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Numerical analysis and experimental measurements of material loadings in cylindrical microwave cavity applicators

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NUMERICAL ANALYSIS AND EXPERIMENTAL MEASUREMENTS OF
MATERIAL LOADINGS IN CYLINDRICAL MICROWAVE CAVITY
APPLICATORS
By
Kadek Wardika Hemawan
A THESIS
Submitted to
Michigan State University
In partial fulfillment of the requirements
For the degree of
MASTER OF SCIENCE
Department of Electrical and Computer Engineering
2003
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UMI Num ber: 1417847
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ABSTRACT
NUMERICAL ANALYSIS AND EXPERIMENTAL MEASUREMENTS OF
MATERIAL LOADINGS IN CYLINDRICAL MICROWAVE CAVITY
APPLICATORS
By
Kadek Wardika Hemawan
The primary objective o f this thesis is to develop an understanding o f the
variation o f cylindrical cavity applicator eigenfrequencies versus different material
loadings and to determine the best electromagnetic coupling and efficient heating
modes to treat silicon wafers, graphite fibers and the magnetic materials. The material
loaded applicator complex eigenfrequencies were first determined numerically by
using the Ansoft HFSS and then were experimentally measured in the laboratory.
The electromagnetic mode excitations that were particularly useful in heating the
selected materials were identified and analyzed. This investigation utilized a seveninch length and probe tunable cylindrical cavity applicator excited with 2.45GHz
microwave energy.
Using the Ansoft numerical analysis results, low power measurements were
conducted at power levels o f less than 25 mW to locate and measure the desirable
electromagnetic mode characteristics for both empty and material loaded cavities.
Based on the numerical analysis and the low power experimental results, a high
power heating process cycle was developed. The engineering design methodology
developed in this investigation, i.e. numerical analysis, low power mode identification
and measurement, and then high power heating process development, can be applied
to aid in the development o f heating processes for a wide variety o f material loads.
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To
the memory of my father, Nyoman Nada Wid
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ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my major advisor, Dr. Jes
Asmussen, for providing opportunity, guidance, editorial, technical suggestions
and encouragement during the course of this research. Along with my advisor, I
would like to thank Dr. Timothy A. Grotjohn and Dr. Donnie K. Reinhard for
serving on my advisory committee. Additional thanks are given to Stanley Zuo
for valuable assistance and Dr. John Hinnant for proof reading the manuscript.
Finally, I would like to thank my family as well as my friends for their support
and understanding throughout my study.
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TABLE OF CONTENTS
LIST OF TABLES............................................ .................................................................. vii
LIST OF FIGURES..............................................................................................................viii
Chapter 1
INTRODUCTION
1.1 Literature Review............................................................................................................ 1
1.2 Motivation for Research................................................................................................. 4
1.3 Research Objectives........................................................................................................6
1.4 Thesis Outline.................................................................................................................. 7
Chapter 2
THEORY OF CIRCULAR CAVITY APPLICATOR
2.1 Introduction...................................................................................................................... 9
2.2 Microwave Circular Cavity Applicator.......................................................................... 9
2.3 The Empty Seven-Inch Cavity Applicator.................................................................... 15
Chapter 3
EXPERIMENTAL SYSTEMS
3.1 Introduction...................................................................................................................... 24
3.2 The Experimental Microwave Cavity Applicator..........................................................25
3.3 Experimental Microwave Systems.................................................................................31
3.3.1 Low Power Coupling Systems..................................................................... 31
3.3.2 High Power Coupling Systems.................................................................... 32
Chapter 4
NUMERICAL FINITE ELEMENT SIMULATIONS
4.1 Introduction...................................................................................................................... 34
4.2 A Brief Review of Ansoft HFSS...................................................................................34
4.3 Complex Eigenfrequencies of a Cylindrical Applicator Loaded with
a Silicon Wafer........................................................................................................35
4.3.1 TM 012 mode..................................................................................................... 37
4.3.2 TMin mode..................................................................................................... 42
4.3.3 TEin Mode..................................................................................................... 46
4.3.4 Resistivity variation in TM012 mode............................................................... 50
4.3.5 Summary of Important Observations............................................................. 52
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4.4 Complex Eigenfrequencies of a Cylindrical Applicator Loaded
with Magnetic Material............................................................................................. 54
4.4.1 TM 012 mode...................................................................................................... 54
4.4.2 TEn2 mode....................................................................................................... 60
4.5 Complex Eigenfrequencies of a Cylindrical Applicator Loaded with Graphite..........65
4.5.1 Eigenmodes solutions......................................................................................65
Chapter 5
EXPERIMENTAL PROCEDURES AND RESULTS
5.1 Introduction..................................................................................................................... 75
5.2 Empty Cavity Experiments............................................................................................ 76
5.3 Silicon Wafer Experiments............................................................................................ 77
5.3.1 Low Power Measurements Procedure............................................................77
5.3.2 Low Power Measurements Results................................................................78
5.3.3 High Power Heating Experimental Procedure.............................................. 82
5.3.4 High Power Heating Experimental Results................................................... 83
5.4 Magnetic Material Experiments.....................................................................................83
5.4.1 Low Power Measurements Procedure............................................................84
5.4.2 Low Power Measurements Results................................................................. 85
5.4.2.1 Stage I .............................................................................................. 85
5.4.2.2 Stage I I ............................................................................................. 88
5.4.3 High Power Heating Experiments Procedure................................................ 91
5.4.4 High Power Heating Experiments Results......................................................91
5.4.4.1 Stage I ............................................................................................. 91
5.4.4.2 Stage II ............................................................................................ 98
5.4.4.3 Summary of Important Observations.............................................105
5.5 Graphite Fiber Experiments.............................
106
5.5.1 Low Power Measurements Procedure.......................................................... 106
5.5.2 Low Power Measurements Results............................................................... 106
5.5.3 High Power Heating Experimental Procedure..............................................108
5.5.4 High Power Heating Experimental Results..................................................108
Chapter 6
SUMMARY AND RECOMMENDATIONS
6.1 Summary of results........................................................................................................110
6.1.1 Numerical Analysis using Ansoft HFSS......................................................110
6.1.2 Experimental Measurements of the Material Loadings.............................. 112
6.2 Recommendations for Future Research........................................................................116
APPENDICES......................................................................................................................114
REFERENCES...............................................
120
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LIST OF TABLES
Table 2.1 -
Selected roots of the Bessel Function......................................................... 16
Table 2.2 -
The eigenmodes and resonance frequencies
for the seven-inch cavity.............................................................................18
Table 4.1 -
The eigenmodes, resonance frequencies, and quality factor
for the seven-inch cavity loaded with graphite material
(Ls =14.4 cm, load radius = 2 mm)............................................................66
Table 5.1-
Fixed resonant frequency of empty cavity
Table 5.2 -
Fixed cavity height of empty cavity............................................................ 73
.......................................72
Table 5.3
Stage II Low power measurements without quartz
tube using TEm mode.................................................................................87
Table 5.4 -
Graphite (16 cm) loaded cavity experiments with
a fixed cavity height.................................................................................... 102
Table 5.5 -
Graphite loaded cavity experiments with a fixed
resonance frequency 16 cm.........................................................................103
Table 5.6 -
Graphite fibers load with a length of 12 cm
at a fixed frequency..................................................................................... 103
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LIST OF FIGURES
Chapter 2
Figure 2 .1 -
Lumped-element equivalent circuit of the microwave
cavity resonator............................................................................................. 11
Figure 2.2 -
A parallel RLC lumped-element equivalent to a microwave
cavity resonator............................................................................................. 14
Figure 2.3 -
Quality factor measurement using sweep oscillator marker........................15
Figure 2.4 -
Resonant mode chart for the seven-inch circular cavity..............................17
Figure 2.5 -
Electric field distributions of TE211 TMno,TMni modes........................... 21
Figure 2.6 -
Electric field distributions of TEon,TEii2 )TMoi2 modes............................ 22
Figure 2.7 -
Electric field distributions of TEon.TMm.TEan modes............................ 23
Chapter 3
Figure 3.1(a) - The seven-inch microwave cavity applicator apparatus............................26
Figure 3.1(b) - The seven-inch microwave cavity applicator with all components..........27
Figure 3.2 -
Side feed cavity applicator apparatus cross-section for
the silicon wafer and magnetic material Stage 1......................................... 27
Figure 3.3 -
Improved design of the microwave reactor for the
magnetic material stage II experiments.......................................................29
Figure 3.4 -
Side feed cavity applicator apparatus cross-section
for the graphite fibers experiments..............................................................30
Figure 3.5 -
Low power diagnostic experimental system................................................31
Figure 3.6 -
High power heating experimental network 1................................................33
Figure 3.7 -
High power heating experimental network II...............................................33
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Chapter 4
Figure 4.1 -
Resonance frequencies of the silicon wafers at various heights................ 38
Figure 4.2 -
Quality factor of the silicon wafers at various heights............................... 38
Figure 4.3 -
Electric field patterns for three-inch and four-inch silicon
wafers at 5,10, and 15 mm pedestal heights in TM 012 .............................. 40
Figure 4.4 -
Electric field patterns for three-inch and four-inch silicon
wafers at 30, 35.5, 60, and 71 mm pedestal heights in TM012 ....................41
Figure 4.5 -
TMi n resonance frequencies of empty, three-inch, and
four-inch silicon wafers............................................................................... 43
Figure 4.6 -
TMi 11 quality factor of empty, three-inch, and four-inch
silicon wafers................................................................................................ 43
Figure 4.7 -
Electric-field patterns for three-inch and four inch silicon
wafers at 5,10, and 17 mm pedestal heights in T M m ...............................44
Figure 4.8 -
Electric field patterns for three-inch and four-inch silicon
wafers at 28.25, 56.5, and 85 mm pedestal heights in T M m .................... 45
Figure 4.9 -
TEi 11 resonance frequencies of the empty cavity, three-inch,
and four-inch silicon wafers......................................................................... 47
Figure 4.10- TEi n quality factor of the empty cavity, three-inch, and
four-inch silicon wafers................................................................................47
Figure 4.11- Electric-field patterns for three-inch and four inch silicon
wafers at 5, 10, and 17 mm pedestal heights in T E m ................................48
Figure 4.12 - Electric field patterns for three-inch and four-inch silicon
wafers at 30, 34, and 60 mm pedestal heights in TEi 11..............................49
Figure 4.13- Resonance frequencies of the three-inch silicon wafer
when resistivity varied in TM012 mode..........................................................51
Figure 4.14- Quality factor of the three-inch silicon wafer when
resistivity varied in TMo 12 mode.................................................................51
Figure 4.15 - Resonance frequencies of the magnetic material in TM012 mode.............56
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Figure 4.16-
Quality factor of the magnetic material in TM012 mode........................... 56
Figure 4.17-
Electric field patterns for the TM 012 on magnetic material
for 5, 13, and 18 load heights....................................................................... 57
Figure 4.18-
Electric field patterns for the TM 012 on magnetic material
for 23, 33, and 43 load heights..................................................................... 58
Figure 4.19-
Electric field patterns for the TM012 on magnetic material
for 53, 63, 73, and 83 load heights...............................................................59
Figure 4.20 -
Resonance frequencies of the magnetic material in TEi 12 mode..............61
Figure 4.21 -
Quality factor of the magnetic material in TE 112 mode.............................61
Figure 4.22 -
Electric field patterns for the TM012 on magnetic material
for 5, 13, and 18 load heights....................................................................... 62
Figure 4.23 -
Electric field patterns for the TM012 on magnetic material
for 5, 13, and 18 load heights....................................................................... 63
Figure 4.24 -
Electric field patterns for the TE 112 mode on magnetic
material for 5, 73, and 83 load heights.........................................................64
Figure 4.25 - Resonance frequencies of the graphite fibers for
the 2 mm load radius....................................................................................71
Figure 4.26 - Quality factor of the graphite fibers for the 2 mm load radius..................71
Figure 4.27 - Electric field patterns for mode 1, 2, 3, and 4 of
the graphite fibers with 2 mm load radius.................................................. 72
Figure 4.28 - Electric field patterns for mode 5,6, 7, and 8 of
the graphite fibers with 2 mm load radius.................................................. 73
Figure 4.29 - Electric field patterns for mode 9, and 10 of the
graphite fibers with 2 mm load radius.........................................................74
Chapter 5
Figure 5.1 -
Resonance frequencies of silicon wafers with fixed cavity
height in the TM 012 mode............................................................................ 79
Figure 5.2 -
Coupling probe depth of silicon wafers with fixed cavity
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height in the TM012 mode............................................................................ 79
Figure 5.3 -
Cavity heights of silicon wafers with fixed frequency
in the TM 012 mode........................................................................................80
Figure 5.4 -
Coupling probe depth with fixed frequency in the
TM012 mode.................................................................................................. 80
Figure 5.5 -
Resonance frequencies on various pedestal height, h
using TM012 mode.........................................................................................86
Figure 5.6 -
Quality factor on various pedestal height, h using TM 012 mode...............86
Figure 5.7 -
Coupling probe depths on various pedestal height, h
using TM 012 mode.........................................................................................86
Figure 5.8 -
Resonance frequencies on various pedestal height, h
using TE 112 mode..........................................................................................88
Figure 5.9 -
Quality factor on various pedestal height, h using TEm mode................ 88
Figure 5.10 - Coupling probe depths on various pedestal height, h
using TE 112 mode.......................................................................................... 88
Figure 5.11- Cavity shorts, Ls, on various pedestal height, h
using TM 012 mode......................................................................................... 89
Figure 5.12- Coupling probe depths, Lp, on various pedestal height, h
using TM 012 mode......................................................................................... 89
Figure 5.13-
Quality factor, Q on various pedestal height, h using TM 012 mode.......... 89
Figure 5.14 -
Cavity shorts, Ls, on various pedestal height, h using TEn2 mode.......... 90
Figure 5.15- Coupling probe depths, Lp, on various pedestal height, h
using TE 112 mode..........................................................................................90
Figure 5 .1 6 -
Stage I cavity lengths versus time using TM012 mode.............................. 96
Figure 5.17 -
Stage I coupling probe depth versus time using TM012 mode..................97
Figure 5 .1 8 -
Stage I cavity lengths versus time using TEi 12 mode............................... 98
Figure 5 .1 9 -
Stage I coupling probe depths versus time using TEi 12 mode..................98
Figure 5.20 - Stage II exp4 sample heating time vs. temperature.................................. 103
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Chapter 1
INTRODUCTION
1.1 Literature Review
Recently, the use of microwave energy to process various materials effectively and
efficiently has increased and has become an important technology.
However, this
technology cannot be utilized to its full potential without a more fundamental
understanding of the sophisticated interaction between the cavity applicator, the
electromagnetic fields and the material loads. Depending on the material loads, incident
microwave energy can be transmitted, reflected, or absorbed during the heating process.
When microwave energy penetrates into a dielectric material, the electric fields excite
translation and vibration motions of free or bound charges and cause internal volumetric
heating. Many rigorous techniques of analyzing cylindrical cavity applicators loaded
with various dielectric materials have been studied and developed [1-2, 4-7]. Examples
include permittivity measurements and microwave heating.
Microwave heating
applications has been established as an efficient heating technique in terms of heating
time, energy needed and controllability of the heating process. In the 70s microwave
heating was employed mainly for food processing industry and a few for the heating of
solid materials. Nowadays, microwave energy and associated cavity applicators have
been used widely for heating composites, semiconductors and biological materials, and
for the excitation of plasma sources.
Booske et al. [21] has performed various
temperature measurements on silicon wafers using microwave energy.
Moreover,
compared to thermal heating, microwave heating has numerous advantages in heating
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applications, such as, compact heating applicators, fast heating rate because of direct
coupling of electromagnetic energy into the material molecules, through volumetric
heating, and also it has process controllability advantages.
At Michigan State University, cylindrical cavity resonators loaded with numerous
material loadings have been developed and studied since the mid 1980’s by Asmussen et
al. [4-8]. These cavity applicator investigations have produced numerous publications as
well as many patents and the potential technologies are currently used by many industries
for their own applications.
Finzel [4] used the resonant cavities to study coupling
efficiencies on ethylene glycol and teflon whereas Frasch [5] employed low power to
determine the effect on the cavity applicator as the loading sample volume was changed.
Manring and Jow [6, 6b, 7] conducted an investigation of single-mode resonant cavity
microwave heating of solid nonreactive materials, and performed dielectric materials
measurements such as nylon, wet wood, and epoxy/amine resins. Uniform microwave
heating was achieved by combining microwave and thermal methods during the heating
process. They concluded that for some applications resonant single mode microwave
heating has advantage of the multimode microwave resonant structure.
Multimode
heating has limited usefulness in some applications, which require the understanding of
electromagnetic/material interactions, precision control, or very high heating efficiency
[2]. It has also been reported in the literature that a single mode tunable microwave
cavity has several advantages compared to a conventional microwave oven [10]. For
example, a tunable cavity has a wide range of resonant frequencies and hence many
potential electromagnetic heating modes, and has high quality factors, which are useful
for permittivity measurements.
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Employing a microwave cavity applicator as a plasma source for both high and low
pressuresmicrowave discharge experiments
has demonstrated
the possibility of
producing plasma torch, ion beam, etching, and plasma assisted (CVD) diamond
synthesis [11, lib ]. This plasma source design which is also commonly known as the
Microwave Plasma Disk Reactor (MPDR™) employs on resonant cylindrical cavity,
coupling probe and sliding short to replace the rectangular wave guide and triple stub
tuner to enhance the coupling efficiency and reduce the tuning complexity.
It is clear that an important element of microwave process development and system
design is the ability to model electromagnetic interactions.
solutions
Nowadays, numerical
are considered to be as important as analytical solutions for many practical
electromagnetic problems.
These typically require extensive
use of computers,
convergence time and careful formulation of the problems. Grotjohn et al. [12], used the
FDTD numerical modeling method to simulate geometrically complex microwave
resonant
cavity structuresfor material processing.
