close

Вход

Забыли?

вход по аккаунту

?

Characterization of time and frequency -varying optoelectronic microwave silicon switches

код для вставкиСкачать
INFORMATION TO U SER S
This manuscript has been reproduced from the microfilm master. UMI films the
text directly from the original or copy submitted.
Thus, some thesis and
dissertation copies are in typewriter face, while others may be from any type of
computer printer.
The quality of this reproduction is dependent upon the quality of the copy
submitted.
Broken or indistinct print, colored or poor quality illustrations and
photographs, print bleedthrough, substandard margins, and improper alignment
can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete manuscript and
there are missing pages, these will be noted.
Also, if unauthorized copyright
material had to be removed, a note will indicate the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning
the original, beginning at the upper left-hand comer and continuing from left to
right in equal sections with small overlaps. Each original is also photographed in
one exposure and is included in reduced form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6” x 9” black and white photographic
prints are available for any photographs or illustrations appearing in this copy for
an additional charge. Contact UMI directly to order.
Bell & Howell Information and Learning
300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA
800-521-0600
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C haracterization o f T im e and F requency V arying
O ptoelectronic M icrow ave Silicon S w itch es
by
K enton Green
Subm itted in P artial Fulfillment
of the
Requirem ents for th e Degree
Doctor of Philosophy
Supervised by
Professor Roman Sobolewski
D epartm ent of Electrical and Computer E ngineering
The College
School of Engineering and Applied Sciences
U niversity of Rochester
Rochester, New York
1999
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
UMI Number:
9947619
UMI Microform 9947619
Copyright 1999, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
To the Im aginative z. w.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Curriculum Vitae
The author was bom in Mt. Pleasant, Michigan on May 8, 1970 to Kirk­
land and Joleen Green. He attended the U niversity of Houston in Texas
and graduated w ith a Bachelor of Science in Electrical Engineering in May
of 1992. He th en began his graduate career in Electrical Engineering at
the University of Rochester in New York. He pursued his research a t the
Laboratory for L aser Energetics under the guidance of Professor Roman
Sobolewski and received the Doctor of Philosophy in July of 1999.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Acknowledgements
I am grateful to m y advisor Roman Sobolewski for being trem endously sup­
portive and helping me tailor my graduate experience to m y benefit. He led
me through m y m any mistakes, while still giving me th e freedom to explore.
As a F ran k J. H orton Fellow a t LLE, not only did I have a t my disposal
nearly any im aginable optoelectronics an d microwave tool, I was also al­
lowed to purchase w hat I needed to advance my research. I worked with
the Pulse Uniformity group on a development project supporting the m ulti­
million dollar OMEGA laser fusion effort. As Pulse U niform ity group leader,
first Wolf Seka in 1994 and later Bob Keck welcomed me, encouraging and
supporting my efforts in m any ways.
I wish to th a n k Tom Hsiang, a champion Go player w hose deep physical
insight has been a valuable resource to me in countless ways.
Sam Letzring showed me th a t a single person can operate a farm, be an
accomplished welder, dem onstrate boundless knowledge of all things elec­
trical, and still be th ere for his family.
I greatly appreciated the assistance of Bill Donaldson, who among other
things graciously let m e misalign his lasers and dot his lab walls w ith laser
bums.
M ark Skeldon fielded my optics questions w ith answ ers even I could
understand, and spend much tim e showing me how to properly write arti­
cles.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Andrey Okishev’s skills on an optical table are amazing. It is m y belief
th a t he could get stim u lated emission from a concrete block. He knows a
staggering am ount o f alignm ent and diagnostic “secrets,” and it is a revela­
tion to watch him work.
I was very lucky to have Lynn Fuller assist m e in navigating dozens of
switch runs through RTFs very busy, large-scale IC fabrication facility.
The “femtoee” group, including ChiaChi, Marc, Doug, Carlo and Ro­
m an, have provided friendship and late-night rounds of pick-up basketball
th a t provided a necessary counterpoint to th e daily grind th a t is graduate
research.
My publications and presentations have been greatly improved by th e
Illustrations D epartm ent (LaDonna, Diane, K athie et al.), and L inda Clement
of Library Services. And Sarah Frasier’s happy smile was a god-send on
those mornings after a n all-nighter when I felt like raw m eat. S arah also
tracked me down like a blood-hound w hen m y wife wanted to tak e our son
to the Emergency Room NOW.
And so I come to: my family, who have blessed me w ith a strong founda­
tion of love and care and plenty of care packages filled w ith cookies, w ithout
which I would’ve easily gotten lost in “the Big City.” Thanks to all of you!
Finally, and foremost, m y wife Wendee. I am inspired by h e r joy and
zest for life, which she possessed even as a child. As a six-year-old she
wrote “I can’t believe I’m alive” in a personal diary. Now that is an early
appreciation for life! She will never realize how much this thesis is truly
owed to her.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Abstract
Optoelectronic microwave devices take advantage of th e interaction of op­
tical and microwave electric fields via the interm ediary of mobile charge
carriers in a semiconductor. This combination of photons and microwaves
m akes possible many unique applications such as photoconductive switch­
ing, which allows unparalleled optical control of electric fields from dc to
THz. However, along w ith these expanded possibilities also comes greater
difficulties in modeling and characterization. For example, the density and
spatial distribution of th e mobile charge carriers evolve on time-scales com­
parable to the microwave electric fields. In this regime th e assum ptions ap­
plied to conventional linear models of tim e-invariant microwave filters and
frequency-invariant m odulators cannot be used. To conquer th is difficulty,
techniques of analysis and synthesis using general time- an d frequencyvarying linear models were developed and applied.
This thesis introduces a technique for the m easurem ent of time-varying
systems based on general tim e- and frequency-varying models. The tech­
nique allows characterization of a class of microwave devices th a t vary tem ­
porally and spectrally on time-scales comparable to th e microwave period,
such as optoelectronic microwave silicon switches. This characterization is
presented as a superset of th e conventional microwave S param eter charac­
terization technique.
To shape laser pulses, th e U niversity of Rochester’s Laboratory for Laser
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Energetics’ OMEGA laser fusion project uses photoconductive microwave
switches to generate and control shaped microwave pulses. By applying the
above analytical technique we were able to observe, for the first time, the re­
lationship between tra n sie n t switching m echanism s (e.g., re-establishm ent
of contact depletion capacitance) and microwave pulse shape. O ur ability
to directly observe the tran sien t evolution of sw itch transm ission proper­
ties allowed the development of a time- and fi*equency-varying linear switch
model. By relating the model to switch fabrication conditions, we were able
to improve the fabrication procedures. Fabrication and characterization of
successive generations of switches perm itted optim ization of the switch per­
formance through an iterative fabrication process. Through optimized per­
formance, the bandw idth of the optical pulse shapes was increased from
3 to 6 GHz. Along w ith bandwidth, the dispersion of the switch tra n s­
mission was reduced. The developed switch m odel and the associated ex­
perim ental characterization technique are accu rate under many different
operating conditions, from cw to SBS-steepened fast-rise-tim e optical illu­
mination. The ultim ate performance lim its of th e OMEGA pulse-shaping
switches were also outlined.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
viii
Table of Contents
Abstract
vi
List of Tables
xi
List of Figures
x ii
1 Introduction
1
1.1 M o tiv a tio n .........................................................................................
2
1.2 Prim ary C o n trib u tio n s ...................................................................
4
1.3 Thesis O v erv iew ................................................................................
5
2 Optoelectronic M icrowave Silicon Sw itch P h ysics
7
2.1 Optical Surface T ra n sm is sio n ........................................................
8
2.2 Photon and C arrier Plasm a I n te r a c tio n .....................................
10
2.3 Complex Perm ittivity C h a n g e s .....................................................
13
2.4 S aturation M echanisms
................................................................
14
2.5 C arrier P lasm a an d Microwave I n te r a c tio n ...............................
14
2.6 Lum ped-elem ent A p p ro x im a tio n .................................................
16
2.7 M etal-Semiconductor Interface E ffe c ts........................................
18
2.8 Switch G eometry D e s i g n s .............................................................
23
2.9 General Switching Operational I s s u e s ........................................
25
2.10 OMEGA Pulse-shaping D e s i g n .....................................................
28
2.11 Summary o f Device Physics C o n sid era tio n s.......................................
36
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
ix
3
Sw itch Model
37
3.1
Standard Microwave M o d e l ..........................................................
38
3.2
Need for New M easurem ent M o d e l..............................................
42
3.3
Background to Tim e-varying M odel..............................................
46
3.4
M athem atical F o rm u latio n .............................................................
47
3.5
Analytical E x a m p le .........................................................................
54
3.6
Sum m ary of Modeling R e s u lts .......................................................
64
4 Experim ental C haracterization
5
67
4.1
Oscilloscope M e a s u r e m e n ts .........................................................
68
4.2
Windowed M e a s u r e m e n ts .............................................................
71
4.3
General L inear Device M e a s u re m e n ts........................................
81
4.4
Model S y n th e s is .................................................................................. 101
4.5
Frequency Response Im p ro v e m e n t................................................ 102
4.6
Summary
of C haracterization R e s u l t s ..................................................... 103
Summary and C onclusions
107
5.1
Advancement of Microwave M easurem ent T e c h n iq u e ...............107
5.2
Construction of M easurem ent S y s te m .......................................... 108
5.3
Complete OMSS Transm ission M easu rem en t.............................. 108
5.4
OMSS O p tim izatio n ............................................................................109
5.5
F u rth er OMEGA Switch Im p ro v e m e n ts....................................... 110
5.6
Application of S{ uj. t) M easurem ent to O ther Devices
.............. 112
Bibliography
114
A M aterial C haracterization
129
A1
OMEGA Single-Crystalline OMSS F a b ric a tio n ........................... 129
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
X
A.2
Polycrystalline Silicon Detectors
A3
Summary
.................................................. 131
of M aterial Characterization R e su lts.......................... 135
B Laser System D etails
139
B .l
OMEGA L aser S y s t e m .....................................................................139
B.2
Nd:YAG L aser S y s t e m .................................................................... 142
B.3
Laser User's Facility
....................................................................... 144
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
xi
List of Tables
2.1
Intrinsic single-crystal Silicon m aterial p aram eters a t 300 K .
2.2
OMSS design param eters and th e ir effect on bandw idth
3.1
A comparison of the transfer functions of lin ear tim e-invariant
...
(LTI) filters an d frequency-invariant (LFI) m odulators.............
3.2
9
36
39
Input-output relationships for all four 2-D system functions. . 50
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
xii
List o f Figures
1.1 Block diagram of th e front-end to the OMEGA laser fusion
system. The oscillator generates a 200 n s G aussian pulse,
which is sliced to a 20 ns square pulse by a Pockel’s cell. The
pulse-shaping system th e n creates the desired optical pulse
shape.....................................................................................................
3
2.1 Schem atic of surface-m ount photoconductive microwave switch
on a m icrostrip transm ission line...................................................
8
2.2 Plot of microwave ‘skin depth’, or penetration of 1 = 67% of the
incident microwave power into the semiconductor plasm a, as
a function of carrier density and fre q u e n c y ................................
