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The design, fabrication and applications of a microfabricated microwave eddy current probe

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THE DESIGN, FABRICATION AND APPLICATIONS OF A MICROFABRICATED
MICROWAVE EDDY CURRENT PROBE
by
Carlton C. Watson
A thesis submitted in partial fulfillment of the requirements
for the Doctor o f Philosophy degree in Physics
in the Graduate College o f The University o f Iowa
July 2001
Thesis supervisors:
Associate Professor Winston Chan
Professor John Schweitzer
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UMI Number: 3018626
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Graduate College
The University o f Iowa
Iowa City, Iowa
CERTIFICATE OF APPROVAL
PH.D. THESIS
This is to certify that the Ph.D. thesis o f
Carlton C. Watson
has been approved by the Examining Committee for
the thesis requirement for the D octor o f Philosophy
degree in Physics at the July 2001 graduation.
Thesis committee:
Thesis supervisor
—
C*J,
Thdsis)sppeiVisi>r
_
- )
^leinber
Member
.
~
VJH t
Smber
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-
To my family, with love
ii
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ACKNOWLEDGMENTS
It is rare that any journey is attempted and completed alone; in this regard, I must
say that it was only through the help, support and even prayers o f many individuals that I
have been able to make it this far. First and foremost, I must give thanks and praise to
God for blessing me with the health and strength to complete this journey. May You
always keep m e humble and obedient. Thanks to my ancestors for paving the way for me,
especially my grandfather Lawrence D ad' Edgecombe - your spirit lives on. To my
parents, two o f the most kind and generous people to walk the face o f this earth, no
amount o f words can folly explain what you mean to me and how much I love you. You
have always supported and continue to support me in every way imaginable. Through
your actions you have taught me how to love unconditionally and to give selflessly. To
my daughter, Alexandrea, may we continue to grow closer together. To my brothers and
sisters, Dellarease, Anthony, Marilyn, Ricardo, Sharon and Kirkwood and their children,
Laura, Ricardo Jr., Lynden Jr., Ashton, Cordell and Lynnard, it was my greatest sacrifice
being away from you, but in a sense the distance brought us even closer.
To my undergraduate mentor at Prairie View A&M University, Dr. Fa-Chung
Fred Wang, thanks for always giving me objective and insightful advice. To Mr. Byron
Hall, Dr. Cory Phillips, Dr. David Staten and Dr. Jacob Willig-Onuwachi, my brothers at
Iowa, thanks for keeping me sane. Thanks to Angie for all the help through the years. I
iii
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am indebted to Dr. Victor Rodgers, Dr. Vincent Rodgers and Dr. Chris Coretsopoulos for
all the help, academic and otherwise. To my friends in the Graduate College, Joe Henry,
Diana Bryant, Paul Meintel and Dean William Welbum, I truly appreciate all the help and
encouragement you have provided for me along the way. Thanks to Dr. Fred Olchowski
for always making time to help me with many technical questions and to Yousef Awad
and Dr. Mohammed Yousef for all your help during the 'eleventh hour'. To all my
friends, classmates and lab mates (especially the people within the physics office) that I
have not mentioned by name, I am no less thankful to you for your help and support. To
my committee members, Professors John Schweitzer, Tom Boggess, John Goree and
David Andersen, thanks for all the help and for being so understanding. I realize that you
have all made great sacrifices in terms o f time and energy to provide constructive input
concerning my dissertation and research.
Last but not least I would like to thank my advisor, Dr. Winston Chan. It was
through your financial support via the NSF grant and graduate assistantships that I was
able to start and continue this research. However, it was only through your patience and
technical and emotional support that I was able to complete it. I have learned many things
from you and was always in awe as to the breadth and depth o f your knowledge. Beyond
technical matters, however, you have taught me a great deal about professionalism and
ethics. For all these things I am eternally grateful.
iv
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TABLE OF CONTENTS
Page
LIST OF TA B LES................................................................................................................... viii
LIST OF FIGURES.....................................................................................................................ix
CHAPTER
1. INTRODUCTION...............................................................................................................1
1.1 Introduction.................................................................................................................1
1.2 Principles.....................................................................................................................2
1.2.1 Eddy Current.................................................................................................2
1.2.2 Microwave Reflection................................................................................. 2
1.3 H istory......................................................................................................................... 3
1.3.1 Eddy Current.................................................................................................3
1.3.2 Microwave Reflection................................................................................. 4
1.4 Present A ctivity.......................................................................................................... 5
1.4.1 Eddy Current Devices...................................................................................5
1.4.2 Capacitive Devices....................................................................................... 6
1.4.3 Microwave R eflection..................................................................................6
1.5 M otivation...................................................................................................................7
1.6 Scope o f This T hesis..................................................................................................8
2. DESIGN............................................................................................................................. 13
2.1 G eneral...................................................................................................................... 13
2.1.1 Maxwell’s Equation..................................................................................13
2.2 C oil............................................................................................................................. 14
2.2.1 Physical D esign...........................................................................................14
2.2.2 Optimization................................................................................................ 15
2.2.3 Fabrication Considerations........................................................................ 16
2.2.4 The Classic Problem................................................................................... 16
2.2.4.1 Mathematical D erivation.......................................................16
2.2.4.2 Qualitative Dependence.........................................................17
2.3 Transmission L ine.................................................................................................... 19
2.3.1 G eneral.........................................................................................................19
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2.3.2 Basic Concepts........................................................................................... 19
2.3.2.1 Fundamental Equations......................................................... 19
2.3.2.2 Modes......................................................................................20
2.3.2.3 Impedance.............................................................................. 21
2.3.2.4 Losses, Dispersion and Distortion....................................... 21
2.3.3 Physical Design..........................................................................................22
2.3.4 Geometric Considerations.........................................................................24
2.3.4. 1 Characteristic Impedance......................................................24
2.3.4.2 Losses......................................................................................25
2.3.5 Fabrication Considerations....................................................................... 27
2.4 Impedance Matching............................................................................................ 28
2.4.1 Circulator ................................................................................................. 28
2.4.2 Transmission Line Basics......................................................................... 29
2.4.2.1 Reflections............................................................................. 29
2.4.2.2 Stub Tuning............................................................................ 29
3. FABRICATION.............................................................................................................. 55
3.1 Common Processes..................................................................................................55
3.1.1 Hot Solvent C lean..................................................................................... 55
3.1.2 Substrate Preparation................................................................................. 55
3.1.3 Single Layer Photolithography.................................................................56
3.1.4 Double Layer Photolithography...............................................................56
3.1.5 Silicon Nitride Deposition........................................................................ 58
3.1.6 Metal Deposition........................................................................................58
3.1.7 Silicon Nitride Etch....................................................................................59
3.2 Common Terms.......................................................................................................59
3.2.1 Photoresist.................................................................................................. 59
3.2.2 Spin-coating................................................................................................ 59
3.2.3 M ask........................................................................................................... 60
3.2.4 Etch..............................................................................................................60
3.2.5 Bi-level Liftoff............................................................................................60
3.3 Layers.......................................................................................................................60
3.3.1 Layer 1: Straps and Interconnects.............................................................60
3.3.2 Second Layer: Vias.................................................................................... 61
3.3.3 Third Layer: Coil....................................................................................... 62
3.3.4 Fourth Layer: Transmission L ine............................................................ 62
3.4 Verification.............................................................................................................. 62
4. APPLICATION I: SCANNING METAL LINES........................................................ 70
4.1 Introduction........................................................................................................... 70
4.1.1 Significance of the Experim ent................................................................ 70
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4.2 Experimental Procedures.........................................................................................71
4.2.1 Sample Preparation......................................................................................71
4.2.2 Stub Tuning................................................................................................. 72
4.2.3 Experimental Set-up and Technique.........................................................72
4.3 Results...................................................................................................................... 73
4.4 Conclusions..............................................................................................................74
5. APPLICATION H: LIFETIME MEASUREMENT OF A THIN IN 0 .5 3 GA 0 .4 7 AS
FILM................................................................................................................................. 82
5.1 Introduction..............................................................................................................82
5.1.1 Significance o f Experiment........................................................................82
5.2 Radiative and Nonradiative Recombination M echanism s.................................. 83
5.3 Lifetime Measurements...........................................................................................85
5.3.1 Photoluminescence......................................................................................85
5.4 Experimental Technique..........................................................................................85
5.4.1 Sample Preparation......................................................................................85
5.4.2 Stub Tuning................................................................................................. 87
5.4.3 Experimental Set-up....................................................................................8 8
5.5 Results...................................................................................................................... 89
5.6 Conclusions..............................................................................................................90
6
. CONCLUSIONS..................................................................................................................105
APPENDIX.............................................................................................................................. I l l
REFERENCES........................................................................................................................ 116
vii
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LIST OF TABLES
Table
Page
2-1. Qualitative comparison o f the various microwave integrated circuit lines..................43
viii
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LIST OF FIGURES
Figure
Page
1-1. Diagram showing the generation o f eddy currents in a conductive material. By
Faraday’s law o f induction, the original current J(t) produces an associated H(t)
that generates J(t)eddy that flows in the opposite direction o f J(t) in accordance with
Lenz’s Law............................................................................................................................ 9
1-2. Schematic o f one type o f microwave reflection measurement system. The fact that
the sample often has to be cut to fit the waveguide is a drawback of this
arrangem ent........................................................................................................................ 1 0
1-3. Examples o f eddy current devices. The top drawing is a schematic o f an atypical
eddy current probe. It uses changes in the spatial position o f a small magnet on a
cantilever to produce eddy currents. The bottom figure is a classic multi-turn coil.
The turns can be in a plane or graduated out of the p lane............................................. 11
1-4. Examples o f near-field capacitance or evanescent probes. The coaxial probes
developed at Berkeley were the basis o f future developments elsewhere.................... 12
2
- 1 . Complete schematic of a microwave eddy current probe showing the relevant
sizes......................................................................................................................................32
2-2. Concentric orientation o f a two system excitation and sensing eddy current probe.
The major drawback of this orientation is added capacitance due to the coupling of
electromagnetic fields of two separate transmission lines............................................. 33
2-3. Coaxial orientation of a two-system excitation and sensing eddy current probe. The
major drawback o f this orientation is lack of flexibility in arranging the sample to
be tested.............................................................................................................................. 34
2-4. Schematic o f an actual coil. Rectangular features aid in the mask fabrication while
not altering the underlying physics.................................................................................. 35
2-5. Diagram showing the relevant parameters and variables for the classic problem, i.e.
a circular coil above conducting sheets.......................................................................... 36
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2-6. Diagram showing variation o f normalized impedance with lift-off (11). Here the
normalized impedance is defined as the change o f the coil’s impedance due to the
presence o f the conducting layer divided by the impedance o f the unperturbed coil.
The thickness o f the coil is 1 pm, f = 10 GHz, rl and r2 are 5 and 7.5 microns
respectively and c l and ct2 are 0 and 106 (ohm-m) -I respectively. These variables
are based on Figure 2-5......................................................................................................37
2-7. Diagram showing variation o f normalized impedance with coil radius. Here the
normalized impedance is defined as the change o f the coil’s impedance due to the
presence o f the conducting layer divided by the impedance o f the unperturbed coil.
The thickness o f the coil is 1 pm, f = 10 GHz, r2 = 1.5 r l, 11 = pm, crl and <t2 are 0
and 106 (ohm-m ) - 1 respectively. These variables are based on Figure 2-5.................38
2-8. Diagram showing variation o f normalized impedance with frequency. Here the
normalized impedance is defined as the change of the coil’s impedance due to the
presence o f the conducting layer divided by the impedance o f the unperturbed coil.
The thickness o f the coil is 1 pm, r l =1 pm, r2 =1.5 rl, 11 = 5 pm, crl and ct2 are 0
and 106 (ohm-m) -I respectively. These variables are based on Figure 2-5.................39
2-9. Diagram showing variation o f normalized impedance with conductivity. Here the
normalized impedance is defined as the change o f the coil’s impedance due to the
presence o f the conducting layer, divided by the impedance o f the unperturbed coil.