Manring
and Asmussen [2]
numerically calculated Q and resonant frequency for a cavity applicator loaded with lossy
filaments and rods.
electromagnetic model
One of their findings from the investigation using
the
is that the electric fields that are impressed tangential to the
electric boundary couple better than electric fields that are perpendicular to the boundary.
There are several
fundamental techniques that are commonly used in
the
electromagnetic fields computation such as the method of moment, the Rayleigh-Ritz
method, the finite element method, and the finite-difference method.
The numerical
method used in this thesis is the finite element method. This technique was developed
originally for problems in structure mechanics. However, in recent years it has been
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applied to many other physical problems, which include radio frequency (RF) and
microwave components, antennas and arrays, high-speed integrated circuits (ICs), printed
circuit boards (PCBs) and IC packages.
1.2 Motivation for Research
Despite the many numerous past investigations and applications of microwave
energy, a precise knowledge of how the microwave heating takes place inside the
coupling applicators is still poorly understood. This is in part because material loads are
often of irregular shape and have unknown and non-uniform material properties and as
the temperature increases during the processing, the material load properties vary in an
unknown fashion.
Additionally, as the heating takes place and material properties
change, this leads to the changes of the heating mode fields in an unknown fashion.
Finally, it is often believed that certain materials such as semiconductors (silicon wafers),
graphite fibers, metal, etc. are difficult if not impossible to heat. Thus it is clear that the
microwave heating of materials is still a poorly understood process, and hence, there is a
need to develop combined experimental and analytical intuitive process “to engineer” the
microwave applicator design and to understand the microwave heating process itself.
The research in this thesis addresses the problem:
given an unknown or poorly
understood material or a difficult to heat material, how does one go about designing an
optimum heating process? Thus, in this thesis an experimental/analytical methodology
was developed to determine how to heat unknown and difficult to heat materials. The
process utilizes the simple cylindrical, tunable microwave cavity applicator technology
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patented by MSU investigators. See for example U.S. Patent 4, 777, 336,4,792,772, and
5,008,506. The simple, cylindrical nature of the cavity allows commercially available
numerical analysis software packages to be readily applied to analyze the material load
cavity. Each electromagnetic mode is numerically identified and then the material loaded
electromagnetic fields, resonant frequencies, and loaded Q are calculated. They then can
be calculated versus material properties, size, shape, and location.
By observing the
changing in Q, Af (the change in resonant frequency) and the variation of the electric
field patterns versus material properties and material position, “good” and “bad” heating
modes can be determined from the simulations.
Then an experimental process is applied to determine the best heating method. Using
the results of the numerical analysis, the material loads are placed in the experimental
cavity applicator and excited with low microwave power experiments.
The resonant
frequencies o f the “good” and “bad” microwave heating modes are then located and then
loaded Q, resonant frequencies, EM field patterns are then checked against the analytical
calculations. Based on these experiments, specific “good” modes are then chosen for
high power heating experiments.
High power heating experiments are then performed and the cavity coupling
parameters, such as the changes in cavity height (ALs), the coupling probe depth (ALp),
Af (change in resonant frequency), AQ (change in quality factor), and material
temperature (AT) are observed. During the experimental heating tests, additional cavity
loaded material modeling can be performed and the material properties versus heating,
applicator walls losses, can be estimated, thereby achieving a better understanding of
experimentally observed heating processes. Finally, using the knowledge of how the
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material properties are changed versus temperature, a numerical analysis of the heating
versus cavity size, mode, wall materials, can be carried out and then the optimized
microwave coupling applicators can be designed to optimize the heating process.
In this thesis, this process is developed and applied to several specific material loads.
The loads were chosen, in part, for their heating difficulty and also their potential for
commercial application.
Several material loads are evaluated: (1) silicon wafers, (2)
graphite fibers, and (3) unknown magnetic materials.
Each of these materials has a
simple cylindrical shape, i.e. a wafer, disk, or a very thin cylindrical filament. Thus the
shapes match with the shape of the cylindrical applicator.
This allows for efficient
numerical modeling and also simple experimental evaluation.
1.3 Research Objectives
The primary objective of this thesis is to develop an experimental/analytical
methodology to enable the design of optimum microwave material processing applicators
and systems, to develop an understanding of the variation of cylindrical cavity applicator
eigenfrequencies versus different material loadings and to determine the best coupling
positions to heat the silicon wafer, graphite fiber and the magnetic material loads most
efficiently. To achieve these goals, the pedestal height, which holds the material load,
was varied. The objective of varying the pedestal height is to find the best height to
achieve the lowest Q. By finding the lowest Q, the material is in the best position to be
heated. In addition to finding Q, the resonance frequency of the cavity was also
investigated.
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The material loaded applicator complex eigenfrequencies are first determined
numerically by using the Ansoft HFSS software package and then are experimentally
measured in the laboratory. The electromagnetic mode excitations that are particularly
useful in heating the selected materials are identified and analyzed. This investigation
utilizes a seven-inch cylindrical cavity excited with microwave frequencies around 2.45
GHz.
The material loads used during this study are various sizes of silicon wafers,
graphite fibers, and a magnetic material with different electrical properties.
The objective of the numerical analysis is to develop a model of the cylindrical cavity
applicator loaded with dielectric materials given specific cavity applicator geometry and
electrical properties of the loading materials. Based on this model, the eigenfrequencies,
the quality factor, and the eigenmodes field patterns are investigated and used as a
foundation for optimum initial heating positions in the high power experiments. The
objective of the experimental measurements is to compare and study the simulation
model result with the low power experiments and eventually design and develop high
power heating experiments techniques for efficient microwave coupling and optimum
heating o f the silicon wafer, the magnetic material, and the graphite fibers.
1.4 Thesis Outline
The main parts of this thesis include: theory of circular cavity applicator, discussion
of a numerical finite element method using the Ansoft HFSS software package, a
description of the experimental system, a presentation of experimental measurements
procedures and results, and the conclusions drawn from this investigation. In chapter 2,
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the theoretical background of circular cavity applicator is presented. In chapter 3, the
experimental systems are described. These include the seven-inch cavity applicators for
the silicon wafers, magnetic material, and the graphite fibers low and the high power
microwave system networks. In chapter 4, the simulation model of the cylindrical cavity
applicator with loaded material using Ansoft HFSS is given. The chapter begins with a
brief introduction to the software program. This is followed by the empty cavity problem
set up with its solution. Then material loaded cavity simulation problems set up which
consists of silicon wafer, magnetic material, and graphite fiber are presented followed by
the solutions to their complex eigenfrequencies versus material size and position.
Presentation of the experimental procedures and results begins in chapter 5 where the low
power measurements and the high power heating experimental procedures are conducted
using several modes and a single mode respectively. In the low power measurements, the
cavity length, the resonance frequency, and the material loaded Q experimental data are
presented and discussed. Chapter 6 concludes the thesis with a summary of the work of
the numerical simulations and the experimental measurements and also recommendations
for future research.
Attached in the appendices are the mechanical drawings of the
various parts of the microwave cavity applicator, such as brass plug, and quartz tube
chimney. Also, included in the appendices are the resistivity table which was used to
compute the silicon wafer’s conductivity, placement set up of the silicon wafer inside the
cavity applicator, pyrometer set up for the unknown magnetic material, and quart tube
connection set up for the graphite material. Some of the figures presented in this thesis
are in color.
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Chapter 2
THEORY OF CIRCULAR CAVITY APPLICATOR
2.1 Introduction
This chapter describes the theoretical background of a circular cylindrical cavity
resonator. It is intended to give a brief review and to gain a better understanding of the
electromagnetic wave behavior inside a microwave cavity applicator. The theoretical
background discussed in this chapter covers the following:
i)
A lumped-element equivalent circuit of the empty cavity applicator
ii)
Quality factor, which is commonly known as Q
iii)
Formulation of the electromagnetic mode chart between resonance frequency
versus cavity length
iv)
Field patterns that exist in an ideal empty cavity applicator
2.2 Microwave Circular Cavity Applicator
A microwave cavity applicator is essentially an enclosed conducting segment of a
waveguide with closed end faces. A conducting short termination at each end of the
waveguide causes the incident waves to bounce back and forth along its length
repeatedly. This type of waveguide structure is commonly known as a cavity resonator.
The conducting metal tube of circular cavity applicator usually has a uniform circular
cross section. The general electromagnetic propagating waves along straight, uniform
cross section, guiding tubes can be divided into transverse electromagnetic (TEM),
transverse magnetic (TM), and transverse electric (TE) waves. However, for the circular
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cavity applicator, only the TM and TE waves can propagate because it is a single
conductor waveguide. The TEM waves cannot exist in a single conductor hollow or
dielectric filled waveguide of any shape [13-14]. Both the TM and TE modes have
characteristic cutoff frequencies, i.e. frequencies below which mode propagation cannot
take place. If the mode frequencies are below the cutoff frequency then the mode waves
will decay and cannot propagate along the cavity axis.
Conversely, if the wave
frequencies are above the cut off frequencies then the electromagnetic mode will
propagate and the power will be transmitted along the guide axis.
Since a microwave cavity applicator is a resonant waveguide, its operation can be
understood using a lumped-element resonant circuit. It can be modeled either by a series
or parallel RLC lumped-element circuit [18]. As an example, a lumped-element and a
parallel RLC equivalent circuits are presented here to better understand the concept of
resonance and quality factor in a microwave cavity.
Figure 2.1 shows the equivalent circuit of cavity applicator, which is connected
via a transmission line. The cavity is treated here without a material load, i.e. it is empty
and is excited at a single mode resonance. Yg denotes the microwave generator source
admittance.
Zo is the intrinsic impedance of the transmission line, Zjn is the input
impedance to the microwave cavity at the reference plane Zo, m represents an ideal
transformer of turns ratio of the coupling probe and the cavity fields, jX is the reactance
and susceptance due to the coupling probe. Lc and Cc are the equivalent inductance and
capacitance of the cavity respectively, and Gc is the conductance due to ohmic losses in
the cavity walls.
10
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Zo
c a v ity
a p p lic a to r
Lc
source
feed
transmission
line
cavity applicator
Cc
Gc
circuit
Figure 2.1 - Lumped-element equivalent circuit of the microwave cavity resonator
Yg = microwave generator source admittance
Zo = intrinsic impedance of the transmission line
Zin = input impedance to the microwave cavity at the reference plane Zo
m : 1 = ideal transformer of turns ratio of the coupling probe and the cavity fields
jX = reactance and susceptance due to the coupling probe
Lc, Cc, Gc = inductance, capacitance, and conductance lumped elements
11
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The elements of the equivalent circuit of the microwave cavity can be expressed as
Zc oc - JJ jju0\H\2dv
2
v- v.
C c oc -
JJ J f 0|E \2 dv
2
(magnetic field stored energy)
(1)
(electric field stored energy)
(2)
(wall loses)
(3)
V -V '
Gc 00 R
s
The input impedance of the empty cavity system looking into the reference plane Z0 in
Figure 2.1 is given by
Zm_ r . + J W ' - W ' K K+JXm
(4)
Where Pt is total time average power coupled into the cavity, Wm and We are the
time average stored magnetic and electric energy in the cavity, co is the radian microwave
excitation frequency, and Io is the input current on the coupling probe at the reference
plane Zo. The Rjn and jXjn are the real resistive and imaginary reactive terms of the Z-m
respectively. This complex impedance is the microwave cavity input impedance sensed
by the feed transmission line from at the Zo reference plane. At resonance, when the time
average magnetic and electric stored energies or equal to each other, and then the input
impedance becomes purely resistive.
In terms of matching condition of the cavity resonator, the reactance and the
resistance o f the input impedance can also be expressed as
Z in = m\ (— ) + j ( X + ------ ^
\
' Gc
coLc + co LcCc
12
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(5)
V}
The diagonal arrow drawn in Figure 2.1 indicates that they are variable.
The input
impedance of the cavity can be varied by making adjustment of either the cavity length,
which results in the changes of Lc, Cc, Gc, and jX, or coupling probe depth, which results
in the changes of m and jX. These adjustments can make the cavity matched to the input
transmission line, i.e. it makes the input reactance equal to zero and resistance,
R jn
equal
to intrinsic impedance of the transmission line, Zo.
A cavity resonator stores electromagnetic energy in the electric and magnetic
fields for each field pattern. Since the cavity walls have a finite conductivity, which
means that there is a nonzero surface resistance, and the resulting power loss causes a
decay of the stored energy. Quality factor, Q, of a microwave cavity resonator is given
by [13-14,18]
(total energy stored)
Q = w (average power loss/second)
(6)
(7)
Thus Q is a measure of the electromagnetic energy loss per cycle of the resonator circuit.
Lower loss implies a higher Q. For the parallel resonant circuit of Figure 2.2, in the
absence o f any loading effects caused by external circuitry, the unloaded Q, Qun is a
characteristic of the resonant cavity itself. Also, due to the fact that Wm = We at
resonance, give
(8)
13
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Resonant
circuit
Q
RL
Zin
J
L
Figure 2.2 - A parallel RLC lumped-element equivalent to a microwave cavity resonator
In practice, if a resonant circuit is coupled to other external load, R l, in parallel
RLC circuit, the effective resistance in equation 8 is RRl/(R+Rl), shown in Figure 2.2
Then the loaded Q, Ql can be expressed as
RRL / (R + R L) _ 0)oL | co0L
coaL
R
(9)
R,
If we define an external Q, Qext, as
O - ^
V ext
for parallel circuit
conL
(10)
Therefore the loaded Ql can be expressed as
Ql
Qun
( 11)
Qe-
It can be inferred from equation 11 that the loaded Q is a function of the degree of
coupling between the resonant circuit and the external circuitry. Also, since a quality
factor is a measure o f the bandwidth of the resonator, Q can be defined as
(12)
Qi =
/* -/>
14
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fO z e r o r e f l e c t e d
p o w e r line
f O is t h e r e s o n a n c e
f r e q u e n c y = 2 , 4 5 GHz
f l and f2 a re th e h a lf
power point
f 2
fl
absorp
power
Figure 2.3 - Quality factor measurement using sweep oscillator marker
Shown in Figure 2.3 is the sweep frequency versus reflected power line used for
quality factor calculation, fr and
£2
are the half power points of the absorption power
curve and fo is the resonance frequency which is equal to 2.45 GHz. When the absorption
power reaches the zero reflected power, all the incident power is absorbed by the cavity.
Equation 12 was used to calculate the quality factor during the experiments in the
laboratory.
2.2.1 The Empty Seven-Inch Cavity Applicator
As discussed earlier, the electromagnetic field propagation for each waveguide
can be divided into transverse electric (TE) and transverse magnetic (TM). Each of these
modes has a natural eigenfrequency that exists in the cavity. This natural eigenfrequency
is a sinusoidal steady-state solution of Maxwell’s equations that exists at certain
frequency, which is also commonly known as the resonant frequency. For an empty,
15
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perfectly conducting, cylindrical cavity applicator, the natural eigenfrequency is
governed by the following equations [14-16]
(13)
(14)
Where b and Ls are the radius and length of the cylindrical cavity, Xnp and Xnp'
correspond to the p* zeros of the Bessel functions Jn and J 'n. For TM modes, the indices
n, p and q may be any integer value and only n and q are allowed to be zero. The indices
n, p, and q for TE modes may be any integer value but only n is allowed to be zero.
Some values of the Bessel function are given below:
Table 2.1 - Selected roots of the Bessel Function
Roots of J,
Roots of J',
Xoi = 2.405
X 02 = 5.520
X u = 3.832
Xi2 = 7.016
X'oi = 3.832
X ' 02 = 7.016
X '„ = 1.814
X ' 12 = 5.331
The empty circular cavity applicator, either rectangular or circular has an infinite
number of discrete, real, natural frequencies, generally called electromagnetic modes.
Each of these electromagnetic modes has an individual electromagnetic focus and a
distinctive field pattern. Both equations 13 and 14 imply that the resonance frequency for
an electromagnetic mode depends on the cavity radius and cavity length. A seven-inch
(17.78 cm) diameter microwave cavity applicator was used during this study.
16
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Shown in Figure 2.4 is the mode chart for the seven-inch cavity with a radius of
8.89 cm. The mode chart is useful in determining the frequency range over which a
particular resonance can be tuned without interference from other modes. This mode
chart corresponds to plotting the frequency versus the cavity length using both equations
13 and 14. The resonant frequencies in this chart were calculated for the cavity lengths
within the range of 6 cm to 21 cm. The actual cavity length was adjustable and it can be
set to a certain height, which at a specific excitation has frequency corresponds to a
particular eigenmode. Since the operating frequency for this thesis research is 2.45 GHz,
the resonant frequency range was swept from 1.8 to 3.2 GHz to observe possible
eigenmodes that exist in the empty cavity. As can be seen from the mode diagram, T E m ,
T M on, TE2n ,
TMin and TE 0n (degenerate mode), T E n 2, TM012, TE311, TE212, and TE113
modes can be excited for the seven-inch cavity resonator when operating at 2.45 GHz.
3.2E+09
TE212
TE311
3.0E+09
TE113
2. 2.8E+09
TE211
® 2.6E+09
2.4E+09
TM111 &TE011
g 2.2E+09
TM012
TE112
2.0E+09
TE111
1.8E+09
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Cavity Length (cm)
Figure 2.4 - Resonant mode chart for the seven-inch circular cavity with diameter of
17.78 cm
17
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Given a cavity length, one can also use the Ansoft software (see chapter 4) to
calculate the eigenfrequencies that exist in the cavity aplicator. Described below is the
empty cavity simulation with the following problem setup: cavity height and radius were
set to 14.4 cm and 8.89 cm, material property was equal to vacuum, cavity boundary
conditions was a perfect conductor, permittivity and permeability was set to
1,
initial
frequency was equal to 1.95 GHz. The empty cavity simulation results were used as a
benchmark check to make sure that the simulation results were close to the theoretical
approximations.
In Table 2.2, nine eigenmodes are displayed and identified with their
corresponding resonance frequencies.
Using the electrical field patterns, which are
displayed in Figures 2.5-2.7, identification of the transverse magnetic and transverse
electric fields modes are possible. In addition to the field patterns, the eigenmodes are
determined by comparing the resonance frequencies obtained from the simulation and the
theoretical calculation using equations 13 and 14. The eigenmodes obtained from the
simulation match with the eigenmodes displayed in the mode chart in Figure 2.4.
