 4.3b.

Note that the variable Lsm is used to represent the cavity length position of a reﬂected
power minima. In Figure 4.3b Lsm vs. Lp curves are plotted in the Ls Lp plane below the
nine reﬂected power trace curves.

Data points for each reﬂected power vs. Ls curve, such as shown in Figure 4.3a, were
not taken at ﬁxed intervals. More data points were taken where the reﬂected power showed
a large change vs. cavity length, such as near reﬂected power minima. Fewer points were
taken where little change was observed. This method was used to avoid missing important
maximum and minimum data points that might otherwise be omitted in taking data at stan-

dard 0.5 cm intervals. Note, for all data points taken there was always a discharge present.

55

 

 

 

 

A
=3 '1 _ _ __ _ EWISPEWLLEW'
E _
a) 1‘13 _
E - \f\ I
D- - —~ Reﬂected Power
g _ Minima,Lsm
é’ _
32 1 l 1 1 1 W l 1 1 1

Cavity Length - Ls (cm)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/
// g Mode Curves
:1"? // _ Lsm vs.Lp
.5 T N."
.. w :
\
D N N
g ‘ ‘0 . Z >3
a, A \ 11 L
3 I q?
E - I Q
0 /
n: F

 

1 1 1 1 1 1 1 1
Cavity Length - Ls (cm)

Figure 4.3 - a) An example single reﬂected power curve for one loop length Lp’
b) An example set of nine curves tracing out a reﬂected power contour surface.

56

The range of movement of the sliding short was limited by the contact of the loop with
the quartz discharge chamber. See Figure 4.4. When the loop was made shorter the range
of the sliding short was increased. For example when the 6.9 cm tall discharge was used
and the loop was set to a length of LI) = 5.5 cm the range of the sliding short was L5 = 8.2
cm to 13.35 cm. When the loop was set to Lp = 1.5 cm the range of the sliding short was
Ls = 4.2 cm to 13.35 cm. The shortest Ls point of each reﬂected power curve was mea-

sured when the loop was in contact with the discharge chamber.

 

 

 

 

 

.— L.

l8: :8

 

 

 

 

Figure 4.4 - Loop in contact with discharge chamber

The measured reﬂected power curves, as seen in Figures 4.5 through 4.8, reveal values
of Ls and 1..p where reﬂected power is minimized at a speciﬁc discharge pressure and reac-
tor conﬁguration. For example, in Figure 4.5a for a pressure of 40 mtorr and loop length of
2.5 cm there are two well matched regions or local reﬂected power minima at sliding short
positions of 8 cm and 9.4 cm. These minima of reﬂected power are the regions of greatest
absorbed power or best electromagnetic match. These regions correspond to conditions

when electromagnetic input energy is coupled and matched efﬁciently to the discharge.

57

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For some conditions of pressure and discharge height one repeatable reﬂected power
curve could be obtained when the cavity length was varied from low to high values of Ls
and another different curve could be obtained when the cavity length was varied from high
to low Ls. Making a record of this hysteresis phenomenon required the recording of two
separate curves, one for increasing Ls and one for decreasing LS, for every loop length
investigated. This is seen in Figure 4.6b for a pressure of 0.75 mtorr and loop length of 3.0
cm where the direction of hysteresis is shown with arrows. Note in this example that the
decreasing Ls curve passes over the sharp reﬂected power minimum achieved by the
increasing Ls curve. When no signiﬁcant hysteresis effect was observed only one reﬂected
power vs. cavity length curve was taken as cavity length was decreased from high to low
cavity length, Ls, as shown in all the curves in Figures 4.5a-c.

In the following section (Section 4.5) reﬂected power curves are presented for the four
reactor geometry conﬁgurations. Three pressure ranges were investigated for each conﬁg-
uration. In those conﬁgurations with ECR magnets the pressures investigated were 0.75,

40, and 100 mTorr. In the conﬁgurations without magnets pressures investigated were 40,

70, and 100 mTorr.

 

61

4.5 Reﬂected Power Measurements:

4.5.1 Reﬂected Power vs. Ls Curves for a 5.6 cm tall Discharge with ECR Magnets:

This experimental conﬁguration used a 5.6 cm discharge chamber, that extends 1.4 cm
into the microwave cavity. An eight pole magnet array (see Figure 2.10) was used to create
an 875 Gauss ECR zone approximately 0.5 to 1 cm from the quartz walls of the discharge
chamber. The pressures investigated in this group were: 0.75 mtorr, 40 mtorr, and 100
mtorr. For each pressure nine loop lengths (LP) were investigated: 5.5 cm, 5.0 cm, 4.5 cm,
4.0 cm, 3.5 cm, 3.0 cm, 2.5 cm, 2.0 cm, and 1.5 cm. The reﬂected power vs. cavity length
Ls curves are shown in Figures 4.5a-c where pressure increases from 0.75 to 40 to 100
mtorr from left to right and loop length Lp increases from 1.5 cm at the bottom of Figure
4.5a to 5.5 cm at the top of Figure 4.5c. Very little hysteresis was observed for this conﬁg-
uration. Thus, only one curve was plotted for each pressure and loop length.

It can be observed from the plots in Figures 4.5a-c that there are two distinct and well
matched cavity length positions for most loop lengths and pressures. For example, in Fig-
ure 4.5b at a pressure of 40 mtorr and a loop length of 3.0 cm two minima of reﬂected
power are shown with one minima at a cavity length of 7.6 cm and a second more narrow
minima at a cavity length of 9.3 cm. In Chapter 5 these two well matched positions are
identiﬁed as two different electromagnetic modes of Operation. Field pattern measure-
ments for the higher cavity length mode (around L5 = 9 cm) demonstrate that it has a TB“
electric ﬁeld mode pattern. Field pattern measurements for the lower cavity length mode

(around L8 = 7 cm) show a circumferentially constant E-ﬁeld pattern indicative of a 4)

62

symmetric excited waveguide mode. It is noted here that this Low Ls mode is wider in its
Ls proﬁle for many reﬂected power curves, shown in Figures 4.5a-c, than the TB“ like
mode. In most cases the Low Ls mode appears to be approximately 1 cm wide at the 50

Watt level, whereas the T1311 mode is around 0.5 cm wide at the 50 Watt level.

4.5.2 Reﬂected Power vs. Ls Curves for a 6.9 cm tall Discharge with ECR Magnets:

This experimental conﬁguration used a 6.9 cm discharge chamber, that extends 2.7 cm
into the microwave cavity. A multipolar magnet ring (see Figure 2.10) was used to create
an 875 Gauss ECR zone approximately 0.5 to 1 cm from the quartz wall of the discharge
chamber. The pressures investigated in this group were: 0.75 mtorr, 40 mtorr, and 100
mtorr. For each pressure nine loop lengths (LP) were investigated: 5.5 cm, 5.0 cm, 4.5 cm,
4.0 cm, 3.5 cm, 3.0 cm, 2.5 cm, 2.0 cm, and 1.5 cm. The reﬂected power vs. cavity length
1.8 curves are shown in Figures 4.6a-c where pressure increases from 0.75 to 40 to 100
mtorr from left to right and loop length Lp increases from 1.5 cm at the bottom of Figure
4.6a to 5.5 cm at the top of Figure 4.6c. Considerable hysteresis was observed for this con-
ﬁguration so two curves were plotted, one for decreasing Ls and another for increasing Ls,
for each pressure and loop length.

For most reﬂected power curves only one mode is observed. For example in Figure
4.6b at a pressure of 40 mtorr and a loop length of 3.0 cm a single minima is observed at a
short length of 10.9 cm. Electric ﬁeld pattern measurements presented in Chapter 5 indi-
cate that this mode has TE“ electromagnetic excitation. Near zero reﬂected power can be

achieved for this mode for all three pressures investigated.

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66

Evidence of a second reﬂected power minima is seen in Figure 4.6a at a pressure of
0.75 mtorr and a loop length of 2.5 cm. Here the second mode or Low Ls mode appears at
a cavity length L8 = 5.9 cm. The TE“ mode is seen in this reﬂected power curve at L5 =
9.1 cm. The Low Ls mode is observed for this conﬁguration in ﬁve cases: from 1..p = 3.5
cm to Lp = 1.5 cm at a pressure of 0.75 mtorr.

Hysteresis is observed in reﬂected power as the cavity length is ﬁrst decreased and
then increased. This is shown in Figure 4.6a at a pressure of 40 mtorr and loop length of
2.5 cm. In this plot the reﬂected power curve follows one path for decreasing L8 (as indi-
cated by the arrows) and another path for increasing Ls. As can be seen at other pressures
and loop lengths the best matched operating conditions were only achieved as the sliding
short increased toward the mode from the low Ls side. Note that, hysteresis is found at
pressures of 0.75 and 40 mtorr while very little is found at 100 mtorr.

At a pressure of 100 mtorr and loop lengths between Lp = 3.0 and 1.5 cm more power
is absorbed for values of Ls off resonance than at any other pressure or loop length. Off
resonance regions are deﬁned as those regions where no minima of reﬂected power or
mode exist. For example in Figure 4.6a at 100 mtorr and Lp = 2.5 cm the off resonance Ls
regions are those where the reﬂected power curve is almost horizontal, whereas the TB“
mode region is identiﬁed by the steep slope of the curve in the vicinity of Ls = 11.4 cm.

At 100 mtorr and loop lengths from 3.0 cm to 5.5 cm, in Figures 4.6b-c, the average
off resonance reﬂected power was approximately 100 Watts. For the same pressure at loop
lengths of 2.5 cm, 2.0 cm, and 1.5 cm the average off resonance reﬂected power was 90
Watts, 80 Watts, and 65 Watts, respectively. For lower pressures of 0.75 mtorr and 40

mtorr, in Figures 4.6a-c, the off resonance reﬂected power is generally over 100 Watts.

 

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67

4.5.3 Reﬂected Power vs. Ls Curves for a 5.6 cm Tall Discharge Without Magnets:

This experimental conﬁguration used a 5.6 cm discharge chamber, that extends 1.4 cm
into the microwave cavity. The ECR magnets were removed in order to investigate the
behavior of a non-magnetized discharge. The pressures investigated in this group were: 40
mtorr, 70 mtorr, and 100 mtorr. Note that higher pressures are used in this conﬁguration
because a discharge could not be sustained at 0.75 mtorr without magnets. For each pres-
sure nine loop lengths (Lp) were investigated: 5.5 cm, 5.0 cm, 4.5 cm, 4.0 cm, 3.5 cm, 3.0
cm, 2.5 cm, 2.0 cm, and 1.5 cm. The reﬂected power vs. cavity length Ls curves are shown
in Figures 4.7a-c where pressure increases from 40 to 70 to 100 mtorr from left to right
and loop length Lp increases from 1.5 cm at the bottom of Figure 4.7a to 5.5 cm at the top
of Figure 4.7c.

The absence of a multipolar ECR magnet ring in this conﬁguration appears to restrict
the range of Ls, Lp and p/f where the discharge is sustainable and also reduces the range
where the discharge is well matched (as compared to the 5.6 cm discharge with magnets).
It was very difﬁcult to sustain a plasma at 40 and 70 mtorr, consequently reﬂected power
curves were only taken at a loop length Lp = 3.5 cm for 40 mtorr and from LP = 4.5 to I.p =
2.5 cm at 70 mtorr. The blank areas of Figures 4.7a-c represent conditions where the dis-
charge could not be sustained. For example, in Figure 4.7a there is no reﬂected power
curve at 70 mtorr for loop lengths of Lp = 2.0 and 1.5 cm. Discharges struck in these
regions were easily extinguished by slight movements of the sliding short or loop. A
reﬂected power curve was only taken if a discharge could be maintained over a large con-

tinuous region of Ls.

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In most reﬂected power curves in Figures 4.7a-c two reﬂected power minima are
present. For example, in Figure 4.7b, at 40 mtorr and 1.9 = 3.5 cm one minima is observed
in the area of 6.5 cm and another is observed near 9.3 cm. Also for loop lengths of 3.0 cm,
3.5 cm, and 4.0 cm, at 100 mtorr two distinct reﬂected power minima are present. These
two minima are similar in sliding short position to the two minima observed (with the 5.6
cm discharge) with magnets present. Field patterns presented in Chapter 5 indicate that
these minima are the TB“ mode and the circumferentially symmetric Low 1.8 mode.

The TE“ mode is well matched (with near zero reﬂected power) at 70 mtorr at 100p
lengths of 4.0 cm and 3.5 cm. Another well matched minima is observed at 100 mtorr and
a loop length of I.p = 1.5 cm. However, as seen in Figures 4.7a-c, a reﬂected power of 30
to 50 Watts is the best match for most reﬂected power curves taken for both modes for this
conﬁguration. Note that the maximum reﬂected power for most curves is in the range of
110 to approximately full reﬂected power of 150 Watts. Hysteresis was observed in all

proﬁles.

4.5.4 Reﬂected Power vs. L, Curves for a 6.9 cm tall Discharge without Magnets:

This experimental conﬁguration used a 6.9 cm discharge chamber, that extends 2.7 cm
into the microwave cavity. No ECR magnets were used in this conﬁguration in order to
investigate the behavior of the non-magnetized discharge. The pressures investigated in
this group were: 40 mtorr, 7O mtorr, and 100 mtorr. Note that higher pressures are used in

this conﬁguration because a discharge could not be sustained at 0.75 mtorr without mag-

nets. For each pressure nine loop lengths (113) were investigated: 5.5 cm, 5.0 cm, 4.5 cm,

 

72

4.0 cm, 3.5 cm, 3.0 cm, 2.5 cm, 2.0 cm, and 1.5 cm. The reﬂected power vs. cavity length
Ls curves are shown in Figures 4.8a-c where pressure increases from 40 to 70 to 100 mtorr
from left to right and 100p length LP increases from 1.5 cm at the bottom of Figure 4.8a to
5.5 cm at the top of Figure 4.8c.