17
2.3 Current-voltage curve of an unillum inated Si sw itch (solid)
and fitted curve (dashed) based on model. The shape of the
curve indicates a ‘leaky’ reverse-biased diode is dom inating
the response, m eaning th a t the current is prim arily due to
carriers diffusing across th e depletion region, not conduction
across a n ohmic-like contact............................................................
19
2.4 Actual m easured values (solid) and modeled curve fit (dashed)
of current-voltage curve of an illum inated Si switch. This
curve bends upward, indicating a shunted reverse-biased diode,
and now th e (leaky) forward-biased diode has th e larg est in­
fluence on th e I-V curve....................................................................
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
20
T in
2.5 The best fit to our m easured photoconductive switch S(uJ. t) re­
sulted in a lum ped-elem ent model, w ith th e Rs decaying ex­
2.6
ponentially. .........................................................................................
21
Schematic of OMEGA pulse-shaping subsystem ........................
29
2.7 Side view of OMSS showing different m etallization layers and
top view showing dimensions of finished OMSS................
3.1
32
(a) Two-port lin e ar tim e-invariant device, w ith a representa­
tive tem poral (b) in p u t and (c) output, (d) associated spectral
input and output, and (e) transfer function S( jc)................
3.2
40
(a) Two-port lin ear frequency-invariant device, w ith a repre­
sentative spectral (b) in p u t and (c) output, (d) associated tem ­
poral input and output, and (e) m odulation function k(t). . . .
41
3.3 (a) Linear tim e an d frequency varying device. Time varia­
tion is shown schem atically by the application of (b) two im ­
pulses and th e ir subsequent (c) differing im pulse responses.
Frequency variation is shown similarly, by (d) different input
sine waves an d (e) output spectral response, (f) Representa­
tive sketch of a S(uj.t) showing exponential tem poral decay
(modulation) an d spectral attenuation sim ilar to a low-pass
filter w ith an exponential amplitude d e c a y ...............................
43
3.4 Representative tran sfer function for a filter (lower left), mod­
ulator (upper right), separable (upper left) and inseparable
transfer functions..............................................................................
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
44
xiv
3.5 An example linear device w ith a time-varying capacitance rep­
resenting a tim e-varying pole location (bandwidth). The timevarying frequency response cannot be completely character­
ized by either a filter or modulator model.....................................
54
3.6 Magnitude of the tran sfer function S2 1 (a;) of a low-pass, single­
pole filter, which is equivalent to the circuit in Fig. 3.5 but
with a constant (unmodulated) capacitance.................................
56
3.7 Magnitude of the tran sfer function S-n (u;. t) of a low-pass, single­
pole filter w ith sinusoidally varying capacitance, plotted over
one cycle of m odulation and 150% of the bandw idth..................
56
3.8 A series of cross-sections through S2I (ur, t) along th e tim e axis,
showing the change in the m agnitude and phase of th e modu­
lation for different signal frequencies............................................
57
3.9 A series of cross-sections through S21(u>.t) along th e frequency
axis, showing the change in instantaneous bandw idth for dif­
ferent tim es........................................................................................
57
3.10 Surface density plot of |S2i(cu, t)\ with six cycles of modula­
tion along the time axis and dem onstrating low-pass filtering
along the frequency axis..................................................................
58
3.11 Plot of input and output signals showing the D U T s low-pass
filtering effect. D ashed line is input signal; solid line is the
output signal......................................................................................
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
59
XV
3.12 Magnitude-only plot of th e o u tput signal spectrum, as a spec­
tru m analyzer would display it. The two major frequencies
are th e input signals, and th e different side-lobes show th e
variations in modulation characteristics for different frequen­
cies, which a modulator model is unable to account for. . . . .
59
3.13 Time-frequency representation (ambiguity function) of a 2GHz sine wave th a t tran sitio n s abruptly to a 20-GHz sine
wave. Due to window trade-offs, low frequencies are sm eared
vertically and high frequencies are smeared out horizontally.
In addition, some w rap-around from top to bottom is caused
by th e FFT. Areas of g reater signal energy are proportionately
lighter.
...............................................................................................
62
3.14 Time-frequency representation of the output signal, after m ul­
tiplication of the input tim e-frequency distribution w ith th e
system function
t). The effect of the system function in
shown by the attenuation of th e high-frequency signals an d
the tem poral ripple in th e different spectral components. . . .
63
3.15 Time-domain comparison of output signals u sin g th e tech­
nique described in th is thesis (thin line), and th e windowing
m ethod (thick line). Windowing can be applied successfully to
th e high-frequency segm ent of the signal where th e m odula­
tion is slow compared to th e cycle; however, it averages over
th e system function for th e first segm ent......................................
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
64
xvi
4.1 Oscilloscope m easurem ents of th e shaped electrical signal be­
fore and afte r reflection from th e variable-impedance line (left
plot) and before and after transm ission through the sw itch
(right plot) are shown. The signal attenuation in th e spectral
domain is also given as an inset, to indicate bandw idth............
69
4.2 The top plot graphically dem onstrates the incident and tra n s ­
m itted signals. The middle plot shows the incident signal an d
the signal after transm ission, w ith an inset of th e spectral
distribution. The frequency response can be approxim ated by
dividing th e spectrum of the tran sm itte d signal by the spec­
trum of th e incident signal, show n in the bottom plot w ith a
linear fit, indicating the initial 3-dB bandw idth of th e OMSS
(before optim ization) was approxim ately 3 GHz..........................
70
4.3 Transient microwave bandw idth m easurem ent system. The
gated in teg rato r allows accurate m easurem ent of the S p a­
ram eters w hen th e OMSS conductance is constant....................
73
4.4 D ata used to derive S param eters of OMSS and microstrip.
The “th ru ” connected m easurem ent calibrates th e m easure­
m ent system. The “microstrip” an d “microstrip and switch”
m easurem ents allow the m icrostrip transm ission and OMSS
transm ission functions to be determ ined se p a ra te ly .................
78
4.5 S2 1 param eters of activated OMSS an d microstrip. These d a ta
were derived from the data in Fig. 4.4 and dem onstrate th a t
the m icrostrip attenuation dom inates the illum inated OMSS
attenuation..........................................................................................
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
80
xvii
4.6 Block diagram of a te st and m easurem ent system capable of
m easuring time- and frequency-varying DUTs. The m easure­
m ent is asynchronous, in th a t the power (envelope) is detected
rath e r th an the microwave signal electric field. Thus th e os­
cilloscope m ust only span the modulation bandw idth................
83
4.7 Photograph of experim ental setup for m easuring the tran sfer
function of OMSS’s. In the foreground on the optical table is
the te st fixture and th e microwave cabling. In the background
is the laser system th a t creates th e 200-ps fast risetim e opti­
cal pulse to trigger the OMSS’s.......................................................
84
4.8 Block diagram of a synchronous te st and m easurem ent sys­
tem capable of m easuring time- and frequency-varying DUTs.
This system is shown using either a sam pling scope, requiring
the trigger and microwave signal be in phase, or a single-shot
digitizer, which doesn’t require the phase-locked signal b u t
has degraded noise values due to the lack of averaging. . . . .
86
4.9 Signal transm ission during triggering of the OMSS. Notice
the nearly n/4 phase shift as the tran sm itted signal tra n si­
tions from capacitive to conductive coupling. ............................
87
4.10 Comparison of the m agnitude of the frequency response, be­
tween a commercial 20-GHz network analyzer and our m ea­
surem ent system................................................................................
91
4.11 Comparison of the phase of the frequency response, between a
commercial 20-GHz netw ork analyzer and our m easurem ent
system..................................................................................................
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
92
xviii
4.12 Frequency response o f th e microstrip test fixture alone (solid)
and w ith old (gray) an d new (dashed) OMSS’s.............................
95
4.13 The decrease in th e am plitude of the low-frequency transfer
function as shown h ere is consistent with the reform ation of
a depletion region..............................................................................
97
4.14 Temporal evolution of the phase of S shown by line-outs along
the tim e axis, dem onstrating th e reformation of th e metalsemiconductor depletion region capacitance.................................
98
4.15 Full S( uj. t) m agnitude plot of an OMSS before and afte r opti­
cal illum ination..................................................................................
99
4.16 Full S( uj. t) m agnitude plot of an under-illum inated OMSS,
showing am plitude variations consistent w ith a n increased
on-state resistance an d consequently increased reflection co­
efficient................................................................................................... 100
4.17 Lumped elem ent model of an OMSS, compatible w ith th e mea­
sured S . The resistance Rimik initially drops upon applica­
tion of the optical trigger, and subsequently retu rn s to the in­
trinsic, unillum inated value. The contact capacitance
C c (m ta c t
drops im m ediately afte r the trigger. The other two elem ents
rem ain approxim ately tim e-invariant over the m easurem ent
range........................................................................................................102
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
4.18 Improvement of OMSS frequency response from a 3-dB band­
width of 3 GHz to over 5 GHz. The g rap h on the left shows in ­
put and o u tp u t signals a t th e beginning of the pulse-shaping
campaign, in 1995. By dividing the spectrum of th e signals,
the approxim ate bandw idth can be indirectly m easured. The
graphs to th e rig h t show a more recent m easurem ent, show­
ing th e im proved bandw idth............................................................
104
4.19 M easured an d f it5 ( w J ) , an d a lumped-elem ent model corre­
sponding to th e fit. The variable resistance has a n exponen­
tial d ecay ............................................................................................. 106
A.1 Step-by-step procedures for OMSS fabrication as performed
at R IT ................................................................................................... 130
A.2 An SEM im age of th e polySi surface ta k e n after preferential
etching at grain boundaries reveals grain sizes of th e order of
30 n m ....................................................................................................
133
A.3 An SEM cross-section image showing th e m etal m ultilayer on
the 2.3-^m polySi la y e r....................................................................
134
A.4 Transm ission spectra of the polySi sam ple (solid line), cor­
rected for thin-film etalon effects (dashed line)...........................
135
A. 5 Experim ental setup for both optoelectronic and oscilloscope
m easurem ents of polySi interdigitated switches discharging
a m icrostrip transm ission line......................................................... 136
A.6 Impulse response m easurem ents of polySi as a function of
bias voltage. The linear relationship of th e peak response to
bias indicates a n ohmic-like contact............................................... 137
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
XX
A. 7 Impulse response m easurem ents of polySi as a function of op­
tical power. The linear relationship of th e peak response to
power also indicates an ohmic-like contact..................................... 137
A. 8 EO sampling of polySi......................................................................... 138
B .l Block diagram of the fro n t end of LLE’s fusion laser system,
including the Nd:YLF monomode Q-switched OMEGA ringoscillator and the Nd:YLF mode-locked oscillator a n d OMSS
activation system...................................................................................140
B.2 Top and side views of the diode-pumped Nd.'YLF ring-oscillator
laser system. This laser can produce 3 W in CW mode and 10
m J in pulsed mode, up to 300 H z.......................................................141
B.3 Detailed block diagram of pulse-shaping laser system from
after the oscillator, to OMSS’s. A 10-mJ, 150-ps, 5-Hz pulse is
split among m any OMSS’s using a large-diam eter core fiber
optical power distribution schem e.....................................................142
B.4
Block diagram of the Nd:YAG laser system ....................................143
B.5 Block diagram of the experim ental setup used for electro-optic
sampling and m aterial characterization. The laser shown is
b u t one p art of a complete system capable of sub-picosecond,
1-nJ pulses from 400 nm to 12 nm .................................................... 145
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
1
Chapter 1
Introduction
We describe the development and application of a characterization tech­
nique to the optim ization of the transm ission function of optoelectronic m i­
crowave silicon switches (OMSS’s). In th is thesis and in other publications,
OMSS’s will also be referred to as photoconductive switches (PCS) and
optically-activated silicon switches (OASS), depending on the performance
aspect being emphasized. This m easurem ent technique can be used to de­
term ine the properties of similar semiconducting microwave devices such
as photoconductive attenuators and phase shifters [1, 2, 3, 4, 5], as well as
other devices th a t effect the propagation of microwave electrical fields, ei­
th er through the influence of mobile charge carriers or through other mech­
anisms independent of the propagating electric field.