Table 2.2 - The eigenmodes and resonance frequencies for the seven-inch cavity (Ls =
14.4 cm)
Eigenmodes
Frequency (GHz) simulation Frequency
(GHz)
calculation
results using Ansoft HFSS
results using Equations 13-14
1.96251
1.9431
Mode 1 = TE211
2.0581
Mode 2 = TMno 2.07995
2.3133
Mode 3 = T M m 2.32668
2.32761
2.3133
Mode 4 = TEon
2.33081
2.3326
Mode 5 = TE 112
2.4501
Mode 6 = TM 012 2.46705
Mode 7 = TE311
2.50443
2.4851
2.67340
2.6515
Mode 8 = TE212
2.7584
Mode 9 = TM210 2.77377
18
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As can be seen in Table 2.2, both the simulation and calculation resonance
frequencies are very close, with absolute error of less than 1 %. Thus the simulation
results are in close agreement with the theoretical results.
The electromagnetic field distributions within a cylindrical circular perfectly
conducting cavity applicator are governed by equations 15 and 16 [14, 18-19] listed
below. The tangential component of the electric field is equal to zero at the conducting
wall boundaries.
For the TM modes, the transverse magnetic waves do not have a
component of the magnetic field in the direction of propagation, i.e. Hz = 0, but have
axial electric fields, i.e. Ez j- 0. Likewise for the TE modes, the transverse electric waves
do not have a component of the electric field in the direction of propagation, Ez = 0, but
have axial magnetic fields, Hz ^ 0.
TM mode,
Where
r cos(n0)cos
(15)
Eoz = amplitude of the electric field
J„ = Bessel function of the first kind
Xnp = pth x value at which Jn(x) = 0
n = number of periodicity in <j>direction (n=0 ,l ,2 ,...)
p = number of zero fields in radial direction (p=l ,2 ,3 ...)
q = number of half waves in axial direction (q = 1 ,2 ,3 ...)
TE mode,
Where
r cos(n^) sin
H oz
= amplitude of the magnetic field
Jn = Bessel function of the first kind
X'np = p* x value at which Jn’(x) = 0
19
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(16)
n = number of periodicity in (j) direction (n= 0 ,l, 2 ,...)
p = number of zero fields in radial direction (p=l ,2,...)
q = number of half waves in axial direction (q = 1 ,2,3...)
Figure 2.5, 2.6, and 2.7 show the field distribution patterns for various TM and
TE modes in an empty 17.78 cm diameter. These field patterns were obtained from the
Ansoft HFSS simulation results. These electric field patterns solutions reveal the spatial
electric and magnetic fields distribution within the cavity applicator. The electric field
patterns are plotted in two different plane (XY and YZ planes) cross sections to allow the
easier identification of the eigenmodes since the distributions of the electromagnetic
fields are functions of angular, radial, and axial positions. Red, orange, green, and blue
color is the plot of the electromagnetic field intensity. The red color of the electric field
pattern indicates that the electric field concentration is greater than the orange, green or
blue color. The blue color spots indicate that the electric field in this area is very weak.
An eigenmode is a natural resonance frequency of the cylindrical cavity
applicator.
Some of the eigenmodes, namely the
T M npo
modes are equal to the
waveguide cut off frequencies meaning that there is no length dependence in the z
direction of the field. Also, some of the eigenmode are dipole modes. For example, the
T M j io
mode is a dipole mode.
For the empty cavity simulation, a perfect conductor is chosen for the boundary
condition in order to simplify the numerical solution. This result the Q equal to infinity.
Furthermore, for time-varying electromagnetic waves the tangential component of an
electric field should be zero at the surface of the cavity walls.
20
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TE211
TE211
TM! 10
TM 110
TMin
TMin
Figure 2.5 - Electric field distributions of TE211 T M n o ,T M m modes
21
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TM 0 12
TM 012
Figure 2.6 - Electric field distributions of TEon,TEi 12, TM012 modes
22
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T M 2io
T M 2 io
Figure 2.7 - Electric field distributions of TEoii,TMih;TE 3 h modes
23
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Chapter 3
EXPERIMENTAL SYSTEMS
3.1 Introduction
The experimental systems consisted of seven-inch cavity applicator and
associated microwave networks. The seven-inch cavity applicator used during this study
was a side feed cavity applicator. It is described in more detail in section 3.2. The
microwave networks consisted of a low power diagnostic coupling system and a high
power heating experimental transmission network. The low power microwave circuit set
up utilized a function sweep generator, circulator, oscilloscope, and a cavity applicator.
The purpose of the low power experiments was to provide an experimental system
calibration prior to the high power heating experiments. The high power heating set up
can be divided into two microwave systems, Stage I and Stage II. Stage II microwave
network set up is a modification of the Stage I transmission network.
The main
difference between the two stages is that in Stage II, there are additional components,
such as, nitrogen gas, argon gas and a pyrometer for temperature measurements.
24
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3.2 The Experimental Microwave Cavity Applicator
Figures 3.1(a) and 3.1(b) display photographs of the microwave cavity applicator
employed in the experiments. Figure 3.1(a) displays the seven-inch cavity main system
while Figure 3.1 (b) shows the cavity applicator with all of its associated components.
Figure 3.2, Figure 3.3, and Figure 3.4 display cross sectional views of the several
cylindrical microwave cavity applicators employed in this investigation. It is a side feed
cavity applicator. The cavity applicator can be operated either manually or automatically.
In this research, the cavity length and coupling probe depth were adjusted manually.
As depicted in Figure 3.2, the microwave side feed cavity applicator consisted of
a section of circular wave-guide with shorting plates located at each end. These plates
are perpendicular to the wave-guide axis. The top shorting plate, which is referred to as
the sliding short, is adjustable allowing the cavity length, Ls, to be varied. In order for
the sliding short to maintain contact with the cavity walls, it is ringed with silver fingerstock. The sliding short is rigidly suspended by three threaded rods from a plate that is
attached to the top of the wave-guide with removable bolts. The bottom short plate is
removable, allowing for the insertion of material into the cavity for processing.
As
shown in Figure 3.2-3.3 a snout with a two-inch diameter wide provides an opening an
outlet for the gases or smoke during the heating process.
In order to couple the
microwave energy into the cavity, an adjustable coaxial probe of length, Lp, is inserted
through a cylindrical port in the cavity sidewalls. The 50-Ohm coaxial coupling probe
has an inner diameter of 0.965 cm and an outer diameter 2.52 cm in diameter. As shown
in the Figure 3.1-3.4, an observation window was located on the side of the cavity
applicator to allow visual viewing of the material while heating the material load.
25
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Figure 3.1(a) - The seven-inch microwave cavity applicator apparatus
26
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Figure 3.1(b) - The seven-inch microwave cavity applicator with all components
27
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■cavity s n o u t
c a vity
wall
to p
p la te
silve r
f inger s
co u p lin g
Ls
po
V
silicon
w a fe r
L,
'
viewing
window
q u a rtz
ped e sta l
Figure 3.2 - Side feed cavity applicator apparatus cross-section for the silicon wafer and
magnetic material Stage I
28
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Figure 3.3 displays the modifications of the microwave cavity applicator required
for heating the unknown magnetic material. The new design consisted of a quartz glass
tube, a modified brass base plate plug, and a brass block. The quartz glass tube surrounds
the material excitation zone. It acts as a chimney that allows the smoke produced during
high power heating to stream out of the cavity chamber into an exhaust hood. The brass
plate plug has two holes in it as shown in Figure 3.3. The center hole is to enable the
measurement of material temperatures while the other hole is to allow the injection of
nitrogen gas. The pyrometer probe tip is inserted axially through a small tight-fitting
threaded hole as shown in Figure 3.3 into the center of the brass plug. The brass block,
which is located underneath the brass base plate, is used to hold and mount the
pyrometer. See the appendices section for further detailed drawings of the brass plug,
quartz tube chimney, and the brass block.
Shown in Figure 3.4 is a cross section of microwave cavity applicator used for
heating the graphite fiber load. Brass plugs at each end of the top and bottom plates were
installed to replace the top snout and the temperature access hole that were used for the
magnetic experiments. A 3.2 mm hole is located in the center of each of the brass plug,
which allows the insertion of the quartz tube.
The quartz tube has inner and outer
diameter of 2 mm and 3 mm respectively. Graphite fibers are inserted inside the quartz
tube via a thread and a needle. The filled quartz tube was then placed axially in the
center and along the cavity applicator axis. The bottom end of the quartz tube was glued
to a quarter-inch plastic tube using an epoxy and the plastic tube was then attached to a
T-shaped swage lock connector. This allows the argon gas flow into the tube during the
heating process o f the graphite fibers. See appendices for photograph.
29
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cavity
cavity
snout
wa l l
top
plate
silver
f inger s
quartz
tube
coupling
port
Ls
quartz
dish
viewing
wi ndow
quartz
crucible
brass
plug
tem perature
a c c e s s hole
nitrogen
Figure 3.3 - Improved design of the microwave reactor for the magnetic material stage II
experiments
30
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cavity
wa l l
brass
plug
top
plate
silver
f inger s
quartz
tube
coupling
port
Ls
graphite
fibers
brass
plug
gas
swagelock
connector
inlet
Figure 3.4 - Side feed cavity applicator apparatus cross-section for the graphite fibers
experiments
31
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3.3
Experimental Microwave Systems
The experimental microwave systems can be divided into two microwave circuits.
The first one is the low power diagnostic coupling system and the second is the high
power heating system. Each of these microwave systems is describe in the following
section.
3.3.1
Low Power Coupling Systems
Shown in Figure 3.5 is the low power heating experimental system.
The
microwave power source was a Hewlett Packard 8350B Sweep Oscillator connected to a
three-port circulator (UTE Microwave, CT-3695-N). A 50-Ohm coaxial cable was used
to connect the incident power via the circulator into the cavity applicator (Wavemat BK4443). The reflected signal was rectified by a crystal detector (RF ID 9931 model 50D-1)
and displayed on X-Y oscilloscope (Tektronix 2215A 60 MHz).
Circulator
Microwave
Sweep
Function
Generator
Pin
Microwave
Cavity
Applicator
Pref
Crystal
Detector
Oscilloscope
Figure 3.5 - Low power diagnostic experimental system
32
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3.3.2
High Power Coupling Systems
Shown on Figure 3.6 is the high power heating experimental system I. This
microwave system network was used for the silicon wafers and Stage I magnetic material
experiments. The microwave power oscillator (Micro-now Instrument Co. Inc model
420B1 or Opthos) was connected directly into the circulator. A 30-dB directional coupler
was used to measure the incident power and a 20-dB directional coupler was used to
sense the reflected power. The reflected signal was fed into a matched load (coaxial
resistor model 8201). Both the incident and the reflected power were measured using HP
435A power meters, which are connected to HP 8481A thermistor power sensors.
The actual incident and reflected power were calculated using the following
formula:
Where
Pin
Pin or P ref
={10 exp [K/l 0]} x
= Power incident (W),
P ref
(17)
P meter
= Power reflected (W), K = Total attenuation
(incident power = 51.5 dB and reflected power = 29.5 dB),
P meter =
Power meter reading
(mW). The high power heating experimental system II is shown in Figure 3.7. This
microwave system network was used for the graphite fibers and Stage II magnetic
material experiments. It is similar to the microwave system I with the exception of an
additional pyrometer to measure the temperature of the magnetic material, and an inlet to
pass gases over the magnetic material and graphite fibers. The pyrometer (Raytek, MTB
model) with a temperature range of 200° to 1,200° C was mounted on the bottom base
plate of the cavity applicator. In the magnetic material experiments, nitrogen gas was
injected through the gas inlet port on the bottom base plate of the cavity floor to keep O2
from entering into the heated material while in the graphite experiments, used argon gas
to prevent the O2 from entering into the heated fibers.
33
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Incident
Attenuator
Circulator
pin
r—^
^
M
e
P ow er
t
e
r
P ow er Sensor
M icrow ave
M icrow ave
P ow er
Oscillator
Cavity
Directional Coupler
I
Applicator
Directional Coupler
Load
Attenuator
P ow er Sensor
Figure 3.6 - High power heating experimental network I
Incident
Attenuator
Circulator
pin
p
_
*
^
Power
Meter
Power Sensor
Microwave
Microwave
Power
Oscillator
Directional Coupler
Applicator
Pref
Directional Coupler
Load
Pyrometer
— b Y V V V W iAttenuator
Power Sensor
Figure 3.7 - High power heating experimental network II
34
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Gas Tank
Chapter 4
NUMERICAL FINITE ELEMENT SIMULATIONS
4.1 Introduction
An important first step in the engineering design methodology developed in this
thesis is to identify “good” electromagnetic modes for coupling input microwave power
into the material. The initial mode identification can be made from experiments and
know-how o f the investigators.
However, most potential users have little of any
microwave technologies experience or education. Performing a numerical simulation of
the material loaded applicator can facilitate this mode selection.
In the simulation
process the numerical results replace the required experience and know-how.
The
numerical simulation search for the material loaded cavity eigenfrequency. Once the
eigenfrequency is located and identified then loaded Q, resonance frequency,
electromagnetic field patterns are determined. Good heating modes are then identified
and the exact cavity dimension can be determined for 2.45 GHz heating excitation.
Numerous numerical simulations were performed to determine the good heating
modes for silicon wader, graphite, and magnetic material loads examples considered in
this thesis research.
Thus, this chapter only presents representatives numerical
calculations. Each o f the examples can be examined in greater details. However, this is
left for follow-on research investigations. This chapter describes the use of Ansoft HFSS
for numerical analysis of the material loaded cavity applicators. Each problem is initiated
with the set up parameters and then followed by its solution.
The numerical results
consist of resonance frequencies, quality factors, and electromagnetic field patterns for
each eigenmode. Representative examples of these calculations are given in section 4.2
35
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to 4.5. In section 4.2 a brief review of Ansoft HFSS is presented, in section 4.3 the cavity
applicator is loaded with both three-inch and four-inch silicon wafers. In the silicon
loaded simulation, three different modes were simulated, the TM 012 , TM m, and the TEm
modes. The silicon wafer resistivity variation is simulated in the TM 012 mode. In section
4 .4
the cavity applicator material load is an unknown magnetic disk shaped material.
Simulation for two modes, i.e. the TM 012 and the TEn 2 modes, are presented in 4.4.
Finally, in section 4.5 the graphite fiber simulation is presented. Two different radii of
the same material were simulated. Each of the material loaded cavities was searched for
the lowest ten eigenmodes that exist in the cavity applicator.
4.2 A Brief Review of Ansoft HFSS
Ansoft HFSS is a software package for calculating the electromagnetic behavior
of a structure. Examples of the electromagnetic behavior computations are characteristic
port impedances, propagation constant, scattering parameters, near and far field radiation,
and eigenmodes. Ansoft HFSS is commonly used in microwave applications, millimeterwave and wireless devices such as antennas, microwave transitions, launchers, wave­
guide components, RF filters, and three-dimensional discontinuities. In this research,
Ansoft HFSS was used to compute the following:
i) Applicator eigenmodes ii) natural resonant frequencies iii) quality factor of the material
loaded cavities and iv) electromagnetic fields patterns for different resonant frequencies
inside the cavity. The numerical results of these simulations were used to identify the
good heating modes and also can be employed to help understand the high power
material heating experiments.
36
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Introduced in 1990, Ansoft HFSS is the first commercial software tool to simulate
complex 3D geometries. Ansoft HFSS is a finite element method (FEM), which means
the geometric model is automatically divided into a large number of tetrahedra, where a
single tetrahedron is basically a four-sided pyramid. Dividing a structure into thousands
of smaller regions or elements allows the system to compute the field solution separately
in each element. The smaller the system elements, the more accurate the final solution
will be.
Ansoft HFSS program runs both under Windows and Unix operating systems.
The simulation in this thesis was done using the Sun Solaris UNIX based workstations
located in the engineering computer laboratory under Division of Engineering Computing
Service (DECS), Michigan State University. The general procedure of the simulation
includes the drawing of the geometric model, assigning the material properties of the
drawn model, setting up boundary conditions, specifying the solution, and analyzing the
simulation results.
When specifying solution, one has to determine the initial sweep
frequency, number of eigenmodes, and number of iteration passes for convergence.
Analyzing solution includes recording the resonance frequency, Q and plotting the
electric or magnetic fields patterns. The numerical result in Ansoft HFSSS is called the
eigenmode solutions. Furthermore, the solution is referred to a complex eigenfrequency
because o f the real and imaginary solution of the resonance frequency and quality factor.
37
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4.3 Complex Eigenfrequencies of a Cylindrical Applicator Loaded with a Silicon
Wafer
Three different excitation modes were simulated for the silicon wafer material
load.
They were identified as the TM 012 , TM m, and the TEm modes.
The mode
nomenclature was chosen because of electric and magnetic field intensities, field patterns,
and eigenfrequencies were close to the empty cavity mode simulations.
The resistivity of the silicon wafer is determined by using the resistivity versus
dopant concentration graph (see appendix 4). The silicon wafer has n type doping with
1015 cm ' 3 electron concentration. Given the resistivity of the silicon, the electric loss
tangent can be calculated using the following formula:
a
(18)
= -
P
S
<7
E0£ r
C08a£ r
loss tan gent = ------= --------
(19)
The general problem set up for the silicon wafer load consisted of the following
procedure: i) the excitation mode was first determined; ii) the cavity height was then
calculated using the cavity length equation, iii) the cavity model was then drawn with a
fixed cavity length and radius, iv) once the material load properties and boundary
conditions are assigned, the geometric model then simulated to generate solutions.
The output parameters for each mode of the silicon wafer simulation are Af
(change in resonant frequency), AQ (change in quality factor), and AE (change in the
electromagnetic field patterns) versus h (material height position inside the cavity),
silicon wafer diameters (three-inch and four-inch), and silicon wafer resistivity.