This 6.9 cm discharge conﬁguration without ECR magnets demonstrates a greater
ability to sustain the discharge over a large variation of Ls and L.p and match the discharge
at pressures of 40 and 70 mtorr than does the 5.6 cm discharge conﬁguration without mag-
nets. A plasma could be sustained at all loop lengths and pressures in this investigation.
Several reﬂected power curves that show minima with near zero reﬂected power are seen
in Figures 4.8a-b.

For this conﬁguration only one mode is observed for all reﬂected power proﬁles. For
example, in Figure 4.8b at 70 mtorr and loop length of 3.5 cm one distinct reﬂected power
minima is observed at 11.5 cm. In Chapter 5 this minima is shown to be the TB” mode.
No evidence of the Low Ls mode was observed.

Hysteresis is observed at loop lengths of 5.5 cm, 5.0 cm, 3.5 cm, 3.0 cm and 1.5 cm for
70 mtorr and between loop lengths of 1.5 cm and 3.0 cm for 100 mtorr. However, note that
the hysteresis observed in Figures 4.6a-c for this discharge height with magnets is much
more pronounced, i.e. the curves for increasing Ls are much different than for decreasing
Ls, than the hysteresis displayed in ﬁgures 4.8a-c. Note that hysteresis is observed at 100
mtorr without magnets while very little is observed at 100 mtorr when magnets are
present. At 100 mtorr the reﬂected power curves with (Figures 4.6a-c) and without mag-
nets (Figures 4.8a-c) appear very similar. Even the reduction of background reﬂected

power at shorter loop lengths is present in both conﬁgurations. In both conﬁgurations the

73

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76

p off resonance reﬂected power at 100 mtorr for loop lengths of Lp = 2.5 cm to 1.5 cm is
generally lower than for the same loop lengths at 40 mtorr and 70 mtorr. For example, in
Figure 4.8a at 100 mtorr and loop length of 1.5 cm the off resonance reﬂected power is
approximately 80 Watts, whereas at 70 mtorr and 40 mtorr the average off resonance

reﬂected power for Lp = 1.5 cm is approximately 125 Watts and 115 Watts, respectively.

4.6 Analysis of Electromagnetic Mode Behavior:

4.6.1 Observations of Mode Behavior for the Four Source Geometry Conﬁgurations:

In order to facilitate the comparison of the electromagnetic mode behavior of each
conﬁguration (for a constant incident power of 150 Watts) vs. variation in Ls, Lp and p/ f
summary graphs are shown in Figure 4.9a-d. The summary graphs plot the cavity length
positions of each minima of reﬂected power for each loop length and pressure investi-
gated. The points on these summary graphs are obtained by recording the reﬂected power
minima locations on Figures 4.5 through 4.8. These summary graphs provide an overall
picture of changes in position of matched conditions as the cavity length LS, and loop
length LP, is varied. They can be thought of as the minimum points of a contour surface, as
shown by Figure 4.3b. The minimum points of the trace curves in Figure 4.5a—c are plotted
and connected by lines in Figure 4.9a. Note that more than one discharge pressure, and

hence more than one curve for the same mode, is plotted on each summary graph.

Loop Length - Lp (cm)
3" N s» .w .A .e :4- s»
O UI O Ut O Ut O U.
|

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77

I Denotes that mode is well matched <10% Reﬂected Power
El Denotes that mode is between 10% and 60% Reﬂected Power

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 4.9a - Best matched positions for the 5.6 cm discharge with ECR magnets

Loop Length - Lp (cm)
1" 1° 5" P" :5 P S" S"
O U! 0 VI 0 LII 0 U0

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Cavity Length - Ls (cm)

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Figure 4.9b - Best matched positions for the 6.9 cm discharge with ECR magnets

Loop Length - Lp (cm)

Loop Length - LP (cm)

55
50
45
4D
35
3D
25
20

15

78

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Figure 4.9c - Best matched positions for the 5.6 cm discharge without magnets

55
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Figure 4.9d - Best matched positions for the 6.9 cm discharge without magnets

 

 

79

On each summary graph solid squares indicate reﬂected power minima where less
than 10% of forward power (i.e. 15 Watts) is reﬂected. Empty squares indicate reﬂected
power minima positions that have between 10% and 60% (or between 15 and 90 Watts)
reﬂected power. No minima were deﬁned when reﬂected power was greater than 60%.
Collections of data points taken for a constant pressure and the same mode are connected
by lines. The resulting curves are identiﬁed as Lsm vs. Lp mode curves or constant pres-
sure mode curves (recall that Lsm is the variable representing the cavity length position for
a minima of reﬂected power for a particular mode). For example in Figure 4.9a the TB“
mode has three such Lsm vs. Lp curves for pressures of 0.75 mtorr, 40 mtorr, and 100
mtorr. Solid black lines connect two well matched points, whereas grey lines connect all

other points.

4.6.2 Pressure Dependent Changes in Mode Cavity Length:

For each mode change in mode cavity length vs. discharge pressure can be studied
with the aid of Figures 4.9a-d. Signiﬁcant changes in mode cavity length can be seen for
changes in discharge pressure. For the 5.6 cm discharge with magnets, shown in Figure
4.9a, the average increase in mode cavity length for the TE“ mode is 0.825 cm from the
0.75 mtorr mode curve to the 40 mtorr curve and 0.16 cm from 40 mtorr to 100 mtorr.
Note that the discharge pressure increase from 0.75 mtorr to 40 mtorr is a 50 fold increase,
while the increase from 40 mtorr to 100 mtorr is only a 2.5 fold pressure increase. For the
6.9 cm discharge with magnets, shown in Figure 4.9b, the average cavity length increase is

1.63 cm from 0.75 mtorr to 40 mtorr and is 0.35 cm from 40 mtorr to 100 mtorr.

80

In the conﬁgurations without magnets the pressures studied were 40, 70, and 100
mtorr and therefore covered a much smaller range of discharge pressure than the conﬁgu-
rations with ECR magnets present. The change in mode curve position from 40 mtorr to
70 mtorr or to 100 mtorr is difﬁcult to determine, because only one point was obtained at
40 mtorr. However, one signiﬁcant observation is that this single point is 0.2 cm higher in
cavity length than the mode curves for 70 and 100 mtorr. The average difference between
the 70 mtorr curve and the 100 mtorr curve is very small at 0.1 cm. It should be noted that
the pressure of 70 mtorr provides the best matching conditions for the TE“ mode for this
conﬁguration. For the TE" mode in the 6.9 cm discharge, see Figure 4.9d, the average
increase in mode curve position from 40 to 70 mtorr is 0.18 cm. The average increase from
70 mtorr to 100 mtorr is 0.37 cm. Consequently, the total average increase from 40 mtorr
to 100 mtorr is 0.55 cm. Note that as pressure is increased from 40 mtorr to 70 mtorr and
from 70 to 100 mtorr a deviation or local increase in cavity length is observed for portions
of the mode curves between loop lengths of Lp = 3.5 cm and 1.5 cm.

For the low Ls mode with ECR magnets, shown in Figure 4.9a, when there is a change
in pressure from 0.75 mtorr to 40 mtorr the average change in mode cavity length is 2.1
cm. When the pressure is further increased from 40 mtorr to 100 mtorr the mode cavity
length, surprisingly, decreases in length on average 0.4 cm. In the 6.9 cm discharge with
magnets, shown in Figure 4.9b, the Low Ls mode is only found at 0.75 mtorr and can not
be compared vs. other pressures. In the 5.6 cm discharge without magnets, shown in Fig-
ure 4.9c, when the pressure is changed from 40 mtorr to 70 mtorr the mode cavity length is

seen to decrease about 0.7 cm, but then as pressure is increased to 100 mtorr the mode

81

cavity length increases once more about 0.8 cm. For the 6.9 cm discharge without mag-

nets, shown in Figure 4.9d, the Low Ls mode could not be found.

4.6.3 Increase in mode cavity length with decrease in loop length:

For all cases of the TB” mode observed in Figures 4.9a-d the cavity length of the
mode increases as the loop length is decreased. This can be seen for 0.75 mtorr with a 5.6
cm tall discharge, in Figure 4.9a, where at a loop length of 5.5 cm the mode cavity length
is Ls = 7.4 cm. The cavity length steadily increases to L8 = 8.4 cm as loop length is
decreased to Lp = 3.0 cm and levels off somewhat at L8 = 8.5 cm as the loop is further
decreased to Lp = 2.0 cm. Other curves for the TB“ mode at other pressures, discharge
sizes, regardless of magnetic conﬁnement show the same type of behavior.

A large increase in cavity mode length is also observed in the Low Ls mode with
decrease in loop length. However a somewhat different behavior is observed with the Low
Ls mode than with the TB“ excited mode. The slope of all the TE" I.p vs. Ls mode
curves, seen in Figure 4.9a, appear to start out at some negative value and then become
almost vertical as the loop length is decreased from 5.5 cm to 1.5 cm. In contrast, the Low
Ls mode curves, as seen in Figure 4.9a, appear to start out with vertical slope and then
level off to small negative and almost horizontal slope as the loop is decreased from 5.5

cm to 1.5 cm.

82

4.6.4 Change in Mode Cavity Length vs. Discharge Height:

Using the data presented in Figures 4.9a-d it is possible to compare cavity length posi-
tions of constant pressure mode curves vs. discharge chamber height. The cavity lengths
and loop lengths for each speciﬁc mode at a speciﬁc pressure can be taken from separate
ﬁgures and plotted on the same graph to make direct cavity length comparisons. These
mode position vs. discharge height comparison graphs are shown in Figures 4.10 - 4.12.

The graph comparing cavity length of the TB“ excited mode in the 5.6 cm discharge
(at 0.75 mtorr with ECR magnets) vs. the same mode in the 6.9 cm discharge is shown in
Figure 4.10a. As can be seen from the two constant pressure mode curves there is an
increase in cavity length on the order of 0.8 cm between curves from the 5.6 cm discharge
to the 6.9 cm discharge. The cavity length difference of 0.8 cm is signiﬁcantly smaller
than the difference in discharge height which is 1.3 cm. The shape and slope of the mode
lines are generally the same for both discharge chambers.

In Figure 4.10b the TB“ mode at 40 and 100 mtorr is compared for the two conﬁgura-
tions with ECR magnets. At 40 mtorr the average increase in mode curve cavity length is
1.5 cm from the 5.6 cm discharge to the 6.9 cm discharge. For 100 mtorr this average
increase is 1.7 cm. The general shape of the mode curves appears the same, both having a
segment of steep negative slope from Lp = 5.5 cm to I.p = 3.5 cm and another segment that
is almost vertical from L1) = 3.5 cm to Lp = 1.5 cm. Note that the sloped segment has a
steeper (i.e. more a negative) slope in the 5.6 cm discharge than in the 6.9 cm discharge
where the slope is more gradual.

A comparison of mode curve position vs. change in discharge height can also be made

83

for the conﬁgurations without ECR magnets for pressures of 40, 70, and 100 mtorr. This
comparison is displayed in Figure 4.11.

At 40 mtorr only one loop length, Lp = 3.5 cm, could sustain a discharge in the 5.6 cm
discharge chamber. Thus, only one point can be compared against the full 6.9 cm dis-
charge chamber mode curve. This is shown in ﬁgure 4.1la. As can be readily seen, the dif-
ference in cavity length is 1.3 cm from the 5.6 cm discharge to the 6.9 cm discharge.

At 70 mtorr ﬁve loop lengths could be sustained for the 5.6 cm discharge chamber. The
average increase in mode curve position, as shown in Figure 4.11b, is 1.8 cm. The curves
for both discharge lengths appear similar except for a noticeable deviation in the 6.9 cm
discharge mode curve for loop lengths between 2.5 and 3.5 cm.

At 100 mtorr the average increase in cavity length is 2.0 cm from 5.6 cm to 6.9 cm dis-
charge, shown in Figure 4.11c. Notice the large deviation in the mode curve in the region

of Lp = 2.0 cm to Lp = 3.0 cm for the 6.9 cm discharge chamber.

Loop Length - Lp (cm)
1" .N S" E” :5 P .V' 5"
O UI O U: C U: C VI

—0
M

T1311 Mode, 0.75 mtorr

 

 

 

 

 

 

 

 

 

 

 

 

g “l

3 5.6cm 6.9cm

5M: mm
- III III] ”III IIII IIII
7.0 8.0 9.0 10.

 

 

 

Cavity Length - Ls (cm)

(a)

 

84

3.5

3.0

2.5

2.0

1.5

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3
5
E.
8. 9.0 10.0 1 1.0 12.0
Cavity Length - Ls (cm)
(b)

Figure 4.10 - Comparison of Cavity Lengths for the TB“ Mode With Magnet Ring
vs. Discharge Chamber Height

85

 

 

Wm
H 40 mtorr WM
5.5 : / 5-5 : lumton'
1 \. 3 . /
5.0 _ W 5.0 g
A : : /
E 4.5 d 4.5 _ —
O 4 _
‘3 1 :
.1 4.0 2 4.0 1
a 3.5 : / a 3.5 :
‘3 : / :
,3 3.0 - 3.0 _ ,1
Q 3 5. cm hambgr -_-
3 2.5 ‘_‘ 40 mt 2.5 : , ..
2 0 E 2 0 3 5.6 cm Phanm
° 3 ° : 70 mtorr
1'5 - III IIII III ITII IIII VI 1'5 -IIII IIII VII IIII rm [III III II
8.0 9.0 11 .0 11.0 8.0 9.0 10.0 11.0 12.
Cavity Length - Ls (cm) Cavity Length - Ls (cm)
(a) (b)
5.5 n 52
5.0 A 5 100 ﬁto
"‘ 4.5 = I
5. a ’
3 4.0 g j)
3°50 3.5 f \K
s: 3 N
:5 3.0 3 N
a. : \
g 2.5 3 56 ~ ham:—
._1 : 100 mtorr
2.0 3
1'5 d I IIII IIII IIII IIII IIII IITI
8.0 9 0 10.0 11.0 12.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

cavity Length - Ls (cm)

 

 

 

 

 

(C) .