The thickness o f the coil is 1 pm, f = 10 GHz, rl =1 pm, r2 =1.5 rl, 11=5 pm, crl
=0. These variables are based on Figure 2-5...................................................................40
2-10. Schematic o f a microstrip line. The major drawback o f this configuration is that the
ground and signal planes are separate. As a result, to make contact to the ground one
must drill through the substrate....................................................................................... 41
2-11. Schematic o f a triplate line. This configuration is similar to the microstrip tine. The
fact that the signal center conductor is completely within a homogenous dielectric
aids in the transmission o f a pure TEM mode................................................................ 42
2-12. Diagram o f a coplanar strip (CPS) and coplanar waveguide (CPW) transmission
line. Neither o f the two conductors o f the CPS needs to be grounded........................ 44
2-13. Perspective o f a CPW showing the two sets of variables (a, b and S, W) used to label
the relevant conductor and ground planes widths and/or spacing................................ 45
2-14. Diagram showing the characteristic impedance and effective permittivity as a
function o f a/b parametric in h/b. Here h is the substrate thickness. These plots are
based on GaAs (sr = 13).................................................................................................... 46
x
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2-15. Diagram o f even and odd quasi-TEM mode for a CPW. N ote that for the even mode
the electric fields are in phase while for the odd mode the electric fields are anti­
phase.................................................................................................................................... 47
2-16. Top and perspective view o f ground straps on a CPW. The straps keep the ground
planes at the same potential thereby ensuring the propagation o f the even mode
quasi-TEM m ode................................................................................................................48
2-17. Schematic o f a circulator. The circulator is a key element o f our experimental set­
up. It allows us to measure the reflected power using one coil and one transmission
line. The circulator is constructed using magnetic and ferrite materials that help
circulate the microwave signal originating from port 1 into the ports in the direction
o f the arrow (counter-clockwise). Port 2 is connected to the MECP. Any reflection
back to port 2 is circulated into port 3............................................................................. 49
2-18. Simple model o f a transmission line terminated with a load such that Z^ad is not
equal to the characteristic impedance, therefore resulting in a reflected signal
50
2-19. Simple model o f a transmission line with an open stub. The impedance at A-A’ is
just the impedance o f the open stub and the load translated to A -A ’ and added in
parallel................................................................................................................................. 51
2-20. Actual schematic o f stub-tune CPW; compare with Fig. 2-19....................................52
2-21. Screenshot o f stub matching Java program. This program allows for real time
variation o f stub position, transmission line length, index o f refraction, Z ^ d and
frequency. Inner window shows a Smith chart.............................................................. 53
2-22. Screenshot o f stub matching Java program. This programs allows for real time
variation o f stub position, transmission line length, index o f refraction, Zo, Zu>ad and
frequency. An inner window shows a plot o f the reflection, R=r2, as a function o f
distance along the transmission line, d............................................................................ 54
3-1. Schematic showing the various layers to be fabricated................................................. 64
3-2. Process steps for first level straps.................................................................................... 65
3-3. Process steps for first level straps continued.................................................................. 6 6
3-4. Photograph o f completed M ECP......................................................................................67
3-5. Photograph o f close-up of larger c o il.............................................................................. 6 8
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3-6. Photograph o f close-up o f smaller coil
69
4-1. Schematic o f chromium/gold lines that were scanned.................................................. 75
4-2. Schematic samples showing holder and translation stage. The PZT oscillates the
sample in the vertical direction. The purpose o f the PZT is to increase the sensitivity o f
the measurement by allowing phase sensitive detection........................................................76
4-3. Schematic o f experimental set-up for scanning o f thin metal films. Our reflected
microwave signal is then the incident signal amplitude modulated
The
microwave component o f this signal is converted to dc at the crystal detector with the
only ac signal being/^od- This signal is sent to the lock-in for phase sensitive
detection............................................................................................................................... 77
4-4. Scan across the edge o f the 50 pm line. Imperfections at the edges may contribute to
errors in our data................................................................................................................. 78
4-5. Scan o f a 125 pm wide line............................................................................................... 79
4-6. Schematic o f 250 micron wide gold and titanium stripes on the left are gold while the
stripe on the right is titanium. The calculated sheet resistances o f the gold and
titanium are 0.08 and 1.3 Q/square respectively.............................................................80
4-7. Figure showing results from three separate scans across the schematic shown in
Figure 4-6.............................................................................................................................81
5-1. Schematic showing the process o f radiative generation and emission. The
semiconductor is initially in equilibrium. Incident light causes electrons to be
injected into the conduction band thus leaving holes behind in the valence band.
If the incident light is turned o ff the electron-hole pairs will combine and emit
photons................................................................................................................................. 91
5-2. Schematics showing both band diagrams o f an indirect and a direct semiconductor.
Going from valence to conduction band in an indirect semiconductor requires a
change in momentum that is usually accomplished by emitting a phonon..................92
5-3. Schematic o f the Shockley-Read-Hall recombination mechanism o f electron capture
and emission in an n-type semiconductor. This is a nonradiative process
distinguished by traps near mid-gap. Initially the electron-hole pair is created..........93
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5-4. Schematic o f the Shockley-Read-Hall recombination mechanism o f hole capture and
emission in an n-type semiconductor. This is a nonradiative process distinguished by
traps near mid-gap.............................................................................................................94
5-5. Example o f a set-up for the steady state photoluminescence measurement............... 95
5-6. Schematic illustrating our dilemma when working with bulk InGaAs/InP sample. In
the first scenario the InGaAs is too far removed from the coil to be inductively
coupled to the coil. In the second scenario the InGaAs is close to the coil but
essentially no laser power reaches the sample because it is absorbed within the InP.
We can avoid the limitations o f this second scenario in the fixture by choosing the
laser wavelength so that it does not absorb significantly into the InP......................... 96
5-7. Process steps for achieving epitaxial lift-off. The black wax served two very
important purposes: it provided chemical protection from the HC1 and it provided
structural support during handling................................................................................... 97
5-8. A typical Reflected power vs. distance from the open end o f the CPW plot obtained
with stub tuning. The Plot shows reflection curves at 13, 15 and 18 GHz................. 98
5-9. Plots showing qualitative agreement between measured and calculated reflected
power as a function o f position along the CPW .............................................................99
5-10. Experimental set-up for lifetime measurement. We modulated the carriers at the
coil by modulating the laser. Our reflected microwave signal was then the incident
signal amplitude modulated a tfmod. By beating our reflected microwave signal to
base band we generated a plot of reflected power as a function of/nod..................... 1 0 0
5-11. Schematic showing qualitative explanation o f Lorentzian-like dependence. At low
modulation frequencies the carriers within the InGaAs can ‘follow’ the laser.
However at high frequencies the carriers cannot fully recombine before they are
excited again. This results in a decrease o f the reflected signal............................... 101
5-12. Plot o f reflected power versus modulation frequency/mod- This shows the
Lorentzian dependence that we expected.....................................................................102
5-13. A Linear regression of our lifetime data allows us to calculate the minority carrier
lifetime f r o m / m0d on the graph..................................................................................... 103
5-14. Plot o f lifetime vs. doping concentration N [Ahrenkiel, 1998]. Based on the MBE
grower’s estimate o f a few times 1 0 1 5 cm ' 3 our results fall within our expected range
and agree well with the literature................................................................................... 104
xm
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6-1. Side view o f an alternative experimental set-up for lifetime measurement...............109
6-2. Another alternative experimental set-up for lifetime measurement............................110
A -l. Set-up o f coarse tuning method. The microwave frequency is incremented by
i*Af.................................................................................................................................. 114
A-2. Schematic showing fine stub tuning.............................................................................. 115
xiv
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1
CHAPTER 1
INTRODUCTION
1.1
Introduction
This thesis describes the design, fabrication and applications of a microfabricated
microwave eddy current probe (MECP) [Watson and Chan, 2001]. The MECP combines
elements from two traditional electromagnetic noncontact and nondestructive
measurement techniques: 1 ) the eddy current technique and 2 ) the microwave reflection
technique. For the most part, the physics at the coil is dictated by eddy current
generation while the delivery o f the microwave signal to the coil, via a coplanar
waveguide, and most o f the instrumentation, is characteristic o f the microwave reflection
technique. In this chapter, we will present an outline for the principles, history and
current activity o f both the eddy current and microwave reflection techniques. In
addition, we w ill review a few o f the capacitive devices that have also been o f great
interest recently. Our MECP is a significant improvement on existing devices since it
extends the frequency into the 10-18 GHz range and reduces the inner and outer diameter
o f the coil, by an order of magnitude, for better sensitivity and spatial resolution.
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2
1.2
1.2.1
Principles
Eddy Current
An eddy current test device operates such that a time-varying current, J(t), flowing
through a coil will produce a time varying magnetic field, H(t), that is perpendicular to
the plane o f the coil as shown in Figure 1-1. If a conducting material is close to the coil,
the effect o f H (t) will be to induce a current J eddy(t) in the material, the eddy current,
which flows in the opposite direction to J(t). Furthermore, J eddy(t) will in turn produce
an associated magnetic field, Heddy(t), that will be directly opposite to H(t) and will
interact with the coil to change the impedance Zco,i by AZc0 ,i. The size o f AZCOii can be
related to properties o f the conducting material. Although in our design we will employ a
coil arrangement, however, it should be noted that eddy current probes can be produced
in an alternate, coil-less arrangement. Instead o f a time varying current, eddy currents are
induced in a conducting material if we periodically vary the sample to probe distance,
provided that the probe or the sample has some magnetic properties.
1.2.2
M icrowave Reflection
The microwave reflection technique makes use o f the wave properties of
electromagnetic waves to be reflected at the interface o f two media with different
material properties. Microwaves exhibit the same reflection and refraction properties o f
visible light. F or metals, microwaves impinging at the surface will be reflected.
However, when microwaves propagate through a nonmetallic material, polarization
within the sample causes changes to the amplitude and velocity of the propagating beam.
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3
A reflecting metal plate can be placed after the sample or a detector can be placed
directly after the sample to measure the change in reflection or transmission. In this way,
the dielectric properties of the material can be ascertained. For semiconductors, the
reflection technique often involves using a magnet to apply a magnetic field through the
sample (see Figure 1-2). A relationship between the reflected power, the sheet resistance
and/or mobility o f the carriers within the sample and the magnetic field can then be
obtained [Coue’,1994].
1.3
1.3.1
History
Eddy Current
Ever since the first applications by Hughes in 1879 [McClung, 1974],
nondestructive testing using eddy current techniques has found a large range o f industrial
uses [Bray and McBride, 1992] and [Mclntire, 1986]. Traditional applications o f eddy
current testing include detecting surface or subsurface voids, inclusion or cracks, as well
as thickness gauging in thin plates or coatings. Hughes used his first device to sort
metals. Eventually, during the 1960s, these techniques were extended to semiconductors.
Proheler and Liben [Proheler and Liben,1964] were among the first to do so. They
measured the change in the Q of a radio frequency solenoid due to eddy current losses.
Crowley and Rabson [Crowley and Rabson, 1976] used two sets o f driving and sensing
coils for a phase-sensitive detection method. One group [Miller, et al.,1976] monitored
the change in current o f a radio frequency tank circuit while another [Bianchi, et al.,
1985] measured bulk HgCdTe material at 77K using a commercial instrument. Chen
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4
[Chen, 1989] extended this measurement to epitaxial HgCdTe and Si samples using
Crowley and Rabson’s configuration. Because no physical contact is made with the
sample, eddy current probes are also well suited to monitor the growth or deposition o f
materials. The two most common are monitoring the growth o f semiconducting crystals
[Stefani, et al., 1990] and the chemical vapor deposition (CVD) o f metals like aluminum
[Ermakov and Hinch,1997]. In addition, eddy current probes have also been used to
measure the thickness o f superconducting materials [Gauzzi, et al., 2000] and magnetic
thin films [Tai,
1.3.2
2 0 0 0
]
Microwave Reflection
The use o f microwave techniques has a much shorter history [Bray and McBride,
1992]. The impetus for microwave measurement was provided by developments during
World War 13. Microwaves were used to analyze the dimensions of, and to test for flaws
within, microwave components used with radar devices. These tests were aided by the
fact that the microwave source was inherent with the radar. Microwaves are also used for
moisture analysis.
It was during the early 1950s that interest in the applications o f microwaves to the
studies of semiconductors began to grow. Benedict and Schockley [Benedict and
Schockley, 1953] presented a pioneer paper in 1953, and Bhar [Bhar, 1963] conducted
the first review o f the field in 1963.
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1.4
1.4.1
Present Activity
Eddy Current Devices
Recently there has been increased interest in microfabricated coils. Previous
works were performed with wire wound coils with diameters on the order o f a few
millimeters; see for example [Chen, 1989]. These devices are primarily used for flaw
detection in metals or conductivity measurement in semiconductors. In regards to
microfabricated coils, the spatial resolution o f these coils is at best in the 50-100 pm
range; see for example [Xue, 1998]. These coils are usually multi-turn (see Figure 1-3)
devices, which in essence contribute to the inability to increase the spatial resolution.
However the sensitivity is proportional to N2. Here TVis the number o f turns. Therefore,
careful balance must be struck between sensitivity and resolution.
In regards to frequency, most micro fabricated and wire wound coils seldom
operate above a few gigahertz. It has only been recently reported that microfabricated
coils operate at or above 5 GHz [Watson and Chan, 2001] and [Sakran, 2001].
A radical departure from typical eddy current probes was conducted by two
separate groups [Hoffman, et al., 1998] and [Lantz, et al., 2001]. They made use o f a
spatially changing magnetic field, as opposed to a time varying magnetic field, to create
eddy currents. Instead o f using a coil, Lantz used small spherical FeNdBLa magnets,
radii ranging from 650 nm to 1000 nm, at the end o f a cantilever tip, as shown in Figure
1-3. The frequency o f the eddy currents is the oscillating frequency o f the cantilever tip
Looking at the change in the damping o f the oscillating tip as it scans over a material
enabled them to perform microscopy.
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6
1.4.2
Capacitive Devices
Even though the focus o f this dissertation is that o f an eddy current probe, it is
important to note and discuss the complementary, near-field capacitive devices. In recent
times, these devices have seen the most activity o f all electromagnetic nondestructive
devices with significant independent work carried out at Case Western Reserve
University [Tabib-Azar, et al.,1999,2000], The University of Maryland [Steinhauer, et
al., 1998] and Hebrew University [Lann, et al.,1998, 1999 ] and [Govolsky, et al., 2000]
as shown in Figure 1-4. Some o f the earlier work using coaxial probes was also carried
out at The University o f Califomia-Berkeley and Lawrence Berkeley National Labs [Wei
and Xiang, 1996] and [Gao, C., et al.,1997,1998]. The basic idea o f all o f these
capacitive devices is to overcome the classical Abbe limit (spatial resolution A./2) by
bringing the tip close to the sample. In doing so, the exponentially decaying evanescent
waves (waves with spatial frequency higher than 1A.) interact with the sample. These
devices have been used to map resistivity o f semiconductors, and to scan metals and
insulators.