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.1 TM on mode
The following are the problem setups for the empty and silicon loaded cavities:
the cavity height was set to 14.4 cm while the cavity radius was equal to 8.89 cm. The
cavity material property was assigned as vacuum, the cavity walls were assigned to be
aluminum, and end plates were brass. The initial sweep frequency was set to 2.4 GHz. It
was found that for the loaded T M o n mode, the resonance frequency was equal to 2.47405
GHz. Thus, the initial sweep must be assigned below 2.47405 GHz to guarantee that the
mode is around 2.45 GHz.
Both the three-inch and four inch silicon wafers were
assigned with the following properties: silicon thickness was set to 0.038 cm, permittivity
was equal to
12
farad/meter, permeability was set to
1
henry/meter, conductivity was
equal to 1/3 siemen/cm, electric tangent loss was set to 0.204 using equation 19. The
silicon wafer was placed at seven different heights inside the cavity as follows: 5 mm,
8
mm, 15mm, 30 mm, 35.5 mm, 60 mm, and 71 mm.
Figures 4.1-4.2 display the resonance frequency and quality factor while Figures
4.3-4.4 depict the electric field patterns inside the silicon wafer at resonance. The electric
field patterns for each pedestal height inside the silicon wafer are plotted in a normalized
scale from magnitude of -0.0182001 V/m to 2.2214 V/m. By plotting the electric filed
patterns in normalized scale fashion, the electric field intensity changes at each pedestal
height can be examined. Since the YZ cross-section is the same as shown in Figure 2.52.7, all plots are displayed only in the XY plane cross-section. These cross sections are
plotted through the silicon wafer and each of the solution describes the electric fields at
the resonant frequency. The plot on the left and the right side is for the three-inch and the
four-inch silicon wafers respectively.
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3Jnch_silicon
2.475E+00
c 2.460E+00
0
10
20
30
40
50
60
70
80
Pedestal Height (mm)
Figure 4.1 - Resonance frequencies of the silicon wafers at various heights for the TM 012
mode (Ls = 14.4 cm)
^
S |
£
s
§
c
® E
O =5
8.0E+03
7.0E+03
3_inch_silicon
■ — 4_inch_silicon
6.0E+03
5.0E+03
4.0E+03
3.0E+03
2.0E+03
1.0E+03
0.0E+00
0
10
20
30
40
50
60
70
80
P edestal H e ig h t (m m )
Figure 4.2 - Quality factor o f the silicon wafers at various heights for the TM 012 mode
(Ls = 14.4 cm)
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The effects that the silicon wafers on the frequency and the quality factor are the
two main observations. Loading the cavity with silicon wafers disrupts the electric and
magnetic fields slightly. The eigenfrequency for the empty cavity is 2.46705 GHz (see
Table 2.2), whereas the eigenfrequency for the loaded cavity is 2.44971 GHz.
The
change in frequency, Af, is equal to 17.34 MHz. The introduction of the silicon wafer
and the quartz pedestal perturb the cavity resonator. Given a cavity at resonance, the
average stored magnetic and electric energies are equal. If a small perturbation is made
inside the cavity, this will in general change one type of energy more than the other, and
resonant frequency would then shift by an amount necessary to again equalize the
energies. The lowest quality factor for the loaded cavity is 293 and 871 at pedestal height
35.5 mm for the four-inch and three-inch respectively. By loading the cavity with silicon
wafer, at a height of 35.5 mm, it only changed the eigenfrequency slightly but changed
the quality factor dramatically. The wavelength of the cavity is 14.4 cm and 35.5 mm is
approximately a quarter wavelength. Thus, in this mode, it can be inferred that the
optimal position for the silicon is one quarter of a wavelength from the cavity bottom
plate. When the TM 012 mode is being excited with a cavity height equal to 14.4 cm, the
electric fields inside the cavity are tangential to the silicon wafer. With the electric fields
tangential, it means that strong surface currents are induced on the silicon. The electric
loss tangent of the silicon affects the strength of these surface currents. The higher the
electric loss tangent, the lower the Q and the easier the material is to heat. These surface
currents create a Joule heating effect, which quickly heats the material.
In the electric field patterns below, since the YZ cross-section is the same as
shown in Figure 2.5-2.7, all plots are displayed only in the XY plane cross-section.
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Three-inch silicon wafer
Four-inch silicon wafer
Pedestal height 5mm
Pedestal height 5mm
Pedestal height 10mm
Pedestal height 1Omm
Pedestal height 15mm
Pedestal height 15mm
Figure 4.3 - Electric field patterns for three-inch and four inch silicon wafers at 5, 10,
and 15 mm pedestal heights in TM 012 (Ls = 14.4 cm, cross section through the wafers)
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pedestal height 30mm
Pedestal height 30mm
Pedestal height 35.5mm
Pedestal height 35.5mm
Pedestal height 60mm
Pedestal height 60mm
Pedestal height 71mm
Pedestal height 72mm
Figure 4.4 - Electric field patterns for three-inch and four-inch silicon wafers at 30, 35.5,
60, and 71 mm pedestal heights in TM012 (Ls = 14.4 cm, cross section through the wafers)
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.2 TMni mode
The problem setup for the silicon load cavities using the TM m is as follows:
cavity height was
set to 11.3 cm, cavity radius was equal to 8.89 cm.The material
property was assigned as vacuum, cavity boundary condition for the walls was set to
alum inum while the ends plate were equal to brass. The initial frequency was swept up
from 2.4 GHz.
The silicon wafer has the following material load properties: silicon
thickness equal to 0.038 cm, silicon resistivity was equal to 3 Ohm-cm, permittivity was
equal to 12 farad/m, and permeability was set to 1 henry/m. A three-inch and four-inch
silicon wafer were simulated, the pedestal material was quartz glass, the pedestal outer
radius was set to
2 .8 6
from 5 to 10 to 17
cm, and the pedestal height was varied inside the cavity applicator
to 28.25 to 56.5 to and to 85 mm.
Shown in Figure 4.5 and Figure 4.6 are plots of the cavity Qand resonance
frequency versus the pedestal height for the three-inch and four-inch silicon wafers using
TM m
mode. Both the three-inch and four-inch silicon wafers behave similarly. The
frequency shifts lower because the silicon wafer and the quartz glass position are moved
around inside the cavity. The cavity quality factor also changes with varying pedestal
height. The lowest Q was found at pedestal height 56.5 mm for both the three-inch and
four-inch silicon wafers equal to 372 and 316 respectively. At this height, which is about
a half wavelength, the silicon wafer can be heated most efficiently. Compared to the
TM012
mode, these Q are slightly higher.
As shown in Figure 4.7-4.8, the electric field patterns for each pedestal height is
plotted through the silicon wafer with a constant scale of electric field magnitude from
V/m to 1 V/m.
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
^
2.47E+00
N
x
|
3
4_inch_silicon
3_inch_silicon
g . 2.46E+00
2.45E+00
£ 2.44E+00
u.
O 2.43E+00
«
o 2.42E+00
W
0>
“
2.41 E+OO
0
10
20
30
40
50
60
70
80
90
Pedestal Height (mm)
Figure 4.5 - T M m resonance frequencies of the three-inch and four-inch silicon wafers
(Ls = 11.3 cm)
4.00E+03
3_inch_silicon
4Jnch_silicon
3.50E+03
j- aT 3.00E+03
o v>
0 |
2.50E+03
>, "55 2.00E+03
1 |
1.50E+03
° S
1.00E+03
5.00E+02
0.00E+00
0
20
40
60
80
Pedestal Height (mm)
Figure 4.6 - T M m quality factor of the three-inch and four-inch silicon wafers
(Ls = 11.3 cm)
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
Three-inch silicon wafer
Four-inch silicon wafer
Pedestal height 5 mm
Pedestal height 5 mm
Pedestal height 10 mm
Pedestal height 10 mm
Pedestal height 17 mm
Pedestal height 17 mm
Figure 4.7 - Electric-field patterns for three-inch and four inch silicon wafers at 5, 10, and
17 mm pedestal heights in TMi n (Ls = 11.3 cm, cross section through the wafers)
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pedestal height 28.25 mm
Pedestal height 28.25 mm
Pedestal height 56.5 mm
Pedestal height 56.5 mm
Pedestal height 85 mm
Pedestal height 85 mm
Figure 4.8 - Electric field patterns for three-inch and four-inch silicon wafers at 28.25,
56.5, and 85 mm pedestal heights in TMm (Ls = 11.3 cm, cross section through the
wafers)
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.3 TEin Mode
The simulation problem setup is as follows: cavity height was set to
6 .8
cm,
cavity radius was equal to 8.89 cm, and material property assigned was vacuum. The
cavity boundary condition at the walls was equal to aluminum and end plates were equal
to brass. The initial frequency was set to 2.4 GHz. The silicon thickness was equal to
0.038 cm, silicon resistivity was set to 3 Ohm-cm, permittivity and permeability were
equal to 1 F/m and H/m. The pedestal material was quartz glass, the pedestal outer and
inner radius were equal to
2 .8 6
cm and 2 . 6 6 cm respectively.
Displayed below in Figure 4.9-4.12 are the simulation results. As can be seen in
Figure 4.9, the four-inch silicon wafer has slightly lower resonance frequencies for all
pedestal height position compared to the three-inch silicon wafer. The lowest resonance
frequency is found at the pedestal height equal to 10 mm high, which is equal to 2.404
GHZ and 2.409 GHz for the four-inch and three-inch wafers respectively. In Figure 4.10,
it can be observed that there are two locations of low Q for both silicon wafers. At
pedestal height of 10 mm, the four-inch Q is equal to 137 and the three-inch Q is 156.
Additionally, the Q is equal to 415 and 253 at pedestal height of 34 mm for the three-inch
and four-inch silicon wafers respectively. These Q are greater compared to the TM012
mode, especially at pedestal height 34 of mm. For this particular mode, there are two
possible optimum positions, i.e. 10 mm and 34 mm to place and heat the silicon wafer.
Shown in Figures 4.11-4.12 are the electric field patterns for the silicon wafers in
TEin mode. The electric field patterns are plotted in a constant scale magnitude from 0.058337 V/m to 1.2189 V/m and from -0.002.5724 V/m to 2.1184 V/m for the threeinch and four-inch silicon wafer respectively.
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-2 .5 6
g
2 54
^ 2.52
o
c 2 .5 0
CD
O- 2.48
CD
i£ 2.46
8 2.44
| 2.42
o
co 2 .4 0
CD
^ 2.38
3_inch
10
0
30
20
40
4_inch
50
70
60
Pedestal Height (mm)
Figure 4.9 - TEm resonance frequencies of the three-inch and four-inch silicon wafers
(Ls = 6 . 8 cm)
1 .2 E + 0 3
3_inch
4 inch
1 .0 E + 0 3
2 $ 8 .0 E + 0 2
cc c
o
ll
6 .0 E + 0 2
* c
^ - i 4 .0 E + 0 2
O
X3
2 .0 E + 0 2
0 .0 E + 0 0
0
10
20
30
40
50
60
Pedestal Height (mm)
Figure 4.10 - TEm quality factor of the three-inch and four-inch silicon wafers
(Ls = 6 . 8 cm)
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
Three-inch silicon wafer
Four-inch silicon wafer
Pedestal height = 5 mm
Pedestal height 5 mm
Pedestal height = 10 mm
Pedestal height 10 mm
Pedestal height = 17 mm
Pedestal height 17 mm
Figure 4.11 - Electric-field patterns for three-inch and four inch silicon wafers at 5, 10,
and 17 mm pedestal heights in TEm (Ls = 6 . 8 cm, cross section through the wafers)
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pedestal height = 30 mm
Pedestal height 30 mm
Pedestal height = 34 mm
Pedestal height 34 mm
Pedestal height = 60 mm
Pedestal height 60 mm
Figure 4.12 - Electric field patterns for three-inch and four-inch silicon wafers at 30, 34,
and 60 mm pedestal heights in TEm (Ls = 6 . 8 cm, cross section through the wafers)
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.4 Resistivity variation in TM012 mode
The problem setup for the silicon wafer resistivity variation parameter is as
follows: cavity height and cavity radius were set to 14.4 cm and 8.89 cm respectively,
cavity walls was equal to aluminum with an ends plates equal to brass. The silicon wafer
thickness was set to 0.038 cm. The pedestal height was set to 35.5 mm. This height was
chosen because of the best optimum position to place the material load based on the
TM012 silicon wafer simulation. The pedestal material was equal to quartz glass, and
pedestal outer and inner radii were set to 2.86 cm and 2.66 cm. The initial frequency was
assigned to 2.4 GHz. The resistivity was varied from 0.08,0.5,3,10, and 15 G-cm.
Presented below in Figure 4.13 and Figure 4.14 are the simulation results for the
silicon wafer using the TM 012 mode with resistivity values were varied: From the graphs,
it can be observed that the resonance frequency increases as the resistivity of the silicon
wafer is higher. However, when the resistivity reaches a certain value, the resonance
frequency started to reach a steady state.
The increase of the frequency has to do with
the changes in the silicon conductivity. Because of the changes in the electric tangent
loss, as the resistivity of the silicon getting higher, the quality factor is increasing
approximately linearly. Qualitatively, resistivity is a measure of a material’s inherent
resistance to current flow. Thus, if the silicon wafer has a very high resistivity value, it
will be harder to heat the load.
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.470E+00
'Xn
2.465E+00
2- 2.460E+00
>*
oc
3 2.455E+00
C
T
O
_
LkL
2.450E+00
3 inch silicon
2.445E+00 4
6
8
10
Resistivity (Ohm-cm)
Figure 4.13 - Resonance frequencies of the three-inch silicon wafer when resistivity
varied in TM 012 mode
4.000E+03
3.500E+03
*O «T
(0 3.000E+03
O I 2.500E+03
•§ 2.000E+03
'■5 | 1.500E+03
3 E
o
1.000E+03
5.000E+02
3 inch silicon
0.000E+00
5
10
15
20
Resistivity (Ohm-cm)
Figure 4.14 - Quality factor of the three-inch silicon wafer when resistivity varied in
TM 012 mode
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.5 Summary of Important Observations
Around the silicon wafer there is considerable change from the empty cavity in
the electric field, which implies that silicon is a conductive material and affects the
electric field. For example, the electric field also does not appear to be the TM012 mode
when the electric field on the plane of the silicon is viewed. The material loaded fields
change from the unloaded fields. The electric field intensity is relatively less in the
center of the silicon compared to the outer edges. There is also an abrupt change in
electric field intensity at the edges of the silicon; i.e. it dramatically increases in intensity.
Based on the silicon wafers in various modes simulation results, the resonance
frequency of the three-inch and the four-inch silicon wafer only differ slightly. It can be
implied that small changes in silicon geometric dimension does not alter resonance
frequency significantly. The lowest quality factor for the three-inch and four-inch silicon
wafer loaded cavities was found at pedestal height 35.5 mm for the TM012 mode, 56.5
mm for the T M m mode, and both 10 and 34 mm for the T E m mode.
The optimal position to heat the silicon wafer is mainly dependent on how the
electric fields are arranged in the cavity. The wafer is heated the most efficiently when
the electric fields are tangential to the surface of the silicon wafer. The electric fields,
which are tangential, induce a surface current creating a Joule heating effect. Depending
on which modes to couple, the electric fields are tangential in different locations. By
looking at the electrical field pattern for both silicon wafers, it can be approximated that
the most optimal position to heat the silicon wafer is possibly at pedestal height 34 mm.
This material load position is where the electric field is tangential to the surface of the
silicon wafer.
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.4 Complex Eigenfrequencies of a Cylindrical Applicator Loaded with Magnetic
Material
The cavity applicator with the magnetic material load is divided into two
excitation modes. The first mode is the TM 012 while the second is the TEm mode. In the
TM 012 mode, the pedestal heights were varied at 5, 13, 18, 23, 33, 43, 53, 63, 73, and 83
mm. The load material is referred as the magnetic material is because of the assigned
permeability of the material is complex, meaning that the permeability value has a real
and an imaginary number.
The unknown magnetic material is a disk shaped with a
certain thickness and it is placed above the pedestal quartz surface at a various discrete
heights.
Similar to the silicon wafer, the output parameters of each mode for the unknown
magnetic material are Af (change in resonant frequency), AQ (change in quality factor),
and AE (change in the electromagnetic field patterns) versus h (material height position
inside the cavity).
4.4.1 TM 012 mode
The problem setup for the magnetic material load is as follows: cavity radius was
set to 8.89 cm, cavity height was equal to 14.615 cm, cavity walls were set to brass. The
load radius was set to 1.905 cm, load thickness was equal to 0.3175 cm.
conductivity was
1 0 e- 0 2
siemen/meter, load permittivity was set to
6
The load
farad/meter, and
load permeability was equal to 4-j3 henry/meter. The pedestal height was incremented at
5, 13, 18, 23, 33, 43, 53, 63, 73, 83 mm. The pedestal outer and inner radii were equal to
2.54 cm and 2.34 cm respectively. The initial frequency was swept from 2.4 GHz.
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Displayed in Figure 4.15-4.19 are results obtained from the TM 012 mode
simulation. The resonance frequencies of the magnetic material decrease linearly as the
material load heights increase as shown in Figure 4.15.
The material load height
becomes higher due to the increment of the pedestal heights inside the cavity applicator.
As can be seen in Figure 4.16, the highest quality factor among the various material load
heights is at pedestal height equal to 33 mm. It is more likely that at this height, when the
magnetic material is placed and heated using the high power microwave energy it will not
heat efficiently and effectively. The optimum position to heat the material load would be
at pedestal height 63 mm because of the lowest Q value equal to 849.
Shown in Figures 4.17-4.19 are the electric field plots for the TM 012 magnetic
material load. As the pedestal height increases inside the cavity applicator, the electric
field patterns and the magnitude of the electric field distribution changes. At 5 mm
pedestal height, the temperature at the edge of cavity applicator in the radial direction is
very low compared to the center of the cavity. The desired temperature and electric field
distributions are that they must be uniform in both the angular and radial directions. By
comparing the electric field patterns on each height in the figure above, probably the best
choice to heat the magnetic material using the TM 012 mode excitation would be at
pedestal height 63 mm. The different prediction between the Q and the field pattern will
be compared with the low power measurements. It is also important to note that having
strong field intensity alone does not guarantee efficient and maximum coupling of the
electromagnetic energy into the material load. The magnetic field intensity determines
the efficient heating of this material load.