Figure 4.11 - Comparison of Cavity Lengths for the TB“ Mode Without Magnets
vs. Discharge Chamber Height

86

Observation of the Low Ls mode behavior vs. change in discharge height can also be
made. See Figure 4.12. At a pressure of 0.75 mtorr the Low Ls mode is observed in the 5.6
cm discharge with magnets. At a loop length of Lp = 3.5 cm the Low LS mode cavity
length is L3 = 5.2 cm. As loop length is reduced to Lp = 1.5 cm the cavity length of the
Low Ls mode increases to L8 = 8.9 cm as loop length is reduced to 1.5 cm. At the same
pressure in the 6.9 cm discharge (with magnets) the Low Ls mode is present at a cavity
length of L5 = 5.9 cm at a loop length of LD = 2.5 cm and moves up to a cavity length of L5
= 9.4 cm as the loop length is reduced to 1.5 cm. The average increase in mode cavity
length for the Low Ls mode from the 5.6 cm discharge to the 6.9 cm discharge is approxi-
mately 0.2 cm. This is a very small change in cavity length considering that the difference
in discharge chamber size is 1.3 cm. It must be noted that for the 6.9 cm tall discharge the
Low Ls mode could not be observed at longer loop lengths than 5.2 cm because the dis-
charge dome came in contact with the loop and prevented further movement of the sliding
short. See Figure 4.4.

At higher pressures of 40, 70, and 100 mtorr the Low Ls mode is present in the 5.6 cm
tall discharge, shown in Figure 4.9c, but it is not present in the 6.9 cm tall discharge for
these pressures with or without magnets. Consequently no comparison of mode cavity

length between 5.6 cm and 6.9 cm discharges can be made at these pressures.

87

5.5

 

 

5.0

 

 

 

 

4.5

 

 

0. 5 torr

 

\\

4.0

 

 

 

\\

3.5

 

 

 

 

3.0

 

 

Loop Length - Lp (cm)

.75 rhtorr
2.5

 

 

/\
\
CD

2.0 P<

' IIII IIII IIII IIII IIII IIII IIIIIIIII IIII II ITII III1 I".II IIIT

7.0 8.0 9.0 10.0 1 1.0 12.0
Cavity Length - Ls (cm)

 

 

 

 

 

1111 111] Ill] 1111 1111 [Ill 1111 111]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

&L
o
1"
c
a
c

Figure 4.12 - Comparison of Cavity Lengths for the Low Ls Mode With Magnet Ring
vs. Discharge Chamber Height

88

4.6.5 Comparison of Mode Cavity Length With and Without Magnets:

A study of the mode curve Ls position vs. the presence or absence of the multipole
magnet ring can be made. Both TE“ and Low Ls modes were studied. Pressures of 40
mtorr and 100 mtorr were the only conditions where non-magnetized and magnetized dis-
charges were compared, since a non-magnetized discharge could not be maintained at 0.75
mtorr.

For the TB” mode at 40 mtorr in the 5.6 cm discharge, shown in Figure 4.13a, mag-
netic vs. non-magnetic discharges are compared. Note squares indicated magnetized mode
points and triangles indicated non-magnetized mode points. Note that for this comparison
only one point is available for the non-magnetized mode. Yet, it is possible to observe that
this point is approximately 0.2 cm from the comparable Lp = 3.5 cm point on the magne-
tized mode curve. For 100 mtorr, shown in Figure 4.13b, both mode curves have very sim-
ilar shape and cavity length position. For the TE“ mode in the 6.9 cm discharge at 40
mtorr, shown in Figure 4.13c, both magnetized and non-magnetized mode curves also
show similar shape and Ls position. At 100 mtorr, shown in Figure 4.13d, both modes
appear to follow the same path from loop lengths of 1..p = 5.5 cm to 4.0 em, but between Lp
= 3.5 cm and 1.5 cm the non-magnetized mode curve is on average 0.4 cm higher in cavity
length than the magnetized mode curve.

Magnetized vs. non-magnetized discharge comparisons can also be made with the
Low Ls mode in the 5.6 cm tall discharge chamber. See Figure 4.14. At 40 mtorr only one
point was observed for the non-magnetized discharge and we note that this point is 0.4 cm

lower in cavity length than the comparable point on the magnetized mode curve. When

 

 

 

 

 

 

 

 

89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.6 cm Discharge at 40 mtorr 5.6 cm Discharge at 100 mtorr
5.5 _ 5.5 _
5.0 f 5.0 f
E 4.5 f E 4.5 f
3 : 3 :
f 4.0 : 3 4.0 3
a 3.5 3 +3 3.5 1
1: : TE“ MOdC 15:? 1 TE“ MOdB
3 3.0 2 ,3 3.0 3
a. : o. :
§ 2.5 3 g 2.5 3
2.0 f 2.0 f
1'5 - III 1111 III IIII II IIII 1'5 ‘ Ill llll III III] III
7.0 8.0 9.0 10.0 7.0 8.0 9.0 10.0
Cavity Length - Ls (cm) Cavity Length - Ls (cm)
(a) (b)
6.9 cm Discharge at 40 mtorr 6.9 cm Discharge at 100 mtorr
5.5 1 ‘ 5.5 3—5: ‘
5.0 E 1 5'0 :
E 4.5 f E 4.5 f
8 1 3 :
f 4.0 3 3- 4.o :
: _,'= :
= d = .1
3 3.0 3 ,3 3.0 3 t
a. 1 TE“ N C a. : TE” MOdC
g 2.5 : .81 2.5 “
2.0 f 2-0 f
1'5 ‘ III 1111 III III IIII IIII 1'5 ‘ III IIII IIIII IIII
9.0 1 .o 1 .o 12.0 9.0 13.0 1 1.0 12.0
Cavity Length - Ls (cm) Cavity Length - Ls (cm)
(C) (d)

Figure 4.13 - Plots Comparing Magnetized and Non-magnetized TE“ Mode Curves

[:1 With Magnets A Without Magnets

89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.6 cm Discharge at 40 mtorr 5.6 cm Discharge at 100 mtorr
5.5 q 5-5 -
5.0 3 5.0 f
E 4.5 3 E 4.5 f
3 : 3 :
3 4.0 3 4°- 4.o :
go 3 s f 2 5 3.5 f
I: : TE“ MOdC 20 : TE“ MOdB
,3 3.0 3 ,3 3.0 3
c1. 2 CL 1
g 2.5 3 g 2.5 3
2.0 f 2-0 f
1'5 - III IIII III IIII II IIII 15 - III IIII III IIII II
7.0 8.0 9.0 10.0 7.0 8.0 9.0 10.0
Cavity Length - Ls (cm) Cavity Length - Ls (cm)
(a) (b)
6.9 cm Discharge at 40 mtorr 6.9 cm Discharge at 100 mtorr
5.5 1 A 5'5 -1 A
5.0 f 5.0 f
E 4.5 f \ E 4.5 f
3 : 3 :
.4“ 4.0 ‘_‘ j- 4.0 2
5 3 5 f 5 3.5 f
E” : 2” : \
3 3.0 3 ,3 3.0 1 1
CL 2 TE” Node 0. 2 TE” MOdC
— o —1
g 2.5 d 3 2-5 -
2.0 f 2.0 f
1'5 "' III IIII III III III IIII 1'5 -IIII VIII III IIII I IIII
9.0 13.0 1 .0 12.0 9.0 13.0 1 .0 12.0
Cavity Length - Ls (cm) Cavity Length - Ls (cm)
(C) (d)

Figure 4.13 - Plots Comparing Magnetized and Non-magnetized TE“ Mode Curves
C] With Magnets A Without Magnets

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.6 cm Discharge Chamber
5.5
I
A i
E 5.0 _‘
3 2
n- 4.5 '
-) g mtorr
5 4.0 : Magncts
DD .1
= :
.3 35 -_1
0- E
g 3.0—_
2.5 I
20 E \
' E WithoutMa c
1'5 -WII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII “I ”II
40 5.0 60 70 8O 90 10.0 11.0 12.0

Cavity Length - Ls (cm)

Figure 4.14 - Comparison of Magnetized and Non-Magnetized Low Ls Mode Curves
[j Mth Magnets A Mthout Magnets

91

Low Ls mode curves are compared at 100 mtorr we ﬁnd that the shape and location of both

magnetized and non-magnetized mode curves are similar.

4.6.6 Cavity Length Hysteresis in Reﬂected Power:

Hysteresis can be observed in many of the reﬂected power curves recorded in Figures
4.5—4.8. The most signiﬁcant hysteresis is observed for 0.75 mtorr and 40 mtorr for the 6.9
cm discharge with magnets. The reﬂected power curves for this conﬁguration are shown in
Figures 4.6a-c. Some hysteresis is observed at 70 mtorr and 100 mtorr for the 6.9 cm dis-
charge without magnets, in Figure 4.8a-c. Hysteresis is also observable in most of the
reﬂected power curves for the 5.6 cm discharge without magnets, shown in Figures 4.7a-c.

Most of the hysteresis observed follows the same format: the decreasing Ls curve fol-
lows a high reﬂected power path and passes over a well matched point, while the increas-
ing Ls curve follows a much lower reﬂected power path and at some point achieves an
excellent match. In addition most increasing and decreasing curves for an individual graph
follow the same path vs. Ls for the highest and lowest regions of Ls, but generally follow
separate paths near a minima in the mid Ls range of the curve. This is observed, for exam-
ple, in Figure 4.6b at a pressure of 0.75 mtorr and loop lengths of Lp = 3 cm, 3.5 cm, and

4.0 cm.

92

4.7 Summary of Important Observations:

In the investigation presented in this chapter the only internal variable measured was
reﬂected power, Pref. Measurement of reﬂected power was used to locate and study the
behavior of resonant modes in the plasma cavity system. Input parameters varied in this
study were: cavity length Ls, loop length LP, discharge chamber height h, and magnetic
ﬁeld. Two important input parameters were not independently varied: incident power Pine,
and ﬂow rate 1". Incident power was held constant at 150 Watts and ﬂow rate was coupled
to discharge pressure. Thus the data presented in this chapter should be viewed as a subset
of the total data that must be obtained to fully understand the discharge behavior. How-
ever, even under the limitations of constant Pine and dependent i- valuable observations
can still be made.

It is important to emphasize that cavity length Ls, the distance between the sliding
short and the bottom of the cavity, can be considered the sum of several transmission line
sections Lp’ L', and Lc. In order to gain further insight into mode behavior and to develop

an equivalent circuit (in Chapter 6) it will be necessary to consider Ls and its subsections

A summary of important observations made in the previous section are as follows:

WM:

- l) The TE“ mode was found in all four source geometry conﬁgurations and is
present for the entire pressure range investigated.

- 2) A low Ls mode was found in the 5.6 cm discharge chamber at all pressures
measured, with and without magnets. In the 6.9 cm discharge the low Ls mode was
only found at 0.75 mtorr with magnets, and was not observed at any pressure with-
out magnets.

93

MW:

- The shape of the TB“ mode curve vs. 1..p and L8 is different than the shape of the
Low Ls mode curve.

- Low Ls mode reﬂected power minima appear to have more gradual magnitude of
(APref/ALS) slope than do the minima for the TB” mode. Many TE” mode min-
ima have a very large magnitude of slope and a “sharp” appearance, while most
Low Ls minima have a wider “bowl” shaped appearance.

- For all modes a decrease in loop length leads to a compensating increase in mode
cavity length, Lsm.

- For the TB“ mode an increase in discharge pressure leads to an increase in mode
cavity length, Lsm. For the Low Ls mode increase in pressure from 0.75 mtorr to 40
mtorr leads to an increase in Lsm, but an increase in pressure can also lead to a
decrease in Lsm for some pressures ranges higher than 40 mtorr.

WW:

- For the TB“ mode an increase in discharge chamber height always results in a
shift in the mode curve to larger cavity length.

- For the Low Ls mode at 0.75 mtorr an increase in discharge chamber height had
very little effect on the mode cavity length. Behavior at higher pressures could not
be determined conclusively.

WWI

- The presence of magnets allowed a discharge to be maintained at 0.75 mtorr
(with ECR heating) whereas the lowest pressure a plasma could be maintained
without magnets was 40 mtorr (non-ECR heating).

- The presence of magnets improves matching at higher pressures.

- Mth the magnet ring both 5.6 cm and 6.9 cm discharge chambers sustain a dis-
charge, but without magnets the 6.9 cm discharge sustains the plasma much better
than the 5.6 cm discharge.

- Presence or absence of magnets did not have a major inﬂuence on the LS location
of the mode curves. Changes in Ls observed were within the margin of experimen-
tal error (approximately 2 mm). However, at higher pressures of 40 to 100 mtorr in
the 6.9 cm discharge without magnets a “bow” of increased L8 is observed for
short loop lengths.

94

- At 100 mtorr for the 6.9 cm discharge chamber either with or without magnets
the measured reﬂected power is 50 to 70 Watts at low loop lengths in the “off-reso-
nance” Ls regions. For all other pressures and loop lengths the “off-resonance”
reﬂected power is 100 Watts or more.

WW:

- Hysteresis is observed to a great extent in the 6.9 cm discharge with magnets, and
to a lesser extent in both 5.6 cm and 6.9 cm discharges without magnets.

- Hysteresis does not exist in the 5.6 cm discharge with magnets or the 6.9 cm dis-
charge with magnets at 100 mtorr.

- Almost all hysteresis observed is counterclockwise, i.e. the decreasing path fol-
lows a high curve while the increasing path follows a lower curve.
Conclusions drawn from the observations listed above as well as observations made in

Chapter 5 will be presented in Chapter 6.

Chapter 5

Electromagnetic Evaluation of the ECR Microwave Plasma Cavig

5.1 Introduction:

There were two groups of experiments performed in this chapter. The ﬁrst group was a
measurement of spatial electric ﬁeld patterns. The ﬁeld patterns were used in to determine
the speciﬁc waveguide mode present in the cavity at each resonance. Speciﬁcally the spa-
tial electric ﬁeld patterns of the two modes observed in Chapter 4. The second group of
experiments performed in this chapter was a preliminary investigation of the inﬂuence of
absorbed power on charge density and internal cavity electric ﬁeld. Absorbed power, rela-
tive charge density, and relative electric ﬁeld strength were all measured as Ls was varied
and curves vs. Ls similar to the reﬂected power curves of Chapter 4 were obtained. Note,
however, that in all experiments performed in this chapter the loop length was held con-

stant at Lp = 3.5 cm.