1.4.3
Microwave Reflection
There has been a decrease in the number o f papers relating to the classical
microwave reflection technique where the sample to be characterized must be cut to fit
the particular dimensions o f the waveguide (see Figure 1-2). In most current set-ups, the
sample is not restricted by shape since it is placed outside an open waveguide. Typically
reflection methods focus on measuring the bulk or sheet resistance o f doped or undoped
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7
semiconductors [Bhimnathwala and Borrego, 1994], or in the case of photoconductance
measurements, the lifetime and surface recombination velocity.
1.5
Motivation
There are a number o f applications for an inductive (eddy current) electromagnetic
nondestructive device that approaches the spatial resolution o f a few microns. This
would be an order o f magnitude improvement over existing eddy current devices. Such a
probe could be used to map the resistivity or spatial profile o f metals and semiconductors
as well as key semiconductor properties like the recombination lifetime. The drive
towards higher spatial resolution is warranted by the continuous shrinkage o f devices
within the semiconductor industry. In addition, such a device could be used to detect the
concentration of a conductive species within chemical or biological samples. Because, in
principle, samples measured with the MECP require no special preparation, it is ideal for
the manufacturing environment.
In addition, there have been electromagnetic capacitance probes that have been
used to map the resistance o f thin films. However, thus far they have been unable to
measure films with low sheet resistances
(R Sh <
1 Q/square) [Sakran, et al.,2001].
Furthermore, capacitance probes have the added constraint that the conducting sample be
biased. These probes are electric dipole antennas, so they couple most strongly to an
axial electric field that induces an axial polarization in the sample. In contrast, eddy
current probes are magnetic dipole antennas, so they couple most strongly to an axial
magnetic field that induces an azimuthal current in the sample. These probes are
complementary, so one m ay be better suited than the other for a particular measurement.
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8
For example, an eddy current probe would be better suited for measuring transport in a
thin film, such as in an epitaxial layer in a semiconductor, since the induced currents are
in the plane o f the film.
1.6
Scope of This Thesis
In Chapter 2, we elaborate on the various choices o f our design. This will include
the coil, the transmission line and a method for nulling the background signal. In Chapter
3, we describe the fabrication o f the complete probe and show a step-by-step schematic
o f the first layer o f fabrication. Chapter 4 will focus on our first application, which
illustrates that with the appropriate refinement, the MECP could be useful for scanning
across a thin metal and relating the reflected power to the physical profile o f the metal.
We will also present preliminary results showing that the MECP can be used to
differentiate between thin films with different sheet resistances RSh.
In Chapter 6 , we make suggestions for further development o f our device and
present concluding remarks.
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9
Figure 1-1 Diagram showing the generation of eddy currents in a conductive
material. By Faraday’s law o f induction, the original current J(t) produces an
associated H(t) that generates J ( t ) e d d y that flows in the opposite direction of J(t) in
accordance with Lenz’s Law.
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10
P o w er
M eter
W aveguide
w ith T E
M ode
Adjustable
ShorC*-
C irculator
A ttenuator
Sample
I
M icrow ave
Source
M agnet
Figure 1-2 Schematic of one type of microwave reflection measurement system. The
fact that the sample often has to be cut to fit the waveguide is a drawback of this
arrangement.
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11
Cantilever
H (z)
Magnetic Particle on a Tip
Classic Multi-turn Coil
Figure 1-3 Examples of eddy current devices. The top drawing is a schematic o f an
atypical eddy current probe. It uses changes in the spatial position of a small
magnet on a cantilever to produce eddy currents. The bottom figure is a classic
multi-turn coil. The turns can be in a plane or graduated out o f the plane
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12
center conductor
of coaxial
perpindicular
^ / t o sa m p le \^
-7 ?
1
E Parallel to
sample
Case Western
Reserve University
University of
Maryland, Berkeley
Hebrew University
Figure 1-4 Examples of near-field capacitance or evanescent probes. The coaxial
probes developed at Berkeley were the basis of future developments elsewhere.
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13
CHAPTER 2
DESIGN
2.1
General
Our MECP testing system, like most eddy current test systems [Libby, 1971], will
consist o f the following components: a generator, a coil for excitation and detection, a
waveguide for efficient transmission o f power to the coil from the generator, a method o f
nulling the background reflected signal, and an indicator or means o f displaying our
results. Since the generator is commercially available, our design considerations will
focus on the coil, the transmission line and background null (stub tuning). In this chapter,
we will discuss the principles that governed our selection o f the various design
components and at times give reasons for not choosing alternative designs. In many
instances, ideal solutions will have to give way to practical solutions based on the
materials and equipment available to us. Figure 2-1 is a complete micro fabricated design
of our device that shows the relevant sizes and gives a better picture of how each element
integrates into the whole.
2.1.1
Maxwell’s Equation
Below we write down M axwell’s equation in differential form, since they will be
useful for future reference when we discuss some aspects o f the coil design as well as the
general description o f the wave properties on transmission lines.
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14
dt
V • D = p
(2 . 1)
(2.2)
(2.3)
V »B = 0
(2.4)
where D = eE and H = (l/p)B for linear and isotropic materials.
2.2
2.2.1
Coil
Physical Design
In the interest o f simplicity, we will employ a single coil to serve as both the
excitation (driver) and the detection (pick-up) coil. By using a single coil, the fabrication
is greatly simplified since there is no need to make critical alignment with a second coil.
Also, the use o f two coils would require two separate transmission lines. Furthermore, a
design which employs separate connected driver and pick-up coils concentric in the
sample plane, as shown in Figure 2-2, has increased capacitance between the two lines
which normally is not desired. In addition, many designs employ a configuration with
the driver and pick-up coils along the same axis (see Figure 2-3) which creates major
constraints on the measurement conditions since this arrangement requires that the
sample be inserted between the two coils. Although this arrangement is commonly used,
the size o f the coils and spacing between the coils are typically at least one to two orders
o f magnitude greater than our coils, making this arrangement unfeasible at the micron
scale. Although Figures 2-2 and 2-3 depict the coils as circular, our actual
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15
microfabricated coils are single-tum square coils with a gap to facilitate the connection of
a separate ground and signal, as shown in Figure 2-4. The reason w e choose a square coil
is that it is much easier to have a mask fabricated with small straight features as opposed
to circular or curved features. The choice o f using a square coil should not, however,
change any o f the underlying physics.
2.2.2
Optimization
One o f the most important considerations in optimizing the coil is that the ratio of
the inductive reactance and the resistance be made as large as possible. If possible, we
would prefer that this ratio be greater than 1 , i.e.
2 7 ifL /R > l,
(2.5)
where R, L and f are the coil’s resistance and inductance and the operating frequency of
the microwave generator, respectively. Equation 2.5 illustrates that, in principle, we can
increase f to meet our condition. This condition ensures that most o f the power supplied
to the coil is used to create eddy currents in the sample and not lost in ohmic heating o f
the coil. By treating the coil as a series o f straight-line segments, we obtain approximate
equations for the resistance and inductance [Wadell,1991].
(2.6)
2 . 0 d2
L » 0.001842d{logIO[]} + 0.004[2.823d + 0.0447(w + T)](p) ) (2.7).
2.41d(w + T)
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Here
crCOii
is the conductivity o f the coil in (ohm-cm ) ' 1 and s is the length o f the gap
within the coil as illustrated in Figure 2-4. In addition w, d and T are the coil’s width,
average radius and thickness, respectively. The value o f s, d, w and T are given in
centimeters in Equations 2.6 and 2.7. Substituting R and L into Equation 2.5 and using
values o f 5, 10 and 1 pm for the coil’s inner diameter, outer diameter and thickness, we
get a frequency o f approximately 4 GHz or greater. In essence, this is the first constraint
on our system.
2.2.3
Fabrication Considerations
Finally, in designing our coil, w e m ust pay attention to fabrication constraints.
For the most part, these are size and material constraints. Our photolithography
processes define the minimum coil radius. Under ideal conditions, using optical
lithography, we can fabricate coils with minimum inner diameters o f about 1 micron. We
chose to fabricate our coils from gold because gold is a very good electrical conductor.
In addition, during the deposition o f nitride, the coil will have to be heated to 300 °C. At
such temperatures, other low resistivity metals oxidize much more easily than gold.
2.2.4
2.2.4.1
The Classic Problem
Mathematical Derivation
Once w e have selected our coil design and configuration, w e can solve the classic
problem , the change in impedance, AZ, o f a circular coil of radius, a, held at a distance I
(normally referred to as lift-off) above electrically conductive sheets. Refer to Figure 2-5
for the relevant illustration o f the various variables. The fact that the coil in our
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calculation is circular is o f minor importance, since in general we are more concerned
with a qualitative understanding o f the various factors that influence AZ and a feel for the
orders o f magnitude involved. In this way, we will have a better idea o f what range o f
conductivity, a , we will be able to detect. Dodd and Deeds’ [Dodd and Deed, 1968]
treatment o f the classic problem represents a ‘closed form’ solution whereby sinusoidal
driving currents and linear, isotropic homogenous medium are assumed. They arrive at
the following expression for AZ
2(1, - l , ) + a ‘l {2e'a(u-'ll) - 2 + e~2al’ + e '2al‘ - 2 e a^ ' ' ]} X '
AZ=
y c o jj.
7 j “Tl2(r2-ri)
( I2 - I,)2( r2 - r.) 2 o<*
da
( a + a , ) ( a l - a .,) + ( a - a , ) ( a , + q .,)e 2aicN
( a —a ,) ( a , - a , ) + ( a + a , ) ( a , + a , ) e 2a,c
(2.8)
I------------------
where a , = ^ a 2 + jcopcT; , I(r2 ,r,)=
J x J / x j d x , (where Ji(x) is the Bessel’s
arj
x=ar.
Function o f the first kind).
2.2.4.2
Qualitative Dependence
Using our equation for AZ, we can make impedance vector plots of the resistive
and reactive components to visualize the dependence of relevant parameters. However,
since we are only concerned with the total change in impedance, we will make a plot o f
the total impedance, AZ normalized to Zair.
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18
A plot o f AZ as a function o f lift-off illustrates near-exponential dependence as
shown in Figure 2-6. Apart from the lift-off, the other important parameter is the coil
radius a. As we can see from Figure 2-7, the impedance increases almost proportional to
a. This condition places a constraint on our system such that we must choose a careful
balance between resolution and sensitivity. In general, as is the case in Figure 2-6, the
change in impedance falls off after approximately one coil diameter. By decreasing our
coil so that it is much less than the wavelength of our signal and by choosing our lift-off
accordingly, we enter what is referred to as the near zone. In the near zone, we are able
to resolve spatial changes in conductivity much less than the signal’s wavelength and on
the order o f the coil radius, a. In other words, we are beyond the diffraction limit.
From Figures 2-8 and 2-9, we see that the impedance increases linearly with both
conductivity cr and frequencyf . Consequently, it is important to note that the effects o f
changing cr , f and a are interdependent and that constant 2n[ifaa2 yields lines o f constant
impedance. Theoretically, we can overcome the size/sensitivity dilemma by increasing
the frequency.
It is important to point out that the constant term 27tp.f<ra is actually equal to 1/8
where
8
is called the skin depth. The skin depth is defined as the depth at which the
current density has decreased to 1/e o f its maximum value. Therefore,
8
is sometimes
called the equivalent conducting layer thickness. The decrease in current, within the
interior o f the conductor, becomes an issue at radio frequencies or greater. In general, we
would like to make the coils as thick as possible; however, when we consider the skin
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19
depth, there is a thickness above which we receive no significant benefit. For gold at 10
GHz, the skin depth is approximately 0.8 microns.
2.3
Transmission Line
2.3.1
General
A transmission line is a metallic structure that guides the transmission of
electromagnetic power from one point to another. There are m any different types o f
transmission lines, but many o f these can be eliminated when we consider our frequency
range, size, and fabrication techniques. In this section, we will first discuss basic
concepts and terminology that are general to most transmission lines. We will explore
reasons that support our choice o f transmission line, the relevant geometrical
considerations, and finally, we will discuss the fabrication o f the transmission line.
2.3.2
2.3.2.1
Basic Concepts
Fundamental Equations
From M axwell’s equation one obtains the source free homogenous vector wave
equations for both the magnetic H and electric E fields.
(2.9)
V xE = where u = (pe)
1 /2
SB
dt ’
(2 . 1)
is the speed o f the wave in the medium (u= c in air). For linear
media H = (l/p )B
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20
For harmonic fields such that E (r,t) = i?e[E(r)e,"t] and H(r,t) = /te[H (r)eI'tot], the
equation yields the homogenous vector Helmholtz’s equation, i.e.
V2E + k 2E = 0
(2.10)
where k = <a/u.
2.3.2.2 Modes
In the case o f a generic transmission line type, it is often desirable to transmit one
mode. The concept o f mode here is the same as that encountered when describing the
field distribution o f laser beams. Furthermore, it is usually desirable to transmit the
lowest order mode. Often this is the transverse electro-magnetic (TEM) wave. The TEM
mode o f a waveguide is one in which the electric and magnetic fields are perpendicular to
each other and both are transverse to the direction o f propagation o f the wave. For
example, a uniform plane wave characterized by E =a XEX= axE’oe'Y(z‘ut) propagating in the
+z direction that has an associated magnetic field H = ayHy= -ay( 1!r\ )£,oe'Y(z'"t)’.where y
and r| are the propagation constant and the intrinsic impedance, respectively. The form o f
y and rj depends on the quality o f the conductor and dielectric o f the transmission line.