The OMSS characterization and optimization is accomplished by ap­
plying a novel technique which accounts for variations in the tem poral and
spectral response, unlike conventional Laplace-transform-based approaches
which require either tim e or frequency invariance within a windowed re­
gion. Our more general characterization allows us to achieve an accurate
and intuitive m easurem ent of the changing OMSS properties. W ith this
m easurem ent in h an d we are th en able to find a suitable device model.
The elements of th e (lumped-element) model correspond to properties of
the OMSS th a t can be optimized, so th a t a direct relationship betw een fab­
rication and performance can be realized.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
2
Chapter 1. Introduction
We show the complete characterization, of a n example device: OMSS’s
used on the OMEGA laser fusion system a t th e U niversity of Rochester’s
Laboratory for L aser Energetics (LLE) for laser pulse-shaping. O ur char­
acterization, despite tem poral and spectral variations comparable to th e
transm itted signal’s period an d bandwidth, allowed us to observe for th e
first time the m echanism s responsible for th e perform ance limitations. Based
on these observations we modified the OMSS design param eters. O ur mod­
ifications led to a deeper understanding of OMSS performance principles
and to substantial perform ance improvements.
1.1 Motivation
The investigation of OMSS characterization was driven by the observed per­
formance lim itations of OMSS’s in the pulse-shaping system of th e OMEGA
laser. A block diagram of th e OMEGA front-end, including laser pulse
shapes before and a fte r pulse shaping, is shown in Fig. 1.1. By m easuring
shaped pulses at various points in the pulse-shaping system, it was deter­
mined th a t the OMSS’s were th e foremost elem ent lim iting the optical pulse
envelope bandw idth. The desired properties of OMSS’s relevant to OMEGA
are their ability to: a) hold off large (>100 V) bias voltages while in th e
OFF (unillum inated and non-conducting) state, b) generate long (>3 ns)
electrical pulses w ith short (<30 ps) tran sien ts during turn-on (illumination), and c) tra n sm it or pass these pulses w ith m inim al distortion while in
the ON
( illu m in a t e d
an d conducting) state. The tem poral pulse length and
risetim e of the shaped pulses correspond to a 3-dB transm ission frequency
response th a t extends from approximately 0.1 to 10 GHz. The bandw idth of
the shaped pulse can be lim ited by the OMSS’s in two ways. First, the high-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
3
Chapter 1. Introduction
frequency en d of the pulse b andw idth is directly related to th e leading edge
of the electrical square pulse, which is generated by the in itial OMSS tu rn ­
on: delays in th e turn-on tran sitio n tran slate into reduced bandw idth. Sec­
ond, changes in the complex OMSS transm ission (am plitude decay or phase
dispersion) th a t occur w hen th e shaped pulse passes through th e OMSS to
reach th e modulator, detrim entally effect the pulse bandw idth.
M aster
oscillator
M
.
1
1.2
1
t
TF
0.8
\
I ------------ 1
-200 ns "
0.0
2.0
1.6
fiber
i
\ -20 ns
1.2
0.8
0.4
O '
----
0.0
— T -"
0.2
1
0.4
,
TF
Optical
system
Optical
fiber
1
i
To
regen
Poiseshaping
i
0.6
---0.8
1.0
0.4
0.0
Time ((is)
< 30-ps risetime
- and > 3-ns
duration
I
10
20
30
Time (ns)
Time (ns)
Figure 1.1: Block diagram of th e front-end to the OMEGA laser fusion sys­
tem. The oscillator generates a 200 ns Gaussian pulse, w hich is sliced to a
20 ns square pulse by a Pockel’s cell. The pulse-shaping system th e n creates
the desired optical pulse shape.
For microwave signal transm ission, we found th a t such mechanisms
as photoconductive decay and depletion-region capacitance effect the mi­
crowave transm ission and occur on time-scales comparable to th e microwave
spectrum of th e shaped electrical pulse. Since these effects are independent
of the microwave fields, linear models are appropriate; however the timeand frequency-varying aspects resu lt in inaccuracies w ith conventional lin­
ear analysis, which uses filter models. Therefore a more flexible characteri­
zation technique was developed, as described in th is thesis.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
Chapter 1. Introduction
4
1.2 Primary Contributions
This research describes our development of a novel, more general m ethod of
OMSS characterization, th a t incorporates (conventional) filter and m odula­
tor characterization as special cases. This more general tran sfer function
characterization is accomplished by considering th e OMSS as a lin ear de­
vice with both filtering and modulating properties. These two properties
are complementary in tim e and frequency, and a n experim ental technique
taking advantage of th is viewpoint is applied to the m easurem ent of the
transfer function. The characterization technique uses the fact th a t all real
devices can be modeled as separable m odulators and filters, to apply an
appropriately-modified form of Fourier transform . However it does not rely
on windowing nor th e experimental separation of time-varying m odulation
effects and frequency-varying filter effects. The freedom from assum ptions
regarding tim e and frequency invariance is balanced by th e g reater impor­
tance of careftd system design and extensive d ata processing, however this
freedom allows tran sien t device phenom ena to be observed w ith unprece­
dented clarity. The expanded observation capabilities led to b etter model­
ing, and ultim ately improved device performance.
The m easurem ent system based on th is development was dem onstrated
by characterizing a variety of devices, such as conventional microwave timeinvariant filters, frequency-invariant optoelectronic modulators, and opto­
electronic microwave switches. The filter and modulator m easurem ents
matched the resu lts of conventional m easurem ent techniques.
Based on th e m easurem ents, th e performance of OMSS’s on OMEGA
were optimized by a series of fabrication improvements. The im portant
performance criteria were initial electrical pulse risetime, and subsequent
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter I. Introduction
5
microwave tran sfer function bandwidth. The optim ization resulted in an
OMSS bandw idth comparable to the rest of the pulse sh ap in g system.
1.3 Thesis Overview
To explain the operation of OMSS’s, Chapter 2 begins by providing back­
ground concerning the physics of the interaction of lig h t and microwaves
through the interm ediary of charge carriers in a semiconducting m aterial.
The detailed m aterial characterization of silicon samples, used for OMEGA
photoconductive switches, is presented in Appendix A T hen the applica­
tion of OMSS’s to the generation an d gating of microwave signals is intro­
duced. In particular, we will discuss the operation of th e se switches in the
OMEGA laser pulse-shaping system. The fabrication step s for the switches
used in our work are explained as well. The details of th e OMEGA laser
and other laser systems relevant to the work in this th esis are overviewed
in Appendix B.
Due to th eir non-standard device properties, OMSS’s are exceptionally
well-suited for use in LLE pulse-shaping. However, th e se sam e properties
also make it difficult to characterize the performance of th e switches using
conventional microwave techniques. Chapter 3 develops th e linear system
m easurem ent theory necessary to comprehensively m odel th e switch per­
formance. Conventional microwave device modeling and characterization is
presented in such a way as to n atu rally lead to the derivation of the exten­
sion of filter and m odulator analysis to microwave switches.
From the developed theory, C hapter 4 describes a m easurem ent tech­
nique capable of adequately characterizing the perform ance of switches
used on OMEGA and th e corresponding experimental resu lts (including the
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C hapter 1. Introduction
6
resulting performance improvements).
Finally, C hapter 5 sum m arizes th e thesis by drawing conclusions from
th e m easurem ents and discussing future research directions.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
7
Chapter 2
Optoelectronic Microwave Silicon Switch Physics
This chapter opens by covering the basic solid sta te physics concepts ger­
m ane to a n u n d erstanding of OMSS operation. Following this, we detail
the operation of OMSS’s, emphasizing m icrostrip-based geometry, as im­
plem ented on OMEGA. For our research, th e m ost influential aspect of the
interaction of microwave fields with optically-created charge carrier plas­
m as tu rn s out to be th e temporal and sp atial dynamics caused by sur­
face/interface (semiconductor-vacuum and metal-semiconductor) effects in
long-carrier-lifetime silicon. Our consideration of the temporal dynamics
will em phasize th e picosecond and nanosecond time-scales, w hereas spatial
dynamics are considered to the extent th a t th ey influence the microwave
lum ped-elem ent elem ents used to model th e switch. We discuss th e bene­
fits and limitations of applying lumped-element analysis in Sec. 2.6.
The general sw itch geometry we are considering is shown in Fig.
2
.1 .
Initially (before optical illumination of the switch) a bias electric field ex­
ists between one electrode and the other electrode and the ground plane.
The physical dimensions controlling the in itial electric field distribution in­
clude th e gap w idth (or length) I, switch w idth w, electrode-to-ground plane
distance h, and complex relative perm ittivity of the transm ission-line sub­
strate eJL, and OMSS
[6 ]. The photoconductive switch perm ittivity will
in general be a function of time and space, due to illumination, plasm a
carrier dynamics, an d energy-band effects such as doping, defect an d de­
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 2. Optoelectronic M icrowave Silicon Switch Physics
8
pletion region/surface effects [7, 8 ]. O ther im portant aspects of switch ge­
om etry th a t affect the creation and distribution of th e charge carriers are
anti-reflective (AR) and high-reflective (HR) coatings. In addition carrier
distribution is affected by optical power PQ and w avelength A [9].
Light pulse
A., Pn
Figure 2.1: Schematic of surface-mount photoconductive microwave switch
on a microstrip transm ission line.
For convenience we’ve collected in Table 2 . 1 some relevant properties of
nearly-intrinsic silicon a t room tem perature, under both uniUuminated and
illum inated conditions.