5.2. Parameter Space:

As described in Chapter 4 the experimental variables inﬂuencing the plasma source

were classiﬁed as: macroscopic controllable input variables U1, reactor geometry vari-

ables U2, process variables U3, internal variables X, and output variables Y. A block

95

96

Reactor Geometry Variables, U2

 

 

”II-W

5.6 cm or 6.9 cm

”121331191539QO

Magnets Present or Not Present

 

 

Macroscopic Controllable

Input Variables, U1

 

 

1)p/r' {maxim
1,10, 50 mtorr

2)Lp-me_ls.nzth

Constant at 3.5 cm

3) Ls - W
4.5 - 13.35 cm

4) Pine - mm
Constant at 150 Watts

 

Internal Variables, X

Output Variables, Y

 

 

1)Pabs-Ah§szth¢.d_ﬁo_m

0 to 150 Watts

 

 

 

2) Enl- -R§latil¢_E:Ei:ld
-25 mWatts

 

 

 

 

 

Process Variables, U3 ,

1) Isa-112nm
Cum

0 to 8000 uAmps

 

 

 

 

None Measured

 

 

 

Figure 5.1 - Block Diagram of Experimental Variables

97

diagram of the experimental variables is shown in Fig. 5.1.

The macroscopic controllable variables were: 1) discharge pressure/ﬂow rate, 2) loop
antenna length, 3) cavity length, and 4) incident power. In this chapter discharge pressures
investigated were 1, 10, and 50 mtorr where discharge pressure, p, and ﬂow rate, r‘, were
interdependent, p/f . The cavity length, Ls, was varied from 4.5 cm to 13.35 cm. The loop
length, LP, was held constant at 3.5 cm. Input power, Pine, was also held constant at 150
Watts.

The discharge geometry variables were: 1) discharge height, and 2) magnet geometry.
As discussed in Section 4.2, four discharge geometry conﬁgurations were investigated.

Internal variables investigated in this experiment were: 1) absorbed power, Pabs, and 2)
relative electric ﬁeld strength, Ere]. Absorbed power ranged from close to zero power
absorbed to almost complete absorption of 150 Watts. Relative electric ﬁeld strength was
measured using a microwave power meter. Measured power ranged from zero Watts to 25
mWatts.

The only output variable measured in this experiment was ion saturation current, 1“,,
which is a relative measure of plasma charge density. The currents measured in this exper-
iment ranged from 0 to 8000 microampere. Process variables were not measured in this

investigation.

5.3 Start-up Procedure and Experimental Setup:

The experimental start-up procedure for this set of experiments is the same as that dis-

cussed in Section 4.3. The basic experimental setup is also similar except that two

98

measurement devices were added. A diagram of the experimental setup is shown in Figure
5.2.

A microcoaxial electric ﬁeld probe (1) was used to measure relative electric ﬁeld
strength and electric ﬁeld patterns. Power coupled into to microcoaxial dipole antenna was
measured by a Hewlet Packard power meter (2) with a thermistor (3) used to convert
microwave power to a DC signal.

A double Langmuir probe (4) was placed approximately 1 cm below the ECR magnet
ring (5) at the circular opening of the discharge chamber (6). The Langmuir probe was
electrically connected to the measurement circuit (7) through an electrical feed through (8)
in the vacuum chamber wall. The measurement circuitry is described in detail in Section
5.4.2.

Microwave power was delivered to the plasma source with the same microwave net-

work (9) as used in Chapter 4 and the same method of measuring reﬂected power (10) was

used.

99

    

Microwave Network

 

 

O
.0

 

 

 

 

 

 

“.:.:...:.:.:.:.:.:.:.:.:.‘V.
O

 

    
 

 

 

 

 

 

 

 

 

 

 

:- _ __
lllllll- I
I
/ 10 ' |
l
l .
v To dummy load :
l
l
L ____________ .1
Double Probe
Measurement
Circuit

 

 

 

Figure 5.2 - Experimental Setup for Source Evaluation

 

 

 

 

 

 

 

 

  
  
 

 

 

 

 

 

100

5.4 Experimental Procedure:

5.4.] Relative Measurement of Electric Field:

Relative measurements of electric ﬁeld were taken with a microcoaxial probe. A cross-
sectional diagram of an electric ﬁeld probe is shown in Figure 5.3. It was constructed from
5 to 7 cm sections of 3 mm diameter ﬂexible copper coaxial stock (1) obtained from Pas-
temack, Inc. One end of each stock section was soldered to an SMA connector (2). Two
millimeters of the copper shielding was carefully cut away from the other end. The dielec-
tric (3) surrounding the center conductor was not cut away in order to provide a mechani-
cal shield and prevent the accidental bending of the center conductor (4). The extension of
the center conductor into the cavity forms a 2 mm long dipole antenna.

When inserted into small holes in the wall of the cavity this probe acts as a dipole
antenna, coupling to the radial time varying ﬁelds normal to the wall of the cavity. See
Figure 5.4. The microwave power absorbed by the probe was measured by a thernistor (l)
aided Hewlet Packard microwave power meter (2). Since electric ﬁeld strength is propor-
tional to the square root of microwave power the measurement of microwave power was

used as a relative measurement of radial electric ﬁled strength.

 

 

Figure 5.3 - Cross Sectional Diagram of a Microcoaxial Electric Field Probe

101

As shown in the inset of Figure 5.4, the inner wall of the cavity (3) acts as the ground
plane of the dipole (4). In order to maintain consistent depth of extension into the cavity an
adjustable brass collar (5) was placed on the probe [18]. This also ensures that the end of
the copper outer conductor is ﬂush with the inner wall of the cavity. When a measurement
is made the probe is inserted into a probe hole in the cavity until the collar makes full con-
tact with the outer wall of the cavity.

To accommodate the above described E-ﬁeld probe many 3mm diameter holes were
drilled into the side walls of the cavity. In order to measure the 11) variation of radial E-
ﬁelds three circumferential rings of holes (with holes spaced 10° apart) were drilled at
planes 1 inch (2.54 cm), 2 inches (5.08 cm), and 3 inches (7.62 cm) from the bottom of the
cavity. These can be seen clearly in the photograph in Figure 2.5 in Chapter 2. A cross sec-
tional diagram of the circumferential ring of holes at 2 inches from the bottom of the cav-
ity is shown in Figure 5.5. A zero degree reference point is chosen at the center of the
screened window (1). The plane of the coupling loop (2) is the plane that passes through
both 90° and 270° sampling holes.

In order to measure the variation of radial E-ﬁeld along the length of the cavity four
linear groups of holes were drilled at 0°, 90°, 180°, and 270° around the circumference
with reference to the screened window at 0°. These can also be seen clearly in the photo-
graph in Figure 2.5 in Chapter 2. The ﬁrst hole of each line was placed at 0.75 inches
(1.905 cm) from the bottom of the cavity. Holes were drilled at 0.25 inch (0.635 cm) inter-
vals up to 4.25 inches (10.795 cm) from the bottom of the cavity. A 3/ 16” (0.476 cm) thick
stainless steel strip was welded to the outside of the cavity at each line and ring of holes.

These strips were used to provide larger hole depth in order to increase electrical contact

102

 

      

 
   

       
 
    
       
 

_ Illllll

'l’ll’ll

 

 

 

 

/

 
  

1. 3'
’4‘?" ﬁ‘fé‘“ W 1“».
3 ‘5 5.12-V43». . .2 ~ ~ _‘. ,—
' ‘J’SVJ- 2.109 5.9."? . ' -
D D

.O..-‘.-...-....‘

 

 

 

Figure 5.4 - Measurrnent of Electric Field Strength

103

 

 

 

 

 

Figure 5.5 - Cross-Section of a Circumferential Ring of E-Field Sampling Holes

104

and to ensure that the probes would ﬁt securely and not wobble while measurements were
performed.

Electric ﬁeld measurements were taken in two types of experimental procedures. The
ﬁrst procedure was intended to determine cavity mode patterns and the second was to
measure relative electric ﬁelds in the cavity vs. L5. This relative electric ﬁeld measurement
was part of the correlated measurement of absorbed power, relative charge density and rel-
ative electric ﬁeld strength vs. LS.

In order to determine the electromagnetic modes present in the cavity the spatial varia-
tion of radial electric ﬁelds was investigated. In this procedure all parameters of the
plasma source, such as Ls, LP, input power, and discharge pressure, etc., were held con-
stant. The microwave power (relative electric ﬁeld strength) was then measured at each
probe hole around the cavity. These measurements were then plotted vs. circumferential
angle or longitudinal distance. These curves facilitated the identiﬁcation of the electro-
magnetic mode present in the cavity.

The second experimental procedure involved the measurement of relative electric ﬁeld
strength as the sliding short position Ls was varied. A microcoaxial electric ﬁeld probe
was placed and kept at one sampling hole 90° from the center of the screened window and
2 inches from the bottom of the cavity. Periodic readings were taken from the electric ﬁeld
probe at this constant sampling position as the sliding short was lowered and then raised.
All input variables other than Ls were held constant. Note, since electric ﬁeld patterns may
be different for different modes accessed by varying Ls one to one comparisons of ﬁeld
strength from one mode to the next may not be possible for this ﬁxed sample. However,

the relative E-ﬁeld vs. Ls curves make it possible to identify positions of Ls where E-ﬁeld

105

is signiﬁcant and observable. They also make it possible to make comparisons between
absorbed power, relative charge density, and relative electric ﬁeld strength when all are

varied vs. Ls.

5.4.2 Measurement of Absorbed Power:

Power absorbed by the plasma cavity system is calculated from measurements of
reﬂected power. A reﬂected power curve is ﬁrst taken by measuring reﬂected power while
varying the cavity length Ls and holding loop length, discharge pressure and forward
power constant. An example reﬂected power curve is shown in Figure 5.6a. The absorbed
power curve is obtained by subtracting the reﬂected power curve from the value of inci-
dent power (150 Watts in this investigation). Such an absorbed power curve is shown in

Figure 5.6b. The regions of good matching and low reﬂected power appear as minima in

 

 

 

 

 

g - Forward Power Level :3: - Forward Power Level
a J. ___________ a:
E E
I— " 1..
D
‘3’ - a
8 _ n.
B — E
.D
82 ‘ <
llllllfIlIl lllllllllll
Cavity Length - Ls (cm) Cavity Length - Ls (cm)
(a) (b)

Figure 5.6 - Reﬂected and Absorbed Power Proﬁles

106

the reﬂected power curve and as maxima in the absorbed power curve. The presentation of
reﬂected power curves as absorbed power curves facilitates their comparison with relative
charge density and relative electric ﬁeld curves vs. LS. Note the total power absorbed in the
plasma source is the sum of the power absorbed by: the cavity walls, the coupling antenna,

and the plasma discharge.
5.4.3 Relative Measurement of Charge Density:

Ion saturation current was measured vs. Ls at the same time absorbed power was mea-
sured vs. Ls. These simultaneous measurements allowed relative charge density vs. Ls
curves to be plotted and compared with absorbed power vs. Ls curves. The ion saturation
current vs. Ls curves also indicated the values of Ls for speciﬁc discharge geometries and
pressures where the charge density was highest.

Ion saturation current measured by a double Langmuir probe at a ﬁxed bias voltage (40
Volts in this experiment) can be used to provide a quick relative measurement of charge
species density. Ion saturation current, 1”,, is related to charged species density, ni,

through the approximate relation [26]:

kTe
[W s 0.6nieA (7')
where 0.6 is a constant of proportionality, e is the charge on an electron, A is the area of
the probe, k is Boltzman’s constant, m,- is the mass of an Argon ion, and T, is the electron
temperature. Since e, A, k, and m,- are normally constant then direct proportionality

between Isa, and ni is only possible if electron temperature, Te, is held constant. Electron

107

temperature is controlled by: discharge gas composition, discharge pressure, and dis-
charge geometry. If each of these three parameters are held constant then Isa, can be used
as an indicator of n,- as other parameters such as input power and microwave matching are
varied. Therefore, the measurements of [W vs. L8 in this experiment strongly indicate the
relative variation of n,- vs. Ls. Note that the area of the DC sheath surrounding the probes
(i.e. the effective collection area) may change with changing ni introducing a small source
of error into the relative measurements. Nonetheless this method is a good general indica-
tor of relative charge density.

Note also that ion saturation current measurements alone can not be used to determine
absolute charge density. A current vs. voltage curve must be obtained to make absolute
charge density measurements.

A diagram of the setup used to make ion saturation current measurements is shown in
Figure 5.7. The double Langmuir probe (1) was mounted along the central axis of the
plasma source with the tips of the probes 1 cm from the bottom of the ECR magnet ring
(2). The Langmuir probe was constructed from two 0.95 mm diameter Tungsten rods (3)
encased in fused quartz (4) with 0.9 cm of the Tungsten rods exposed to form the probes.
The double probe was connected through a electrical vacuum feedthrough (5) to the mea-
surement circuit outside the vacuum chamber. The measurement circuit consisted of two
digital multimeters and a ﬂoating DC power supply. The power supply was set to 40 Volts
and held constant throughout the experiment. DMM #2 was used as a volt meter to moni-
tor voltage produced by the DC power supply. DMM #1 was used as an ammeter and mea-
sured the current ﬂowing through the double probe. The current measured by DMM #1

was deﬁned as the ion saturation current.