For example, for a perfect dielectric medium and a perfect conductor y =y'(3 = yco(|j.s) 1 /2
and r| = (p/e)l/2. There is no longitudinal component of the wave, so the wave is guided
within the dielectric medium, which is why we concern ourselves with source free
equations. The two other common modes are the transverse electric (TE) and the
transverse magnetic (TM). As their names suggest, these modes are characterized by
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21
waves that have electric and magnetic field components normal to their direction o f
travel.
2.3.2.3 Impedance
In addition to the intrinsic impedance, rj, we have the wave impedance Z tem and
the characteristic impedance
Zo- Z tem
is defined as the as the ratio o f E x/H y in the
transverse direction, provided we are using the orientation o f the traveling wave above.
Using this definition, it can easily be shown that for a T E M wave
Z tem =
The characteristic impedance Z q is defined as the ratio o f the voltage to the
current at any point along the transmission line. For an infinitely long transmission line
Zo=V(z)/I(z) = Vo/Io- In general we can relate Zo to the inductance (L) and/or capacitance
(C) (per unit length) o f a transmission line. Depending on the type o f transmission line,
the L and/or C values can be found to give Zo- Often Zo is related to r\.
The surface impedance Zs is the ratio o f the tangential component o f the electric
field to the surface current density, i.e. Zs = Et/Js. In a transmission line Zs is associated
with a waveguide made with imperfect conductors and is a source o f losses.
2.3.2.4 Losses, Dispersion and Distortion
To understand the concept o f dispersion and distortion, we must consider the
difference between phase and group velocity. Furthermore, our general description thus
far has been based on perfect conductors and insulators. In reality, the introduction o f
imperfect low loss dielectric medium means that we introduce a dielectric material with
permittivity e and nonzero conductivity ct and a (3 that is not a linear function of
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22
frequency. Consequently, the phase velocity up will differ for different frequencies since
up = to/p (assuming again a wave traveling in the + z direction).
All real signals are composed o f a band o f signals that travel w ith a group velocity
u Since up for an imperfect conductor w ill not be independent o f frequency, different
components o f the signal will travel with different phase velocities causing the signal
shape to distort leading to what is termed dispersion. In addition to the dispersion due to
the dielectric medium, there is also modal dispersion which is the result o f the non-TEM
nature o f a transmission line. There is also the possibility of exciting the Longitudinal
section electric (LSE) waves and Longitudinal section magnetic (LSM) waves, which are
characterized as having no electric and magnetic field perpendicular to the conductordielectric boundary, respectively. The LSE and LSM modes are usually excited when the
wave is not travelling in a purely homogenous medium.
Distortion is due to changes in a signal that involves the addition o f spurious tones
at frequencies not present in the original incident waves. In harmonic distortion, the
spurious tones are at integral multiples o f the original frequency. In intermodulation
distortion, non-harmonic tones appear at the sums and differences o f two original
frequencies.
2.3.3
Physical Design
There are many types of transmission lines ranging from the comm on coaxial
cable to the rectangular box type waveguides. These lines can transmit electromagnetic
waves with frequencies ranging from near dc to hundreds o f gigahertz. The most logical
type of transmission line required for our device belongs to the group o f transmission
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23
lines commonly referred to as planar transmission lines. As its names suggest, planar
transmission lines are transmission lines that occupy a plane. This group includes many
variations, which are often subtle. However, the four most distinct types are the
microstrip, slotline, coplanar waveguide (CPW), and the coplanar strip (CPS). The
microstrip line shown in Figure 2-10 is the most classic type o f planar transmission line.
Its popularity is based primarily on the fact that the dominant mode o f propagation is
almost transverse electro-magnetic (or quasi-TEM) which makes the analysis simple and
allows for the design wide band circuits [Gupta, et al.,1996]. The major drawback o f the
microstrip line for our purpose is the fact that the separate ground plane requires drilling
through the substrate. The stripline shown in Figure 2-11, sometimes referred to as a
triplate line, is similar to the microstrip line except that the signal o f the triplate line is
fully imbedded into a homogenous dielectric, which allows for the propagation o f a pure
TEM mode.
The slotline can be integrated into microstrip circuits by etching the slotline
circuit in the ground plane. The wave within a slotline propagates along the slot such that
the major electric field component is oriented across the slot in the plane o f the metal on
the dielectric substrate. This is a non-TEM mode o f propagation and closer to a TE
mode. Coplanar strips and waveguides have similar characteristics as illustrated in Table
2-1. Even though both CPS and CPW shown in Figure 2-12 allow for series and shunt
integration o f components, a fact that makes them attractive in the design o f microwave
circuits, CPS are far less popular than CPW for such purposes. This is due to the fact that
CPW typically have slightly better performance at higher frequencies.
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2.3.4
Geometric Considerations
Thus far the treatment o f the basic concepts has been void o f any relationship to
the physical properties, dimensions and type o f transmission line. Even though the CPW
is a newer structure, most o f the relevant properties o f its quasi-TEM mode, such as
characteristic impedance, cut-off frequency, dispersion, mode propagation, etc., have
been calculated and related to its physical geometry. Quite often look-up graphs are
provided for some o f the more common material substrates used for microwave IC’s,
such as AI2 O 3 and GaAs. Although fullwave analysis methods are more accurate, the
level o f complication and rigor required for these methods go beyond the scope o f this
dissertation. Therefore, we will use quasi-static analysis methods since they are adequate
for frequencies below 40 GHz.
Figure 2-13 is an isometric representation showing a CPW with the various
geometric variables. There are two sets o f conventional variables used, (S and W) and (a
and b), where S is the width of the center conductor and W is the spacing between the
edge o f the center conductor and the adjacent ground plane. Alternately, a = SI2, the
width o f the center conductor, and b = ( 2 W + S)/2, the distance between the near edges of
the two ground planes.
2.3.4.1
Characteristic Impedance
In the quasi-static approach, the phase velocity up and the characteristic
impedance can be written, up = c( er e ) ' 1 /2 and Zo = 1/(C up). Here c is the speed o f
electromagnetic waves in free space, ere = C/Ca, C is the total capacitance per unit length
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25
o f the coplanar line and Ca is the capacitance o f the corresponding line if we replaced the
dielectric with air. The method o f conformed transformation involves relating the
capacitance to the geometry and size o f the CPW. For our geometry, a CPW with finite
dielectric thickness and finite width ground plane as shown in Figure 2-13. Zo is an
expression consisting o f several elliptical integrals. It is often much more convenient to
view a parametric graph relating it to physical quantities. Figure 2-14 shows Zo as a
function of a/b. Therefore, by choosing the width o f our center conductor and gap
between the ground planes, we can design for a particular Zo. In particular, 50 Q is one
o f the industry standards for cable assemblies at microwave frequencies.
2.3.4.2 Losses
Losses associated with the CPW are either dielectric, ohmic, or radiation due to
surface waves. The expression for the dielectric attenuation is given as
a d=
2
71
er (ere - 1 ) tan 5
r - D
dB/unit length,
(2.11)
^0
where tan5 is the ratio o f the energy loss in the dielectric to the energy stored, and er and
sre are the dielectric constant and the effective dielectric constant, respectively. The
effective permittivity is in essence a weighted measure of the proportion o f the wave
traveling within the dielectric medium to that traveling in air (assuming the waveguide is
open to air). For conductor losses, the attenuation constant may be written as
) dB/unit length,
'0
5
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(2.12)
26
where Ca is the capacitance o f the line in air and Cg is the new capacitance obtained by
recessing all the metal surfaces by 6/2
(8
is the skin depth) [Gupta et al., 1996].
Radiation due to surface waves occurs when parasitic or unwanted waves are
excited in a CPW. This unwanted wave is an odd mode quasi-TEM (see Figure 2-15),
which is distinguished by anti-phase voltages in the two slots [Riaziat et al., 1990]. To
avoid exciting this, mode straps, which join the two ground planes and are placed at
regular intervals —A.d/4 (see Figure 2-16), ensure that the even mode as shown in Figure 215 is maintained. Here A.d is the wavelength o f the electromagnetic wave in the dielectric
medium. These straps, which are placed over the CPW and electrically isolated by
silicon nitride (SiNx), have the disadvantage that they increase the capacitance o f the
waveguide. This potentially may lower the cut-off frequency o f the TEM mode.
Alternatively, wirebonds may be used, but these tend to add more inductance to the
device. In addition to attenuation, there are also phase considerations, which are
influenced by the relative thickness o f the substrate to the dielectric wavelength
For a
CPW with an infinitely thick substrate, there are two modes o f propagation, the CPW
mode with
(3/ko = ((sr + l) /2 ) 1/2,
(2.13)
where ko = co/c,
and the TEM mode of the substrate with
ps/ko = (er)1/2.
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(2.14)
27
For a CPW in general, if the CPW mode travels faster than the TEM mode, then
the waveguide becomes leaky. Since p < ps for the infinitely thick CPW, the guided TEM
mode is always leaky and radiates into the substrate with «p = c/(er)1/2.
The CPW with finite thickness substrates can also be leaky. However, instead o f
propagating a TEM substrate mode, the odd TE modes and the even TM modes are
propagated.
2.3.S
Fabrication Considerations
As is the case with the coil, it is necessary to consider the processing that is
involved with making the transmission line. Since dining fabrication the transmission
line will be subjected to temperatures around 300°C, gold will be the most suitable
material. W hen we consider the skin depth, a thickness on the order of a micron will be
adequate. Additionally, one end o f the coplanar waveguide should be tapered so that the
coil can easily be aligned to it. It should be noted that although the ratio o f the signal
electrode width to the ground spacing determines Zo, one should not overlook the fact
that as the spacing becomes smaller, the losses along the transmission line increase.
Therefore, it is in our best interest to make the tapered region as short as possible. The
wider end o f the CPW should be able to facilitate connection by commercial microwave
probes and wirebonding. Therefore, we should ensure that the signal strip is greater than
50 pm, which is typically minimum for wirebonding applications. At the same time, we
should ensure that gaps be less than
1 0 0
pm, which is a common spacing for commercial
probes.
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28
2.4
2.4.1
Impedance Matching
Circulator
We wish to use a single coil and a single transmission line for both excitation and
detection. One way o f doing this is by using a circulator; see Figure 2-17. A circulator is
used to separate a reflected signal from the transmitted or incident signal. The circulator
is constructed with ferrite pucks, striplines, a magnet and a metallic disk. The center
metallic disk is sandwiched between the two ferrite pucks, which are housed between two
ground planes. Three stripline conductors, 120° apart, are attached to the periphery o f the
center metallic disk. These three striplines form the three ports o f the circulator. In
operation, the ferrite disk forms a resonant cavity. Without a bias field, the cavity is in
the lowest order mode. In the presence o f a bias field, which is supplied by the magnet,
the singled lowest order mode will break into two resonant modes with slightly different
frequencies. The operation frequency o f the circulator can be chosen such that in
superposition the modes add at one port and cancel at the other. From our figure, a signal
entering at port
1
will be ‘circulated’ to port 2 with the signal being directed out through
port 2. Any mismatch at port 2 will result in a signal being reflected back through port 2
and circulated to port 3.
In order to maximize our sensitivity so that we can detect smaller changes at the
coil, we wish to make the reflected signal as small as possible. In order to accomplish
this, we could minimize the mismatch at port 2. Port 2 is connected to our CPW which is
designed to have the same Zo as the circulator, 50 Q. However, the CPW is terminated
with the coil, which is the source o f the reflections. We use the method referred to as
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29
stub tuning to minimize the reflections due to the coil. Stub tuning has the added
advantage that it not only minimizes reflections from the coil, but it also maximizes the
power to the coil. The added power equates to more energy being used to generate eddy
currents in the sample.
2.4.2
2.4.2.1
Transmission Line Basics
Reflections
An ideal lossless transmission line has characteristic impedance Zo and load
impedance ZLoad that terminates it. The voltage reflection coefficient T can be written as:
r = (ZLoad —Zo)/(ZLoad + Zo),
(2.15)
where T is a measure o f the ratio o f complex amplitudes o f the reflected and incident
voltage waves at the load. Therefore, the power reflected is then directly proportional to
•y
|T| . We can calculate T due to the load at any point along the line d which is the distance
measured from the load (see Figure 2-18) by calculating the impedance at d as
Zd = Z0[(ZLoad + Zotanhyd)/( Z0 + ZLoadtanhyd)].
(2.16)
We then substitute this value as ZLoad into equation 2.15 to solve for T.
2.4.2.2
Stub Tuning
2.4.2.2.1 The Ideal Case
A tuning stub is essentially a second transmission line place in parallel with the
main transmission line as shown in Figure 2-19. In our illustration, we have our stub
terminated with an open; however, this could have easily have been a short. As a
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30
practical matter it is easier to realize a short as opposed to an open at microwave
frequencies. Furthermore, the characteristic impedance o f the stub Z qs need not be the
same as the characteristic impedance o f the m ain transmission line Zom. However, for
simplicity we w ill make our design such that Zos = Zom = Zo = 50 Q. If we change the
length o f the stub /, we change the impedance ZSd at d due to the stub. An open translated
a distance I will have an impedance o f Zi0Pen = -y'Zo cotp I (assuming a lossless line). Here
P is the phase constant. Furthermore, if we change the distance d that the stub is from the
load, then in the same manner we change the impedance ZiLoad at d. The total impedance
is just the translated impedances added in parallel Zr- Here ZT=l/(l/Z,open + 1/ Z,Load)
The goal o f stub tuning, therefore, is to vary I and d such that the total impedance
Z t is the same as the characteristic impedance o f the line. Recall from our equation for T
that if Zo = Z^ad then there are no reflections. It is important to note that with a single
stub, it is possible to tune to any ZLoad as long as the total length o f the transmission line
(d + 1) is approximately the wavelength Xd o f the microwave signal in the dielectric
medium.