2.1 Optical Surface Transmission
Before the photons can be absorbed in the semiconductor bulk, they m ust
pass through the interface. The optical intensity (photon) transm ission
function a t the interface betw een free-space and a dielectric is
4e0.5
r = < T T ^ ’
(2-«
where er is the real p art of the relative perm ittivity of the substrate (which
can be effected by carrier density, as discussed below in Sec. 2.3). W ithout
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 2. O ptoelectronic Microwave Silicon S w itch Physics
9
Table 2.1: Intrinsic single-crystal Silicon m aterial param eters a t 300 K
Param eter
Symbol
Value
U nit
Band Edge Wavelength
^9
1.09
ixm
Excess C arrier Density
Tla
1.4 x 10xo cm~z
Ambivalent Mobility
Pa
1800
cm2/ \ ' - .s
Ambivalent Mobility
Pa
300
cm2f \ '
Recombination Lifetime
Tr
1 0 0
lis
Auger Recombination Time
‘
9
flS
do
1
mm
dj
1
mm
Thermal Conductivity
K
1.5
IV/cm ■K
Specific H eat
Cp
0.7
J/g - A'
Resistivity
Pi
2.3 x 105
Q • cm
Breakdown Field
Eb
300
kV/cm
Density
5
2.33
g/cm z
-s
at na = 1018 cm-3
Auger
at na = 101 8 cm ~ 3
Optical Absorption Depth
at A = 1.06 fim
Free-carrier Absorption D epth
at nQ = 1018 cm~z
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Chapter 2. O ptoelectronic Microwave Silicon Sw itch P hysics
10
thin-film coatings, th e reflection loss of optical energy a t th e transition from
a ir to Si is initially [(er —1 ) / (er + l ) ] 2 = (2.4/4.4 ) 2 = 0.30. By placing a n AR
coating on th e incident side and an HR coating on th e opposite (metal con­
tact) side (see Fig. 2.1), the percentage of absorbed laser pulse energy can
be increased to nearly
(1
—e~2ctd) of th e incident energy, where a is th e ab­
sorption depth a n d d is the thickness of the OMSS. The AR layer improves
th e transm ission for a given value of perm ittivity er, however since the per­
m ittivity changes w ith carrier density the transm ission across the interface
(and hence absorption in the bulk) decreases. This effect is one of th e lim ­
iting mechan ism s to increasing carrier density. O thers are mentioned in
Sec. 2.4.
2.2 Photon and Carrier Plasma Interaction
The operation of a n OMSS relies on the m odulation of the complex dielectric
constant of a semiconducting substrate by th e optical generation of mobile
electron-hole pairs. At high enough carrier densities th e interaction be­
tween the mobile carriers begins to take on th e characteristics of a plasm a.
This carrier p lasm a w ithin the bulk of intrinsic or nearly-intrinsic Si (where
density of tra p s n t is much less th an th e density of carriers nc) consists of
an electrically-neutral (on the ensemble average) plasm a of mobile electrons
and holes.
Once th e photons reach the semiconductor, ignoring surface effects and
assum ing a q u an tu m efficiency 77 th a t is independent of carrier density (i.e.,
single-photon absorption), absorption of the photons by conversion to free
carriers (decrease in optical irradiance or in stan tan eo u s optical power /)
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 2. Optoelectronic M icrowave Silicon Sw itch Physics
11
will be proportional to th e num ber of photons:
(2 . 2 )
where dopt is th e optical absorption depth. Solving for I,
I{z) = I0e~z/dopt.
(2.3)
w here I q is th e optical power tran sm itted into the b u lk a t the surface.
The absorption depth is a function of frequency, so the absorption depth
profile can be tailored for best charge carrier/microwave electric field inter­
action. For OMSS geometries where th e illum ination and the penetrating
microwave field are on opposing surfaces, this is accomplished by choosing
a wavelength such th a t the absorption depth is comparable to the switch
thickness. This choice strikes a balance between maximum (shallow) ab­
sorption which would only occur a t th e surface and separates the carriers
from the field lines (at least initially, u n til diffusion has time to occur), and
deep absorption which would spread th e generated carriers evenly through
th e
bu lk ,
b u t would lower th e total
large transparency.
I llu m in a t io n
am ount
of created carriers, due to th e
from the microwave field side would al­
low maxim um (shallow) absorption, b u t causes “current pinch” at the edges
of the contacts because the contacts are opaque to the illum ination and
shadow the semiconductor bulk.
D uring and after illum ination, w hen the population of free carriers in
th e bulk Si substrate is large enough th a t the interaction between carriers
becomes significant, equations for plasm a dynamics can be applied. An im ­
portant param eter of th is plasm a is carrier density, which varies through­
out the bulk during illum ination, and after illumination further evolves ac­
cording to Maxwell’s equations and th e charge continuity/transport differ-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 2. Optoelectronic Microwave Silicon Switch Physics
12
ential equation (defined for each point in th e bulk)
(2.4)
where
J = finEt + D Vn.
(2.5)
n is the excess carrier plasm a density (cm -3 ), G is generation a n d R is re­
combination (cm -3 .s-L, huj is the photon energy (eV), J is th e conductive
current component incorporating drift and diffusion as first-order approx­
imations to Boltzm ann’s transport equations, r r is the recom bination life­
tim e^), p. is plasm a mobility, E is the electric field, and D is th e diffusion
coefficient. These equations show th a t a non-uniform creation of a plasm a
in the bulk of th e device creates internal electric fields, which combine w ith
diffusion to cause the carriers to disperse throughout the bulk. These fields
influence the carrier transport (current flow) and therefore th e microwave
properties of th e switch.
When the optical pulse is much shorter th a n the excess ca rrie r recom­
bination lifetime, carrier diffusion and surface recombination are less im ­
portant during th e initial excitation, which simplifies determ ination of the
initial spatial distribution of the plasma. P lasm a density n is th e n greatest
at the surface, follows the spatial profile of th e illum ination across the face
of the OMSS, an d as a function of time is
(2.6)
where the variables such as recombination tim e in the in teg ratio n can change
over the duration of the pulse. For illum ination of long-lifetime OMSS’s in
the geometry of Fig. 2.1, th is equation says th a t the rate of change in charge
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
13
C hapter 2. Optoelectronic M icrowave Silicon Switch P h ysics
carrier plasm a density is th e integration of th e absorbed optical pulse en ­
ergy. Thus, the im portance of minimizing a n y incident optical energy p re ­
ceding th e
m a in
i l l u m i n a t io n
optical illumination: we w a n t th e in itial rise of the optical
to be steep a t least until the conductivity is negligible (relative
to th e microstrip characteristic impedance). Because of the long carrier lifetime, even pre-pulse energy much earlier th a n th e m ain illum ination (e.g.,
from prelim inary round-trips through the la se r am plifier cavity) will create
free carriers th a t will p ersist until the m ain pulse arrives, lengthening th e
tran sitio n tim e from th e OMSS being com pletely O FF (no excess carriers)
to completely ON.
2.3 Complex P erm ittivity Changes
A change in su b stra te perm ittivity has a d etrim en tal effect on the perfor­
mance of the AR coating, which is a function of th e index of refraction differ­
ence a t the air/sw itch interface. The perm ittivity of th e plasm a generated
in the substrate is found by considering th e polarization of the m aterial
P =
60
/y E which is m ost conveniently rep resen ted in Maxwell’s equations
by using
€qE + P
D
(2.7)
V x H = juiY) + <rE = juj'E e —j ie" H— )
(2.8)
(f; — jt") E
—
6
q ( 1 -f- \
e)
E
—
—
and
w here the relative perm ittivity in the su b stra te is th a t of a plasm a u n d er
optical excitation conditions, and
(2.9)
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
14
Chapter 2. Optoelectronic M icrowave Silicon Switch Physics
where th e plasm a frequency ujp =
2
m
f*
^ is the microwave frequency, m*
is the carrier effective m ass, v is the carrier collision frequency, q is charge
and e0 is the perm ittivity of free space [10, 11, 12, 13].
2.4 Saturation Mechanisms
As the irradiance of th e laser illum ination I qcontinues, th e switch bulk con­
ductivity increase p~l will continue to follow the optical energy integration
due to carrier density by th e equation
p _l = qpn.
(2.10)
A saturation regime will be reached where q u an tu m efficiency
77
decreases
due to increased surface reflection, decreased free-carn er absorption depth,
and decreased e a rn e r recom bination time (Auger effect). These mecha­
nism s conspire to create a n asymptotic approach to a n effective maximum
achievable carrier density; for our experiments th e sa tu ra tio n carrier den­
sity is approximately 101 8 cm -3 [14, 15,16].
2.5 Carrier Plasma and Microwave Interaction
The equations relating th e interaction of an ensem ble of charge carriers
(plasma) with a microwave signal involve such variables as skin depth,
parasitic reactance effects, an d complex perm ittivity. In Si the carrier ex­
citation is a quantum sta te change of approxim ately
1
eV energy differ­
ence therefore the tran sitio n occurs during a single optical cycle, and so
the sw itch response to illum ination is considered in stan tan eo u s on the m i­
crowave (sub-nanosecond) tim e scale. By ensuring uniform switch illum ina­
tion, th e excitation or switch turn-on occurs as a single, complete transition
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C hapter 2. Optoelectronic M icrowave Silicon Sw itch Physics
fr o m
15
insulating to conducting by th e uniform collapse of th e electric field
across the OMSS gap [17]. This resu lts in the generation of a single fastrise-tim e propagating square pulse w ith no additional, unw anted picosec­
ond or nanosecond structure [18, 19]. Therefore from th e perspective of mi­
crowave signal influence, the m ost im portant issue involving th e excitation
of th e switch is the density of carriers and their distribution throughout the
bulk of the semiconductor. A fter excitation, the tem poral an d spatial evolu­
tion of the created carrier p lasm a begins, and may have a significant effect
on the subsequent microwave signal propagation through th e device.
Both the real and im aginary p arts of the relative perm ittivity are al­
tered by the plasm a state: w hen th e microwave frequency is small com­
pared to the collision frequency u:p <C v and the plasm a frequency is much
sm aller th a n the collision frequency u p <C u, the change in th e real part
of the plasm a perm ittivity can be neglected and th e sw itch is then con­
sidered to be operating in the ‘photoconductive’ regime. As th e microwave
frequency approaches the plasm a frequency the real p a rt of th e permittiv­
ity of the plasm a begins to increase and this influences th e propagation of
the microwave signal. However this dielectric mode of operation occurs, for
Si, above 30 GHz and so is not a significant factor in th e operation of the
switches discussed in this work [2 0 ].
In th e photoconductive regime
e' = e f ,
a = nqua-
(2-1:L)
In the OMEGA arrangem ent, th e electric field penetrates th e switch from
beneath, on the opposite side of th e switch from th e optical illumination
w ith the dependence
Et = Exe~yz,
H t = j^ E y e ~ yz,
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
(2.12)
Chapter 2. O ptoelectronic Microwave Silicon Sw itch P hysics
16
where the atten u a tio n factor
7 = {junvy-
“s
(2.13)
has a real an d im aginary parts and is inversely proportional to th e charac­
teristic ‘skin’ depth, defined as
^ =
(2-14)
and shown in Fig. 2.2. The im aginary p a rt of th e microwave atten u atio n
factor is positive and therefore the effect is inductive, causing th e phase of
the current to lag the electric field as it penetrates the m etal. A lthough
the absorbed optical power and hence carrier density is initially g reatest on
the side opposite th e electric field, diffusion an d drift distribute th e carriers
roughly evenly throughout the bulk of the semiconductor on th e order of th e
dielectric relaxation tim e Tre[ = e/a, which is on th e picosecond tim e-scale
[2 1 ]. Both of th e se effects cause dispersion of the microwave signal. If th e
dielectric co n stan t changes with carrier density and hence w ith time, th e
displacement cu rren t across the gap begins to change w ith tim e (or from
the lum ped-elem ent viewpoint, the series gap capacitance becomes tim evarying). If th e effect is large enough, it strongly impacts the m odulation of
the microwave signal and leads to difficulties w ith conventional microwave
modeling, as w ill be explained later.