108

  
 

Measurement Circuit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

—‘ | | | l— DMM #1
+ | 1:] Used for Current
- O O
40 V Measurement
DMM #2
Z: Used for Voltage
0 0 Measurement
I: Floating DC Power Supply
0 o 0 Set to 40 Volts

 

 

 

Figure 5.7 - Setup for Measurement of Ion Saturation Current

109

5.5 Spatial Electric Field Patterns:

5.5.1 Description of the Experiment:

The ﬁeld pattern measurements presented in the next two sections were intended to aid
in the identiﬁcation of the two mode like phenomena noted in Chapter 4. Field pattern
measurements were taken by ﬁrst striking the discharge and adjusting to the intended pres-
sure. Then the sliding short was tuned to the speciﬁc cavity length where the mode in
question was observed and the plasma source was perfectly matched. When this condition
was reached all input parameters were then held constant. At this point the electric ﬁeld
probe was inserted into each of the appropriate E-ﬁeld sampling holes and the power
absorbed by the probe was recorded. Once a power reading from each of the sampling
holes was obtained the ﬁeld pattern measurement was complete. The power measured for
each sampling hole was then plotted vs. circumferential and longitudinal distance. These
plots are presented in the next two sections. Field pattern measurements were taken in all
four source geometry conﬁgurations for the TB" mode, while pattern measurements with
the Low Ls mode were only taken in the two conﬁgurations with the 5.6 cm discharge.

It is important to note that all ﬁeld pattern plots display power coupled into the probe.
This power is proportional to the square of electric ﬁeld. Thus these plots should be
viewed as plotting the square of relative electric ﬁeld.

Also, note that the objective of these experiments is to determine relative ﬁeld patterns
and not absolute ﬁeld strength. At the beginning of each ﬁeld pattern measurement the

depth of the probe was optimized to provide the best resolution of ﬁeld pattern. This

98

measurement devices were added. A diagram of the experimental setup is shown in Figure
5.2.

A microcoaxial electric ﬁeld probe (1) was used to measure relative electric ﬁeld
strength and electric ﬁeld patterns. Power coupled into to microcoaxial dipole antenna was
measured by a Hewlet Packard power meter (2) with a thermistor (3) used to convert
microwave power to a DC signal.

A double Langmuir probe (4) was placed approximately 1 cm below the ECR magnet
ring (5) at the circular opening of the discharge chamber (6). The Langmuir probe was
electrically connected to the measurement circuit (7) through an electrical feed through (8)
in the vacuum chamber wall. The measurement circuitry is described in detail in Section
5.4.2.

Microwave power was delivered to the plasma source with the same microwave net-

work (9) as used in Chapter 4 and the same method of measuring reﬂected power (10) was

used.

Microwave Network

Illllll- l

10 I

/ 7

 

Double Probe
Measurement
Circuit

 

 

 

O
..
"0:020:02.IOIOIOZOZOZOIOIO‘s

 

2

.;o'o'o¢ \
.0 a.

’0
O

 

  

Figure 5.2 - Experimental Setup for Source Evaluation

100

5.4 Experimental Procedure:

5.4.1 Relative Measurement of Electric Field:

Relative measurements of electric ﬁeld were taken with a microcoaxial probe. A cross-
sectional diagram of an electric ﬁeld probe is shown in Figure 5.3. It was constructed from
5 to 7 cm sections of 3 mm diameter ﬂexible copper coaxial stock (1) obtained from Pas-
temack, Inc. One end of each stock section was soldered to an SMA connector (2). Two
millimeters of the copper shielding was carefully cut away from the other end. The dielec—
tric (3) surrounding the center conductor was not cut away in order to provide a mechani-
cal shield and prevent the accidental bending of the center conductor (4). The extension of
the center conductor into the cavity forms a 2 mm long dipole antenna.

When inserted into small holes in the wall of the cavity this probe acts as a dipole
antenna, coupling to the radial time varying ﬁelds normal to the wall of the cavity. See
Figure 5.4. The microwave power absorbed by the probe was measured by a themistor (1)
aided Hewlet Packard microwave power meter (2). Since electric ﬁeld strength is propor-
tional to the square root of microwave power the measurement of microwave power was

used as a relative measurement of radial electric ﬁled strength.

 

 

Figure 5.3 - Cross Sectional Diagram of a Microcoaxial Electric Field Probe

101

As shown in the inset of Figure 5.4, the inner wall of the cavity (3) acts as the ground
plane of the dipole (4). In order to maintain consistent depth of extension into the cavity an
adjustable brass collar (5) was placed on the probe [18]. This also ensures that the end of
the copper outer conductor is ﬂush with the inner wall of the cavity. When a measurement
is made the probe is inserted into a probe hole in the cavity until the collar makes full con-
tact with the outer wall of the cavity.

To accommodate the above described E-ﬁeld probe many 3mm diameter holes were
drilled into the side walls of the cavity. In order to measure the 4) variation of radial E-
ﬁelds three circumferential rings of holes (with holes spaced 10° apart) were drilled at
planes 1 inch (2.54 cm), 2 inches (5.08 cm), and 3 inches (7.62 cm) from the bottom of the
cavity. These can be seen clearly in the photograph in Figure 2.5 in Chapter 2. A cross sec-
tional diagram of the circumferential ring of holes at 2 inches from the bottom of the cav-
ity is shown in Figure 5.5. A zero degree reference point is chosen at the center of the
screened window (1). The plane of the coupling loop (2) is the plane that passes through
both 90° and 270° sampling holes.

In order to measure the variation of radial E-ﬁeld along the length of the cavity four
linear groups of holes were drilled at 0°, 90°, 180°, and 270° around the circumference
with reference to the screened window at 0°. These can also be seen clearly in the photo-
graph in Figure 2.5 in Chapter 2. The ﬁrst hole of each line was placed at 0.75 inches
(1.905 cm) from the bottom of the cavity. Holes were drilled at 0.25 inch (0.635 cm) inter-
vals up to 4.25 inches (10.795 cm) from the bottom of the cavity. A 3/16” (0.476 cm) thick
stainless steel strip was welded to the outside of the cavity at each line and ring of holes.

These strips were used to provide larger hole depth in order to increase electrical contact

102

 

      

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Figure 5.4 - Measurrnent of Electric Field Strength

103

 

 

 

 

 

Figure 5.5 - Cross-Section of a Circumferential Ring of E-Field Sampling Holes

104

and to ensure that the probes would ﬁt securely and not wobble while measurements were
performed.

Electric ﬁeld measurements were taken in two types of experimental procedures. The
ﬁrst procedure was intended to determine cavity mode patterns and the second was to
measure relative electric ﬁelds in the cavity vs. Ls. This relative electric ﬁeld measurement
was part of the correlated measurement of absorbed power, relative charge density and rel-
ative electric ﬁeld strength vs. Ls.

In order to determine the electromagnetic modes present in the cavity the spatial varia-
tion of radial electric ﬁelds was investigated. In this procedure all parameters of the
plasma source, such as Ls, LP, input power, and discharge pressure, etc., were held con-
stant. The microwave power (relative electric ﬁeld strength) was then measured at each
probe hole around the cavity. These measurements were then plotted vs. circumferential
angle or longitudinal distance. These curves facilitated the identiﬁcation of the electro-
magnetic mode present in the cavity.

The second experimental procedure involved the measurement of relative electric ﬁeld
strength as the sliding short position Ls was varied. A microcoaxial electric ﬁeld probe
was placed and kept at one sampling hole 90° from the center of the screened window and
2 inches from the bottom of the cavity. Periodic readings were taken from the electric ﬁeld
probe at this constant sampling position as the sliding short was lowered and then raised.
All input variables other than Ls were held constant. Note, since electric ﬁeld patterns may
be different for different modes accessed by varying Ls one to one comparisons of ﬁeld
strength from one mode to the next may not be possible for this ﬁxed sample. However,

the relative E—ﬁeld vs. Ls curves make it possible to identify positions of Ls where E-ﬁeld

105

is signiﬁcant and observable. They also make it possible to make comparisons between
absorbed power, relative charge density, and relative electric ﬁeld strength when all are

varied vs. Ls.

5.4.2 Measurement of Absorbed Power:

Power absorbed by the plasma cavity system is calculated from measurements of
reﬂected power. A reﬂected power curve is ﬁrst taken by measuring reﬂected power while
varying the cavity length Ls and holding loop length, discharge pressure and forward
power constant. An example reﬂected power curve is shown in Figure 5.6a. The absorbed
power curve is obtained by subtracting the reﬂected power curve from the value of inci-
dent power (150 Watts in this investigation). Such an absorbed power curve is shown in

Figure 5.6b. The regions of good matching and low reﬂected power appear as minima in

 

 

 

 

 

:3: Forward Power Level £9, — Forward Power Level
g 1 ____________ g ﬁr
:— '1 ‘- '—
D
: _ g _
a? _ a. _
-o
B - a -
o _ .o
a: < "
IlIlIlﬁlfll 111111111r1
Cavity Length - Ls (cm) Cavity Length - Ls (cm)
(a) (b)

Figure 5.6 - Reﬂected and Absorbed Power Proﬁles

106

the reﬂected power curve and as maxima in the absorbed power curve. The presentation of
reﬂected power curves as absorbed power curves facilitates their comparison with relative
charge density and relative electric ﬁeld curves vs. Ls. Note the total power absorbed in the
plasma source is the sum of the power absorbed by: the cavity walls, the coupling antenna,

and the plasma discharge.
5.4.3 Relative Measurement of Charge Density:

Ion saturation current was measured vs. Ls at the same time absorbed power was mea-
sured vs. Ls. These simultaneous measurements allowed relative charge density vs. Ls
curves to be plotted and compared with absorbed power vs. Ls curves. The ion saturation
current vs. Ls curves also indicated the values of Ls for speciﬁc discharge geometries and
pressures where the charge density was highest.

Ion saturation current measured by a double Langmuir probe at a ﬁxed bias voltage (40
Volts in this experiment) can be used to provide a quick relative measurement of charge
species density. Ion saturation current, 130,, is related to charged species density, n,,

through the approximate relation [26]:

kTe
I =0.6nieA (—)

sat mi

where 0.6 is a constant of proportionality, e is the charge on an electron, A is the area of
the probe, k is Boltzman’s constant, m; is the mass of an Argon ion, and Te is the electron
temperature. Since e, A, k, and m,- are normally constant then direct proportionality

between I”, and n,- is only possible if electron temperature, 7;, is held constant. Electron

107

temperature is controlled by: discharge gas composition, discharge pressure, and dis-
charge geometry. If each of these three parameters are held constant then Isa, can be used
as an indicator of n,- as other parameters such as input power and microwave matching are
varied. Therefore, the measurements of Isa, vs. L5 in this experiment strongly indicate the
relative variation of It, vs. Ls. Note that the area of the DC sheath surrounding the probes
(i.e. the effective collection area) may change with changing 72,- introducing a small source
of error into the relative measurements. Nonetheless this method is a good general indica-
tor of relative charge density.

Note also that ion saturation current measurements alone can not be used to determine
absolute charge density. A current vs. voltage curve must be obtained to make absolute
charge density measurements.

A diagram of the setup used to make ion saturation current measurements is shown in
Figure 5.7. The double Langmuir probe (1) was mounted along the central axis of the
plasma source with the tips of the probes 1 cm from the bottom of the ECR magnet ring
(2). The Langmuir probe was constructed from two 0.95 mm diameter Tungsten rods (3)
encased in fused quartz (4) with 0.9 cm of the 'Ilungsten rods exposed to form the probes.
The double probe was connected through a electrical vacuum feedthrough (5) to the mea-
surement circuit outside the vacuum chamber. The measurement circuit consisted of two
digital multimeters and a ﬂoating DC power supply. The power supply was set to 40 Volts
and held constant throughout the experiment. DMM #2 was used as a volt meter to moni-
tor voltage produced by the DC power supply. DMM #1 was used as an ammeter and mea-
sured the current ﬂowing through the double probe. The current measured by DMM #1

was deﬁned as the ion saturation current.

108

  

Measurement Circuit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

—‘l' ' "i— :1
+ O O
40 V
T
O O
I: Floating DC Power Supply
0 o 0 Set to 40 Volts

 

 

 

 

DMM #1
Used for Current
Measurement

DMM #2
Used for Voltage
Measurement

Figure 5.7 - Setup for Measurement of Ion Saturation Current

109

5.5 Spatial Electric Field Patterns:

5.5.1 Description of the Experiment:

The ﬁeld pattern measurements presented in the next two sections were intended to aid
in the identiﬁcation of the two mode like phenomena noted in Chapter 4. Field pattern
measurements were taken by ﬁrst striking the discharge and adjusting to the intended pres-
sure. Then the sliding short was tuned to the speciﬁc cavity length where the mode in
question was observed and the plasma source was perfectly matched. When this condition
was reached all input parameters were then held constant. At this point the electric ﬁeld
probe was inserted into each of the appropriate E-ﬁeld sampling holes and the power
absorbed by the probe was recorded. Once a power reading from each of the sampling
holes was obtained the ﬁeld pattern measurement was complete. The power measured for
each sampling hole was then plotted vs. circumferential and longitudinal distance. These
plots are presented in the next two sections. Field pattern measurements were taken in all
four source geometry conﬁgurations for the TB“ mode, while pattern measurements with
the Low Ls mode were only taken in the two conﬁgurations with the 5.6 cm discharge.

It is important to note that all ﬁeld pattern plots display power coupled into the probe.
This power is proportional to the square of electric ﬁeld. Thus these plots should be
viewed as plotting the square of relative electric ﬁeld.

Also, note that the objective of these experiments is to determine relative ﬁeld patterns
and not absolute ﬁeld strength. At the beginning of each ﬁeld pattern measurement the

depth of the probe was optimized to provide the best resolution of ﬁeld pattern. This

110

optimization was dictated by two concerns: 1) providing enough probe length to couple to
the weakest ﬁelds, and 2) ensuring that the highest ﬁeld measurements did not exceed the
power limit of the probe and thermistor (30 mWatts).Therefore in the ﬁeld graphs pre-
sented any apparent increase in coupled power from one discharge pressure or conﬁgura-
tion to the next should not be taken as evidence, for example, that E-ﬁeld strength
increases with discharge pressure. This kind of observation can only be made with abso-
lute measurements of electric ﬁeld strength. These measurements will be made in future

investigations of this source.
5.5.2 Identiﬁcation of the TE“ Mode:

Electric ﬁeld pattern measurements for the TB“ Mode were performed for the conﬁg-

urations and pressures listed in Table 5.1 below:

 

Table 5.1 - Summary of the Discharge Pressures Investigated in the Evaluation
of the Spatial Electric Fields of the TE“ Mode

5.6 cm Discharge 6.9 cm Discharge 5.6 cm Discharge 6.9 cm Discharge

W Magnets W915 MW
1 mtorr 1 mtorr .. --
10 mtorr 10 mtorr -- --

50 mtorr 50 mtorr 50 mtorr 50 mtorr

 

 

 

111

Note that a discharge could not be maintained at 150 Watts for pressures of 1 mtorr and 10
mtorr for the conﬁgurations without magnets.