2A.2.2.2 Real Tuning
To realize our method o f stub tuning in any real sense, we have the option o f
purchasing a commercial stub tuner that can be placed some distance away from our
probe. This is a valid option; however, it runs counter to our desire to further miniaturize
(in the future) and simplify our probe. It is also possible to incorporate stubs directly
onto the transmission line, but in doing this we do not have much flexibility in varying I
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31
and d. If we compare Figures 2-19 and 2-20, we see that we can create a single stub
without adding any extra elements to the main transmission line. The stub length / (in
Figure 2-20) is defined as the distance from where we place our commercial probes (AA ’) to the open end o f the transmission line. The distance from the load d is the distance
from the probe to the load. Changing the probe position and changing the frequency vary
I and d in different ways. Only with the combination o f the probe position and changing
the frequency, w e can obtain / and d.
Figures 2-21 and 2-22 are two screen shots o f a Java program written by Dr.
Winston Chan that easily allows for the manipulation o f I and d. A plot o f |F|2 vs.
frequency and |F|2 vs. d can be generated. These plots are not only important in helping
us to decide where to tune our circuit, but they also give us an indication as to whether
we are exciting the correct mode (even mode quasi-TEM). If we were exciting, to any
large degree, the hybrid modes or the odd quasi-TEM mode, we would not expect good
qualitative agreement between experiment and theory.
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32
20 |xn
C
coil
P W
10 pm
via
240fjm
i
shorting straps
(~ lOjxn wide )’
120jjm
Figure 2-1 Complete schematic of a microwave eddy current probe showing the
relevant sizes.
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Figure 2-2 Concentric orientation of a two-system excitation and sensing eddy
current probe. The major drawback of this orientation is added capacitance due to
the coupling o f electromagnetic fields of two separate transmission lines.
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34
To Transmission Line 1
To Transmission Line 2
Figure 2-3 Coaxial orientation of a two-system excitation and sensing eddy current
probe. The major drawback of this orientation is the lack of flexibility in arranging
the sample to be tested.
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Figure 2-4 Schematic of an actual coil. Rectangular features aid in the mask
fabrication while not altering the underlying physics.
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36
Figure 2-5 Diagram showing the relevant parameters and variables for the classic
problem, i.e. a circular coil above conducting sheets.
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37
Change o f Impedance with Lift-off
0.2
0.18
0.16
w
S 0.14
iB
9i
0.12
■e 0.1
j§
0.08
S
0.06
0.04
0.02
0
10
15
20
25
30
L ift-off (microns)
Figure 2-6 Diagram showing variation of normalized impedance with lift-off (11).
Here the normalized impedance is defined as the change o f the coil’s impedance due
to the presence of the conducting layer divided by the impedance o f the unperturbed
coil. The thickness of the coil is 1 |im, f = 10 GHz, r l and r2 are 5 and 7.5 microns
respectively and <rl and o2 are 0 and 10ti (ohm-m) -1 respectively. These variables
are based on Figure 2-5.
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38
C hange o f Im p ed a n ce w ith coil radius
0.6
oo
c
(B
"O
0
Q.
E
TJ
O
N
75
E
o
z
0.5
0.4
0.3
0.2
0.1
0
10
15
20
25
30
35
r1 (m icrons)
Figure 2-7 Diagram showing variation of normalized impedance with coil radius.
Here the normalized impedance is defined as the change of the coil’s impedance due
to the presence of the conducting layer divided by the impedance of the unperturbed
coil. The thickness of the coil is 1 jam, f = 10 GHz, r2 = 1.5 r l, II = fim, a l and cr2
are 0 and 106 (ohm-m)-1 respectively. These variables are based on Figure 2-5.
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39
Change o f Im pedance with frequency
0.0012
0 . 0 0 1
-
U 0.0008
&
i -g 0.0006
I
0.0004
e
0.0002
10
20
30
40
50
60
Frequency (GHz)
Figure 2-8 Diagram showing variation of normalized impedance with frequency.
Here the normalized impedance is defined as the change of the coil’s impedance due
to the presence of the conducting layer divided by the impedance o f the unperturbed
coil. The thickness of the coil is 1 (im, rl =1 (im, r2 =1.5 r l, 11 = 5 p.m, crl and o2 are
0 and 106 (ohm-m) ~ l respectively. These variables are based on Figure 2-5.
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40
|
|
Change of Impedance with Conductivity
0.0016
« 0.0014
g 0.0012
i
i
0.001
0.0008
0.0006
0.0004
t
0.0002
i
i
!
O.OE+OO 1.0E+07 2.0E+07 3.0E-+07 4.0E4O7 5.0E-+07 6.0E+O7 7.0E+07 8.0EH)7
a2
(1/ohm-meter)
Figure 2-9 Diagram showing variation of normalized impedance with conductivity.
Here the normalized impedance is defined as the change o f the coil’s impedance due
to the presence o f the conducting layer, divided by the impedance of the
unperturbed coil. The thickness of the coil is 1 ^m, f = 10 GHz, rl =1 pirn, r2 =1.5 r l,
11 = 5 fim, crl =0. These variables are based on Figure 2-5.
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41
center
conductor
ground
Figure 2-10 Schematic of a microstrip line. The major drawback of this
configuration is that the ground and signal planes are separate. As a result, to make
contact to the ground one must drill through the substrate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ground
center
conductor
substrate:
ground
Figure 2-11 Schematic of a triplate line. This configuration is similar to the
microstrip line. The fact that the signal center conductor is completely within
homogenous dielectric aids in the transmission o f a pure TEM mode.
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43
Table 2-1 Qualitative comparison o f the various microwave integrated
circuit lines.
Characteristic
Microstrip
Slotline
Coplanar
Waveguide
Coplanar
Waveguide
Effective Dielectric Constant
(e r=*I3. h-100
nm)
8.6
5.07
Power Handling capability
High
Medium
Medium
Medium
Radiation Loss
Low
Medium
Medium
Medium
Dispersion
Small
Large
Small
Small
Components Mounting:
Shunt
Series
Technical difficulties
Enclosure Dimensions
Difficult
Easy
Easy
Difficult
7
7
Easy
Easy
Easy
Easy
Ceramic holes
Edge plating
Small
Large
Large
Large
Note: Adapted from Hoffman, R.K., Handbook of Microwave
Integrated Circuits (Artech House, Boston, 1987), Chap. 2-3, 13.
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s u b s tr a te
gr
s u ,b s tr. a te.
gr
Figure 2-12 Diagram o f a coplanar strip (CPS) and coplanar waveguide (CPW)
transmission line. Neither of the two conductors of the CPS needs to be grounded.
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45
2b
XL
Figure 2-13 Perspective of a CPW showing the two sets of variables (a , b and S , W )
used to label the relevant conductor and ground planes widths and/or spacing.
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46
7.5
160
140
120
UJ
L 6.5
QC
100
80
O 5.5
UJ
60
UJ
40
20
XI
4.5
10-1
a/b
Figure 2-14 Diagram showing the characteristic impedance and effective
permittivity as a function of a/b parametric in h/b. Here h is the substrate thickness.
These plots are based on GaAs (sr = 13).
Note: Diagram taken from Gupta, K.C., Garg R., Bahl, I., Bhartia, P., Microstrip Lines
and Slotlines, 2nd ed. (Artech House, Boston, 1996), p. 383.
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Even Mode
Q ddM ode
Figure 2-15 Diagram o f even and odd quasi-TEM mode for a CPW. Note that for
the even mode the electric fields are in phase while for the odd mode the electric
fields are anti-phase.
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48
n
ii
n
ii
Figure 2-16 Top and perspective view o f ground straps on a CPW. The straps keep
the ground planes at the same potential thereby ensuring the propagation o f the
even mode quasi-TEM mode.
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Figure 2-17 Schematic o f a circulator. The circulator is a key element of our
experimental set-up. It allows us to measure the reflected power using one coil and
one transmission line. The circulator is constructed using magnetic and ferrite
materials that help circulate the microwave signal originating from port 1 into the
ports in the direction of the arrow (counter-clockwise). Port 2 is connected to the
MECP. Any reflection back to port 2 is circulated into port 3.
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50
Vs
Reflected Signal
Figure 2-18 Simple model of a transmission line terminated with a load such that
ZLoad is not equal to the characteristic impedance, therefore resulting in a reflected
signal.
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51
d
Om
Figure 2-19 Simple model of a transmission line with an open stub. The impedance
at A-A’ is just the impedance of the open stub and the load translated to A-A’ and
added in parallel.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 0 j- im
(E
240 jam
<
>
S I
M
f
A -A '
P r o b e P o s itio n
120 um
B -B ’
Figure 2-20 Actual schematic of stub-tune CPW; compare with Fig. 2-19.
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53
rrr:
9
TO
IT T2 T3 14
Frequency (CKO
T5
16
T7
T8
T9
20
2T
22
23
24
25
TT 4 6 G H Z
LOAD
5.000
5.000
Figure 2-21 Screenshot of stub matching Java program. This program allows for
real time variation o f stub position, transmission line length, index of refraction,
ZLoad and frequency. Inner window shows a Smith chart.
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54
Transmission Line Impedance Matching By Single Stub Tuning
Po w er Reflection Coer.
10
!am bda/2n
11 12 13 14
F requency (GHz)
12.5Q GHz
15
16
17
18
19
20
21
22
23
24
25
Probe Position (m m )
l&V/xW /l!
LOAD
Figure 2-22 Screenshot of stub matching Java program. This programs allows for
real time variation of stub position, transmission line length, index of refraction, Zo,
ZLoad end frequency. An inner window shows a plot of the reflection, R = r2, as a
function of distance along the transmission line, d.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
CHAPTER 3
FABRICATION
Eddy current coils have traditionally been fabricated by winding thin wires into a
coil. However, such methods are not useful for making coils with a diameter less than
approximately a millimeter. To overcome this size limitation, we use photolithography
or planar processes. Figure 3-1 shows a schematic o f the device to be fabricated. We will
first list and describe some o f the processes and terms that are associated with
microfabrication. We will then describe with appropriate diagrams the step-by-step
fabrication o f the first layer o f the MECP as shown in Figures 3-2 and 3-3.
3.1
3.1.1
Common Processes
Hot Solvent Clean
Place wafer in boiling acetone for 3 minutes.
Place wafer in boiling methanol for 3 minutes.
Place wafer in boiling isopropanol for 3 minutes.
3.1.2
Substrate Preparation
We first start with a 2-inch diameter alumina substrate.
To remove impurities we perform a hot wash.
In the event o f additional moisture the wafer is placed on a hot plate to dry.
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56
Blow-dry immediately with nitrogen.
Note: It is important that at no point the sample be allowed to air dry, as this results in
contaminants remaining on the wafer.
3.1.3
Single Layer Photolithography
Place wafer on the spinner chuck.
Use micropipette to deposit photoresist in a circular motion starting with center.
Spin at appropriate speed for 40 seconds.
Remove from chuck.
Place on hot plate (soft bake) at appropriate temperature and time.
Remove and place on Suss MJB3.
I f necessary, align.
Expose for appropriate time. The wavelength o f the MJB3 is 365 nm and the intensity is
15 mW/cm2.
Remove from m ask aligner.
Develop in photoresist developer using the appropriate water to developer ratio for the
appropriate time
Rinse in de-ionized (DI) water for 2 minutes.
3.1.4
Double Layer Photolithography
Place wafer on the spinner chuck.
Deposit PMGI S.F. 11 photoresist in a circular motion starting at the center o f the wafer.
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57
Spin at 4000 rpm for 40 seconds.
Remove and place on hot plate at 200 °C for 2 minutes.
Allow to cool and place wafer on the spinner chuck.
Use micropipette to deposit top layer photoresist in a circular motion starting at the center
o f the wafer.
Spin at appropriate speed for 40 seconds.
Remove from chuck.
Place on hot plate (soft bake) at appropriate temperature and time.
Remove and place on Suss MJB3.
If necessary, align
Expose for appropriate amount time. The wavelength o f the MJB3 is 365 nm and the
intensity is 15 mW/cm
Remove from mask aligner.
Develop in photoresist developer using the appropriate water to developer ratio for the
appropriate time.
Rinse in DI water for 2 minutes.
Remove and place in deep UV (DUV) system.
Expose for 12 minutes.
Remove from DUV.
Develop in non-dilute PMGI developer for 1 minute.
Rinse in DI water for 2 minutes.
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58
3.1.5
Silicon Nitride Deposition
Equipment: CVD 1000 MPB by Ion and Plasma Equipment Inc.
Place sample on stage
Pump down chamber to 25 mTorr
Heat stage to 300 °C
Flow Silane (70%) and Ammonia (100%) into chamber
Throttle at 350 mTorr
Turn on RF power Supply at 30 percent
Note: Deposition rate is about 10 nm/min.
3.1.6
Metal Deposition
Equipment: Edwards Coating System E306A
Load gold pellets into turret and load chromium rod into holder
Mount wafer onto sample holder
Pump system down to 1.2 10'6 Torr
Slowly turn on power.
Allow chromium to deposition onto the shutter. (This is done so that in the event o f any
contaminants within the metals, they are evaporated onto the shutter and not the sample).
Open shutter.
Deposit 30 nm o f chromium.
(Chromium is used to promote adhesion to the alumina wafer, since gold does not adhere
well to most substrates.)
Close shutter.
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59
Deposit gold in the same manner as the chromium
3.1.7 Silicon Nitride Etch
Equipment: March Plasmod with the GCM 200 gas controller.
Place wafer on sample stage.
Pump down to 0.2 Torr.