2.6 Lumped-element Approximation
To most efficiently model and thereby improve the transfer function of th e
OMSS’s, we u se a lumped-element approxim ation [22]. The complete m i­
crowave transm ission response can be modeled by solving Maxwell’s equa­
tions, including complex perm ittivity an d excess charge carrier continuity
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C h apter 2. Optoelectronic M icrowave SUicon Sw itch P h ysics
E
3.
£
a.
a>
■o
c
17
1000
1 GHz
100
10
10 GHz
CO
1016
1017
1018
1 0 19
1020
C arrier d e n s ity (c m -3 )
Figure 2.2: Plot of microwave ‘skin depth’, or p en etratio n of ± = 67% of th e
incident microwave pow er into the sem iconductor plasm a, as a function of
carrier density and frequency.
w ith drift and diffusion, as given in Secs. 2.2 a n d 2.3, w ith the additional
relationship from Maxwell’s equations
V x E = jcjfiH.
(2.15)
However, by considering th e physical conditions we employ on OMEGA,
w ith a) time-scales g reater th a n a picosecond, b ) dimensions much sm aller
th a n th e wavelength of the highest frequency o f in terest (30 GHz) so th a t
th e phase of the microwave signal is approxim ately constant across th e
length of the device a n d equivalent currents a n d voltages can be uniquely
defined [23], c) a quasi-TEM transm ission line [24], it is observed th a t the
effort required to find complete solutions is o u t of proportion to th e ben­
efit [25]. A more fru itful approach comes from th e analysis standpoint:
by appropriate m easurem ents of the tran sfer function, one can construct
a lumped-element model of resistors, capacitors, diodes and inductors th a t
relates aspects of th e tra n sfe r function to properties of the switch th a t can
be modified.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
C hapter 2. Optoelectronic M icrowave Silicon Sw itch Physics
18
2.7 Metal-Semiconductor Interface Effects
D uring illumination, th e carriers are created in the bulk according to the
absorption depth and spatial beam distribution. The carriers will th en im­
m ediately begin to drift in the com bination of the applied field and internal
fields (e.g., due to the rectifying metal-semiconductor contacts). The carri­
ers will also diffuse because of th e concentration gradients, and on a much
longer time-scale (nanoseconds to microseconds), recombine.
2 . 7.1 Lumped-element Diode Contact Model
For the linear lumped elem ent model to fit the observed m easurem ents of
th e Si switch, there should be negligible nonlinearities in th e switch oper­
ation. The prim ary source of possible nonlinear mechanisms is non-ohmic
contacts. To identify this we m easured current-voltage (I-V) curves of the
switches a t various cw optical illum ination intensities [26, 27]. In the unillum inated case shown in Fig. 2.3, th e I-V curve is dom inated by a leaky (resistively shunted) reverse-biased contact. In this graph, one of the reversebiased diodes had a sm all zener break-down voltage th a t was reduced by
therm al loading.
U nder cw illum ination (1 W average power) the OMSS has an I-V curve,
shown in Fig. 2.4, th a t indicates th e forward-biased diodes dominate the
curve. This is due to the large reduction in Rd and R s under illumination,
as shown in the fit to this curve, Fig. 2.4. The smaller Rd shunts the reversebiased diode and its effect on th e I-V curve.
The best fit model to these I-V curves incorporates two back-to-back
diodes and is shown in Fig. 2.5 w ith the element values calculated from the
I-V curves. The element R c is th e contact resistance in series w ith the de-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
19
Chapter 2. Optoelectronic Microwave Silicon Switch Physics
Actual
>■*—s
Fit
<
o
fc
3
U
S
-5
-1 0
-3 0
-2 0
-10
0
10
20
30
Figure 2.3: Current-voltage curve of an unilluminated. Si switch (solid) and
fitted curve (dashed) based on model. The shape of the curve indicates a
‘leaky 5 reverse-biased diode is dominating th e response, meaning th a t th e
current is prim arily due to carriers diffusing across the depletion region,
not conduction across an ohmic-like contact.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C h apter 2. Optoelectronic M icrow ave Silicon Switch P h ysics
20
Actual
<
c
8
3
u
-5
-1 0
-
Fit
----------- ^
0.3
-
--------------------> -
0.2
-
0.1
0
0.1
0.2
0.3
Figure 2.4: Actual m easured values (solid) and modeled curve fit (dashed) of
current-voltage curve of an illum inated Si switch. This curve bends upward,
indicating a shunted reverse-biased diode, a n d now the (leaky) forwardbiased diode has th e largest influence on the I-V curve.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C h apter 2. Optoelectronic M icrowave Silicon Switch Physics
21
pletion capacitance Cd, R s is the resistance of th e semiconductor betw een
th e contacts, and Rd is th e contact resistance sh u n tin g the depletion re­
gions. The values of th ese equivalent elements are heavily dependent on
th e metal-Si contact quality, and can be greatly affected by impurities, p as­
sivation and dislocations or other defects [28]. As such it was found th a t th e
two metal-semiconductor contacts can be significantly different; in fact, we
found variations of alm ost 50% of th e resistance an d a n order of m agnitude
in capacitance. Slow drifts of the I-V curve on the o rder of milliseconds were
also observed, mostly prevalent for earlier switch fabrication runs, and re ­
lated to the quality of th e evaporated metal-semiconductor interface.
rVH>h
R
di
r f H
■W
Rs
MRci
t i
R D2
- W
f t -
-
1
RC2
R d (Q)
Rc(Q )
RS (Q)
Unill.
-104
-105
-105
Ilium.
- 1 0
- 1 0
- 1 0 2
Figure 2.5: The best fit to our m easured photoconductive switch S( uj. t) re ­
sulted in a lumped-elem ent model, w ith the Rs decaying exponentially.
These contact elem ent values dem onstrate th a t to improve the linear­
ity of the photoconductive switches, minimize th e frequency-dependent ele­
m ents (which contribute bandw idth-lim iting dispersion to the transfer func­
tion), and reduce the effects of th e time-varying m odulation, the capacitive
Schottky-contact m ust be elim inated, or a t least m ade as negligible as pos-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
C hapter 2. Optoelectronic M icrowave Silicon S w itch Physics
22
sible through careful fabrication [29, 30, 31, 32].
2.7.2
Contact Capacitance Dynamics
Before illumination, th e energy band diagram of th e Si a t th e metal-Si interface resembles the p side of a p —n+ junction, and therefore (ignoring
possible surface states) a potential b arrier exists for the holes and the electrons between the Fermi surface of th e m etal and the respective valence and
conduction bands of th e bulk Si. We m anipulate the energy band a t the in­
terface (e.g., by introducing shallow dopants, creating th in barriers allowing
quantum-mechanical tunneling) to promote the creation of an ohmic-like
current-voltage relationship betw een th e electrodes. Ultimately, the metal
and Si energy level differences will resu lt in some type of non-ohmic effect,
and the best th a t we can achieve is th e minimization of th is effect.
Because of the interface junction, in the unillum inated state a region
n ear the interface is depleted of mobile carriers and the average distance
between the metal and the mobile carriers can be approxim ated by the stan­
dard junction diode relationship
(2.16)
qn
where V is the applied voltage and
is th e “built-in” potential
(2.17)
<$£ is the difference in work functions between the m etal and th e Si substrate and Eg is the Si band gap. U sing values for these variables appropri­
ate to the switches used on OMEGA er = 11.8, <&b = 0.7 eV, p = 40 kQ ■cm,
Na =
1 0 13
cm-3, the calculated depletion distance comes out to a quite deep
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 2. Optoelectronic Microwave Silicon S w itch Physics
23
4 microns. Further, from the initial capacitance per unit area of the contacts
C±
A
2
(V* - V)
qnereQ
(2.18)
we get 2400pF /cm 2, or for the contact pad area of 5 mm by 2.4 m m used
on OMEGA: 28 pF. However carrier recom bination and tran sp o rt dynamics
will change during switch operation due to th e effects mentioned above, as
well as carrier-density dependent carrier-to-carrier scattering, which low­
ers the mobility by an order of m agnitude [33, 34]. The depletion region
a t the metal-semiconductor causes a signal-dependent capacitance to form,
sim ilar to a varactor diode. In th e lum ped-elem ent model, th is contact ca­
pacitance is in series w ith the OMSS b u lk resistance and in parallel w ith
the contact resistance.
Importantly, the contact capacitance or depletion region is filled dur­
ing optical illum ination, assuming th e optical pulse is short enough to ig­
nore carrier tran sp o rt [35]. After the carriers are created and illum ination
ceases, they d rift and diffuse out of th e depletion region, w ithout being re­
placed by the generation of new free carriers [36]. Their drift velocity is
close to 106 cm/s, which implies a depletion region of 4 ^m thickness will
re-form in approximately 0.4 ns. This is on the time-scale of the electri­
cal pulse, therefore establishm ent of th e depletion region and its resul­
ta n t lumped-element capacitance will occur during the transm ission of the
shaped electrical pulse.
2.8 Switch Geometry Designs
This section discusses various issues affecting the choice of th e physical de­
sign of the switch, especially in regard to those choices th a t have an im pact
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Chapter 2. Optoelectronic M icrow ave Silicon Switch P h ysics
24
on the propagation of th e microwave signal an d th e absorption of the optical
trigger.
2.8.1 Photoconductive Substrate
A configuration which can potentially lead to m onolithic integration of the
entire pulse-shaping system , including optical an d electrical components,
is the use of a photoconductive m aterial as th e dielectric between th e m i­
crostrip electrode and th e ground plane. V ariations on this them e also exist
[37]. By selective
i l l u m i n a t io n
of specific a re a s of th e substrate, on can
achieve switching, p h ase shifting, attenuation, a n d other effects [38, 39, 40,
41, 42, 43, 44, 45]. For OMEGA pulse shaping, th e requirem ent of 4-ns
shaped pulses dictates th a t a length of Si tran sm issio n line should be a t
least 40 cm. This introduces difficulties such as folded lines or th e ab u t­
m ent of m ultiple wafers. Most importantly, for signal propagation over long
distances, dispersion a n d attenuation due to th e dielectric properties of Si
a t microwave frequencies becomes a significant issue [46, 47].
2.8.2 Discrete Surface-m ount Switch
The geometry currently used on OMEGA is show n in Fig. 2.1. This design
creates greater p arasitic reactances th a n other, more integrated options
such as the one above (which degrades the frequency response). However it
has the advantages of ease of construction a n d placem ent, due to com pati­
bility w ith standard microwave surface-mount device technology. Therefore
the OMEGA pulse-shaping system has chosen to use th e surface-mount ap­
proach. A prim ary goal of th e research in th is th esis is to reduce th e detri­
m ental effects of using th is OMSS architecture.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 2. Optoelectronic M icrowave Silicon Sw itch Physics
25
A related approach is to place a small, thin sliver of photoconductive
m aterial in th e gap between th e m icrostrip line. However, to achieve suffi­
ciently low resistance values, th e OMSS m ust be significantly thicker th an
the m etal due to the much lower carrier density (1018cra-3 vs. 1022cm-3 for
copper a t room tem perature). To minimize microwave cu rren t discontinu­
ities and th e resulting parasitic reactances, the dielectric in th e gap can be
partially rem oved or “dug out”, increasing the capacitance to the ground
plane an d allowing the thicker sw itch to be placed in th e gap. However this
method requires ohmic end-pad contacts to be evaporated on th e edge of
the Si sw itch wafers. These kinds of contacts m ust be created after dicing,
and consequently is much more difficult th an evaporating contacts on the
surface of th e wafer, before dicing. The OMSS performance is unpredictable
and unrepeatable for this and o th e r reasons, and therefore th is approach
was not pursued.