For the 5.6 cm discharge with magnets at a discharge pressure of 1 mtorr the ﬁeld pat-
tern measurements taken are shown in Figures 5.8 and 5.9.

In Figure 5.8 circumferential variance of radial electric ﬁelds is plotted. The data
points marked by squares were taken from the ring of E-ﬁeld sampling holes 5.08 cm from
the bottom of the cavity. Data points marked with diamonds were taken from the ring of
sampling holes 2.54 cm from the bottom of the cavity. These rings of sampling holes can
be seen clearly in the photograph in Figure 2.5. There are three rings in total: one at 2.54
cm from the bottom of the cavity, the second at 5.08 cm from the bottom (shown inter-
rupted by the screen window), and the third at 7.62 cm from the bottom. Fields could not
be sampled from the third ring in Figure 5.8 because the sliding short obstructed the region
of these holes.

It can be seen, in Figure 5.8, that both groups of data points follow a double lobe pat-
tern. The peak of the ﬁrst lobe occurs at 100° from the center of the screened window. The
peak of the second lobe occurs at 280° a difference of 180° from the ﬁrst lobe. This type of
circumferential ﬁeld pattern is strongly indicative of a TE,“ type cavity mode, shown in
Figure 3.10a. The maxima of the lobes are very close to the plane of the coupling loop (the
90° 270° plane) which is what would be expected for a TB] 11 mode. In this case, magnetic
ﬁelds couple through the loop and induce electric ﬁelds in the central volume of the cavity
that are parallel to the plane of the loop.

Note that the lobes centered at 100° have a higher peak than the lobes centered at 280°.

This is explained by the fact that the thickness of the cavity wall was found to be 14 mills

112

(or 0.36 mm) thicker in the 280° region than the 100° region. In regions where the wall is
thicker the probe does not penetrate as far into the cavity volume. This reduces the amount
of power absorbed by the probe and causes ﬁeld readings to appear lower than for readings
taken at thinner areas of the wall.

In Figure 5.9 longitudinal variance of radial electric ﬁelds are plotted. These data
points were taken from the linear group of sampling holes 90° from the center of the
screened window. This linear group of holes can be seen at the right side of the cavity in
the photograph in Figure 2.5. This curve shows an approximate half wave sinusoidal
dependence that is consistent with the radial electric ﬁelds of a TB] 11 cavity mode. Paral-
lel electric ﬁelds must approach zero at a conducting surface, and hence the radial electric
ﬁelds measured at the cylindrical wall must be to zero at each end of the cavity.

Figures 5.10, 5.11, 5.12, and 5.13 show similar ﬁeld patterns for the same conﬁgura-
tion at the higher pressures of 10 mtorr and 50 mtorr. Figures 5.10 and 5.12 display two
lobes in the circumferential variation similar to Figure 5.8. Figures 5.11 and 5.13 show a
half wave sinusoidal dependence in the longitudinal variation similar to Figure 5.9. These
plots are all consistent with ﬁeld patterns in the TB] 11 cavity mode.

The next six Figures present the ﬁeld pattern measurements for a different source con-
ﬁguration: the 6.9 cm discharge with magnets. Figures 5.14 and 5.15 present the ﬁeld pat-
terns for this conﬁguration at 1 mtorr. Figures 5.16 and 5.17 present ﬁeld patterns for 10
mtorr. Figures 5.18 and 5.19 present ﬁeld patterns for 50 mtorr. All circumferential plots,
Figures 5.14, 5.16, and 5.18, demonstrate a two lobe structure consistent with the TEm
mode ﬁeld pattern. All longitudinal plots, Figures 5.15, 5.17, and 5.19, demonstrate a half

wave sinusoidal structure. In Figures 5.20 and 5.21 the ﬁeld patterns are presented for the

113

1:] Field Pattern 2 inches from bottom of cavity
0 Field Pattern 1 inch from bottom of cavity

 

5.00

.4"
o
o

9"
o
o

I“
o
o

1.00

RADIAL E—FIELD — MEASURED POWER (mWatts)

 

 

0.00

 

 

YIIIIIIIIIIIII IIIIIITIIIIIYY

0 100.00 200.00 300.00
HOLE POSITION AROUND CIRCUMFRENCE OF CAVITY (DEG)

bl1111111111L11111111l1111111111111111111l111111111

0

Input Power: 150 Watts Cavity Length (La): 8.45 cm
Reflected Power: 4.5 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm
Pressure: 1 mTorr Extension into Cavity (L9): 1.4 cm
Flow Rate: 27.8 sccm ECR Magnets: Present

Figure 5.8 - 360° Circumferential Electric Field Proﬁle for TB] 11 Mode at 1 mTorr

114

0 Field Pattern at 90° of Circumference

 

 

 

 

“5.00 q
3 _
“6 I
E I
f; :
Q: 4.00 '3
LL] 3
g _
O 3
a. j
0 j
E 3.00 :
:3 _
(f) .1
< ‘
LU 3
2 I
I 1
2.00 :
Q _
__J _
LLJ _.
17'. :
m E
g .
Q -I
< 2*
o: _
0.00—IIIIIIIIIIIIIITIIIIIIIIIIIIIIIIIIIIIIII
0.00 2.00 4.00 6.00 8.00
HOLE POSITION FROM BOTTOM OF CAVITY (cm)
Input Power: 150 Watts Cavity Length (Ls): 8.45 cm
Reflected Power: 4.5 Watts Loop Length (L,,): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm
Pressure: 1 mTorr Extension into Cavity (La): 1.4 cm
Flow Rate: 27.8 scorn ECR Magnets: Present

Figure 5.9 - Longitudinal Electric Field Proﬁle for TB] 11 Mode at 1 mTorr

115

13 Field Pattern 2 inches from bottom of cavity
0 Field Pattern 1 inch from bottom of cavity

 

10.00

8.00

6.00

4.00

2.00

RADIAL E—FIELD — MEASURED POWER (mWatts)

lJLlllllllllllllllIlLlllllllllllllllllllllllllll

 

 

 

 

0.00 YYIIIIIIIIIIIIII ITIIIIIIIIIYY

0.00 100.00 200.00 300.00
HOLE POSITION AROUND CIRCUMFRENCE OF CAVITY (DEG)

Input Power: 150 Watts Cavity Length (Ls): 9.05 cm
Reﬂected Power: 19.5 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm
Pressure: 10 mTorr Extension into Cavity (La): 1.4 cm
Flow Rate: 45.2 sccm ECR Magnets: Present

Figure 5.10 - 360° Circumferential Electric Field Proﬁle for TB] 11 Mode at 10 mTorr

116

El Field Pattern at 90° of Circumference

 

10.00

8.00

6.00

4.00

2.00

RADIAL E—FIELD —— MEASURED POWER (mWatts)

lllllllLiIllllllLllllllILllllllllLlILLlLlllllllll

 

 

 

0.00 IITIIIIIIIVIIIIIIIIIIIIIIIIIIIIIIIIIIII

0.00 2.00 4.00 6.00 8.00
HOLE POSITION FROM BOTTOM OF CAVITY (cm)

Input Power: 150 Watts Cavity Length (Ls): 9.05 cm
Reflected Power: 19.5 Watts Loop Length (LP): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm
Pressure: 10 mTorr Extension into Cavity (L9): 1.4 cm
Flow Rate: 45.2 sccm ECR Magnets: Present

Figure 5.11 - Longitudinal Electric Field Proﬁle for TB, 11 Mode at 10 mTorr

117

C1 Field Pattern 2 inches from bottom of cavity
0 Field Pattern 1 inch from bottom of cavity

 

 

 

 

 

A1500
3 _.
+6 ..
3 —1
é _.
a: -
LL] .1
3 _
8 _

10.00 -
D ..
EL; 4
D —1
U) ..
<
LL] —1
2 -

I I
9 —I
1.. 5.00 —
L? i
LLJ _
_, _
g —
Q —1
< _
Eh -I

0.00 ‘~ -~

0.00 100.00 200.00 300.00

HOLE POSITION AROUND CIRCUMFRENCE OF CAVITY (DEG)

Input Power: 150 Watts Cavity Length (Ls): 9.35 cm
Reﬂected Power: Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm
Pressure: 50 mTorr Extension into Cavity (L9): 1.4 cm
Flow Rate: 95.1 scorn ECR Magnets: Present

Figure 5.12 - 360° Circumferential Electric Field Proﬁle for TB] 11 Mode at 50 mTorr

118

D Field Pattern at 90° of Circumference

 

10.00

8.00

6.00

4.00

2.00

RADIAL E—FIELD — MEASURED POWER (mWatts)

IIIIIIIIILIII111111111111111111111111l111111111

 

 

 

0.00 IIITIIIIIIIIIIIIIIIIIIIIIIIIIIIIIFIIIII

0.00 2.00 4.00 6.00 8.00
HOLE POSITION FROM BOTTOM OF CAVITY (cm)

Input Power: 150 Watts Cavity Length (Ls): 9.35 cm
Reﬂected Power: Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm
Pressure: 50 mTorr Extension into Cavity (L9): 1.4 cm
Flow Rate: 95.1 scorn ECR Magnets: Present

Figure 5.13 - Longitudinal Electric Field Proﬁle for TB] 11 Mode at 50 mTorr

119

5.6 cm discharge without ECR magnets at a discharge pressure of 50 mtorr. These plots
also indicate a TE 11 mode ﬁeld pattern.

The ﬁeld plots for the 6.9 cm discharge without ECR magnets at 50 mtorr are pre-
sented in Figures 5.22 and 5.23. The ﬁeld plots taken at 5.08 cm and 7.62 cm from the bot-
tom of the cavity show the two lobe pattern. However, the ﬁeld plot taken at 2.54 cm from
the bottom of the cavity, which is the closest to the discharge, shows a possible four lobe
pattern. Note that this is a non-magnetic discharge so the impressed electric ﬁelds would
not be inﬂuenced by any magnetically generated anisotropy of the discharge. No indica-
tion of this type of four lobe pattern was observed in any of the other ﬁeld patterns
recorded. This type of ﬁeld pattern would normally be consistent with a TF4” type of cav-
ity mode, however T5211 is in cutoff for this cavity diameter. It may be possible that an
evanescent TE” waveguide excitation exists in the region of the discharge. However,
more investigation is necessary in order to determine the exact cause of this anomaly. The
longitudinal plot, shown in Figure 5.23, demonstrates a half wave sinusoidal dependence
observed in the other longitudinal plots presented for this mode.

It is observed that as pressure is increased from 1 mtorr to 50 mtorr for both 5.6 cm
and 6.9 cm discharge that the relative strength of the electric ﬁeld measured near the dis-
charge (the longitudinal sampling hole at 2.5 cm) is decreased. For example in Figure 5.8
the power measured at the 2.5 cm sampling hole was 68% of the maximum measured
along the cavity length. In Figure 5.10 the power measured at the 2.5 cm distance is 58%
of maximum. In Figure 5.12 the power measured at this sampling hole is 40% of the max-
imum. The ﬁeld plot in Figure 5.12 appears more symmetric on each side of its peak than

do the longitudinal plots in Figures 5.8 and 5.10.

120

Plots taken for the 6.9 cm discharge with magnets display a similar phenomenon. In
Figure 5.15 at 1 mtorr the power sampled closest to the discharge is 35% of the maximum
power measured in this plot. In Figure 5.17 at 10 mtorr the power sampled at the 2.5 cm
sampling hole is zero. In Figure 5.19 at 50 mtorr the power sampled at both 2.5 cm and
3.15 cm was zero.

From the data observed in this section we can conclude with a high degree of certainty

that the high Ls mode observed in the data from Chapter 4 is in fact the TB] 11 mode.

A500

52

*6

g

E

Q: 4.00

LL]

2:

O

Q.

Q

‘3; 3.00

I)

(D

<{

LLJ

2

' 2.00

O

__.I

LLJ

L?