Run CF 4 -O 2 into chamber for 2 minutes
Throttle pressure 0.5 Torr
Turn on RF power.
Etch rate ~ 80 nm/min.
3.2
3.2.1
Common Terms
Photoresist
Commercially available, photosensitive, organic polymer. The polymer is normally
suspended in a solvent that is removed by baking during the process. Exposure to
ultraviolet radiation renders the exposed areas soluble or insoluble depending on the type
o f photoresist.
3.2.2
Spin-coating
Also referred to as spinning or spin-on. The process o f putting down layers o f dielectric
or organic polymers. The material is dispensed in liquid form onto the wafer, which
spins up to 8000 rpm. The material and the process are engineered to give a smooth and
pinhole free layer that has uniform thickness except near the wafer edges.
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60
3.2.3
Mask
Patterned opaque layer, normally chromium, on a transparent glass substrate. The masks
are normally made commercially with the pattern given by the output o f a computeraided design program.
3.2.4
Etch
The process o f selectively removing a material while using the imaged photoresist as a
mask. Throughout the context o f this chapter, we will refer to dry plasma etch.
Dry (gas) etching uses the reaction o f the CF4 -O 2 plasma ions with SiNx.
3.2.5
Bi-level Liftoff
The removal (lift-off) o f excess gold and photoresist after blanket evaporation. The
wafer is placed in a hot (80 °C) ‘stripping’ solution that dissolves the PMGI photoresist.
Since the PMGI is on the bottom layer, any other layer on top o f the PMGI will be
‘lifted- o ff.
3.3
Lavers
3.3.1 Layer 1: Straps and Interconnects
Approximately a 1 pm thick layer o f silicon nitride (SiNx) is deposited on the bare
alumina substrate. Grooves will be etched into the SiNx and 1 pm thick metal will be
deposited into these grooves to form the metal straps. The surface remains planar
because the SiNx and the metal are nominally the same height. The planarity makes the
subsequent processing steps easier. Though in principle w e could etch the grooves
directly into the alumina to achieve the same results, etching alumina is difficult.
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61
We performed a two-layer photoresist step. We used AZ1518 as our top layer resist and
PMGI SF 11 as the second layer. The spin speeds were 4000 rpm for both resists. We
performed a soft bake at 90 °C for 1 minute for the AZ1518 resist and a 200 °C 2-minute
bake for the PMGI.
We then exposed the AZ1518 resist for 15 seconds and developed using a 1:1 mix of AZ
developer and water for 30 seconds. The wafer was then rinsed with DI water and blown
dry with nitrogen gas. The PMGI layer was then exposed for 12 minutes using the deep
UV system. The PMGI was then developed in undiluted PMGI developer for 1 minute.
We then placed the wafer in the barrel etcher and etched for two minutes. 1 micron o f
gold was then blanket evaporated. The excess gold was removed using a bi-level liftoff
by placing it in PMGI stripper solution heated at 80 °C.
3.3.2
Second Layer: Vias
A second layer of 150 nm o f SiNx is deposited over the strap layer.
We then performed a single layer photolithography step. We used Shipley 1805
photoresist. The photoresist was soft baked at 90 °C for 1 minute. We exposed the 1805
for 6 seconds and developed in a 1:1 AZ Developer and water solution for 30 seconds.
Vias were then etched in the exposed areas o f the SiNx using a C F 4 - O
2
plasma. After the
etch, the sample was placed in an oxygen plasma (thus process is sometimes called
photoresist ashing) for 5 minutes to remove any photoresist that may have reacted with
the
C F 4 -O 2
plasma to form a compound that is insoluble in acetone. The remaining
photoresist was then removed using acetone and methanol.
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62
3.3.3
Third Layer: Coil
A hot wash was performed.
The coil layer was patterned using the same two level photoresist process as the first
layer. We also evaporated 0.5 to 1 micron o f gold to form the coils. After removal from
the evaporator, the excess gold was removed using a bi-level lift-off.
3.3.4
Fourth Layer: Transmission Line
The transmission line layer was patterned and created using identical steps as the coil
layer the only exception being that 0.5 micron o f gold was evaporated.
3.4
Verification
After fabrication o f the MECP, we needed to verify that the device was working
as expected. Figures 3-4 to 3-6 show photographs o f the fabricated MECP. We needed to
ensure that the SiNx was properly etched and that there was good electrical contact at the
ends o f the connector joining the coil to the transmission line. To do this, we measured
the DC resistance between the ground and signal strips o f the CPW. A low reading
indicates that there is good DC electrical contact from the series connections o f the CPW
connecting straps and the coil. We got resistance values o f less than 5 ohms, which is in
good agreement with what we expected. It is important to note that we would expect
higher resistances at microwave frequencies due to the skin effect.
By moving the picoprobes along the CPW and by looking at reflected power at
various frequencies, we were able to compare theoretical and experimental plots o f
frequency versus distance for a CPW. Good agreement is an indication that the CPW is
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63
in quasi-TEM mode. We got good qualitative agreement with the only significant
difference being that the physical length had to be replaced by a larger effective length in
the simulation. This would seem reasonable since the CPW is open at one end, and we
would expect coupling to nearby structures, thereby increasing the effective length.
Finally, to verify that the MECP was operating like a typical eddy current probe,
we placed a thin gold wire at the end o f a manipulator and moved it along the coil area of
the MECP and then replaced the gold wire with a dielectric fiber. Since we know that the
magnitude of the eddy current is dependent on the conductivity o f the sample, we would
expect a large signal for the gold wire and no response for the dielectric. These
expectations were in agreement with what we observed.
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64
coil
CPW
via
shoning straps
Figure 3-1 Schematic showing the various layers to be fabricated.
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65
S id e
Start w*h bars alumina
wafer and d e a n
T op
9999999
222222Z222Z2Z22Z
alumina
Deposit Nitride
PMGI S.F11
m
AZ 1518
SiNx
Mask
Spin-on PMGI S.F.
11 & AZ
1518 photoresists
use mask to expose
with ufltra violet
radiation
Figure 3-2 Process steps for the first level straps.
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66
Side
Top
nn
?yy&7yyyyyyyyyyyyyyyyy/.
Develop
AZI518
yyyyyyyyyyyyyyyyyyyyyyyA
Place wafer in deep (JV
and develop PMGI
n m m r ri
byyyyyy/
Etch
Nitride
Blanket Evaporate
Chrome and Gold
^99999999^
'^s^vyyyyyy ww /zxm
Lift-off
photoresist
Figure 3-3 Process steps for the first level straps continued.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3-4 Photograph of completed MECP.
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Figure 3-5 Photograph of close-up o f larger coil.
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69
i 0 um
Figure 3-6 Photograph o f close-up of smaller coil.
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70
CHAPTER 4
APPLICATION I: SCANNING METAL LINES
4.1
4.1.1
Introduction
Significance o f the Experiment
One o f the first applications of eddy current probes was the sorting o f metals. Over
100 years later, this application still finds its use within the semiconductor industry. In
particular, the ability to accurately determine the thickness or uniformity o f metals like
copper or gold is extremely important. Furthermore, the ability to image and distinguish
these metals against the background o f another conductive substance, for example a
GaAs semiconducting substrate, is invaluable. At present, there are several ways to do
this, including laser ultrasonic techniques, scanning electron microscopy, x-ray
fluorescence and stylus profilometry. However, each o f these methods has drawbacks,
including poor spatial resolution, sample contact damages, long data collection time, or
high capital investment [Banet, et al. 1998] Another important application is the ability
to detect failure modes such as electromigration in ultra thin metal films.
In this chapter, we will demonstrate the utility o f the MECP by using it to map gold
and titanium lines. In doing so, we will demonstrate the spatial resolution o f our probe as
well as its sensitivity to changes in sheet resistance RSh-
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71
Recently it has been demonstrated using an eddy current probe [Sakran, et al.,
2 0 0 1
] that the sheet resistance o f copper lines varying in height from 0 . 2 to
1 .2
pm can be
determined. However, the size o f the eddy current probe was on the order o f a
millimeter, which is more than two orders o f magnitude greater than our coil.
4.2
4.2.1
Experimental Procedures
Sample Preparation
We prepared two sets o f samples. The first set was used to scan across metal
lines and was made by patterning and thermally evaporating chromium/gold 20/50 nm.
The second samples were prepared by patterning and electron beam evaporating 0.36 pm
thick titanium/gold (0.03/0.33 pm) and 0.36 pm thick titanium metal lines. Both sets o f
samples were on microscope cover slides. The widths o f the lines ranged from 50 pm to
250 pm (see Figure 4-1). The slides were then broken up into small pieces on the order
o f I -2 mm. The pieces were then sorted for those with straight edges, since we only
wanted to scan the ends o f the slides. Scanning indiscriminately in the plane o f the coil
would require having pieces o f the slide over the CPW, which would cause interactions
with the CPW guided microwave traveling along the CPW. These interactions would be
undesirable, since they would decrease the resolution o f the probe from approximately
the coil diameter to that o f the gaps in the CPW.
The sample was then mounted with epoxy onto the end of a probe tip that was
glued at the thick end to a piezoelectric transducer (PZT) that vibrated along the vertical
axis. The PZT was then mounted onto an arm that was in turn mounted onto a
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72
commercially available 5-axis translation stage. This stage was mounted onto the arm o f
our probe station, which allowed for coarse x-y translation as well (see Figure 4-2).
4.2.2
Stub Tuning
Once the sample was fully prepared, we were ready to impedance match the probe
using the stub tuning method. The tuning was performed in three steps: first a rough
semi-automatic tuning was performed, then the tuning was further refined manually using
the crystal detector. Once the frequency was fixed, we performed our final fine-tuning by
varying the distance along the transmission line very slightly and using the spectrum
analyzer. A general but more detailed description is given in the Appendix.
4.2.3
Experimental Set-up and Technique
Figure 4-3 shows a schematic of our experimental set-up. The microwave signal
was sent through the ‘in’ port (port number 1) o f the circulator to the matched CPW
through port number 2. The sample, which is attached to a PZT, was held over the coil.
The audio frequency generator was used to oscillate the PZT and the sample at a
frequency o f approximately 100 Hz. The range o f oscillation o f the sample was
approximately 15 pm vertical to the coil. A signal from the sync port o f the audio
frequency generator was sent to the lock-in amplifier. The change in vertical position of
the conducting sample over the coil resulted in the reflected signal being amplitude
modulated at 100 Hz. The magnitude of the modulation was proportional to the change
in tuning of the CPW. This change in tuning was due to a change in impedance o f the
coil-metal layer combination. The change in impedance of the coil-metal layer
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73
combination was dependent on the sheet resistance, the distance o f the probe from the
sample (lift-off), the microwave frequency and the radius as discussed in section 2 .2 .4 .
The modulated reflected signal was then reflected through port number 3 o f the
circulator to the high frequency low noise amplifier (LNA) and then to the crystal
detector. The amplitude o f the microwave signal was converted to a DC voltage at the
crystal detector. The low frequency modulation o f this signal, however, resulted in this
DC voltage being modulated. This modulated signal was then sent to the ‘signal in’ o f
the lock-in amplifier.
We used a MECP with average diameter o f about 20 microns. The M ECP was
timed at 13.4 GHz. By scanning across on the metal stripes, we were able to generate a
plot showing its physical outline. The sharpness o f the metal-cover slip interface gave us
an indication o f the spatial resolution achievable with our device. The variation in signal
strength o f the different samples gave us an idea o f the achievable sensitivity to sheet
resistance changes.
4.3
Results
We were able to scan and achieve resolution on the order o f the coils average
diameter. Figures 4-4 and 4-5 show the results we obtained by scanning across stripes of
50 and 125 pm, respectively.
Using the second set o f samples, we were able to differentiate between titanium
and gold with calculated sheet resistances o f 1.3 Q/square and 0.08 Q/square respectively
(see Figure 4-6). Figure 4-7 shows the results w e obtained from three separate trials.
The trials give about a factor o f two variations in signal for each metal. Though the gold
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signal is systematically larger than the titanium signal, our theoretical understanding of
the problem and our control o f the lift-off are sufficiently low that these results should be
regarded only as preliminary.
4.4
Conclusions
From this application, we were able to demonstrate that the MECP can be used to
characterize and map metal line and spaces. Although the results are preliminary,
however, we anticipate that we will be able to make measurements that allow us to more
clearly distinguish between lines with different sheet resistances.
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75
Figure 4-1 Schematic of chromium/gold lines that were scanned.
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76
Steel: Arm:
Translation stage
sample
Figure 4-2 Schematic samples showing holder and translation stage. The PZT
oscillates the sample in the vertical direction. The purpose o f the PZT is to increase
the sensitivity o f the measurement by allowing phase sensitive detection.
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77
Data Acquisition
T
Lock-in Am plifier
Crystal
Detecto
Audio Frequent r
T
(iwave “'mod
Amplifier
Mi crowave
Getaerator
p.wave •'mod
L -J r
Matche
CPW
I
XYZ
Translation
Sample
Circulator
Figure 4-3 Schematic of experimental set-up for scanning of thin metal films. Our
reflected microwave signal is then the incident signal amplitude modulated at f mo&.
The microwave component of this signal is converted to dc at the crystal detector
with the only ac signal b e in g /m0d* This signal is sent to the lock-in for phase
sensitive detection.
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78
Area being scanned
from left to right
End to End Scan of W—50 micron Line
30
40
50
Distance (m icreoi)
W
Figure 4-4 Scan across the edge of the SO fim line. Imperfections at the edges may
contribute to errors in our data.
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79
Area being scanned
from left to right
Figure 4-5 Scan of a 125 |im wide line.