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.43
TM012 mode
2.425
2.42
oN
z 2.415
O
2.41
2.405
2.4
20
0
40
60
80
Load heights (mm)
Figure 4.15 - Resonance frequencies of the magnetic material in TM012 mode
1.60E+04
1.40E+04
TM012 mode
*0 to
% 1.20E+04
g |
1.00E+04
> '§ 8.00E+03
1 § 6.00E+03
3 C
O 5 4.00E+03
2.00E+03
0.00E+00
0
20
40
60
80
Load Heights (mm)
Figure 4.16 - Quality factor of the magnetic material in TM012 mode
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
Pedestal height = 5mm
Pedestal height = 5mm
Pedestal height = 13mm
Pedestal height = 13mm
Pedestal height = 18mm
Pedestal height = 18mm
Figure 4.17 - Electric field patterns for the TM 012 on magnetic material for 5, 13, and 18
load heights (Ls = 14.6 cm and XY cross section through material load)
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pedestal height = 23mm
Pedestal height = 23mm
Pedestal height = 33mm
Pedestal height = 33mm
Pedestal height = 43mm
Pedestal height = 43mm
Figure 4.18 - Electric field patterns for the TM 012 on magnetic material for 23, 33, and 43
load heights (Ls = 14.6 cm and XY cross section through material load)
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I ,/
Pedestal height = 53mm
Pedestal height = 53mm
Pedestal height = 63mm
Pedestal height = 63mm
Pedestal height = 73mm
Pedestal height = 73mm
/J
Pedestal height = 83mm
- ........ ... _______
Pedestal height = 83mm
Figure 4.19 - Electric field patterns for the TM 012 on magnetic material for 53, 63, 73, and
83 load heights (Ls = 14.6 cm and XY cross section through material load)
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.4.2 TEm mode
The problem setup for the TEm mode is as follows: the cavity radius was set to
8.89 cm and the cavity height was set to 13.2 cm. The load radius was equal to 1.905 cm,
load thickness was equal to 0.3175 cm, load conductivity was set to 10e-02 siemen/meter,
and load permittivity and permeability were assigned to
6
farad/meter and 4-j3
henry/meter respectively. The pedestal height was incremented at 5, 13, 18, 23, 33, 43,
53, 63, 73, 83 mm. The pedestal outer and inner radiuses were set to 2.54 cm and 2.34 cm
respectively. The cavity walls were aluminum, pedestal material was assigned as quartz
glass, initial frequency was 2.4 GHz, and the number of mode was 1.
The simulation results are displayed in Figure 4.20-4.24.
As expected, the
resonance frequencies decrease gradually as the unknown magnetic material is placed
higher inside the cavity. The 2.45 GHz resonance frequency occurs at around pedestal
height equal to 23 mm. On the other hand, the lowest Q is observed at pedestal height
equal to 63 mm. By comparing the lowest quality factor, the strongest field intensity can
be seen at 63 mm high. Hence, it is more likely that the effective heating might take
place at this pedestal height.
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.465
TE112 mode
2.455
® P 2.445
2.435
2.425
20
40
60
80
Load Heights (mm)
Figure 4.20 - Resonance frequencies of the magnetic material in TEi n mode
8.00E+02
7.00E+02
TE112 mode
5 “g 6.00E+02
tS | 5.00E+02
(0 c
>, 55 4.00E+02
IO“ I5'
3.00E+02
2.00E+02
1.00E+02
0 .0 0 E + 0 0
20
40
60
80
Load H eights (m m )
Figure 4.21 - Quality factor of the magnetic material in TEn 2 mode
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
'/ ■ i
Pedestal height = 5mm
^-------- ---------Pedestal height = 5mm
Pedestal height = 13mm
Pedestal height = 13mm
Pedestal height = 18mm
Pedestal height = 18mm
Pedestal height = 23mm
Pedestal height = 23mm
Figure 4.22 - Electric field patterns for the TM 012 on magnetic material for 5, 13, and 18
load heights (Ls = 13.2 cm and XY cross section through material load)
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pedestal height = 33mm
Pedestal height = 33mm
Pedestal height = 43 mm
Pedestal height = 43mm
Pedestal height = 53mm
Pedestal height = 53mm
Figure 4.23 - Electric field patterns for the TM 012 on magnetic material for 5, 13, and 18
load heights (Ls = 13.2 cm and XY cross section through material load)
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pedestal height = 63mm
Pedestal height = 63mm
Pedestal height = 73mm
Pedestal height = 73mm
Pedestal height = 83mm
Pedestal height = 83mm
Figure 4.24 - Electric field patterns for the TE 112 mode on magnetic material for 5, 73,
and 83 load heights (Ls = 13.2 cm and XY cross section through material load)
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.5 Complex Eigenfrequencies of a Cylindrical Applicator Loaded with Graphite
4.5.1 Eigenmodes solutions
A graphite material size of 2 mm was simulated in the cylindrical cavity
applicator. The material load size was set up to obtain the first ten eigenmodes that exist
inside the cavity applicator loaded with graphite material. The output parameters include
the resonance frequencies, quality factor, and the electric field patterns. The problem
setup for the 2 mm graphite material load is as follows: cavity radius was set to 8.89 cm,
cavity height was equal to 14.4 cm. The graphite load height was set to 14.4 cm, load
conductivity was assigned to 7e+04 Siemen/meter and load permittivity and permeability
was set to 1. The cavity walls were set to aluminum, initial frequency was swept at 2.30
GHz, and number of mode was set to 10.
Displayed in Table 4.1 and Figure 4.30 - 4.34 are the simulation results for the 2
mm graphite load.
Table 4.1 - The eigenmodes, resonance frequencies, and quality factor for the seven-inch
cavity loaded with graphite material (Ls = 14.4 cm, load radius = 2 mm)
Eigenmodes
Mode 1 = TE 112
Mode 2 = TE 112
Mode 3 = TEon
Mode 4 = TMm
Mode 5 = TMm
Mode 6 = TE311
Mode 7 = TE311
Mode 8 = TM 012
Mode 9 = TE212
Mode 1 0 = TE212
Resonance Frequency
(GHz)
2.30760
2.30768
2.32609
2.32749
2.32755
2.50233
2.50251
2.60785
2.65847
2.65872
Quality Factor
(Dimensionless)
1.96E+04
2.03E+04
1.94E+04
1.35E+04
1.31E+04
2.58E+04
2.58E+04
2.02E+03
2.92E+04
2.92E+04
66
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w 2.70
I
2.65
g 2.60
O' 2.55
£ £2.50
g 02.45
g ~2.40
o 2.35
|
2.30
2.25
2 mm
7
5
3
1
9
Eigenmodes (a.u.)
Figure 4.25 - Resonance frequencies of the graphite material for the 2 mm load radius
« 3.5E+04
c 3.0E+04
2
mm
0
1 2.5E+04
®
6 2.0E+04
TJ
r 1.5E+04
0
8 1.0E+04
LL
|« 5.0E+03
1 0.0E+00
o
4
5
6
7
Eigenmodes (a.u.)
Figure 4.26 - Quality factor of the graphite material for the 2 mm load radius
67
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10
Mode 4 = TMm
M ode4 = TMi 11
Figure 4.27 - Electric field patterns for mode 1, 2, 3, and 4 of the graphite material with 2
mm load radius
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Mode 5 = T M m
Mode 5 = TMm
Mode
Mode
6
= TE311
6
= TE3n
Mode 7 = TE 311
Mode 7 = TE 311
Mode
Mode
8
= TM 012
Figure 4.28 - Electric field patterns for mode 5 , 6 , 7, and
mm load radius
8
8
= TM 012
of the graphite material with 2
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Mode 9 = TE212
Mode 9 = TE212
Mode
Mode 10 = TE2 i2
10
= TE212
Figure 4.29 - Electric field patterns for mode 9, and 10 of the graphite material with 2
mm load radius
As can be seen in Figure 4.30, the resonance frequencies increase at each mode.
The highest resonance frequency was 2.65 GHz. This mode was identified as the TE212 .
By observing at the quality factor graph in Figure 4.31, the lowest Q was found at
eigenmode number eight, which is the TMoi2 -mode. The resonance frequency for TM 012
mode o f the 2 mm load radius was found to be 2.60785 GHz. It is slightly higher than
the theoretical value, which is equal to 2.4513 GHz. The TM012 mode has the lowest Q
compared to other modes. It is equal to 2,016. Hence, TM012 mode excitation would be a
good choice to heat the graphite fiber in the cylindrical cavity applicator.
70
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Chapter 5
EXPERIMENTAL PROCEDURES AND RESULTS
5.1 Introduction
The objectives of the experiments presented in this chapter are to use the
numerical simulation techniques and results given in Chapter 4 to help investigate the
microwave heating of specific material loads using single mode cavity applicators. The
chapter begins with the empty cavity experiments, and then is followed by ( 1 ) the low
and high power silicon wafers experiments, (2 ) the low and high power magnetic material
experiments, and (3) finally the graphite fiber low and high power experiments.
The main purpose of these experiments was to determine the best method of
heating these “difficult to heat” material loads. For each material load, the following
experimental procedure was employed.
First the results of the numerical modeling
described in Chapter 4 are used as a guide to determine the initial heating experiments.
That is, the numerical results indicated the “good heating” electromagnetic modes and
also provided some information on optimum placement of material loads in the cavity.
The material loads were then placed in the cavity and then the electromagnetic modes
were located experimentally with low power excitation by adjusting the cavity length, Ls,
coupling probe depth, Lp and by measuring loaded cavity Q. These measurements were
then used for the initial conditions for the high power heating of the material loads. As
microwave heating occurs, the Ls and Lp positions were then readjusted to obtain the
best matching conditions. In some cases the material temperature was then measured as
the heating progressed.
The successful and efficient heating of the material loads
71
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described herein demonstrated the usefulness of the engineering design and test
methodology developed in the thesis research.
5.2 Empty Cavity Experiments
In order to verify that the loaded microwave cavity applicator operated properly,
the experiments were started with calibrating an empty cavity. The empty cavity utilized
was the seven-inch cavity applicator as shown in Figure 3.1.
The empty cavity
experiment provides a calibration or reference position of the mode resonant frequencies,
coupling probe, and sliding short positions for the subsequent material loaded cavity
experiments. Low power measurements were conducted at power levels of less than
25mW to measure the cavity length Ls, coupling probe depth Lp, resonant frequency fo,
and quality factor Q. The eigenmodes excitations investigated were the TM012, T M m ,
TE112,
and T E m eigenmodes.
The data in Table 5.1 were obtained by setting the
resonant frequency of the microwave oscillator fixed at 2.45 GHz and measured the
cavity length and probe depth of the cavity applicator. Likewise, the data in Table 5.2
were obtained by keeping the cavity length fixed at a certain height based on the
theoretical calculation on each mode and then measured the resonance frequency and the
coupling probe depth.
Table 5.1 - Fixed resonant frequency of empty cavity
Resonance Frequency Cavity Height, Ls
Eigenmodes
(GHz)
(cm)
T E U1
2.45
6.82
1 1 .2
T M m & TEon
2.45
13.4
2.45
TE„ 2
2.45
14.6
TM012
TE311
15.8
2.45
Coupling Probe
Depth, Lp (cm)
2 .0
1.5
0 .8
0 .6
0 .6
72
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Table 5.2 - Fixed cavity height of empty cavity
Cavity Height, Ls Resonance Frequency
Eigenmodes
(GHz)
(cm)
6 .8
2.4446
TEm
2.4615
11.3
TMm & TEon
2.4448
13.5
TEm
14.4
2.4779
TM012
TE311
15.8
2.4791
Coupling Probe
Depth, Lp (cm)
2.5
1.5
0 .8
0 .1 2
0 .6
As can be seen from Table 5.1-5.2, the cavity height and the resonant frequency
for each mode is distinctive. These values differ slightly compared to calculation and
simulation results shown in Table 2.2. In the simulation model, the cavity was a perfect
cylinder while in the experiments the cavity has a coupling probe. Furthermore, in the
natural frequency equations, the assumption of the cavity applicator was a perfect ideal
empty cavity. Compared to the mode chart on Figure 2.4 in Chapter 2, these resonance
frequencies are very close to the theoretical calculations.
The T M m & TEon are
degenerates modes.
Since the cavity height was assigned at a fixed height and the resonant frequency
as the output parameters in the simulation, the fixed cavity height empty cavity
experimental measurements were compared with the empty cavity simulation results. On
the other hand, the fixed resonant frequency at 2.45 GHz empty cavity measurements
were used as a reference for the high power heating experiments.
5.3 Silicon Wafer Experiments
5.3.1 Low Power Measurements Procedure
In the silicon wafer experiments, two methods were used to obtain best coupling
position for heating the silicon wafer efficiently. The first method consisted of keeping
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the cavity height fixed and then measuring the resonance frequency. The second method
consisted of holding the resonance frequency fixed at 2.45 GHz and varying the cavity
height. Both the three-inch and four-inch silicon wafers were examined. The cavity
length and quality factors were measured at the critical coupling conditions.
Using the side feed cavity applicators, the cavity height, Ls was fixed at 14.6 cm. The
excitation mode was the TM 012 mode. This mode was chosen because of the electric field
uniformity in the <|>direction and also strong electric field component radial in the center
of the cavity. This information was obtained from the electric field patterns plot in the
simulation results. Two different types and sizes of silicon wafers were examined during
the experiments. The three-inch wafers consisted of n and p type while the four-inch
wafer consisted of only p type. All three silicon wafers were 0.38 mm thick. Both the
three-inch polished, unpolished and four-inch polished silicon wafers have a resistivity
value in the range o f 1 Ohm-cm to 10 Ohm-cm.
The silicon wafer was placed on a
quartz glass pedestals and then were incremented at height, h, at every 5 mm as shown in
Figure 3.2. At low power excitation, the resonance frequency was swept from 2.4 to 2.5
GHz. The resonance frequencies and coupling probe depth measurements were made.
5.3.2 Low Power Measurements Results
Shown on Figure 5.1-5.4 are the results for the side feed cavity resonator with
fixed cavity height, Ls. The coupling probe depth penetration inside the cavity varies
from
10
to 25 mm. Critical coupling could not be achieved using the TM 012 mode at the
pedestal height between 40 to 55 mm for the four-inch polished silicon wafer. This is
probably due to the null o f the electromagnetic fields, which caused harder excitation of
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the mode. At these pedestal heights, it is more likely that the microwave energy will not
be coupled effectively into the material load in the high power experiments. Hence, the
material load should not be placed at this position.
3_inch_p_type
4_inch_p_type
3_inch_n_type
2 .4 7 5
N
x
o
>.
o
c
0)
3
IT
2 .4 6 5
2 .4 5 5
4)
2 .4 4 5
20
0
40
60
80
100
Pedestal Height (mm)
Figure 5.1 - Resonance frequencies of silicon wafers with fixed cavity height in the
TM 012 mode
•— 4_inch_p_type —
0
20
40
3_inch_p_type —* — 3_inch_n_type
60
80
1 0 0
Pedestal Height (m m )
Figure 5.2 - Coupling probe depth of silicon wafers with fixed cavity height in the TM 012
mode
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
146
3_inch_n_type
3_inch_p_type
4Jnch_p_type j
145.5
E
E
145
.c
©
144.5
144
I
143.5
8 143
142.5
142
o
20
40
60
Pedestal Height (mm)
80
100
Figure 5.3 - Cavity heights of silicon wafers with fixed frequency in the TM 012 mode
30
25
20
o 15
O
_o 10
3_inch_n_type
0
20
3jnch_p_type
40
60
Pedestal Height (mm)
4_inch_p_type
80
Figure 5.4 - Coupling probe depth with fixed frequency in the TM 012 mode
76
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100
When the silicon wafer was inserted into the cavity, the resonance frequency
shifted down from the 2.4779 GHz empty cavity resonance frequencies by approximately
37.9 MHz. The resonant frequency of the cavity shifts down because a material with a
high dielectric constant has been added. It can also be observed that as the pedestal
height increases, the frequency seems to somewhat decrease. This is because the pedestal
also acts as a dielectric. The higher the pedestal, the more quartz material is in the cavity.
This perturbs the electric field and shifts the frequencies lower. This implies that the
pedestal should be kept at a certain height in order to avoid major and drastic shift in
resonance frequency. Ideally, the resonant frequency should be in the vicinity of 2.45
GHz. For the three-inch n-type unpolished silicon wafer, the resonance frequency is
lower compared to the three-inch and four-inch p-type polished silicon wafers.
Shown in Figure 5.3-5.4 are experimentally measured cavity heights and the
coupling probe depths for the silicon wafers with fixed frequency. The three-inch n-type
unpolished silicon wafer reached its minimum cavity height when the pedestal height was
at 30-35 mm, which is about a quarter wavelength. For the three-inch and four-inch ptype polished silicon wafers, the cavity height stays constant at pedestal height
20
to 65
mm. The average probe depth penetration is in the range of 15 to 25 mm. It can also be
observed that the three-inch n-type unpolished silicon wafer has shorter cavity height
between 20 to 65 mm pedestal heights compared to the three-inch and four-inch p-type
polished silicon wafers. This is probably due to the difference in resistivity. Since the
resistivity is a measure of a material’s inherent resistance to current flow or quantitatively
defined as the proportionality constant between the electric field impressed across a
homogenous material and the total particle current per unit area flowing in the material.
77
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Therefore, when each type of the silicon wafers was placed inside the cavity applicator,
the difference in material resistivity may have caused the difference in coupling
parameters.