2.9 General Switching Operational Issues
This chapter will discuss the operational details of controlling microwave
signals u sin g photoconductivity, a s it relates to the pulse-shaping system in
OMEGA, including OMSS fabrication. Performance lim itations of OMSS’s
will be discussed, and the need for a characterization technique more com­
plete th a n th a t used for microwave filters and modulators will be explained.
Optim izing an OMSS involves the compromise of m any constraints.
Complete device characterization requires familiarity w ith th e relevant as­
pects of th e interaction of microwave fields with optical photons via the
mediation of th e photoconductive process. The main constraints affecting
performance are summarized below.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Chapter 2. Optoelectronic Microwave Silicon Sw itch Physics ______________
2.9.1
26
Turn-on Dynamics
Although, the bulk of the characterization for this thesis was performed on
the transm ission bandwidth of OMSS’s, the turn-on rise-time is equally
im portant to th e ultim ate OMEGA pulse-shaping bandwidth. Unlike the
transm ission
bandw idth with its large optimization param eter space filled
w ith poorly-known or difficult-to-measure param eters, th e methods for im­
proving the risetim e are well-understood.
The rate of change of the bulk conductivity of the switch is directly
related to the carrier density by Eq. 2.11. The instantaneous voltage V^t
across the transm ission line and the lumped-element series resistance of
the switch Rs is, to a first approximation, related to the bulk conductivity
by
=
=
(2.19)
where ZQis the characteristic impedance of the transm ission line an d Vb is
the initial voltage across the OMSS [48]. This means th a t although th e rise
time of the change in series resistance is linear with respect to th e change
in conductivity (and hence carrier density), the rate of change in th e out­
put voltage is not. Depending on the range of values th a t R s can assum e
relative to Z0, th e greatest rate of change will occur near Z0. W ith th is real­
ization, it is possible to trade-off a swift change in output voltage vs. a low
ON-state resistance. That is, by m aking the difference between OFF- and
ON-state resistance smaller, the energy requirem ents can be minimized,
which for a given optical irradiance will minimize the rise time. For exam­
ple the final ON -state could be Zo/10 instead of 2 or 3 orders of m agnitude
less. A final, non-zero resistance will cause incomplete discharge of the
biased microstrip transm ission line, which will affect the electrical signal
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 2. Optoelectronic M icrow ave Silicon Switch P h ysics
27
level to the electro-optic modulator. However, voltage bias offsets can be
applied to compensate for th is effect.
2.9.2
Transmission and Isolation
The transm ission and isolation performance is affected by the capacitance
and resistance betw een th e contacts in the ON an d OFF states. These two
lum ped elements are effected by the residual dopant density betw een th e
two contacts, the degree to w hich the contacts m ay be non-ohmic (Schottkycontact diodes), which leads to nonlinear current-voltage relationships and
perhaps, more im portantly, depletion regions betw een the m etal contacts
and the semiconductor, th a t evolve after illum ination [49, 50].
2.9.3
Time-domain Performance
The OMSS transm ission function can be m easured in the time-domain, by
m easuring electrical signals w ith sufficient frequency content to allow ex­
ploration of the full desired frequency response.
An experim ental m ethod of determ ining w h at effect the OMSS contacts
have on transm ission perform ance is to take advantage of its sym m etry (i.e.
reciprocity of th e 5 param eters) a t the in p u t an d output ports. If other
variables such as fixture asym m etries can be controlled then differences in
transm ission response w ould be due entirely to asymmetries, which would
occur a t the contacts. Initial efforts in this direction were not successful due
to lack of repeatability, m ost likely due to variations in the soldered connec­
tion between th e pads an d th e microstrip. Subsequently a surface-m ount
microstrip pressure-contact (non-solder) te st fixture was used. The te s t fix­
tu re used precise an d repeatable cam-leveraged pressure from th e fiber­
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 2. Optoelectronic M icrowave Silicon S w itch Physics
28
optic ferrule to hold th e OMSS to th e transm ission line. The repeatability
of th is arrangem ent was high and allowed m easurem ents of th e transfer
function w ith and w ithout th e OMSS to be performed accurately.
2.9.4 Frequency-domain Performance
The transm ission performance of th e OMSS can also be analyzed via the
frequency domain: a single frequency carrier signal can be transm itted
through, and a tim ed receiver can detect the am plitude and phase of the
transm itted signal with high dynamic range, accuracy an d resolution, as
well as low signal-to-noise ration (SNR). However, th e trade-off is added
complexity, and more im portantly th e m easurem ent is very slow (propor­
tional to the capture tim e-constant of th e tuned receiver). This is acceptable
if th e device’s properties are invariant, or a t least changing only slowly dur­
ing the capture tim e of th e receiver. I f th e device is changing more rapidly,
however, th en this approach m ust be modified, since th e assum ptions be­
hind the use of a tuned receiver are now invalid.
2.10
OMEGA Pulse-shaping Design
The details of the U niversity of Rochester’s Laboratory for L aser Energetics
OMEGA fusion research laser system which are relevant to OMSS perfor­
m ance are in App. B. In th is section we describe the operation of th e OMSS’s
in the pulse-shaping subsystem of OMEGA.
OMSS’s are a n atu ra l choice for OMEGA pulse-shaping, since their
strengths and weaknesses align well w ith the tasks th ey are asked to per­
form on OMEGA. They have excellent DC voltage hold-off properties due to
th eir large off-state resistance. They do not have high isolation for higher
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without p erm ission .
Chapter 2. O ptoelectronic Microwave Sihcon Sw itch P hysics
29
GHz frequencies due to capacitive coupling, which makes complete tra n s­
mission easier (except for some am ount of phase shift). They are compact
and integrate well w ith microstrip which is th e technology used to gener­
ate the shaped pulse. They tu rn ON more swiftly than electrical switches,
and there is no jitte r because th e trigger is optical and the electrical signal
does not influence th e tum -on rate. The optical feed is a slim, light-weight
fiber optic instead of a large, bulky high-bandw idth microwave coaxial line.
The optical “overhead”, or equipment requirem ents, is compatible w ith the
optical expertise available at LLE. Finally, because of its simple, solid-state
design it m ay be possible to integrate th e OMSS’s monolithically w ith the
electro-optic modulator.
A schematic of the pulse-shaping subsystem is shown in Fig. 2.6. The
OMSS’s currently used in LLE’s pulse-shaping system sue sm all (0.5 x 2.4
x
2 .0
mm) bulk semiconductors w ith evaporated m etal pads which are sol­
dered across a series gap in a microstrip transm ission line.
, Optical trigger pulses^
0.5 mm
50-Q
term.
Shaped line
(variable impedance)
Optical
square pulse
+75-V dc
Si PC
switch
0.5 m m /
Bonding
50-sl charged
transmission line
o k
Electro-optic
modulator
Fiber optic line
Electrical shaped impulse
Electrical
square pulse
Optical shaped pulse
Figure 2.6: Schematic of OMEGA pulse-shaping subsystem.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
30
Chapter 2. Optoelectronic M icrowave Silicon Switch P h ysics
The pulse-shaping system operation begins by biasing th e m icrostrip
charge line, isolated by the two OMSS’s from th e rest of the system. The
bias voltage U is determ ined by the half-wave voltage VK of the modulator,
the peak reflection coefficient rpeakof the v ariable impedance line, th e m ini­
mum on-state OMSS resistance Rs.mm> and characteristic impedance of th e
transmission line Z Qby
16
=
1 jt ( 2 2 o +
R s.m in ) / ( Z
q
F peak) ■
(2 .2
0)
Upon illum ination, the OMSS closest to th e variable impedance line
acts as an electrical pulse generator, establishing a propagating voltage
transient by the creation of traveling charge a n d discharge perturbations
in either direction along the transm ission line, centered on the OMSS gap.
By the principle of charge preservation the resu ltin g square wave is twice
the length of the charge line, and its am plitude is h alf of the charge voltage.
Some portion of th is square wave is reflected from the variable impedance
line and travels back towards the two OMSS’s in the form of a shaped tr a n ­
sient. The OMSS’s now act as portions of a transm ission line, and after il­
luminating th e second OMSS, they m ust now allow the signal to propagate
with as much of th e frequency content of th e tra n sie n t as possible. To avoid
having to illum inate th e OMSS’s multiple tim es and to prevent “droop” of
the electrical signal during propagation th ro u g h the OMSS’s, carrier life­
times are much g reater th a n the pulse duration.
The shaped electrical transient is th en launched from the m icrostrip
architecture to a short length of coaxial line (tow ards the right in Fig. 2.6),
and the integrated-optic Mach-Zehnder interferom etric am plitude m odula­
tor, where it m odulates the incoming square optical signal.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
31
C h apter 2. Optoelectronic M icrowave Silicon Switch Physics
2.10.1
O M SS Fabrication
Since th e OMSS’s m ust pass nanosecond-length electrical transients for
OMEGA pulse shaping system , long carrier lifetimes a re necessary. We
use intrinsic, single-crystal Si a s our OMSS substrate m a te ria l [51]. The Si
was grown using the Czochralski m ethod into l ”-diam eter boules of [100]
orientation and purified w ith th e float-zone technique to 40 kQ-cm resistiv­
ity, corresponding to a (p-type) dopant density of approxim ately
1 0 12
cm~3.
The boules were sliced in the LLE Optical Fabrication Shop into wafers and
ground to 0.5 mm ± 5/nn and blocked up and carefully m irro r polished to
minimize the surface recom bination velocity, which reduces th e quantum
efficiency [52, 53]. The w afers w ere then cleaned w ith a n electro-optical
grade wax and pitch clearant.
The wafers were cleaned ag ain by dragging or wiping a methanol-wetted
lint-free tissue across both surfaces.
In the LLE T hin Film Deposition
Lab the wafers were placed in a vacuum chamber, pre-cleaned with an
ion etcher, and coated w ith 1140-A of hafnia oxide AR to 1054 nm normalincidence laser illumination.
At th e Rochester In stitu te of Technology (RIT) M icroelectronics Engi­
neering IC Fabrication Lab th e other (non-coated) surface of th e wafers was
cleaned by (in order) acetone, isopropanol, then DI water, th e n dilute HF for
30 seconds and finally a DI rin se an d dry. The wafers w ere m ounted on a 4”
IC -standard industry wafer as a mechanical carrier w ith th e AR-coated side
facing down (unexposed). Next, 3000 A of A1 is evaporated on th e wafers, fol­
lowed by a photoresist spin-on, expose, develop and rin se process to create
a m ask exposing the contact p ad areas (see Fig. 2.7). A
2
* 1 0 1 5 (atoms/crri2)
dose of B n was im planted a t 100 keV, creating a steeply-graded p+ layer be­
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
32
Chapter 2. O ptoelectronic M icrowave Silicon S w itch Physics
neath th e contact pads which promoted ohmic-like contacts. Multiple layers
of metal for th e soldering contacts were b u ilt up by evaporating 1000 A of
Cr, then sp u tterin g 3200 A of Ni, followed by evaporation of 3000 A of Cu.