LLJ

_, 1.00

s

Q

<

o:
0.00

O

b.LllllllllllllLJllllllllllLlllllllIllllliLlilllllll

121

:1 Field Pattern 2 inches from bottom of cavity
0 Field Pattern 1 inch from bottom of cavity

 

 

0 100.00
HOLE POSITION AROUND CIRCUMFRENCE OF CAVITY (DEG)

Input Power: 150 Watts
Reflected Power: 13 Watts

Discharge Gas: Argon
Pressure: 1 mTorr
Flow Rate: 23.9 socm

 

 

200.00 300.00

Cavity Length (Ls): 9.15 cm
Loop Length (L9): 3.45 cm

Discharge Height: 6.9 cm
Extension into Cavity (L9): 2.7 cm
ECR Magnets: Present

Figure 5.14 - 360° Circumferentail Electric Field Proﬁle for TE] 1] Mode at 1 mTorr

122

0 Field Pattern at 90° of Circumference
0 Field Pattern at 180° of Circumference

 

3.00

2.00

1.00

RADIAL E—FIELD ,— MEASURED POWER (mWatts)

llllllllllJLlllllllillLJlllIl

 

 

 

000 A A A4
. llllllllIIIIVIIIVIIYIIITTWTII‘lll‘lllYllIIIIIIIIIIIIIIIIIITTIT

0.00 2.00 4.00 6.00 8.00 10.00 12.00
HOLE POSITION FROM BOTTOM OF CAVITY (cm)

Input Power: 150 Watts Cavity Length (Ls): 9.15 cm
Reﬂected Power: 13 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 1 mTorr Extension into Cavity (Le): 2.7 cm
Flow Rate: 23.9 sccm ECR Magnets: Present

Figure 5.15 - Longitudinal Electric Field Proﬁle for TB, 1] Mode at l mTorr

123

0 Field Pattern 3 inches from bottom of cavity
1:! Field Pattern 2 inches from bottom of cavity
0 Field Pattern 1 inch from bottom of cavity

 

10.00

8.00

6.00

4.00

2.00

RADIAL E—FIELD — MEASURED POWER (mWatts)

 

 

 

0.00 D- ,3

0.00 100.00 200.00 300.00
HOLE POSITION AROUND CIRCUMFRENCE OF CAVITY (DEG)

Input Power: 150 Watts Cavity Length (Ls): 10.75 cm
Reﬂected Power: 17 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 10 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 45.4 socm ECR Magnets: Present

Figure 5.16 - 360° Circumferential Electric Field Proﬁle for TB] 11 Mode at 10 mTorr

124

13 Field Pattern at 90° of Circumference
0 Field Pattern at 180° oi Circumlerence

 

10.00

8.00

6.00

4.00

2.00

RADIAL E—FIELD — MEASURED POWER (mWatts)

111lllLllIllllllllllllLllllllllllllllllllllllllll

 

 

 

 

A
0.00 IIIIIIIIIIII IIYIIYIIIIIIIIIIITIIIIIIIIIIIIIVIIIIIIIIIIIIIII

0.00 2.00 4.00 6.00 8.00 10.00 12.00
HOLE POSITION FROM BOTTOM OF CAVITY (cm)

Input Power: 150 Watts Cavity Length (L3): 10.75 cm
Reflected Power: 17 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 10 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 45.4 sccm ECR Magnets: Present

Figure 5.17 - Longitudinal Electric Field Proﬁle for TB] 11 Mode at 10 mTorr

125

0 Field Pattern 3 inches from bottom of cavity
[:1 Field Pattern 2 inches from bottom of cavity
0 Field Pattern 1 inch from bottom of cavity

 

10.00

8.00

6.00

4.00

2.00

RADIAL E—EIELD — MEASURED POWER (mWatts)

lllA-lllllllllllllllllllllllllllllllllllll1111111

 

 

 

 

0.00 100.00 200.00 300.00
HOLE POSITION AROUND CIRCUMFRENCE OF CAVITY (DEG)

Input Power: 150 Watts Cavity Length (L9): 11.1 cm
Reﬂected Power: 8 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 50 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 87.5 sccm ECFl Magnets: Present

Figure 5.18 - 360° Circumferential Electric Field Proﬁle for TE 11 Mode at 50 mTorr

126

El Field Pattern at 90° of Circumference
0 Field Pattern at 180° of Circumference

 

10.00

8.00

6.00

4.00

2.00

RADIAL E—FIELD — MEASURED POWER (mWatts)

llllllllllllllllllll111111111111llllllilllillLlll

 

 

 

A
0.00 llllllllIIII‘IIIWIIIIITTrjjIII[IllIIIl—ITIIIIIIIIIIIIIIITrllr

0.00 2.00 4.00 6.00 8.00 10.00 12.00
HOLE POSITION FROM BOTTOM OF CAVITY (cm)

Input Power: 150 Watts Cavity Length (Ls): 11.1 cm
Reflected Power: 8 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 50 mTorr Extension into Cavity (La): 2.7 cm
Flow Rate: 87.5 sccm ECR Magnets: Present

Figure 5.19 - Longitudinal Electric Field Proﬁle for TB] 11 Mode at 50 mTorr

127

El Field Pattern 1inch from bottom of cavity

 

10.00

8.00

6.00

4.00

2.00

RADIAL E—FIELD - MEASURED POWER (mWatts)

 

_ . _ 41'
0 100.00 200.00 300.00
HOLE POSITION AROUND CIRCUMFRENCE OF CAVITY (DEG)

 

 

, I

0.00

b.LllllllillllllllllllillllllllJLlllllllllllilllLLll

0

Input Power: 150 Watts Cavity Length (LS): 6.33 cm
Reﬂected Power: 30 Watts Loop Length (L9): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm ‘
Pressure: 50 mTorr Extension into Cavity (L9): 1.4 cm
Flow Rate: 96.6 sccm ECR Magnets: Not Present

Figure 5.20 - 360° Circumferential Electric Field Proﬁle for TB, 11 Mode at 50 mTorr

128

0 Field Pattern at 90° of Circumference

 

 

 

 

.4500
B _
45 ...
g .-
E _
v -I
m -
LL] .I
a -
g -
10.00—
D a
m —1
D:
D —-4
“[2 ‘1
LIJ -I
E ..
I Z
9 —n
m 500--
E I
LL] _
_] —I
g _
O .1
<( _
m —I
0.00 TIIIIITIIITIITIIITIIIIIIIIITTIIITIIIIII
0.00 2.00 4.00 6.00 8.00

HOLE POSITION FROM BOTTOM OF CAVITY (cm)

Input Power: 150 Watts Cavity Length (Ls): 6.33 cm
Reflected Power: 30 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm
Pressure: 50 mTorr Extension into Cavity (L9): 1.4 cm
Flow Rate: 96.6 sccm ECR Magnets: Not Present

Figure 5.21 - Longitudinal Electric Field Proﬁle for TB] 11 Mode at 50 mTorr

129

0 Field Pattern 3 inches from bottom of cavity
0 Field Pattern 2 inches from bottom of cavity
0 Field Pattern 1 inch from bottom of cavity

 

10.00 - 3

8.00

6.00

4.00

2.00

RADIAL E—FIELD — MEASURED POWER (mWatts)

  
 

 

 

  

'P
'1 2
1:

IIIIIIITTIITIIY

0 100.00 200.00 300.00
HOLE POSITION AROUND CIRCUMFRENCE OF CAVITY (DEG)

.LAAIIIIIILIIIIIIIIIIIII111IILLIJLLIIILLLJLILthlLI

 

 

0.00
0

'0

Input Power: 150 Watts Cavity Length (Ls): 11.23 cm
Reflected Power: 15 Watts Loop Length (Le): 2.85 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 50 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 91.0 sccm ECR Magnets: Not Present

Figure 5.22 - 360° Circumferential Electric Field Proﬁle for TB] 11 Mode at 50 mTorr

130

El Field Pattern at 90° of Circumference
0 Field Pattern at 180° of Circumference

 

 

 

 

,_. 10.00 ﬂ

.‘9 -I

*6 1

3 2

f, :

a 8.00 E

LIJ ..

3 _

O I

0. _

P 3

E 6.00 :

D ..

(j) _.

< _.

m _

:2 1

' 4.00 E

3 1

LL] —1

LT Z

w E

<_z _

O I

< -

CK -

0.00-IIIIIITTIIIIr" " i
0.00 2.00 4.00 6.00 8.00 10.00 12.00
HOLE POSITION FROM BOTTOM OF CAVITY (cm)

Input Power: 150 Watts Cavity Length (Ls): 11.23 cm
Reflected Power: 15 Watts Loop Length (Lp): 2.85 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 50 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 91.0 sccm ECR Magnets: Not Present

Figure 5.23 - Longitudinal Electric Field Proﬁle for TE] 11 Mode at 50 mTorr

131

5.5.3 Spatial Field Patterns for the Low Ls Mode:

Electric ﬁeld pattern measurements for the Low Ls mode were performed for several
pressures in the 5.6 cm discharge where the Low Ls mode was known to exist. The power
measured by the microcoaxial probe was very low, in the range of O to 5 mWatts, com-
pared to power measured for the TEm mode, which was in the range of O to 25 mWatts.
This reduced power combined with the uneven thickness of the cavity wall made electric
ﬁeld measurements for the Low Ls mode inconsistent and less conclusive. Nevertheless,
these preliminary measurements seem to indicate that the Low Ls mode does not have a
two lobe circumferential pattern indicative of the TB”, mode. Some ﬁeld plots taken
demonstrated a ll? symmetric ﬁeld pattern possibly indicative of a TMOI waveguide mode.
Certainly, more accurate measurements must be performed to conclusively determine the

electric ﬁeld patterns for the Low Ls mode.

5.6 Correlation of Absorbed Power, Charge Density, and Internal E- Fields vs. Ls:

5.6.1 Description of the Experiment:

This was a preliminary experiment designed to investigate the inﬂuence of absorbed
power on plasma charge density and internal electric ﬁeld strength. The experimental
setup was prepared in the same way as described in Section 4.3. In this experiment three

parameters were investigated: 1) absorbed power, 2) ion saturation current, and 3) relative

132

electric ﬁeld strength. Absorbed power was determined from the reﬂected power measured
with a Hewlet Packard analog power meter (item 10 in Figure 5.2). Ion saturation current
was measured with a double Langmuir probe (item 4 in Figure 5.2) centered along the
cavity axis 1 cm downstream from the ECR magnets. For all experiments listed in this sec-
tion the Langmuir probe bias voltage was held constant at 40 Volts. Relative electric ﬁeld
strength was measured with a microcoaxial electric ﬁeld probe (item 1 in Figure 5.2).
Throughout this experiment the microcoaxial probe was kept at a ﬁxed location 1.75”
from the bottom of the cavity and 90° from the center of the screened window.

After the discharge was struck and the correct pressure was selected the experimental
measurements were taken. First the sliding short was set to its highest position at LS =
13.35 cm. Then it was gradually lowered. Simultaneous measurements of reﬂected power,
ion saturation current, and power sampled from the microcoaxial probe were taken at
selected points as the short length was decreased. Another set of measurements were then
recorded as the sliding short was raised from it’s lowest position. These measurements

were taken at 1 mtorr for both discharge chamber sizes with ECR magnets present.

5.6.1 Evaluation of a 5.6 cm Discharge with ECR Magnets at l mtorr:

Data from each of the three measurement variables taken at a discharge pressure of l
mtorr are plotted in Figure 5.24. The absorbed power curve is observed to have two max-
ima. The maxima near L8 = 5.6 cm was shown with ﬁeld pattern measurements to be the
Low Ls mode. The maxima near Ls = 8.5 cm is similarly found to be the TB” mode. The

two maxima on the absorbed power curve correlate well with the location of two maxima

133

also found on the ion saturation current curve. Note that the Isat maxima generated by the
Low Ls mode at LS = 5.6 cm is approximately twice the value of the maxima generated by
the TB” mode. Recall that the microcoaxial probe measures microwave power, thus data
plotted from the probe readings is proportional to the square of the impressed electric
ﬁeld. The relative electric ﬁeld measurements show that there are two electric ﬁeld max-
ima present. The E-ﬁeld maxima measured for the Low LS mode is very small compared
to the E-ﬁeld maxima found at the TB“ mode. Note that there is very little hysteresis

observed in any of the curves shown.
5.6.2 Evaluation of a 6.9 cm Discharge with ECR Magnets at l mtorr:

In Figure 5.25 each of the measurement parameters are plotted vs. Ls for a discharge
pressure of 1 mtorr. Individual plots of Pabs, 138,, Ed are shown in Figures 5.26, 5.27, and
5.28, respectively. From Figure 5.25 we see that there is one major maxima for all param-
eters at approximately L8 = 9.2 cm. Using E—ﬁeld pattern measurements this was found to
be the TB” mode. Note that the absorbed power curve shows some indication of another
maxima in the region of L8 = 6 cm that could possibly be due to the Low Ls mode. How-
ever, ﬁeld pattem measurements need to be made to conﬁrm this.

As seen in Figure 5.26 hysteresis is very pronounced for absorbed power in the range
of L8 = 8 cm to 10 cm. Notice that the highest maxima was reached while Ls was
increased. There is also hysteresis in absorbed power, shown in Figure 5.27, where the
highest maxima is also reached while increasing Ls. Finally, hysteresis is shown in relative

electric ﬁeld measurements as well, shown in Figure 5.28.

AP(Wotts), E— FlELD(O.1-ImWOtts), lON—SAT(I 00*microAmps

134

0 Data points taken while decreasing Ls
A Data points taken while increasing Ls

 

 

 

 

 
 

 

150-00 j l-ABSORBED POWER
- 2 - ION SATURATION CURRENT
: 3 - E-PROBE POWER
- 1
100.00 3
50.00 3
Z _.__. 3
- 2 /
_ , / ‘
Z ‘ \_ - I. - .- -
0.00— I ‘"
4.00 5.00 8.00 10.00 12.00 14.00

 

SLIDING SHORT POSITION — Ls (cm)

Input Power: 150 Watts Loop Length (L,,): 3.45 cm
Discharge Gas: Argon Discharge Height: 5.6 cm
Pressure: 1 mTorr Extension into Cavity (L9): 1.4 cm
Flow Rate: 27.8 seem ECR Magnets: Present

Figure 5.24 - Absorbed Power, Ion Saturation Current, and Probe Power vs. Ls

AP(Wotts), E—FIELD(O.1+mWOttS), lON—SAT(100*micrOAmps

135

0 Data points taken while decreasing Ls
A Data points taken while increasing Ls

 

 

 

 

150.00 : I-ABSORBED POWER
- 2 - ION SATURATION CURRENT
3 3 - E-PROBE POWER
1
1
.I '\
I00.00 -
1
50.00 4
I 3\ I"? ’
0.00: w“. -- -
4.00 6.00 8.00 10.00 12.00 14.00

SLIDING SHORT POSITION — Ls (cm)

Input Power: 150 Watts Loop Length (LP): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 1 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 23.9 sccm ECR Magnets: Present

Figure 5.25 - Absorbed Power, Ion Saturation Current, and Probe Power vs. Ls

ABSORBED POWER (Watts)

136

0 Data points taken while decreasing Ls
A Data points taken while increasing Ls

150.00

 

 

 

 

 

?
100.00—i
50.00%
000 if1'"‘1"T'IIITTTI'l""""'F""""IT“I'T'IT'I
4.00 6.00 8.00 10.00 12.00 14.00

SLIDING SHORT POSITION — Ls (cm)

Input Power: 150 Watts Loop Length (L9): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 1 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 23.9 secm ECR Magnets: Present

Figure 5.26 - Absorbed Power vs. Ls for a 6.9 cm Discharge at 1 mTorr

ION SATURATION CURRENT (100 a: micrOAmpS)

137

0 Data points taken while decreasing Ls
A Data points taken while increasing Ls

150.00

100.00

 

IIIIIIIIIJIIIIIIIILLILLILIIIII

 

 

50.00
0.00 ITIIIItIt]!IrTrIIIIIIIIItIIIIIIIIIIIITIWTIIIIITT]
4.00 6.00 8.00 10.00 12.00 14.00

SLIDING SHORT POSITION - Ls (cm)

Input Power: 150 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 1 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 23.9 secm ECR Magnets: Present

Figure 5.27 - Ion Saturation Current vs. Ls for a 6.9 cm Discharge at 1 mTorr

E—FIELD PROBE — MEASURED POWER (0.1 it mWatts)

138

0 Data points taken while decreasing L,
A Data points taken while increasing Ls

150.00

100.00

50.00

IIIIILLllIIIII11111141114111]

l

 

.0

o

o
I

4.00 6.00 8.00 10.00 12.00 14.00
SLIDING SHORT POSITION — Ls (cm)

Input Power: 150 Watts Loop Length (Lp): 3.45 cm
Discharge Gas: Argon Discharge Height: 6.9 cm
Pressure: 1 mTorr Extension into Cavity (L9): 2.7 cm
Flow Rate: 23.9 seem ECR Magnets: Present

Figure 5.28 - Electric Field Probe Power vs. Ls for a 6.9 cm Discharge at l mTorr

139

5.7 Conclusions:

In this chapter two sets of experiments were performed: 1) to determine the electric
ﬁeld patterns present for all resonances found in plasma cavity, and 2) to correlate the
behavior of absorbed power with that of plasma charge density and internal electric ﬁeld

strength. Conclusions made from these experiments are as follows:

i tt 'm

- The higher Ls of the two modes found in the cavity is conﬁrmed to be the TEm
cavity mode. The TEm mode was observed to produce similar circumferential
ﬁeld patterns for several conﬁgurations and pressures.