Surface of the silicon wafer may also have generated a little shift in cavity length
and probe depth coupling conditions. The uneven or rough surface in the unpolished
wafer may contribute to the shift in cavity length and coupling probe depth because each
surface of the silicon wafer can have different skin depth. These arguments need to be
investigated further. However, it is beyond the scope of this research to study the material
interactions and characteristics of the material loads when they are excited with
microwave energies. However an important result is a slight difference in size of the
silicon wafers does not seem to cause a major shift in the critical coupling positions. The
three-inch and four-inch p-type polished silicon wafers behave very similarly in cavity
length and coupling probe depth measurements.
5.3.3 High Power Heating Experimental Procedure
The TM 012 mode excitation was employed for the high power experiments on the
silicon wafer. The cavity length and the coupling probe depth were set to 14.25 cm and
2.3 cm respectively. The three-inch n-type silicon wafer was placed on the quart tube
pedestal (as shown in Figure 3.2). The pedestal height was equal to 34 mm, which is
approximately a quarter wavelength.
This height was chosen based on the low Q
obtained from the simulation result. Also, the low power coupling measurements indicate
that, at this height, the critical coupling was successfully achieved. High power heating
experimental network I was used for the silicon wafer heating experiments. The Opthos
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
microwave power supply was utilized during the high power heating of the silicon wafer.
The input power was applied to the cavity applicator. The reflected power was measured
and the change in silicon wafer temperature was also observed.
5.3.4 High Power Heating Experimental Results
The microwave input power of 100 watts was applied to the cavity applicator. The
cavity length and the coupling were retuned slightly to critically couple the silicon wafer
load and also to minimize the amount of the reflected power. After a few seconds, the
silicon wafer was glowing orange almost uniformly. The orange color was more
pronounced around the edge of the silicon wafer, compared to the center. When the
silicon wafer was glowing orange, the temperature was approximately 600° - 700° C.
This experiment demonstrates that heating the silicon wafer can be performed using input
power o f
100
watts, TM012 mode, and a single mode cavity applicator.
The temperature and the electric field are directly proportional to each other.
Since the temperature and the electric field intensity are related, the temperature of the
silicon wafer is expected to be experimentally hotter at the edges than in the center.
However, effect is negligible because of the way the heat transfers throughout the silicon,
heating it in an almost perfectly uniform fashion. If this uniformly heated material can be
achieved, there are numerous applications that this heating method can be applied to.
However, it has been shown that the TM012 alone is not a mode to use to create a uniform
heating method.
79
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5.4 Magnetic Material Experiments
The magnetic material experiments consisted of two stages: Stage I and Stage II.
The difference between the two stages is that in Stage II the cavity applicator has a slight
modification both in the microwave applicator apparatus and microwave system used in
Stage I. Furthermore, in Stage I, the starting material to be heated was only in a form of a
gel whereas in Stage II, the initial material consisted of both powder and gel form starting
material samples. In Stage II, some of these starting material products were from Stage I
experiments.
5.4.1 Low Power Measurements Procedure
The seven-inch diameter cylindrical microwave cavity applicators, shown in
Figure 3.2-3.3 were utilized for the experiments. A quartz dish 5.08 cm inner diameter,
1.3 cm height, and 0.3 cm thick was used to contain the material. For Stage I, the quartz
dish was placed on a cylindrical quartz pedestal (5.32 cm inner diameter and 5.52 cm
outside diameter), which had a variable height h.
The material height varied
incrementally from 3 mm height to 83 mm. For Stage II, a quartz crucible was used as a
holder of the quartz dish that acts as a pedestal. The quartz crucible has a dimension of 28
mm base diameter, 51 mm top outside diameter, 2 mm thick, and 51 mm high. As shown
in Figure 3.3, the quartz pedestal or the quartz crucible was placed at the bottom and
along the axis of the cylindrical cavity applicator.
The material loaded measurements for Stage I consisted of: “no product” (empty
quartz glass), “initial product”, “half product”, and “final product”. The material load for
Stage II consisted of: “reference material”, “stage I sample”, “exp4”, “exp6 ” samples.
From the experimental data, the optimum material load position and the best coupling
80
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condition to heat the material were examined. Furthermore, the influence of the material
loadings on the cavity operating parameters such as the resonant frequency, the coupling
probe depth, the cavity Q, and the load heights were also examined. Using the low
experimental system shown in Figure 3.5, experimental measurements for both Sate I and
Stage II were conducted at power levels of less than 25 mW. In Stage II experiments, the
reference sample, empty quartz holder, and the Stage I initial material were utilized to
investigate the effect of the quartz tube inside the cavity applicator.
5.4.2 Low Power Measurements Results
5.4.2.1 Stage I
Shown below in Figure 5.5-5.7 are the resonance frequency, quality factor, and
coupling probe depth for Stage I experiments using the TM 012 mode. Each experimental
measurement was taken under critical coupling conditions. The critical coupling
conditions were obtained by adjusting the cavity height and the coupling probe depth. As
the pedestal height becomes higher, the resonance frequency shifts lower. This is due to
the presence of the quartz pedestal inside the cavity. The resonance frequency of the “no
product” (empty quartz glass) compared to the “final product” is almost identical. The
“initial product”, on the other hand, has the lowest resonance frequency compared to “no
product”, “half product”, and “final product”. This means that the material is lossier in
the initial product stage. The quality factor for the “initial product” also has the lowest Q
for every pedestal height compared to the “half product” and “final product”. This shows
that the initial material is much easier to heat because of the low Q. The coupling probe
depth consistently decreases as the material moves closer to a final product and becomes
lossless.
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.455
£
♦ No Product ■ Initial Product A Half Product ♦ Final Product
2.45 <k
(3
~ 2.445
c
0)
2.44
t
■
o- 2.435
o
it
0)
g
a
§
i
2.43
i
2.425
2.42
<0
« 2.415
I
2.41
0
10
20
30
40
50
60
70
80
90
Load Height (mm)
Figure 5.5 - Resonance frequencies on various pedestal height h using TM 012 mode
3,000
♦ No Product ■ Initial Product A Half Product ♦ Final Product
2,500
| 2,000
♦
♦
♦
♦
♦
♦
♦
♦
£>. 1,500
♦
♦
♦
4M
♦
A
J 1,000
o
A
■
■
■
500
♦
A
A
1
A
■
■
0
10
20
30
40
50
60
80
70
90
Load Height (mm)
Figure 5.6 - Quality factor on various pedestal height, h using TM 012 mode
1.6
n
■
■
1.4
1.2
A
♦
♦
Q.
Q 1
4)
.O 0.8
O
oc> 0.6
fl>
A
♦
♦
1
A
♦
A
u
A
A
♦
♦
♦
♦
t
♦
A
♦
■
m
m
■
A
♦
■
■
I
§■ 0.4
o
0
(♦No Product
0.2
■ Initial Product
A Half Product
♦
Final Product
0
10
20
30
40
50
60
70
80
90
Load Height (mm)
Figure 5.7 - Coupling probe depths on various pedestal height, h using TM 012 mode
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figures 5.8-5.10 display the resonance frequency, the quality factor, and the
coupling probe depth for TE 112 mode.
Both the “initial” and “half products”
experimental measurements were not critically matched using this mode. The “no
product” and “final product”, were taken under critical coupling conditions.
The
resonance frequency for the “initial product” is minimum at 23 mm and 33 mm pedestal
heights. The quality factor for the “initial product” is the lowest at
8
mm and 18 mm
pedestal heights. Above pedestal height 43 mm, the no product, initial product, half
product, and the final product have a very close quality factor. The coupling probe depth
decreases as the material moves closer to a final product and becomes lossless. The
coupling probe depth between the no product and the final product are very close to one
another.
2.460 r
2.450 ! 1
2.440
2.430
2.420
2.410
2.400
2.390
0 2.380
(0
4) 2.370
QC
2.360 --
N
X
<*5
>.
0
c
4)
3
a
4i_>
U.
4)
C
<u
c
♦ No Product ■ Initial Product A Half Product ♦Final Product
♦
■
i
10
20
■
♦
4
30
i
40
«
‘
50
60
70
80
90
Load Height (mm)
Figure 5.8 - Resonance frequencies on various pedestal height h using TE 112 mode
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
800
♦ No Product ■ Initial Product A Half Product ♦ Final Product
700 II
w
600
0
0
500
(0
u.
>. 400
3 300
O
♦
♦
▲
H
■
♦
♦
♦
A
A
♦
♦
A
*
t
200
100
■
I
*
i
i
1
0
10
20
30
40
50
60
70
80
90
Load Height (mm)
Figure 5.9 - Quality factor on various pedestal height h using TEm mode
♦ No Product ■ Initial Product A Half Product ♦ Final Product
10
20
30
40
50
Load Height (mm)
60
70
80
90
Figure 5.10 - Coupling probe depths on various pedestal height h using TE 112 mode
5.4.2.2 Stage II
Shown below in Figure 5.11-5.13 are the cavity short, quality factor, and the
coupling probe depth for Stage II experiments using the TM012 mode. The cavity short
position for the “stage I initial material” was shifted down the most compared to the short
position for the empty quartz holder and the reference material. The coupling probe
depths for the “stage I initial material” were adjusted the most inward compared to the
other two samples. The “stage I initial material” has the lowest loaded Q at each load
height compared to the empty quartz holder and the reference material.
84
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14.4
♦ empty_quartz_holder
a reference material
14.35 0
■ s ta g e jjn itia l
♦ empty_cavity
E
0
14.3
T
O
JZ
CO
14.25
14.2
*
*
>
14.15
■
■
O
14.1
CO
14.05
*
■
-
10
20
30
40
50
60
Load Heights (mm)
Figure 5.11 - Cavity shorts, Ls, on various pedestal height, h using TM 012 mode
2.5
E
2
o
w
■
Cf 1.5
■t—
CL
a>
Q
1
CD
JD
2 0.5
m
♦
A
A
♦ empty_quartz_holder
a reference material
CL
■ s ta g e jjn itia l
♦ empty_cavity
0
10
0
20
30
40
50
60
Load Heights (mm)
Figure 5.12 - Coupling probe depths, Lp, on various pedestal height, h using TM 012 mode
1400
1200
o to 1000
o
cc c
u_ o 800
w
c
600
3
O
E
=6
▲
♦
400
200
♦ empty-quartzjiolder
▲reference_material
0
0
10
20
■ s ta g e jjn itia l
♦ empty_cavity
30
40
50
Load Heights (mm)
Figure 5.13 - Quality factor, Q on various pedestal height, h using TM 012 mode
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
Figure 5.14-5.15 displays the low power measurements with a quartz tube inside
the cavity applicator using the TE 112 mode. The quality factors could not be calculated at
some pedestal heights because of the under coupled condition. This means that the load
was not matched with the microwave system. The presence of the quartz tube caused the
resonance frequency to shift down and, as a result, the critical coupling condition was not
met.
12.6 r— —— r--------------— ----------—— -------------------------------- "-------------- ;-------------------- r—1
12 5 <►
"c
g
12.4
♦
O 12.2
%
stagejJnitial
Jnitial
■■stagej
♦empty
cavity
♦ empty_cavity
------------------------- — --------- ----------- --------------- ---------------- ------------------♦
♦
"ST 12.3
W
♦ empty_quartz_holder
reference
material
referencejnaterial
a
a
A
A
ft
II
A
12.1
12
q
11.9
°
11.8
a
■
♦
m
11.7 J------------------0
10
ii
■
m
,------ ,-------------,------------- ,------------20
30
40
50
60
Load Heights (mm)
Figure 5.14 - Cavity shorts, Ls, on various pedestal height, h using TE 112 mode
a
a>
0)
-Q
Q
o
4
3.9
3.8
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
♦ empty_quartz_holder
■ s ta g e j Jnitial
reference material
♦ empty_cavity
a
10
20
30
40
50
60
Load Heights (mm)
Figure 5.15 - Coupling probe depths, Lp, on various pedestal height, h using TE 112 mode
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Since the critical coupling conditions were not obtained when the quartz tube was
present inside the cavity applicator, another low power experiment was performed
without utilizing the quartz tube. As shown in Table 5.3, a critical coupling condition was
obtained when the quartz tube was not inserted inside the cavity applicator. The material
samples were contained in a quartz dish and the quartz crucible was used a pedestal.
Table 5.3 Stage II Low power measurements without quartz tube using TE 112 mode
TE 112 Mode
Material
Ls (cm)
Lp (cm)
Q
891
Reference (0.141 gram)
13.00
1.55
Stage I initial (10 grams)
13.00
2.80
790
Exp4 (0.34 grams)
12.95
2.40
320
12.90
1.90
445
Exp6 (0.39 grams)
Stage II initial (11.5315 grams) 13.00
2 .0 0
816
5.4.3 High Power Heating Experiments Procedure
A single fixed frequency at 2.45 GHz was utilized for the high power experiments
for both Stage I and Stage II experiments. The quartz crucible was placed in the center of
the cavity bottom floor and was used as a pedestal, while the quartz dish holder was used
to contain the gel or powder material. The material load height was
8
mm for the TM012
mode excitation and 60 mm for the TE 112 mode excitation. For the TEn 2 mode, this
positioned the material load
6
cm above the cavity bottom plate. At this height, the
magnetic field is at a maximum while the electric field is a minimum. The quartz tube
chimney was only utilized in Stage II when the material samples were in a gel form.
In the beginning of each heating experiment, the input power was typically
maintained constant within the range of 150 to 200 Watts to avoid the overflow of the
material onto the cavity floor. The cavity was continuously tuned to critically coupled by
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manually adjusting cavity length and coupling probe depth to minimize reflected power.
Data points of incident power, reflected power, cavity length, and coupling probe depth
were taken periodically during the heating process.
5.4.4 High Power Heating Experiments Results
5.4.4.1 Stage I
In Stage I, eight different samples were produced using high power experiments.
Seven samples were heated using the TM 012 mode and one sample was heated using the
TE 112 mode. Below is the description for each experiment which describe the heating
time versus input power, reflected power, cavity length and probe depth data points from
the beginning until the end of the experiment.
1. Experiment I
The initial position of the cavity length and the coupling probe depth was 14.53 cm
and 1.9 cm respectively. The initial incident power was approximately 175 watts. After
ten minutes of heating, the material started to change color and turned to liquid. Five
minutes later, when the input power was increased to 250 watts, the material became
black but remained a liquid. Smoke started to come out from the top snout of the cavity
after ten additional minutes of heating. While smoke was present inside the cavity, the
incident power meter reading was unstable. This is probably due to the smoke, which
was created inside in the cavity chamber during the heating process detuning the cavity.
The experiment was stopped at the 25-minute mark. The heated product was labeled as
Sample I.
This product was also referred to as the half product for the low power
measurements.
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2. Experiment II
The starting input power was set to 150 watts. The initial cavity length was 14.55 cm
and the coupling probe depth was 1.6 cm. During the first ten minutes of the heating
process, the material started to bubble and changed color from orange to brown. Five
minutes later, the material turned black and became liquid. When the input power was
raised to 300 watts, smoke was emitted from the cavity. The amount of reflected power
started to increase as the amount of smoke increased. To minimize the reflected power,
the coupling probe was adjusted outward a few millimeters. After 30 minutes of the
heating process, the experiment was stopped. The final product was a thick liquid, and
was labeled as Sample II.
3. Experiment III
After the first five minutes of heating, the material started to bubble and boil rapidly
and changed into a liquid state. The color of the material changed slowly from orange to
brownish and eventually became black after about 15 minutes.
During these color
changes, the minimum reflected power was at its highest, which means that this is the
hardest point to match the load. The smoke started to come out from the top snout of the
cavity. A few minutes later, smoke also came out from the sidewalls of the cavity. After
about a half-hour of heating, most of the water evaporated from the material. Six minutes
later, there was a discharge inside the cavity and the experiment was stopped. The total
amount experiment time was 36 minutes. The final product was labeled as Sample III.
4. Experiment IV
The material was weighed prior to the heating process. The weight of the material
before the heating process was 15.668 grams. After the first 15 minutes of heating, the
89
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material bubbled and boiled rapidly. The coupling probe depth was decreased to match
the load. A few minutes later, the color of the material started to change from orange to
brown and eventually to black. The entire material became liquid and smoke started to
appear from the top snout and sidewalls of the cavity. After 39 minutes of heating, the
material became solid. At the 54-minute mark, the material started to glow, producing
different colors (red, blue, green) in several spots inside the quartz glass. The material
was allowed to glow for fifteen minutes before the experiment was stopped at the 69minute mark. The material was removed from the cavity and weighed. The weight of the
heated material was found to be 0.413 grams. The final product was labeled as Sample
IV.
5. Experiment V
The weight of the material prior to the heating process was 14.32 grams. As
expected, after the first half hour of the heating process, the material changed color and
changed from a liquid into a solid. After 57 minutes, the material started to glow. While
the material was glowing, there were occasional discharges inside the cavity. Manual
detuning of the probe depth (and hence decreasing the input power) was performed to
extinguish the discharge in the cavity chamber. The experiment was stopped at the 72minute mark. The material was removed from the cavity and weighed. The weight of the
heated material was found to be 0.966 grams. The area that was glowing turned brown
when the material cooled down. The brown material was found to be a magnetic material
after being tested using a magnet. The final product was labeled as Sample V.
6. Experiment VI
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The weight o f the material prior to the heating process was 14.549 grams. The
input power increased slowly as heating time increased. The material boiled and changed
its color and the smoke started to come out from the snout and sidewalls of the cavity. At
the
68
-minute mark, the material started to glow at several points. Brown color formed
along the edges and inside the quartz glass. The experiment was stopped at the 83minute mark. The material weight after being heated was found to be 0.426 grams. The
final product was labeled as Sample VI.
7. Experiment VII
The TE 112 mode was employed. The initial calibration for the cavity length was
12.85 cm and the coupling probe depth was 2.6 cm. The weight of the material prior to
the heating process was 16.440 grams. After five minutes of the heating process, the
material started to bubble and boil slowly. The smoke gradually came out of the cavity
top at the 9-minute mark. To minimize the reflected power, the coupling probe was
adjusted outward to 2.0 cm.
After 17 minutes of the heating process, the material
changed color but remained in liquid form. The input power was increased to 400 watts
and the material was heated for another 30 minutes. The amount of reflected power was
almost zero when the coupling probe was adjusted to 1.2 cm. After 65 minutes of heating,
the material was still in a liquid state and the color was black brown. At the
8 6 -minute
mark, a brownish material was formed along the top edge of the quartz glass pedestal.