Photoresist an d m e tal was lifted-off w ith acetone and ultrasonic cleaner. An
electroless gold p latin g process at 80°C for 10 m inutes sacrificially replaced
Cu with Au on th e contact pads, and th e A1 is etched away.
(b) bottom view
(a) ade view
T
Laserpu se
>r
A lu m in u m
Chrome
Nickel
CopperGold
>r
t
\f
^
silicon
Boron
implant
OS
mm
coating
2.00 mm
Figure 2.7: Side view of OMSS showing different m etallization layers and
top view showing dimensions of finished OMSS.
After m etallization, the wafers are re tu rn e d to LLE’s Thin Film Deposi­
tion Lab and are drag-wiped clean again a n d placed in the planetary carrier
so th at th e m etal-contact side faces up (towards th e deposition source). An­
other pre-clean process is performed, th is tim e w ith Ar back-filled. Next,
17 alternating layers of high-index/low index are deposited on the surface
to create an HR coating. The odd, high-index layers are approximately 925
A-thick h afnia oxide an d the even, low-index layers are approximately 1270
A-thick silicon dioxide. Each layer thickness was monitored and adjusted
in situ so as to create a reflectance peak a t 1054 nm a t norm al incidence.
The final OMSS fabrication step is perform ed a t RIT and consists of
rem ounting th e processed wafer on a 4-inch carrier wafer, m asking so as
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission .
C hapter 2. Optoelectronic M icrowave Silicon Sw itch Physics
33
to expose only th e contact pads with the sam e photoresist masking step as
before, removing th e HR coating from th e pads w ith HF etchant, placing a
protective photoresist layer on the entire surface and dicing the wafer into
2 mm by 2.38 mm pieces (see Fig. 2.7). The photoresist is removed, a final
clean as before is perform ed and the OMSS’s are prepared and packaged for
delivery. Average yield from a single 1” w afer h as been approximately 50%,
or 40 OMSS’s.
For final assem bly into the pulse shaping system, the OMSS’s are sol­
dered to a fiberglass-reinforced teflon microwave substrate across the m i­
crostrip line gap. The substrate is 1/32” thick, its dielectric constant a t
microwave frequencies is er = 2 .2 , and th e copper for the microstrip line
and ground-plane is pressed to the substrate a t a thickness of 1.5 mils (“1
oz./sq.ft.”). These values set the w idth of a 50 Q line to approximately 2.4
mm, and give an
mm/ps
ee/ /
= 1.9, 0.8 pF/mm an d propagation velocity of 0.2
[54, 55, 56]. The gap between th e OMSS evaporated contacts is
the same value as th e microstrip line gap w idth: 0.5 mm. The OMSS’s are
bonded to the line w ith a very small bead of low-temperature solder, using
a h eat gun.
2.10.2
OMEGA Pulse-shaping O M SS Requirements
The criteria for optim al OMEGA OMSS operation is best judged by th e
shape of the electrical pulse at the launch into th e coaxial line leading to
the electro-optic modulator. Two im portant and interrelated param eters
th a t are easily observed in the pulse are th e risetim e and duration. Both
of these param eters are seen in the frequency-domain as the bandwidth.
The sharp risetim es of th e features w ithin th e desired pulse shapes and th e
R e p ro du ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
C hapter 2. Optoelectronic M icrow ave Silicon Sw itch P h ysics
34
long pulse duration are generated by th e OMSS turn-on rate and carrier
lifetime. Effects th a t are detrim ental to th e tu rn -o n rates (or, in the spec­
tra l domain, these frequency response curves), b y th e OMSS’s inability to
pass those fast risetim es. A nother im portant req u irem en t is pulse am pli­
tude contrast ratio, both betw een the pre-pulse an d the beginning of th e
pulse, and between the minimnm and m axim um values w ithin the pulse
duration. Large pulse am plitude gain and sa tu ra tio n fu rth er dow nstream
in th e laser system combine to present very challenging specifications for
contrast and bandw idth. A very complete microwave model of the OMSS
during these very different operating regimes is necessary to m eet the chal­
lenges of accurate and predictable pulse shaping.
The mechanisms th a t affect an OMSS’s operation span the fields of
optics, solid state physics, and microwave engineering. The task of opti­
mization m ust be m ade manageable by th e careful selection of appropri­
ate simplifications, w hile a t th e same time, approxim ations which obscure
a m eans of performance improvement should be avoided. For example, a
simple param eter used for our OMSS’s is gap distance between deposited
m etal contacts, which defines the distance betw een electrodes. Even w ith
a simple lum ped-elem ent model the trade-offs betw een narrow- and widegap OMSS’s are num erous. Down into th e picosecond regime, the fastest
possible risetim e (and therefore OMSS bandw idth generation) is directly
related to the gap w idth. However for narrow -gap th e re will be an increase
in capacitance, which is detrim ental in a num b er of ways. This capacitive
coupling coefficient will effect th e device in the O N sta te as well as the OFF.
In th e OFF state the second OMSS to be illum inated (closer to the m odula­
tor) shields th e m odulator from large tran sien ts th a t are propagated down
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C hapter 2. Optoelectronic M icrowave Silicon Sw itch Physics
35
the charge line from the tum -on of th e first OMSS; a large capacitance will
increase th e am plitude of the tran sien ts to the modulator. In the ON-state,
the two OMSS’s allow th e signal to propagate both conductively and capacitively, an d a n increase in capacitance will lower th e frequency a t which ca­
pacitive coupling begins to contribute significantly to th e tran sfer function.
This increased capacitive coupling in th e on-state causes those frequencies
to be phase-shifted during propagation. For OMEGA OMSS’s the gap is 0.5
mm. This distance allows for 30 p s risetim e pulse features to be generated
by a suitably fast optical excitation, while a t the sam e tim e lim iting the gap
capacitance to 10 fF, small enough to p resen t negligible sh u n t impedance to
the conductive signal p ath a t th e highest frequencies of in terest (a magni­
tude of 10 kft at 10 GHz) [57, 58].
A nother simple geometric p aram eter w ith m any trade-offs is the thick­
ness of th e OMSS. Should it be th in to lower parasitic lumped-element
equivalent reactances, a t the cost of reducing th e photon absorption vol­
ume? O r is a thick Si layer b etter to increase th e num ber of carriers ab­
sorbed? W hat about the pros and cons of various gap geom etries like interdigitated, simple flat sides, tapered, etc.? These m any design param eters
and architectures can only be evaluated w ith a comprehensive, accurate de­
vice model. This Table 2.2 shows th e effects of device p aram eter variations
on OMSS transm ission bandw idth. These design p aram eters are evaluated
and optim ized using the techniques described in th e following chapters, and
the optim al OMSS architecture for OMEGA pulse-shaping will be presented
later in Ch. 4.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
36
Chapter 2. O ptoelectronic Microwave Silicon Sw itch Physics
Table 2.2: OMSS design param eters a n d th eir effect on bandw idth
OMSS P aram eter
Effect of increase on Microwave B andw idth
Gap w idth
Capacitance 4, Resistance ft, Risetime
ft
OMSS w idth
Capacitance ft, Resistance ft, Risetime
ft
Thickness
Resistance ft, Absorption ft, Parasitics
ft
2.11 Summary of Device Physics Considerations
The physics of OMSS’s spans the realm s of optics, solid state an d plasm a
physics, an d microwaves. Consequently th e opportunities for applying these
devices to w idely-varied disciplines is large. However, w ith so m any inter­
related p aram eters, optimizing performance can be difficult. W hen control­
ling microwave signals via optically-generated mobile carriers, th e effects of
carrier dynamics on the spectral and tem poral characteristics of th e OMSS
microwave tran sm issio n function can m ake conventional microwave device
modeling difficult or impossible. W ithout a technique for carefully investi­
gating and sep aratin g the spectral and tem poral properties, any improve­
ments to th e transm ission function would necessarily be ad hoc. C harac­
terization en tirely in the optical domain, or completely in th e electronic do­
main, are n o t adequate, nor are purely filter or modulator models, as will
be shown in th e n ex t chapter.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
37
Chapter 3
Switch Model
This chapter will introduce th e concepts of linear sy stem theory th a t are
necessary for modeling linear microwave devices w ith rap id ly time-varying
frequency response, such as photoconductive switches [59, 60, 61]. The ap­
plication of linear systems theory to the experimental m easu rem en t of these
switches is performed in the context of the param eters we are interested in
for pulse-shaping (primarily transm ission, or in term s o f th e scattering m a­
trix S param eters, S2i).
Conventional microwave device modeling and characterization is intro­
duced in Sec. 3.1, in such a way as to naturally lead to th e derivation of our
extended 5 parameter. In Sec. 3.2 we summarize why we are motivated to
develop a new microwave model of photoconductive sw itches. In Sec. 3.3 we
briefly discuss the com plem entarity of linear filters and. modulators. From
this perspective we derive an extension of the filter a n d m odulator charac­
terization function S(u) and k(t) to a general linear device characterization
(system function) S(u, t). From considerations of conventional S param eter
limitations, we also give some of the S param eter’s m o re im portant prop­
erties. We then explain conditions under which this fo rm of analysis can
be implemented. In Sec. 3.4, we apply S param eters to device analysis by
considering a lumped-element example model. We determ in e the device’s
tran sfer function from S p aram eter definition and directly from the differ­
ential equations. We also compare output signals th a t r e s u lt from applying
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
38
C h apter 3. Sw itch M odel
our definition to those obtained by windowing, and by so doing we demon­
strate th e lim itations of windowing. In Sec. 3.6 we link our model to the
experim ental characterization of OMEGA photoconductive switches, which
we p resen t in th e next chapter.
3.1
Standard Microwave Model
Conventional microwave device characterization depends on shift-invariant
device models, tak in g advantage of th e property th a t a convolution in the
tim e or frequency domain will Fourier transform to m ultiplication in the
other. Table 3.1 presents the canonical input-output relationships of the
two ideal shift-invariant microwave devices in th e time and frequency do­
m ains to em phasize their com plem entary n atu re. All dependent variables
are complex; t an d r are in seconds; u> an d f are in radians p e r second;
a(oj)
and
b(aj)
are th e Fourier transform s of th e respective in p u t and out­
p u t tem poral power waves A(t) and B(t), S(uj) and h(t) m e th e scattering
p aram eter and its Fourier transform (the im pulse response),
k(t)
and
K (
jj
)
are th e m odulation param eter and its Fourier transform. The subscripts
refer to th e ports of the device. The L FI model of a modulator is valid when
narrow -band in p u t signals (relative to th e m odulator bandw idth) are ap­
plied, an d th e LTI filter is valid w hen th e device’s temporal variations are
much slower th a n th e signal duration. To conform with m easurem ent prac­
tice we use “a/” as notational shorthand for “j u ” throughout th e re s t of the
thesis, and we assum e the use of analytic in stead of real tim e-series signals
w here appropriate.
The lin ear tim e-invariant (LTI) microwave filter is the m ost common
model used for device characterization. N early any microwave device, in
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
39
C h apter 3. S w itch Model
Table 3.1: A comparison of the tran sfer functions of linear tim e-invariant
(LTI) filters an d frequency-invariant (LFI) m odulators.________________
Domain
Time
Freq.