- As pressure is increased the ratio of: electric ﬁeld strength near the discharge to
maximum electric ﬁeld strength along the axis of the cavity, decreases.

- The internal electric ﬁelds produced in the Low Ls mode are very low compared
to the TE] 1] mode. Preliminary ﬁeld pattern measurements indicate a 4) symmetric
ﬁeld pattern for the Low Ls mode possibly indicative of a TMm waveguide mode.

”‘1”. aooor't'0W3 .! “Vans.” ‘1. '0 t'rai'

- For all conditions investigated the maxima of relative charge density vs. Ls
curves are found to correlate with the maxima of the absorbed power vs. Ls curves.

- The maxima in relative charge density vs. Ls is twice the value for the maxima in
relative charge density for the TE] 11 mode.

- Maxima in relative electric ﬁeld strength vs. Ls also correlates with absorbed
power curves, however electric ﬁeld strength for the Low Ls mode appears much
less than for the TE, 11 mode.

- Hysteresis is not observed for the 5.6 cm discharge chamber, but is observed for
the 6.9 cm chamber. Hysteresis is strongly correlated between absorbed power, rel-
ative charge density, and internal electric ﬁeld strength.

Chapter 6

Conclusions and Recommendations

6.1 Summary and Conclusions for this Investigation:

In this thesis the electromagnetic behavior of a compact ECR microwave plasma
source has been investigated over several input parameters. First the electromagnetic mode
behavior was mapped by recording reﬂected power curves vs. Ls for a range of pressures
and four different source geometries. From this mapping the existence and location of all
resonant modes was determined. Electric ﬁeld pattern measurements were taken in oder to
electromagnetically identify these modes. Relative charge density and internal electric
ﬁeld strength measurements were also taken to provide further information about the
modes observed and to better understand the correlation between absorbed power and
plasma charge density.

All experiments in this thesis were conducted with the plasma source described in
Chapter 2 using argon as the discharge gas. The 2.45 GHz incident microwave power was
held constant at 150 Watt for all experiments. The experimental input variables were: cav-
ity length LS, loop length LP, discharge pressure p, discharge chamber height h, and pres-
ence or absence of the multipole magnet ring. Flow rate was coupled to discharge pressure
in the system used. Output variables measured were: reﬂected power Pref, spatial electric

ﬁeld variation, internal electric ﬁeld strength, and relative plasma charge density.

140

141

The general conclusions for this investigation are as follows:

- The plasma source could be tuned to two distinct resonant modes.

- The ﬁrst mode was investigated with electric ﬁeld pattern measurements and was
determined to be the TEM mode. This mode was found to exist at all discharge
pressures and geometry conﬁgurations.

- The second mode (called the Low Ls mode) was more difﬁcult to conclusively
identify. Preliminary results suggest a (I) symmetric ﬁeld pattern indicative of a
TMOI mode. This mode had two signiﬁcant features: 1) it appears to produce twice
the charge density of the TB“ mode at the discharge pressure of 1 mtorr, and 2) it
has a broad Ls proﬁle making it less sensitive to tuning variations than the TE“
mode.

- The presence of the multipole magnet ring was shown to have two advantageous
effects: 1) it allowed a discharge to be sustained at pressures near 1 mtorr (most
likely due to ECR coupling) where the lowest pressure achievable without magnets
is 40 mtorr, 2) it improved the ability to sustain and match the discharge at pres-
sures of 40 and 100 mtorr.

- Three important observations were made in the comparison of two different
height discharge chambers: l) The Low Ls mode could always be observed with
the 5.6 cm discharge chamber and was not observed for most conditions with the
6.9 cm discharge chamber, 2) signiﬁcant hysteresis was observed with the 6.9 cm
discharge for pressures of 0.75 to 40 mtorr (with magnets) and very little hysteresis
was observed for the 5.6 cm discharge in the same range, and 3) at pressures over
40 mtorr without magnets the 6.9 cm discharge was shown to sustain a discharge
much better than the 5.6 cm discharge.

- Relative charge density of the discharge is strongly correlated with measured

absorbed power. Hysteresis of absorbed power is accompanied by a similar hyster-
esis in relative charge density and relative electric ﬁeld strength.

6.2 'h’ansmission Line Model of the Plasma Loaded Cavity:

The microwave plasma source described in Chapter 2 can be divided into four differ-
ent sections based on the modes of electromagnetic propagation in each section. See Fig-

ure 3.11. Section I begins at the z = 0 input plane and consists of a small diameter coaxial

142

feed line ending at the z = 21 plane (the plane of the sliding short). Section II consists of
the dual co-axial region formed by the loop antenna from the z = 21 plane to the z = z2
plane. Note that the dual coax is shorted at z = 22. Section III is the section of empty cylin-
drical waveguide from the z = 22 plane to the beginning of the plasma load at z = 23.
Finally, section IV begins at z = 23 and consists of a series of several short waveguide sec-
tions of different diameter surrounding the quartz discharge chamber that contains the
plasma load.

Section I can be modeled as a transmission line section, shown at the bottom of Figure
6.1, with characteristic impedance 20 = 50 9. Section II can be modeled as a transmission
line section with 20 = 2669. The characteristic impedance for section II was calculated
[27] assuming a dual coaxial line with outer conductor diameter of 9.8 cm and inner con-

ductor radius of 0.476 cm and inner conductor separation of 2.5 cm using the equation:

2 2
20 = 120{ln[2p(-1—_-Z—)-:l 4.2%.“ "4q2)} Eq 3.22

(1+q2) 16p

where p = s/d, q = s/D, sis the separation between dual center conductors, d is the diame-
ter of each center conductor, and D is the diameter of the outer conductor.

Section II] can be modeled as one individual or two parallel transmission line sections
depending on the mode or modes excited in the cavity. This 9.8 cm diameter waveguide is
capable of propagating the TE“ mode and the TM01 mode. Thus, either or both modes of
propagation can be represented as transmission lines. The transmission line representing

the TE“ mode has Z0 = 544.44 9 calculated with the relation:

143

Eq. 3.23

where 1'10 is the characteristic impedance of free space, a) is the radian frequency of micro-
wave radiation, and too is the cutoff frequency of the TB mode. Similarly, the transmission

line representing TMm has Z0 = 109.96 9 calculated with the relation:

we 2
ZTM ‘ “0 “(75) Eq. 3.24

Section IV, shown in Figure 3.11, the region of the plasma discharge can be modeled
as a lumped complex load impedance, Zplasma. The complex impedance of this load is
dependent on the properties of the discharge.

Note that this model does not include the effects of the abrupt discontinuities in the
propagation of electromagnetic waves from one section to the next. These discontinuities
give rise to evanescent modes that store energy in the vicinity of the discontinuity and may
in future models be represented by lumped parameter capacitors. However, more analysis
is required in order to add such elements to this model.

A few important dimensional variables of the plasma source must be identiﬁed. These
variables are shown just below the depiction of the plasma source in Figure 3.11. The vari-
able Ls represents the cavity length and is deﬁned as extending from the sliding short to
the bottom of the microwave cavity. Lp is the length of the adjustable loop antenna extend-
ing from the sliding short to the tip of the loop. L' is the section of empty waveguide

extending from the tip of the loop to the quartz dome of the plasma discharge. Lc is the

I
Section I Sectign II Section III Section IV
. I . I
Coaxral Coaxral l Empty Plasma
Transmission Loop Waveguide
Line Antenna I

I
I
I
Load :
I
I

|
|
|
l
I
|
I
|
I
I

 

 

 

N
E
53
3
re

0
.1

§

 

I———————q———

Figure 6.1 - Four Sections of the Plasma Source and Transmission Line
Equivalent Circuit

145

extension of the quartz discharge chamber into the cavity, deﬁned as the distance from the
top of the discharge chamber to the bottom of the cavity. For the two discharge chambers
used in this thesis L6 = 1.4 cm and L6 = 2.7 cm. Note that the length L8 is the sum of the
lengths LP, L', and Le. The variable h is the total height of the plasma discharge chamber.
For the two discharge chambers used in this thesis h = 5.6 cm and h = 6.9 cm.

Speciﬁc observations of the cavity tuning length for both modes under variations of
discharge pressure, discharge chamber height, magnetic ﬁeld, and loop antenna length are
given below:

- As discharge pressure is increased the cavity tuning length for both modes gener-
ally increases. The larger the increase in discharge pressure, the larger the increase
in cavity tuning length.

- Cavity tuning lengths for the 6.9 cm discharge are generally higher than for the
5.6 cm discharge, however the difference in tuning length can be smaller or larger

than the 1.3 cm difference in the height of the discharge.

- Very little change in the cavity tuning lengths of both modes was observed when
the multipole magnet ring was removed from the system.

- Cavity tuning length for both modes increases when the length of the adjustable
loop antenna is decreased. This supports the hypothesis that the loop antenna
forms a coaxial section at one end of the cavity. The wavelength of TEM propaga-
tion in a coaxial waveguide section is much shorter than for TE“ or TMm modes
in an empty 9.8 cm diameter waveguide. Thus, when the coaxial section is made
shorter by decreasing the length of the loop antenna the length of the empty
waveguide section must show a larger increase to compensate.

The transmission line model can be used to explain the observed tuning behavior of
the plasma source noted above. Changes in discharge pressure and discharge chamber
height change the complex impedance of the plasma load and therefore require a change

in length of the transmission line sections (section II ~ Lp or section III ~ L') in order to

146

maintain the conditions for resonance. When discharge pressure and discharge height are

held constant a change in Lp will require a compensating change in L' to maintain the con-

ditions for resonance.
6.3 Recommendations for Future Research:

For all experiments in this thesis the input power was held constant at 150 Watts.
Plasma properties such as charge density are greatly effected by changes in input power,
thus behavior of the plasma source could be much different for input power levels above
and below 150 Watts. Any future investigation of this source should include observations
of output variables for variation in input power. A variation from 50 Watts to 250 Watts
would be a useful range to investigate.

Variation in the ﬂow rate of the discharge gas may also cause a change in the behavior
of the plasma source. Therefore, evaluation of this source on a vacuum system where pres-
sure and ﬂow rate can be independently varied may also provide a morecomplete descrip-
tion of source behavior.

In this thesis an end fed adjustable loop antenna was used to couple mieorwaves into
the 9.8 cm diameter cavity applicator. For this applicator other types of microwave cou-
pling should be investigated, such as: end fed probe coupling and side fed probe coupling.
Smaller diameter applicators that only propagate the TB” waveguide mode should also be
investigated with: adjustable end feed loop coupling, end feed probe coupling, and side
feed probe coupling.

The primary unanswered question in this thesis is the origin of the Low Ls mode.

147

Future investigation should be directed at understanding what causes this phenomenon. A
primary tool in this investigation will be the detailed measurement of electric ﬁeld mode
patterns and absolute electric ﬁeld strength. Very sensitive electric ﬁeld measurement
techniques may be needed to determine the ﬁeld patterns of the Low LS mode. Absolute
electric ﬁeld strength measurements will also be valuable in assessing the electromagnetic
losses in the walls of the cavity applicator and losses in the discharge.

Other experimental measurements that have yet to be performed on this plasma source
are: single Langmuir probe electron energy distribution measurements, ion energy analy-
sis, measurement of plasma potential, and measurement of radical ﬂux with a quartz crys-
tal microbalance.

An objective in all MPDR research is to develop a working physical model encom-
passing both electromagnetic and plasma theory that accurately predicts (qualitatively and
quantitatively) the behavior of compact and larger diameter microwave plasma disk reac-
tor designs. Development and testing of the physical model should involve computer sim-
ulation of the plasma sources investigated using the proposed model. A fully developed
physical model would aid in the operation and control of present microwave plasma sys-
tems and also serve as a guide in the design of new microwave plasma sources with
improved performance characteristics.

The research presented in this thesis was intended to contribute to this goal of a predic-
tive physical model, however much more investigation will be required to develop and ver-

ify a reliable theoretical model.

LIST OF REFERENCES

[1]

[2]

[3]

[4]
[5]
[6]
[7]

[8]

[9]

REFERENCES

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149

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Wﬁmhws

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[20] L Mahoney. W
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