The entire material was still in a liquid state. The material was heated for another 40
minutes. During heating, the coupling probe was adjusted outward to 1.0 cm. At the
126-minute mark, the material was still in liquid form, but slightly thicker. There was a
viscous material formed in the center of the quartz glass. After an additional 70 minutes
91
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of the heating process, the experiment was stopped. The material was still in liquid form
and labeled as Sample VII.
8. Experiment VIII
The TM 012 mode was used for this experiment. The weight of the material prior to
the heating process was 16.215 grams. The input power was set to 150 watts. After four
minutes of heating, the material started to bubble and boil slowly. The coupling probe
was adjusted outward to minimize the amount of reflected power. At the ten-minute
mark, the input power was raised to 350 watts and smoke came out of the cavity snout.
The color changed to brown then black. After half an hour of heating, most of the water
had evaporated and the material became solid. At the 35-minute mark, the material
glowed and produced a candle-like flame on top of the material. The coupling probe
depth was detuned to extinguish the flame and the experiment was terminated. A brown
substance was formed from the material that was glowing during the heating process.
Shown in Figures 5.16-5.17 are the graphs of the cavity length and coupling probe
depth position versus time for five experiments using the TM 012 mode.
The initial
calibration for cavity length and probe depth differs slightly for each experiment. This is
probably due to the different weight and shape of the material. The coupling probe was
adjusted outward in order to maintain critical coupling as the material became lossless
during the heating process.
When the material started to glow, the cavity length and the coupling probe depth
reached a steady state at 14.5 cm and around 0.6 cm respectively. These values are very
close to the low power measurements. Hence, there is an excellent agreement between
the low power and high power measurement on the final product.
92
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14.6
£o
O
)
c
0)
14.55 t
♦ Experiment III
♦ Experiment VI
♦
■ Experiment IV
• Experiment VIII
a
Experiment V
m
14.5
a
14.45 +
14.4
<>
♦
10
0
20
30
40
50
60
70
80
90
Time (min)
Figure 5.16 - Stage I cavity lengths versus time using TM 012 mode
2.5
♦ Experiment III
♦ Experiment VI
■ Experiment IV
a Experiment VIII
a
Experiment V
Q.
2
0)
X
o)
oc>
1.5
I
o
0.5
0
10
*
*
20
30
40
50
60
70
80
90
Time (min)
Figure 5.17 - Stage I coupling probe depth versus time using TM 012 mode
Figures 5.18-5.19 display the cavity lengths and coupling probe depth versus time
for TE 112 mode excitation. The material sample was placed in the high magnetic field
position (60 mm). When the initial product was inserted inside the cavity, the initial
cavity length was 12.85 cm. As the material changed its dielectric properties, the cavity
length was decreasing a few millimeters. The coupling probe depth was also decreasing
from
2 .6
cm to
1 .0
cm, as the material became lossless and the temperature increased
inside the cavity. The heating time using the TE 112 mode was over 4 hours as shown on
93
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the graph. The long heating time using this mode indicates that after the initial boiling of
the material, the microwave energy is not efficiently coupled to the material.
12.855
12.85
12.845
12.84
2.835
12.83
12.825
12.82
2.815
♦ Experiment VII
0
20
40
60
80
100
120
140
160
180
200
220
240
260
Time (min)
Figure 5.18 - Stage I cavity lengths versus time using TE 112 mode
♦ Experiment VII
° 0.5
0
20
40
60
80
100
120
140
160
180
200
220
240
260
Time (min)
Figure 5.19 - Stage I coupling probe depths versus time using TE 112 mode
5 .4 .4 .2
Stage II
Five high power-heating experiments were performed to heat the various material
s a m p le s .
T h e “ r e f e r e n c e m a t e r ia l ,” e x p 4 , a n d e x p 6 s a m p l e s
were
h e a te d
using
T E 112
mode. The exp4 and exp6 correspond to the experiment IV and experiment VI material
samples obtained from the Stage I experiments. The numbering system of exp4 and exp 6
used for identifying the samples was selected in order to differentiate between the
94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
samples in the two experimental stages. Two initial materials, one from stage I and the
other one from stage II, were heated using both the TM 012 and TEm mode. For the
“stage II initial material” experiment, the quartz tube chimney was utilized during the
TM 012 excitation. The input power was kept constant at around 100 watts during material
samples heating process. Also, the cavity length, Ls, was kept at original height obtained
from low power measurements. Below is the description for each experiment:
1. Reference sample
Two experimental runs were performed on the reference sample before the
reference sample could be heated successfully. The weight of the material sample prior
to the heating process was 0.141 grams. The initial position for the cavity short, Ls, was
13.0 cm and the coupling probe depth, Lp, was 1.55 cm.
On the first run, the initial input power was set at 100 watts with reflected power
reading 15 watts. The coupling probe depth was then adjusted outward and inward to
minimize the amount of reflected power.
However, after 4 minutes of constant
adjustment of the coupling probe depth, the scale reading of the reflected power did not
decrease. The pyrometer did not display any temperature reading, which indicates that
the temperature of the material was below 200° C. The experiment was stopped at the 5minutes mark due to the blue coaxial cable connector becoming warm.
On the second run, the initial input power was 100 watts. The reflected power
was 10 watts. The coupling probe depth was adjusted outward to 1.5 cm and the amount
of reflected power decreased to
8
watts. At the 2-minute mark, the temperature reading
was 317° C. After 5 minutes into the heating process, the material suddenly glowed red.
The coupling probe depth was 1.2 cm inside the cavity chamber.
The temperature
95
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reading was 620° C. The coupling probe depth was adjusted to 0.8 cm at the 15-minute
mark. The reflected power decreased to 5 watts. The temperature reading was 710° C
after 20 minutes of heating. The highest temperature reading was 835° C at the 28minute mark with coupling probe depth of 0.65 cm. The reference sample was heated for
30 minutes with maximum input power of 120 watts. After the heating, the material did
not change color; it remained brown.
2. Stage I initial material sample
The stage I initial material was heated using both the TM 012 and TE 112 modes.
The initial position for the cavity short, Ls, and probe depth, Lp, was 14.415 cm and 2.3
cm respectively. The input power was 100 watts with reflected power of 4 watts. Smoke
came out of the cavity snout after 2 minutes of heating. At the 5-minute mark, the color
of the sample changed to black but the sample was still in liquid form. The cavity short,
Ls, was adjusted to 14.4 cm and the coupling probe depth, Lp, was adjusted to 1.1 cm.
The input power was raised to 150 watts and power reflected increased to
8
watts. After
10 minutes of heating, the material became black and solid. At the 13-minute mark, a
discharge occurred inside the cavity chamber. The experiment was stopped. A low
power measurement was performed to obtain final positions of the cavity short and the
coupling probe depth. The cavity short and coupling probe depth was found to be 14.5
cm and 0 . 8 cm respectively.
The excitation mode then was switched to TEm mode.
The low power
measurement for the cavity short, Ls, was 13.0 cm and coupling probe depth, Lp, was 2.8
cm. The initial input power was 100 watts with reflected power of 2 watts. At the 30second mark, the material was glowing orange and a little smoke was coming out of the
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cavity snout. The input power was lowered to 80 watts to avoid a discharge. White
sparks were occasionally emitted inside the quartz crucible.
adjusted outward to 1.8 cm to minimize the reflected power.
The probe depth was
The experiment was
stopped after 44 minutes. The material became brown and black. The material was
heated for another 16 minutes with input power of 100 watts and reflected of 3 watts.
The material occasionally produced white sparks and glowed red and orange. After the
heating process, some o f the material became brown, gray, and black.
3. Exp4 sample
The weight of the material sample prior to the heating process was 0.34 grams.
The initial input power was 200 watts. The reflected power was 2 watts. After 2 minutes
of heating, the material started to glow and spark. At the 3-minute mark, the temperature
reading from the pyrometer was 875° C. At the 5-minute mark, the temperature reading
increased to 985° C. After 6 minutes of the heating process, the temperature reading was
993° C. A little smoke was emitted from the cavity snout. When the input power was
lowered to 80 watts, the temperature reading was 857° C. The reflected power was
constant at 0.5 watts. The material was glowing and produced red, blue and white sparks.
The experiment was stopped after 26 minutes of heating due to the decreasing
temperature and the increasing amount of reflected power. The material became gray,
brown and black.
To critically match the material load, a low power measurement was performed to
recalibrate the cavity short and the probe depth. The new coupling position for the cavity
short, Ls, was 12.9 cm and the coupling probe depth, Lp, was 2.5 cm. High power
heating resumed with initial input power of 100 watts. After 2 minutes of heating, the
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temperature reading was 228° C. One minute later, the temperature reading was 612° C
and was increasing rapidly.
The material started to glow and emitted sparks at
temperature 606° C. The reflected power was 5 watts. The input power was lowered to
80 watts to minimize the reflected power and to avoid a discharge. At the 5-minute mark,
the temperature reading was 635° C and remained constant at around 650° C. After 15
minutes of heating, the temperature reading slowly decreased to 560° C. The probe depth
then adjusted but no increased in temperature. The experiment was stopped after 18
minutes due to high-reflected power.
A low power measurement was performed again to recalibrate the cavity short
and the coupling probe depth. The new cavity short, Ls, and coupling probe depth, Lp,
was 12.9 cm and 2.4 cm. The high power heating resumed with initial input power 200
watts. At the 2-minute mark, the temperature reading was 285° C. One minute later, the
material started to glow and the temperature reading was 495° C. To reduce the reflected
power, the probe depth was adjusted outward and set to 0.8 cm.
The material was
glowing orange and there were no sparks. At the 5-minute mark, the temperature reading
was stable at around 510° C.
When the input power was raised to 150 watts, the
temperature reading increased slightly to 540° C. At the 25-minute mark, the reflected
power increased to 10 watts.
The probe depth, Lp, was adjusted to 1.3 cm.
The
temperature reading was 538° C. At the 37-minute mark, the temperature reading was
535° C. The experiment was stopped after 40 minutes of heating due to difficulty in
matching the load. The temperature reading was 525° C. The material became gray and
brown.
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1000
o
£
a(0
<D
Q.
E
0)
h-
800
600
400
200
first_run
0
10
second_run
20
30
third_run
40
T im e (m in )
Figure 5.20 - Stage II exp4 sample heating time vs. temperature
Shown in Figure 5.20 is the graph o f exp4 sample heating time versus temperature
reading for all three experimental runs. The first run for the exp4 sample reached a
higher temperature than that achieved in the second and third run. This is probably due
to the critical coupling condition and the material properties. At this stage, the material
has more organic component and the material is lossier. In the first five minutes of the
heating process for all three experimental runs, there was a rapid increase in temperature.
Possibly, the material properties were changing, as the material was being heated and
exposed to microwave radiation.
4. Exp6 sample
The weight of the material prior to the heating process was 0.39 grams. The
initial positions for the cavity length, Ls, was 12.90 cm and the coupling probe, Lp was
1.9 cm. The material was black and in the form of a powder. When the input power of
100
watts was applied, there was a reddish and orange glow produced immediately inside
the cavity chamber. The reflected power was 5 watts and the temperature reading was
increasing rapidly. At the 3-minute mark, the temperature reading was 750° C. The
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experiment was stopped after
8
minutes of heating due to sudden increased in high-
reflected power, and the blue coaxial cable became warm.
The highest temperature
reading was 810° C during the heating process. The material turned gray and brown. The
final position of the coupling probe depth was 1.7 cm, and the cavity short remains
constant at 12.9 cm.
5. Stage II initial material sample
The initial material was heated for 39 minutes using the TM 012 mode and for 17
minutes using the TEm mode. The weight of the initial material prior to high power
heating was 11.5313 grams. The initial input was set to 100 watts. The material started
to boil, and smoke was emitted from the cavity snout. The temperature reading increased
rapidly from 225° to 280° C. After 15 minutes of heating, the material became liquid and
black. After an additional 18 minutes of heating, the material became solid and black;
however, the material was not dry and there was still some oil-like residue remaining. A
low power measurement was performed to obtain critical coupling condition. After
6
minutes o f additional heating, the material became solid, black and dry. During this
additional heating process, the temperature reading was stable at around 280°-295° C.
The excitation mode then switched to the TE 112. The material was placed inside
the quartz dish holder (instead of the crucible) and the quartz crucible was used as a
pedestal to raise the material load position. The height of the material was
6
cm from the
cavity bottom floor, which is approximately half wavelength. After two minutes of the
heating process, the temperature reading was 220° C. There was no smoke emitted from
the cavity chamber. The temperature reading increased to 275° C at the 7-minute mark.
The temperature reading was 292° C after 10 minutes of heating. Sparks were produced
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inside the cavity chamber at the 11 minute-mark. During the brief sparking stage, the
amount of reflected power was unstable, i.e. the readings fluctuated. A few seconds later,
following the sparking phase, a stable orange and reddish glow occurred inside the cavity
chamber. The amount of reflected power was zero and the temperature reading was 560°
C. The experiment was stopped after 17 minutes of heating. The amount of the final
product was reduced and was brown and powdery. The Q was measured and was found
to be 1400. It is very close to the reference material Q.
5.4.4.3 Summary of Important Observations
The dielectric properties vary with temperature. As the temperature of the heated
material loads increase due to heating, the dielectric constants also change linearly with
the temperature.
In addition to the changes in dielectric constant, the resonant
frequencies also change as the material is heated. Thus, the cavity length and the probe
depth position had to be readjusted during the heating process to maintain the material
loaded cavity resonance at 2.45 GHz such that most of the incident power was coupled
into the cavity applicator under critical coupling conditions.
In the low power experiments, for the TM 012 mode, the insertion of the quartz
tube inside the cavity applicator did not affect the critical coupling condition. However,
for the TE 112 mode, the presence of the quartz tube inside the cavity applicator caused the
resonance frequency to shift down and resulted in under coupling condition. When the
starting material is in a gel form, the TM 012 mode excitation should be used first to
remove the water and organic compounds of the material. When the material becomes
dry and produces no smoke, then the TE 112 mode can be applied without a quartz tube
chimney to obtain a solid and brown final product.
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5.5 Graphite Fiber Experiments
5.5.1 Low Power Measurements Procedure
The graphite fiber with a certain length and thickness was placed inside a quartz
tube.
The outer and inner diameters of the quartz tube were 3 mm and 2 mm
respectively.
The quartz tube was placed in the center and along the axis of the
cylindrical cavity applicator. Shown in Figure 3.4 in Chapter 3 is the microwave cavity
applicator cross-section and fiber placement set up. The fibers were bundled together and
the upper end of the bundle was tied using a cotton thread, which was then pulled using a
needle. This method using a thread and a needle allows the insertion of the graphite
fibers into the desired location inside the quartz tube. The fiber enclosed in the quartz
tube was then inserted into the cavity applicator. Using the microwave system network
shown in Figure 3.5, the cavity length, coupling probe depth, Q, and resonant frequency
were measured.
5.5.2 Low Power Measurements Results
The length of the fiber was 16 cm and was approximately 2 mm thick, thus it
passed completely through the cavity electromagnetic excitation zone as shown in Figure
10. The cavity height was fixed at 14.6 cm and the resonance frequency was swept from
2.0 to 2.5 GHz. The fixed cavity height method was employed in order to identify the
eigenmode and the resonance frequency.
Table 5.4 - Graphite (16 cm) loaded cavity experiments with a fixed cavity height
Cavity Height, Ls Resonance
Coupling
Probe Eigenmode
(cm)
Frequency (GHz)
Depth (cm)
14.6
2.2925
0.9
TMin & TEon
14.6
2.308
0.9
TE 112
14.6
2.4845
0 .2
TEm
102
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Table 5.5 - Graphite loaded cavity experiments with a fixed resonance frequency 16 cm
Coupling
Probe Eigenmode
Cavity Height, Ls Resonance
Depth
(cm)
Frequency (GHz)
(cm)
TMni & TE011
0.4
2.45
11.4
0.5
t e 112
2.45
13.425
TE
311
1
.
0
2.45
15.825
As shown both in Table 5.4 and Table 5.5, the TM 012 mode was not listed in the
table because it disappears as the graphite fiber introduced into the cavity. It is possibly
that the graphite fibers short-circuited the cavity resonator due to its high conductivity.
However, this also indicates that the TM012 will excite the graphite fibers since
electromagnetic excitation clearly occurred in the cavity. In contrary, there was no major
change in excitations Q curve observed in the other three modes.
The fibers’ lengths were then reduced to 12 cm, which is about one wavelength.
Each end of the fibers was 1.3 cm away from the cavity top and bottom plates. Since the
cavity height was equal to 14.6 cm, this positioned the mid length fiber inside the quartz
tube was exactly half of the height of the cavity. The quartz tube filled with the graphite
fibers was placed in the center of the cavity applicator. Critical coupling of the TM 012
mode was successfully achieved using the correct length and exact placement of the fiber
load. Shown in Table 5.6 is the measured result of the cavity height, coupling probe
depth and the quality factor obtained for the TM 012 and the TEm modes with a fixed
resonant frequency at 2.45 GHz. The Q of both modes is in low hundreds.
Table 5.6 - Graphite fibers load with a length of 12 cm at a fixed frequency
Cavity Height, Ls Resonance
Coupling
Probe Quality Factor
(cm)
Frequency (GHz)
Depth (cm)
(Dimensionless)
14.5
2.45
1.7
350
13.4
2.45
0 .8
245
103
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5.5.3 High Power Heating Experimental Procedure
Using
the
critical
coupling
conditions obtained
from the
low power
measurements, the fibers were then heated using the high power. The graphite fibers
were heated using the TM 012 and TEm mode excitations.
These two modes were
selected because of their low Q based on the simulation and low power measurements
results. Also, critical coupling or matched conditions were obtained in the low power
experiments. These show that the microwave electromagnetic energy will be coupled
easily into the fibers, thus efficient and optimum heating can be achieved.