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80
w R ^ i-^ ^ w w h w
S ilg lllt p
*»X«K*K
" 's
i**vfy r*
i l |||p
||pM |M I
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£:*<%%*:.....
'Sss. y'"?<<
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: :^:1;::':-:::::rS::::::':->f"':-:^::-7;:::-r>::>r:l>^:::>-:::
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s*
Figure 4-6 Schematic of 2S0 micron wide gold and titanium stripes on the left are
gold while the stripe on the right is titanium. The calculated sheet resistances of the
gold and titanium are 0.08 and 1.3 Q/square respectively.
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81
Reflected Power (arb. units)
Au
Au
Ti
1
8.2
7
2.2
2
7.4
7.3
1
3
3.93
3.0
1.68
Material
Trial
Figure 4-7 Figure showing results from three separate scans
across the schematic shown in Figure 4-6.
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82
CHAPTER 5
APPLICATION Et: LIFETIME MEASUREMENT OF A THIN
IN 0 .5 3 G A 0 .4 7 A S
5.1
5.1.1
FILM
Introduction
Significance of Experiment
The minority carrier lifetime in many instances can determine or dictate the
performance o f semiconductor devices. More specifically, epitaxial InGaAs that is
latticed matched to InP is often used in Heterojunction bipolar transistors (HBT).
Because o f its bandgap (0.73 eV) InGaAs is also used as infrared sensors. All o f these
devices are minority carrier devices. Our experiment was performed using p-type
InGaAs with a doping on the order o f a 101 5 cm'3. The purpose o f this experiment is to
demonstrate that the minority carrier lifetime can be measured using our microwave eddy
current probe (MECP). In this chapter, we will describe some of the basic transitions
involved in the generation/recombination process. W e will also describe the
photoluminescence lifetime measurement because it is so widely used. We will then
describe the MECP experimental set-up and the results we obtained. Finally, we will
conclude by offering suggestions for future development.
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83
5.2
Radiative and Nonradiative Recombination Mechanisms
When we illuminate a semiconductor in equilibrium with light or an
electromagnetic wave o f appropriate wavelength, we can cause an electron in the valence
band to go into the conduction band (see Figure 5-1). This process creates electron-hole
pairs and disturbs the equilibrium. If we were to switch off the light, the number o f
carriers (no+An and po+Ap) eventually decay to their equilibrium value. Here po and no
are the equilibrium electron and hole ‘background’ concentration and An and Ap are the
electron and hole excess generated carriers. The decay o f excess carriers is exponential
with respect to time and goes like e ^ . The time that it takes the excess carriers to be
reduced by a factor o f e is termed the carrier lifetime and is generally denoted as x By
taking the Fourier transform o f e( t/T) we arrive at an expression o f the Lorentzian form in
frequency domain, i.e.
L(to) = —
, ,
(4.1)
7t(C 0o) + © -
where the half width at half maximum (Do is the inverse lifetime ( 1 /x).
In a defect-free, direct gap semiconductor (Figure 5-2), the dominant
recombination mechanism is often radiative recombination, where a photon carries away
the excess energy. Another mechanism is nonradiative recombination, a process
occurring in both direct and indirect semiconductors. The nonradiative recombination
rate is greatly enhanced by defects (Figures 5-3 and 5-4). Defect assisted recombination
is also known as Shockley-Read-Hall (SRH) recombination.
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84
These two mechanisms, along with Auger recombination, are the three most
common recombination mechanisms. They can occur simultaneously, but which is
dominant depends on the injection level and doping level. At low-level injection and low
doping concentrations, N on the order o f 101 5 cm ' 3 or less, Shockley-Read-Hall
recombination dominates. This nonradiative mechanism is characterized by transitions
within deep levels or traps typically near the semiconductor mid bandgap (see Figures 53 and 5-4). The lifetime
t Sr h
is independent o f N such that t Sr h ~ [Br(no + Po)] -1, where
Br is the defined as the coefficient o f band to band transition and is related to the
transition probability. In the doping range o f 101 6 to 10 18 cm'3, the lifetime varies as 1/N.
This behavior is an indication that radiative recombination is dominant. The lifetime is
given as xrad = 1/(BN) where B is the radiation coefficient which is proportional to the
sum o f the dipole matrix elements connecting the valence and conduction band wave
functions. For Ino.5 3 Gao.4 7 As, B is approximately 1.43xlO ' 1 0 cm'3 s' 1 [Ahrenkiel et
al.,1998]. The final m ajor nonradiative mechanism that we will consider is auger
recombination. The lifetime is Tauger = [CN2]"1, where C is defined as the auger
recombination coefficient. All o f the mechanisms have assumed low-injection level. At
high injection level, the form o f the mechanism remains the same, except N is substituted
with An. It is often desirable to express the total lifetime x as a function o f the various
mechanisms, by the law o f addition o f reciprocal lifetimes, the total lifetime is
1/ T =
1 / Tnonrad
~ 1 / ”tSRH
1 / "trad
1 / ^auger
(4 * 2 )
1 / ^rad*
which implies
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85
x=
5.3
5.3.1
[ts rh " 1+
BN + CN2] '1.
(4.2a)
Lifetime Measurements
Photoluminescence
O f the many methods and techniques that are used to make lifetime measurement,
by far photoluminescence lifetime measurements are the most popular.
Photoluminescence measurement in its most simple sense is the measuring o f optical
radiation emitted by a semiconductor driven far from equilibrium when excited by
external light. Although the concept is simple, the technique and equipment use are not.
Figure 5-5 shows a diagram o f a typical steady-state photoluminescence lifetime
measurement system.
The excitation source for most III-V semiconductors (such as InGaAs) is argonion laser. The photoluminescence measurement is usually taken at room temperature.
The purpose o f the cyrostat is to be able to do the measurement as a function o f
temperature. The scanning spectrometer (with a typical resolution o f 0.1 -0 .2 nm) sends
synchronized information about the intensity and spectrum to the recorder.
5.4
5.4.1
Experimental Technique
Sample Preparation
Figure 5-9 is a schematic o f our experimental set-up for measuring the lifetime
within a thin (~ 0.5pm) InGaAs sample. The two most obvious configurations for
orienting our sample with respect to the coil are shown in Figure 5-6. However, if laser
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86
light is directed as shown (from the top), then both o f these configurations pose serious
problems. In the first scenario, the InGaAs is furthest away from the coil. As a result,
there are essentially no eddy currents in this region, since the minimum thickness o f the
thick InP is about 100 pm. We want the conductor layer to be about a coil diam eter away
from the coil so that we can have adequate coupling between the conducting layer and the
coil. The second scenario may not be a problem if a laser with the correct wavelength is
used. However, with the laser available to us, this second scenario was equally
problematic. Although the InGaAs is now situated extremely close (~0.1 pm) to the coil,
because o f the absorbance o f the laser light within the InP, very little if any electron-hole
pairs are actually created in the InGaAs layer. The absorption coefficient a o f InP at 785
nm is on the order o f 104 cm '1. If Io is the intensity at the top o f the InP, then the
intensity Id at a distance d away in the InP sample goes like Ioe'ad, for d = 10'2 cm (100
pm) thick the intensity at the top o f the InGaAs sample is zero for all practical purposes.
We overcame this problem by performing what is known as an epitaxial lift-off
(ELO) [Chan, et al., 1991]. Figure 5-11 shows a schematic o f this process. First, the
InGaAs sample was cut into small pieces (a little less than a mm on each side). Apezion
W (black wax) was then placed on top o f the InGaAs. This wax served two purposes: 1)
it protected the InGaAs from the etching process that follows and 2) it provided
mechanical support to the thin InGaAs after it was Tifted-off”, so that the sample can be
handled with tweezers. Care was taken to ensure no wax hung along the side o f the
sample, since this would have prevented the InGaAs from ‘sitting’ flat onto the coil. The
sample was then placed in a refrigerated HC1 solution for about 11/2 hours. A complete
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87
lift-off was indicated by the samples floating to the top o f the solution. Next the InGaAs
was removed and rinsed in deionized water. While the sample was still wet, it was placed
over the coil, which was electrically isolated by a 100 nm layer o f silicon nitride (SiNx).
The film was roughly aligned and then left to dry overnight with a small weight
(tweezers) placed on the film. During the drying process, attractive forces between the
SiNx and the InGaAs squeezed the water to the edges by a Poiseuille flow. As the water
escaped and the InGaAs and SiNx became closer until the short-range attractive van der
Waals forces held the two together.
AZ 5214 was then spun on the substrate, an image reversal process was
performed using a Ziess microscope with 80X objective for exposure. The purpose o f the
process was to protect the InGaAs over the coil and leave the undesired areas unprotected
so as to be etched away. The unwanted areas o f InGaAs were etched using a solution o f
phosphoric acid, water and peroxide. The photoresist was then removed and the sample
preparation was complete.
5.4.2
Stub Tuning
Once the sample was fully prepared, we were ready to impedance match the probe
using our stub tuning method. The tuning was performed in three steps; first a rough
semi-automatic tune was performed by varying the frequency and the distance along the
CP W. The tuning was further refined by using information from the first tune and by
making smaller increments in varying the distance and frequency. In both cases, the
reflected signal was measured using a crystal detector connected to a multimeter. A
crystal detector is a device that converts the microwave signal to a dc voltage that is
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88
proportional to the power. Once the frequency was fixed, we performed our final finetuning b y keeping the frequency fixed and varying the distance along the transmission
line very slightly. We used a spectrum analyzer to measure the reflected power. A
general but more detailed description is given in the Appendix. Figure 5-8 shows a plot
o f normalized impedance versus frequency for different positions along the CPW. Figure
5-9 shows a comparison between theory and experiment for a plot of normalized
reflected power versus distance along the CPW at a frequency o f 18 GHz. The theory is
based on our simple transmission line model, yet there is fairly good qualitative
agreement between the two. We used a matching impedance o f 9.9 + j8.3 Q which is
consistent with the calculated values o f the coil.
5.4.3
Experimental Set-up
The experimental set-up is shown in Figure 5-10. The coil-sample load was
excited by 5 dBm o f microwave power aty^wave ~ 16 GHz. We can obtain higher
sensitivity by modulating the reflected microwave power at a low frequency^nod and by
using phase sensitive detection. To modulate the reflection, we modulate the sample
mechanically, electrically or optically, depending on the nature o f the experiment. To
measure the minority carrier lifetime optical modulation is most feasible. The InGaAs
sample was irradiated with a 785 nm diode laser that was connected to a current driver
circuit. The current and consequentially the laser light output in the driver circuit was
amplitude modulated at f mo&, which ranged fromlOO Hz to 200 kHz. By performing the
appropriate calibration, we ensured that the laser response was uniform over the entire
modulation frequency range. The laser light intensity incident on the InGaAs was
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89
approximately 1 mW/mm2. The laser light modulated the sample’s conductivity by
creating electron-hole pairs, and this, in turn, modulated the microwave reflection at
frequency^nod- Because the reflections were eliminated with the laser power off, the
amplitude o f the reflected microwave was directly related to the photogenerated carrier
density. Assuming 100 percent quantum efficiency, we calculated that the upper limit o f
the photogenerated carrier density was approximately 5xl016 cm'3. To obtain the
lifetime, we measured this amplitude as a function of/Jnod which has a Lorentzian
dependence with a half width given by the minority carrier lifetime. Figure 5-11 shows a
schematic o f the response o f the carriers within the InGaAs to the laser excitation. At
low frequencies, the carriers are able to ‘follow’ the laser but at higher frequencies, it
becomes more difficult to do so. Therefore, at higher frequencies, the reflected signal
becomes less. Data was taken via GPIB connections and plotted.
5.5
Results
We obtained the reflected power as a function o f the modulation frequency. The
results fitted well with the expected Lorentzian dependence as shown in Figure 5-12.
The fitting was simplified by doing a linear regression of 1/P v s .fmod as shown in Figure
5-13. The results o f the filled yielded a value o f 3.8 ps for the minority carrier lifetime.
We compared this value with a value found in the literature and found that our results
were in good agreement. Figure 5-14 shows a plot o f the lifetime versus doping density
[Ahrenkiel et al.,1998] with our lifetime value overlaid on the curve.
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90
5.6
Conclusions
W e demonstrate that the MECP is a viable tool for making lifetime
measurements. Within its operating regime, the MECP hold several advantages over PL
measurements. First, the light source needed for the MECP, a diode laser, is relatively
cheap and small compared to the large expensive systems needed for PL. Secondly, the
device can be used to measure samples that are not luminescent, a requirement o f
photoluminescence, since we detect electronic and not optical changes. However, it
should be clarified that although our device has many advantages, it cannot supplant the
photoluminescence lifetime measurement. This is primarily because the M ECP cannot
measure lifetimes less than approximately 10 ns. This condition is set primarily by the
speed o f the electronics needed to drive a diode laser. Presently, a few gigahertz is the
maximum available driver frequency. Furthermore, should we choose such an option, we
may have to change our experimental set-up by using a spectrum analyzer instead o f a
lock-in amplifiers since ‘lock-ins’ tend to operate at less than a gigahertz.
It should be reemphasized that although the sample is electrically isolated by the SiNx
layer, it is physically attached to the wafer (directly over the coil). This allows us to
control for the lift-off consistently. However, for further commercial development, we
can easily mount the sample to a stage for the purpose o f scanning in a plane.
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incident EM wave
equilibrium
E
caxccoco Ev
emission: recombination
absorption: creation of
electron-hole pairs
Figure 5-1 Schematic showing the process of radiative generation and emission. The
semiconductor is initially in equilibrium. Incident light causes electrons to be
injected into the conduction band thus leaving holes behind in the valence band. If
the incident light is turned off the electron-hole pairs will combine and emit
photons.