The
microwave system network used for the high power heating is shown in Figure 3.7 in
Chapter 3. The argon gas tank and flow meter controller were connected to the T-shaped
swage lock connector. The microwave input power used during the experiments varied
between 50 to 150 Watts. The temperature measurement was done using a hand held
infrared thermometer (Ultimax - model number EK-3292). The thermometer is capable
of measuring temperature in the range of 600° to 3000° C.
5.5.4 High Power Heating Experimental Results
1. Experiment 1
The excitation mode was the TMoi2 - The location of the fibers inside the cavity
was 1.3 cm above the cavity bottom and top short as shown in Figure 3.4. Argon gas
flow rate was set to 200 seem. Initially, when the input power of 100 watts was applied
to the cavity applicator, the fibers glow orange. Then input power was increased to 150
watts and the cavity length had to be readjusted about 3 mm to minimize the reflected
power. After retuning the cavity length, plasma occurred at the top and bottom end of the
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quartz tube. The region where plasma occurred in the quartz tube was not filled with
fibers. The input power was then lowered to 75 watts and the fibers glow turned reddish
without plasma observed inside the quartz tube. The glow was uniform along the fiber
surface.
The temperature measured was 652° C.
At the end of the high power
experiment, the final cavity height and coupling probe depth positions were equal to 14.5
cm and 2.3 cm respectively.
2. Experiments 2
The excitation mode was the TEm mode. Argon flow rate was set to 120 seem. It
took about 100 Watts of microwave input power to make the fibers glow. Also, plasma
occurred along the graphite fibers uniformly inside the quartz tube. The input power was
then varied in order to examine the presence of the plasma along the fibers. When the
input power was lowered to 75 watts, the plasma and the glow of the fibers became
weaker. Likewise, when the input power was increased to 150 watts, the intensity of the
plasma and the glow increased. After retuning the cavity height, the amount of reflected
power only decreases slightly and plasma remained inside the quartz tube. By using an
optical temperature sensor, the fiber temperature was measured via the observation
window. The recorded temperature was 672° Celsius. The experiment was stopped at 5minutes mark. The plasma occurring in the quartz tube might indicate that some of the
electromagnetic energies are coupled to the argon gas in addition to the graphite fibers.
Furthermore, this might have to do with the electric and magnetic fields distribution
inside the cavity applicator. In this experiment, when the coupling probe was adjusted
inward or outward inside the cavity, it did not have any affect on the reflected power
meter reading.
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Chapter 6
SUMMARY AND RECOMMENDATIONS
6.1 Summary of results
6.1.1 Numerical Analysis using Ansoft HFSS
The simulation of empty cylindrical cavity, silicon wafer (TM 012 , TM m, and
TEin modes), magnetic material (TM 012 and TEn 2 modes), and various material sizes for
graphite fiber were successfully completed. The resonance frequency, quality factor, and
the electric-field patterns for each mode were analyzed.
In the case of the TM012 mode, the optimal position for the silicon wafer is a
quarter wavelength, which is approximately at pedestal height 35.5 mm. At that height
using the TM012 mode excitation, the electric fields are tangential to the silicon wafer.
With the electric fields tangential, surface currents are induced on the silicon.
The
electric loss tangent of the silicon affects the strength of these surface currents. The
higher the electric loss tangent, the lower the Q and the easier the material is to heat.
These surface currents create a Joule heating effect, which quickly heats the material. As
was expected, the quality factor was at its minimum in regions of high electric field. For
the T M m mode with a cavity height equal to 11.3 cm, the lowest Q was found at 5.65 cm
which is one half wavelength. Therefore, the optimal position for the heating the silicon
wafer in T M m is at one half wavelength. For T E m mode with a cavity height equal to
68
mm, the lowest Q was found at two different positions. The lowest Q for the three-
inch and four-inch silicon wafers was found at 10 mm and 34 mm respectively.
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However, by examining the electric field pattern for the three silicon wafers, the optimal
position for heating the silicon in TEm mode is at one half wavelength.
In the magnetic material load simulation, both the TM012 and TEm modes have
been simulated and used as guidance in the experimental measurements. The resonance
frequencies of the magnetic material decrease linearly as the material load heights
increase with the quartz pedestal. By comparing the quality factor and electric field
patterns at each height, the best coupling position to heat the magnetic material for the
TM 012 and TEm modes were
8
mm and 63 mm respectively.
A graphite material size of 2 mm has been simulated in the seven-inch cylindrical
cavity applicator. The material load size was set up to obtain the first ten eigenmodes
that exist in the cavity. Additional output parameters were the resonance frequencies,
quality factor, and the electric field pattern. The resonance frequency for TM 012 mode
was found to be 2.60785 GHz. It is slightly higher than the theoretical value that is
2.4513 GHz. The TM 012 mode has the lowest Q equal to 2,016 compared to other nine
modes. Hence, TM 012 mode excitation is a good choice to heat the graphite material in
the cylindrical cavity applicator.
It is important to note that the Ansoft analysis cannot be directly compared with
the low power experiments. This is due to the fact that the theoretical cavity applicator is
not exactly the same as the experimental system. The theoretical cavity applicator does
not have a snout, coupling probe port, or observation window. Furthermore, the material
properties are not exactly the same either. However, considering these limitations, the
Ansoft HFSS calculations compare well with the experimental measurements.
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The
plotted electric field patterns can be utilized to help understand the heating behavior of
each material load inside the cavity applicator.
6.1.2 Experimental Measurements of the Material Loadings
A microwave heating measurement and procedure using several mode resonant
cavities has been developed to heat the material successfully. Both the low and high
power experiments in silicon wafers, magnetic materials, and graphite fibers have
demonstrated that the heating cycle is repeatable and can be made controllable by
adjustment o f input power, material load position, or mode excitation.
1. Silicon wafers
Two different approaches to heating the silicon wafer more effectively partly
depend on the type of generator, network and circuitry. In one case, the frequency is held
constant while the cavity height dominates the mode excited. In other case, the cavity
height is held constant and a different frequency provides different modes. Both cases
can yield almost identical results, but in industrial applications, fixing the cavity height
and varying the frequency would give the best-desired results. Speed is an important
factor when considering which method is to be used. When using a fixed frequency, the
cavity height must be changed in order to excite a different mode. This can take up to a
few seconds increasing the undesired time delay between the different modes.
If a
constant cavity height is used, changing the frequency of the signal is almost trivial and
instantaneous. Clearly the constant cavity height is the better method for exciting various
modes.
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The optimal position for heating the silicon wafer is mainly dependent on how the
electric fields are arranged in the cavity. The wafer is heated the most efficiently when
the electric fields are tangential to the surface of the silicon wafer. The electric fields,
which are tangential, induce surface currents creating a Joule heating effect. Depending
on the excitation mode, the electric fields are tangential to the wafer in different
locations. High power heating experiments have demonstrated that efficient and uniform
heating of the silicon wafer can be achieved.
The simulation and the low power
experiments play a very useful role in determining the best position to heat the silicon
wafer.
2. Magnetic material
A microwave heating procedure for the magnetic material has been developed for
the stage I experiment. The low power measurements were performed to determine the
best experimental coupling and optimum heating positions of the material inside the
cavity applicator using TM 012 and TE 112 mode excitations. Based on the low power
experimental results, a high power (50-300 W) heating process cycle was developed. A
final product of solid brown color was obtained after the high power heating experiments
using TM 012 mode. The final product was found to be a magnetic material and had low
microwave losses (as compared to the initial product).
In the low power experiments, it was found that, as the pedestal height becomes
higher, the resonance frequency shifts lower. This is due to the presence of the quartz
pedestal inside the cavity. The quality factor for the initial product had the lowest Q
when compared to the half product and final product Q. This indicates that the initial
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material is much easier to heat and has higher losses than the final product. The coupling
probe depth consistently decreased, as the material became less lossy and moved closer to
the position for the final product.
In the high power TM012 experiments, the initial calibration for the cavity length
and probe depth varied slightly for each experiment. This is probably due to the different
initial weights o f the material. During the course o f the experiment, the cavity length and
coupling probe depth had to be adjusted constantly to match the load. The coupling
probe depths consistently decreased, as the material became lossless and the temperature
inside the cavity increased. Once the material glowed, the cavity length reached steady
state at 14.5 cm and the probe depth reached steady state around 0.6 cm. These values
are almost identical to the low power final product load measurements. Hence, there was
a good agreement between the low power and high power final product load
measurements.
The TM012 mode excitation was found to be a faster heating process compared to
the TE112 mode excitation.
For example, a solid brown material was obtained in 35
minutes o f heating process using TM012 in contrast to 256 minutes o f heating process
using TE112 mode. In the TE112 case, solid brown material was only formed along the top
edge o f quartz glass container, while most o f the material was still in a thick liquid form.
A microwave heating procedure for the magnetic material stage II has been also
developed. The initial gel materials were heated using the TM012 mode prior to the TEm
excitation.
Then the material heating was completed with the TEm excitation.
The
powdered material samples were heated using the TEm mode in a region o f high
magnetic field flux.
During the heating process, the temperature o f the material reached
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over 700° C. Final products of solid brown or gray powder were obtained after the high
power heating experiments.
In the low power experiments, for the TM 012 mode, the insertion of the quartz
tube inside the cavity applicator did not affect the critical coupling condition. However,
for the TE 112 mode, the presence of the quartz tube inside the cavity applicator caused the
resonance frequency to shift down and resulted in under coupling condition. When the
starting material is in a gel form, the TM012 mode excitation should be used first to
remove the water and organic compounds of the material. When the material becomes
dry and produces no smoke, then the TE 112 mode can be applied to obtain a solid and
brown final product.
During the course of the experiment, the cavity length and coupling probe depth
had to be adjusted constantly to match the load. The coupling probe depths consistently
decreased, as the material became lossless. The adjustment of the cavity length was very
sensitive. It required only a few millimeters of adjustment to achieve the best match.
3. Graphite fibers
Preliminary heating of the graphite fibers bundle has been performed.
The
minimum amount of input power required to heat the graphite fibers uniformly along the
12 cm length is about 50 watts. Given the correct amount of input power and proper
tuning of the cavity applicator, the TM 012 mode can be used to heat the graphite fibers
without exciting the plasma in the quartz tube. On the other hand, when the TEn 2 mode
was used to heat the graphite fibers, plasma occurred inside the quartz tube when input
power was applied to the cavity applicator. Depending on the applications, either mode
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has demonstrated that heating the graphite fibers are possible with exact placement,
length, and coupling parameters conditions.
6.2 Recommendations for Future Research
This research has examined the methodology used to heat various materials
loading inside the cavity applicator using both numerical analysis and experimental
measurements. There are a few suggestions that can be conducted for future research that
may lead to deeper understanding of the heating process of these materials and to
improve the design of the microwave cavity reactors.
The first suggestion for future research has to do with numerical simulation. A
more detailed problem setup with the Ansoft HFSS software package should be analyzed
to predict the experimental results.
One-unit port cavity applicators that include a
coupling probe should be simulated in order to obtain more precise numerical model
solutions of the quality factor calculation and actual field pattern distribution inside the
cavity applicator.
By adding a coupling probe from the top or side of the cavity,
observation window, and snout in the cavity applicator geometry, it may be useful to help
design more optimum microwave reactors.
The second recommendation has to do with the experimental measurements. In
order to complete this research, a better design of graphite fibers set up in the cavity
applicator should be considered. For example, in the current design, in order to remove
the quartz tube from the cavity applicator, the quartz tube has to be broken at the end of
each experiment to obtain the heated sample. Instead of gluing the quartz tube and the
plastic tubing using an epoxy, a different approached should be employed. This will
speed up the heating process.
Secondly, further investigation on the high power
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experiments of the graphite fibers should be conducted to achieve a more uniform and
higher temperature reading. In order to obtain higher temperature, various mixtures of
gases such as methane and hydrogen can be utilized, and higher input power can be
applied without causing a large mismatch in the system. These exploratory high powerheating experiments on the graphite fibers could be useful for various applications, such
as, fiber coating in chemical vapor deposition, nanodiamond synthesis using graphite
fibers as a substrate, and perhaps growing carbon nanotubes.
113
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APPENDICES
u
1
Signature Checked
Date
RevNo Revision note
in|
Itemref
Quantity
Designed by
K Hemawan
Material Brass
Checked by
J Asmussen
Article No /Reference
Approved by - date
J Asmussen - 2/8/02
Michigan S t a t e U n i v e r s i t y
File name
1 Date
Brass_Plugdwg ' 2/7/D2
Scale
1
1
B R A S S PLUG
Dimensions are in millimeters
eneral Tolerance. +0.2
Edition
Sheet
1/ 1
Appendix 1 - AutoCAD drawing of the brass plug installed in the unknown magnetic
material cavity applicator
114
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u
Itemref
Quantity
Designed by
K Hemawan
Signature Checked
Date
RevNo Revision note
Material Quartz
Checked by
J Asmussen
Article No /Reference
Approved by - date
J Asmussen - 2/8/02
Mi c hi gan S t a t e U n i v e r s i t y
File name
Date
Quartz_Tube dwg 2/7/02
Scale
2 3
Q U ARTZ TUBE
Dimensions are in millimeters
eneral Tolerance- ± 2
Edition
Sheet
1
1/ 1
Appendix 2 - AutoCAD drawing of the quartz tube installed in the unknown magnetic
material cavity applicator
115
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Resistivity (£2 —cm)
Dopant concentration (cm' 3 )
Appendix 3 - Resistivity versus dopant concentration at 300 K
116
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Appendix 4.a - Silicon wafer placement set up at the bottom plate of the cavity applicator
Appendix 4.b - Pyrometer set up for the unknown magnetic material high power
experiments
117
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Appendix 5 - Quartz tube connection with the swage lock connector for the graphite
fibers experiments
118
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REFERENCES
1. Haw-Hwa Lin, Theoretical Formulation and Experimental Investigation of a
Cylindrical Cavity Loaded with Lossy Dielectric Materials, Ph.D. dissertation, Michigan
State University, 1989.
2. Edward B. Manring and Jes Asmussen, Jr., “Numerical Calculations for Single-mode
Continuous Processing of Rods and Filaments”, Polymeric Materials Science &
Engineering, vol 6 6 , pp476-477,1990.
3. Bradford L. Smith and Michel-Henri Carpenter, The Microwave Engineering
Handbook, vol 1, Microwave Components, Van Nostrand Reinhold, New York, 1993.
4. Mark C. Finzel, Microwave Heating of Polar Liquids and Solids, M.S. thesis,
Michigan State University, 1985.
5. Lydell Lemoine Frasch, An Experimental and Theoretical Study of a Microwave
Cavity Applicator Loaded with Lossy Materials, Ph.D. dissertation, Michigan State
University, 1987.
. Edward Benjamin Manring, An Experimental Investigation of the Microwave Heating
of Solid Non-Reactive Materials in a Circular Cylindrical Resonant Cavity, M.S. thesis,
Michigan State University, 1988.
6
6 b. J.Asmussen, H.H. Lin, B.Manring, and R.Fritz, “Single mode or controlled
multimode microwave cavity applicator for precision material processing”, Rev. Sci.
Inst., 58, pp 1477-1482,1987.
7. Jes Asmussen, Jr., Jinder Jow, Martin C. Hawley, and Mark C. Finzel, “Microwave
heating and dielectric diagnosis technique in a single-mode resonant cavity”, Review of
Scientific Instruments, vol.60, N ol, pp96-103,1989.
. Edward B. Manring and J. Asmussen, Jr., “Numerical model for the modes of a lossy,
coaxially-loaded cylindrical cavity”, Microwaves: Theory and Application in Material
Processing II, Ceramic Transactions, vol. 36, pp 201-212, 1993.
8
9. Stanley J. Whitehair, Experimental Development of a Microwave Electrothermal
Thruster, Ph.D. dissertation, Michigan State University, 1986.
10. Martin C. Hawley, Jianghua A Wei, and Valerie Adegbite, “Microwave Processing of
polymer Composite”, Materials Research Society, Symposium Proceedings, Microwave
Processing of Materials V, Volume 347, pp669-680,1994.
11. Leonard J. Mahoney, The Design and Testing of a Compact Electron Cyclotron
Resonant Microwave-Cavity Ion Source, M.S. thesis, Michigan State University, 1989
119
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1lb. Joseph Root and Jes Asmussen, “Experimental performance of a microwave cavity
plasma disk ion source”, Rev. Sci.Inst., 56(8), pp 1511-1519,1985.
12. Timothy A. Grotjohn and Jes Asmussen, “Numerical Simulation o f Resonant Cavity
Microwave Systems for Material Processing”, Materials Research Society, Symposium
Proceedings, Microwave Processing of Materials V, Volume 430, pp357-362,1996.
13. Akira Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering,
Prentice Hall, New Jersey, 1991.
14. David K. Cheng, Field and Wave Electromagnetics, Second Edition, Addison-Wesley
Publishing Company, November 1992.
15. Jes Asmussen and Timothy Grotjohn., “Microwave Applicator Theory - Excitation
and Scaling,” Handouts, October. 2000.
16. Jes Asmussen and Timothy Grotjohn, “A Review of Industrial Microwave Plasma
and Materials Processing Technologies,” Handouts, Department of Electrical and
Computer Engineering, Michigan State University.
17. W.R. Runyan, Silicon Semiconductor Technology, Texas Instruments Electronic
Series, McGraw-Hill Book Company, New York, 1965.
18. D.M. Pozar, Microwave Engineering, Addison-Wesley Publishing Company, Inc.,
Reading, Massachusetts (1998).
19. K-Y. Lee, Microwave Processing of Ceramics and Ceramic Composites Using a
Single-Mode Microwave Cavity, Ph.D. Dissertation, Michigan State University, 1998.
20. “Getting Started: An Antenna Problem”, Handouts, Ansoft High-Frequency Structure
Simulator, October 1999.
21. Keith Thompson, John H. Booske, Reid F. Cooper, Yogesh B. Gianchandani, and
Shiaoping Ge, “Temperature measurement in microwave-heated silicon wafers”,
Microwaves: Theory and Application in Material Processing V, pp391-398, 1999.
120
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