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Direct Semiconductor
k
Indirect Sem iconductor
Figure 5-2 Schematics showing both band diagrams o f an indirect and a direct
semiconductor. Going from valence to conduction band in an indirect
semiconductor requires a change in momentum that is usually accomplished by
emitting a phonon.
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93
electrons
EC
acceptortype traps
holes
OOCCC'XCO v
C
c
o
jx
m
x
Ev
electron capture
EC
------------EV
electron emission and
recombination
Figure 5-3 Schematic of the Shockley-Read-Hall recombination mechanism of
electron capture and emission in an n-type semiconductor. This is a nonradiative
process distinguished by traps near mid-gap. Initially the electron-hole pair is
created.
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electron
trapsholes
^O CCCOOCOO
E
000
0 0 0 v
hole capture
------------ Ev
hole emission and
recombination
Figure 5-4 Schematic of the Shockley-Read-Hall recombination mechanism of hole
capture and emission in an n-type semiconductor. This is a nonradiative process
distinguished by traps near mid-gap.
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95
irror
Laser
Inteference
Filter
I
Lock-in
Am plifier
Photom ultiplier o r Solid
State D etector
I C hopper
Focussing Lens
Focussing
Lens
R ecorder
C olor Glass
Spectrom eter
Filter
Laser B eam L ow Tem perature
Cryostat
Figure 5-5 Example of a set-up for the steady state photoluminescence
measurement.
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96
L
a
s
e
r
InGaAs
A
SiN x
Side View
Figure 5-6 Schematic illustrating our dilemma when working with bulk InGaAs/InP
sample. In the first scenario the InGaAs is too far removed from the coil to be
inductively coupled to the coil. In the second scenario the InGaAs is close to the coil
but essentially no laser power reaches the sample because it is absorbed within the
InP. We can avoid the limitations of this second scenario in the future by choosing
the laser wavelength so that it does not absorb significantly into the InP.
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97
black w a x
jnGaAs_
In P
In P
black wax
black w ax
InuaAs
InOaAs
®l
HC1
-0.5 fim
t
Figure 5-7 Process steps for achieving epitaxial lift-off. The black wax served two
very important purposes: it provided chemical protection from the HC1 and it
provided structural support during handling.
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98
Stub Tuning at 13,IS and 18 GHz
0.E+00
-I.E-04
• | -2.E-04
ja -3.E-04
-2- -4.E-04
— 13 GHz
|
-5.E-04
- 1 5 GHz
“
-6.E-04
— 18 GHz
•5 -7.E-04
1
OS
-8.E-04
-9.E-04
-l.E-03
Distance from open end (mm)
Figure 5-8 A typical Reflected power vs. distance from the open end o f the CPW
plot obtained with stub tuning. The Plot shows reflection curves at 13,15 and 18
GHz.
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99
m easu red
c a lc u la t e d
n = 4 .3 5
|rf
Zfc0ii= 9-9 + jSO
L = 4 .5 5 m m
i
2^=551
\
f=18 GHz
d
D is t a n c e fr o m o p e n e n d
Figure 5-9 Plots showing qualitative agreement between measured and calculated
reflected power as a function of position along the CPW.
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100
Data Acquisition
I
Lock-in Am plifier
Audio Frequency
Mixer
Sample
uw ave
M icrowave
p.wave
J mod
Matched
I
n ( ki a \ s
p.wave
Circulator
Load
Figure 5-10 Experimental set-up for lifetime measurement. We modulated the
carriers at the coil by modulating the laser. Our reflected microwave signal was
then the incident signal amplitude modulated at f mo «j. By beating our reflected
microwave signal to base band w e generated a plot o f reflected power as a function
O f/m o d *
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101
Reflected Power Versus
Frequency
w
o>
S3
Frequency
Time
Time
Time
Figure 5-11 Schematic showing qualitative explanation of Lorentzian-like
dependence. At low modulation frequencies the carriers within the InGaAs can
‘follow’ the laser. However at high frequencies the carriers cannot fully recombine
before they are excited again. This results in a decrease of the reflected signal.
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102
Normalized Reflected Power vs. Frequency
Normalized Reflectef Powei(arb. units)
1
o
0
50
100
150
250
200
Frequency (KHz)
Figure 5-12 Plot o f reflected power versus modulation frequency f
the Lorentzian dependence that we expected.
m0d-
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This shows
103
In v erse R eflected P o w e r V s F re q u en cy 2
1/Reflected Power (Arb. Units)
3
2
0
1000
2000
3000
4000
Frequency2 (kHz2)
Figure 5-13 A Linear regression of our lifetime data allows us to calculate the
minority carrier lifetime from f mo<± on the graph.
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104
Expected Range
o u r d ata point
C 10
N(cm
)
Figure 5-14 Plot of lifetime vs. doping concentration N [Ahrenkiel, 1998]. Based on
the MBE grower’s estimate of a few times 1015 cm'3 our results fall within our
expected range and agree well with the literature.
Note: Ahrenkiel, R. K., Ellingson, R., Johnston, S., and Wanlass, M., Recombination
lifetime o f I n o . 5 3 G a o . 4 7 As as a function o f doping density, Applied Physics Letters, Vol.
72, Number 26, June 29, 1998
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105
CHAPTER 6
CONCLUSIONS
There is an ever-increasing need to increase the spatial resolution o f probes for
the reliable characterization of semiconducting devices. This is due to the fact that in
order to increase the performance and/or for economic reasons, it is almost always better
to decrease the size o f the various components and devices. Within a manufacturing
environment, in addition to achieving the desired resolution, speed is o f extreme
importance. A decrease in the time that it takes to make, characterize and test a device
usually translates into savings to the consumer. The ability to rapidly scan
semiconductors and provide information that can be related to its conductivity, mobility,
permittivity, or carrier lifetime is also o f extreme importance. Because o f the increase in
operating frequencies and current density o f semiconductor devices, the ability to
diagnose the failure in interconnects, for example, is equally important.
For these reasons, we proposed the design and development o f a non­
contact/nondestructive high frequency eddy current probe. In order to make a leap in
improvement o f the spatial resolution, we had to make a departure in the w ay in which
we designed and fabricated our probe. Instead o f the traditional wire wound or
microfabricated multi-turn probe, we used a microfabricated single turn coil. This helped
us to increase the spatial resolution by an order o f magnitude even over micro fabricated
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106
coils. Our increase in frequency up to 18 GHz, though a first for such a probe, was more
a necessity than a choice. Since the sensitivity decreases with decreasing coil radius, we
had to extend the probes operation higher frequencies to ensure that we used as much of
the power to the coil for eddy current generation as opposed to being lost in Ohmic
heating o f the coil. We used a coplanar waveguide to deliver power to the coil because of
its planar nature and ability to ‘handle’ such high frequencies. To further improve
sensitivity, we used a stub tuning method that was integrated into our design with
minimal effort and that achieved a minimization o f the reflected background signal o f 60dBm.
We performed two experiments that not only demonstrated that we had fabricated
a working device but also demonstrated its utility. The ability to distinguish between two
metals with different sheet resistance has implications for scanning metal interconnects
on semiconducting substrates such as GaAs. The measurement o f the lifetime o f p-type
InGaAs is another important example o f the usefulness o f our device. Based on our
experimental results, we should easily be able to measure the lifetime o f many different
types o f semiconducting materials as long as their minority carrier lifetimes are greater
than approximately 10 nanoseconds. With our technique, it does not m atter if the
semiconductor is luminescent or not.
Despite all our successes, this first iteration o f our device demonstrates that there
are still several modifications to our device that can make it more effective and even
more attractive as a commercial device.
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107
Optical lithography limits the diameter o f our coils to about 1 to 2 microns.
W hile electron beam lithography can reduce the diameter much further, it m ay not be
economically feasible to do so. Another possible change to the design and fabrication o f
our coils is incorporating a small high permeability metal ‘rod’ within the inner area o f
the coil. The effect o f this rod will be to concentrate the magnetic flux lines that then
induce the eddy currents into a smaller effective volume and increase the coupling to the
sample. In any event, we will have to account for the large increase in resistance o f such
small coils.
There are also key improvements that can be made to the design o f the
transmission line. In order to facilitate three-dimensional scanning, the CPW can be
made lower than the coil so that the only interaction is at the coil and not from the quasiTEM waves traveling along the CPW (see Figure 6-1. Another possible alteration could
be to attach the coil at the end o f and coax line (see Figure 6-2). In this way, the MECP
could be used in a similar manner as evanescent probes. Additionally, these probes could
be incorporated simultaneously with evanescent probes.
Even though our method o f tuning is very effective and simple, a better method
should be explored so that multi-frequency or microwave frequency scanning
experiments can be made. One method could be the incorporation o f a varactor and
variable resistor within the CPW to facilitate fast electronic stub tuning.
Overall incorporation o f the device onto a more robust scanning stage will greatly
improve our accuracy. A piezoelectric stack with longer travel range will also increase
the maximum range between the coil-sample separation and therefore the sensitivity. By
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108
increasing the vertical distance that the sample is away from the coil, we get less
coupling. These changes, however, can easily be incorporated since these items are
commercially available. Overall, we conclude that the MECP is a useful and important
diagnostic tool. We contend that the information contained in this dissertation w ill
greatly assist in the future developments o f such a probe. The utility of the MECP is by
no means limited to the ones that we have demonstrated; we believe we will eventually
see many more creative and useful applications for the device.
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109
S a m p le
T h ic k
D ie le c t r ic
> 5 pm
CPW
/
Figure 6-1 Side view o f an alternative experimental set-up for lifetime
measurement.
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110
Contact to
coax ground
Contact to
coax Signal
Coxaial transmission line
From the bottom looking up
Dielectric
Sample
Side View
Figure 6-2 Another alternative experimental set-up for lifetime measurement.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ill
APPENDIX
The method o f stub matching has been a widely used method for tu n in g
transmission lines. Often with regard to long cables, one would desire that m in im u m
losses be present. For example, in long-range cable transmission systems, these losses
manifest themselves as echoes and other distortions. Using a stub helps to minimize
these losses. A stub is essentially an open or short in that is usually in parallel with the
load impedance (see Figure 2-19). The length of the stub I and distance that the stub is
from the load d is determined such that the combine parallel resistance o f the stub and the
load is equal to the characteristic impedance of the line, thereby eliminating reflections.
Shorted stubs are generally better suited for lines with purely resistive characteristic
impedance. As an aside, a graphical method using a Smith chart is commonly used to
make it easier to find the values o f electrical lengths needed to tune the transmission line.
This eliminates the need to make calculation with complex numbers.
The stub tuning method is performed in three steps: a coarse semiautomatic scan
using a crystal detector and a multimeter, a fine tune o f the first scan using the same
equipment but better resolution, and finally an even finer method using the spectrum
analyzer.
For our initial coarse stub tuning, we must make sure that the CPW is in a
quiescent state, which means that the coil could be loaded or unloaded (not coupled to a
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112
conductive sample). For example, in our first application, the coil is totally unloaded
whereas in the second application, the coil is initially coupled or loaded with the InGaAs
sample. Both o f these scenarios represent the quiescent state o f the CPW because it is the
changes from this state that are o f interest to us. Figure A -l represents a schematic o f our
coarse tuning method. First w e normalize our measurement by shorting our picoprobes
on one o f the CPW ground planes. We then use the computer via a GPIB connector to
step through either the 6.5- 13 GHz or 10.5-18.5 frequency range depending on which
circulator w e use. We use increments o f 100 or 50 MHz. The reflected microwave signal
is sent to the return port o f the circulator, then sent to a crystal detector. The microwave
signal at the crystal detector is converted to a voltage that is proportional to the
microwave power. Thse data are the sent to the computer, which records this information
as a function o f frequency. After we record the initially calibration data, i.e. reflected
power as a function o f frequency with the picoprobes shorted, we then manually
increment the position o f the picoprobes along the CPW. We typically use increments o f
0.25 pm since the straps that short the ground plane are repeated every 0.5 pm can be
used as a guide. After we have repeated this process all along the CPW, we normalize
our data using the data from the reflected signal when the probes are shorted. We then
arrange our data so that we can plot reflected power versus distance for various
frequencies; for example, see Figure 5-13.
After we have located a point that looks like a point o f minimum reflection (in
Figure 5-13, this would be at around 1.75 mm for a frequency o f 15 GHz), we then
manually move the picoprobes near this area and manually vary the microwave frequency
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113
with a resolution finer resolution (around 10 MHz). Using the reading from the
multimeter, we can eventually determine the point o f lowest reflection Lmjn. Once we
have tuned our device beyond —30dBm, this is beyond the sensitivity of the crystal
detector, we use the spectrum analyzer to perform our final tune.
Scanning frequencies using the spectrum analyzer is slow and cumbersome
because o f the time it takes to regenerate the appropriate graphics on the screen. For this
reason, w e perform our final tune by keeping the frequency fixed and move the
picoprobes a few microns around Ln,m. See Figure A-2 for a schematic.
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114
pvave
output
output
computer
input
Multimeter
DC Voltage
crystal
detector
p.wave
Microwave
Generator
Probe Position
CPW
(j.wave
Circulator
Loaded or
Unloaded Coil
Figure A -l Set-up of coarse tuning method. The microwave frequency is
incremented by i*Af.
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115
Spectrum
Analyzer
(x w a v e
Mi<srowave
Getlerator
Probe Position
o>
Circulator
b*
(j.w a v e
*
CPW
Loaded or
Unloaded Coil
Figure A-2 Schematic showing fine stub tuning.
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116
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