LTI Filter
LFI M odulator
Bid) =
Bdt) =
f-oc M * - r )Aj(r ) dr
kijd) ■Ajd)
bi(uj) =
bi(u) =
SZoK ij^-O ajiO ^
some regime of operation, can be usefully m odeled as a linear filter. W ithin
th a t range of validity, S param eters are popular an d easy to apply. The
sim plest model dem onstrating the characteristics of transm ission a n d re ­
flection is th e two-port model shown in Fig. 3.1(a). The change in am plitude
and phase of the signal as it is tran sferred from port j to port i is described
by th e elem ent Sij{uj) of the m atrix. A sketch of in p u t and output signals in
Figs. 3.1(b) an d 3.1(c) illustrates the unchanging tem poral response of th e
LTI device of the method of determ ining S p aram eters and Figs. 3.1(d) an d
3.1(e) indicate graphically the relationships on th e left-hand side of Table
3.1.
To characterize devices under more complicated circumstances, tech­
niques —such as complex frequency-hopping [62] and “transient” S p aram ­
eters —have been developed for application to exponential tran sm ission
lines [63], nonuniformly-coupled transm ission lines [64], transm ission lines
w ith tim e-vaiying [65] or nonlinear [66, 67] loads, or some com bination of
these [68, 69, 70, 71]. In contrast to filters, th e explicit analysis of lin­
ear frequency-invariant (LFI) m odulators is encountered less often since,
unlike the relative ease of m aintaining th e tem poral stability of a n LTI de-
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C hapter 3. Switch Model
40
(a)
A(t)
LTI device
S(o>) h(t)
a(co)
B (t).
b(co)
(d)
(b)
s(tb) m )
a(co)
b(co)
A(t)
-> CO
to
(e)
(c)
m
atco)
t
CO
22401
Figure 3.1: (a) Two-port linear tim e-invariant device, w ith a representative
tem poral (b) input and (c) output, (d) associated spectral input and output,
and (e) tran sfer function S(u).
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
41
C hapter 3. Sw itch M odel
vice’s response, the ability to m ain tain a constant response over a broad
range of frequencies is much more difficult. Analogous to Fig. 3.1, th e sig­
nals associated w ith a n LFI device are show n in Fig. 3.2.
(a) LFI device
k(t) K(co)
(b) Input spectrum
8(coo)
6(0*,)
A
A
(d) Temporal signals
A(t)
a(co)
B(t)
0*0
CO,
Time
Frequency
(e) Modulation function
(c) Output spectrum
b(CD)
i
/ J.1
/ __A 1
COo
a.
E
<
1
—
>
CO,
Frequency
Time
Figure 3.2: (a) Two-port linear frequency-invariant device, w ith a represen­
tative spectral (b) in p u t and (c) output, (d) associated temporal in p u t and
output, and (e) modulation function k(t).
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C hapter 3. Sw itch M odel
42
3.2 Need for New Measurement Model
The tim e-varying S p aram eter extension and m easurem ent technique pre­
sented in th is chapter are distinct from the above-mentioned methods be­
cause they allow complete characterization of lin ear microwave devices w ith
transm ission properties th a t are both time- an d frequency-varying (i.e., not
shift-invariant on eith er the tim e or frequency axis). The technique is es­
pecially useful w here th e tim e variations (modulation) and the frequency
variations (filtering) are too rapid for windowing, or w hen they cannot be
separated during th e m easurem ent process. As shown in Fig. 3.3, from the
filter point of view th is can happen when th e filter modulates th e input
signal, or from the m odulator point of view w hen th e modulator has signifi­
cantly variable frequency response w ithin the in p u t signal’s bandwidth.
Looking a t a 2-D example of the tran sfer function of a filter, a modu­
lator and a general lin ear device in Fig. 3.4 graphically indicates th e ir dif­
ferences. The m odulator shown in the upper rig h t is frequency-invariant; a
cross-section along th e tim e axis represents an oscilloscope m easurem ent.
The filter in th e lower left is tim e-invariant an d a cross-section along the
frequency axis is a spectrum analyzer m easurem ent. The other two tra n s­
fer functions are of two different general lin ear devices. The one in th e
lower right is simply a filter and m odulator cascaded, which is equivalent
to the m ultiplication of the filter and m odulator tran sfer functions. In th e­
ory a separable device such as this could be characterized conventionally by
holding eith er th e m odulator or the filter constant and m easuring th e re­
sponse of th e other; however experim entally it m ay not be possible to hold
one constant, independently of the other. The tra n sfe r function in th e upper
left represents a device th a t cannot be separated into a modulator and fil-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
43
C h apter 3. Switch M odel
(a) LTV device
(b) Temporal input
i
k
(d) Spectral input
i
ii
j
m
S(«b)
5(0),)
SK )
A(t)
------- >
«o
*1
O lg
Time
CO ,
Frequency
(c) Temporal output
(e) Spectral output
“o
to
“i
Frequency
Time
(t)
ZMM
Figure 3.3: (a) Linear tim e an d frequency varying device. Time variation is
shown schematically by th e application of (b) two im pulses and their sub­
sequent (c) differing impulse responses. Frequency variation is shown sim­
ilarly, by (d) different in p u t sine waves and (e) output spectral response,
(f) Representative sketch of a S(u. t) showing exponential temporal decay
(modulation) and spectral attenuation sim ilar to a low-pass filter with an
exponential amplitude decay.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
44
Chapter 3. Sw itch M odel
ter. N on-separable transfer functions, and separable transfer functions th a t
cannot be experim entally separated, are both candidates for the application
of 2-D m easurem ent techniques.
Modulator
function
Filter
Separable
function
Figure 3.4: R epresentative transfer function for a filter (lower left), m odula­
tor (upper right), separable (upper left) and inseparable transfer functions.
As we dem onstrated in Ch. 2, the ability to m easure 2-D transfer func­
tions is particularly useful for optoelectronic (photoconductive) microwave
devices and circuits [72, 73, 74]. Properties of photoconductive microwave
devices include isolation of electrical and optical in p u t signals, the absence
of a constant conductive (ON) mode after illum ination, and the significant
effect of charge-carrier population dynamics on the microwave device’s tran s-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 3. Switch M odel
45
fer function [75, 76, 77, 78], These properties indicate a change of the de­
vice’s scattering p aram eters due to spatial and tem poral charge-carrier dy­
namics, independent of th e in p u t electrical signal. If the change is rapid
enough, conventional windowed 5-param eter techniques will time- and/or
frequency-average the variations and lead to inaccurate m easurem ents. The
advantage of the scattering param eter defined h ere is th a t no windowing
and therefore no averaging has been performed, because no assumptions
about shift-invariance are m ade [79, 80].
The general concept of a time-vaiying filter is well-established in the
signal processing [81, 82, 83, 84], communication [85, 86, 87] and automatic
control [88] fields. Devices w ith periodic m odulation are also amenable to
calculation and have been analyzed extensively [89, 90, 91, 92, 93, 94, 95].
Although some prelim inary work was done for electrical circuits [96, 97], a
linear tim e-varying filter model in the microwave regim e has been unnec­
essary, however, since th e variation of filter properties is typically caused
by slowly varying (mechanical) effects, generated by a rapid sequence of
transitions between steady-state regimes (e.g., microwave diode switches
or mixers), where th e signal during the tran sitio n is neglected. For these
devices, windowing can provide adequate solutions. The motivation of our
analysis is to introduce a characterization technique analogous to (and a
superset of) the 5 param eters, th a t can be applied to devices such as photo­
conductive microwave switches th a t are linear filters w ith rapid modulation
of am plitude and/or phase.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 3. Switch Model
46
3.3 Background to Time-varying Model
The equations in Table 3.1 cannot rigorously be applied to devices th at
are neither tim e-invariant nor frequency-invariant w ithout introducing the
concept of windowing. A device th a t is not shift in v arian t m ay be considered
a tim e-varying filter w ith different impulse responses a t different times,
or equivalently a m odulator w ith finite frequency response th a t modulates
different frequencies differently. If th e filtering and m odulating aspects of
this general linear device can be controlled independently (i.e., can be made
separable), or if the variations are slow relative to th e signal applied, then
conventional analysis can still be applied using some form of windowing;
inaccuracies will depend on how strongly the LTI or L FI assum ptions are
violated [98, 99]. Otherwise, characterization of th e device u nder te s t (DUT)
using either k(t) modulator functions or S(ui) filter p aram eters cannot ac­
count for complete device behavior. Since conventional m ethods of linear
microwave circuit characterization (e.g., spectrum and netw ork analyzers)
are based on windowing, th e application of Fourier transform s, an d th e con­
volution integral, their use can lead to incorrect or m isleading characteri­
zation results.
M otivated by these lim itations, we combine the sep arate (but comple­
m entary) one-dimensional (1-D) LTI and LFI tran sfer functions into a sin­
gle two-dimensional (2-D) tran sfer (or system) function, calling it S(u,t) to
em phasize its similarity to conventional S( uj) param eters. The determ i­
nation of th is 2-D S(u:) param eter can be more difficult th a n m easuring a
conventional device’s S param eter; however, it is possible to simplify the
m easurem ent process by tak in g advantage of the 2-D n a tu re of S and using
methods th a t are not applicable to 1-D transfer functions. For example, the
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
47
Chapter 3. Switch M odel
theory of generalized projections, as used in 2-D phase retrieval, allows for
th e reconstruction of th e full, vector (complex) 2-D transfer function from
m easurem ents of only the magnitude |5(u;, £)[. This method applies if the
function is zero outside some finite tem poral an d spectral window, th a t is,
if it has known, compact support along both axes [100]. In practice, real
microwave devices will satisfy these criteria.
3.4 Mathematical Formulation
To derive a combined system function S( uj. t) th a t is capable of characteriz­
ing the input-output relationships of tim e- an d frequency-varying devices,
some of the assum ptions used in microwave circuit/network analysis and
synthesis m ust be revisited [101, 102, 103, 104, 105, 106, 107]. We will be­
gin the derivation w ith the time-domain differential equation describing a
linear lumped-element device with tim e-variable coefficients:
n
o
Bi(t) +
h an(t)Bi(t) =
(3.1)
£ij(p,t)Bi(t) = Aj(t),
where the coefficients a are determined by th e (time-varying) dependencies
between the nodes of th e circuit (e.g., th e lumped-element models of resis­
tance, capacitance an d inductance). The ports of the device described by
the circuit model are a subset of the nodes of th e circuit model [108]. The
signals A{t) an d B{t) used in Eq. 3.1 are defined as in Table 3.1. Also, we
have used th e operator notation C{p) = a 0pn -t-aipn~l H
ho;n where p is the
differential operator ^ [109]. Note th a t although the following derivation is
being done for a device w ith a finite num ber of nodes and therefore a finite
num ber of (time-varying) poles and zeros, S{uj,t) like S( uj) is also applicable
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
48
C hapter 3. Switch Model
to distributed-element devices [110].
We will frame the derivation in term s of filters and 5-param eter charac­
terization; however, m athem atically there is no special significance to filters
over modulators; the system function subsum es both LFI an d LTI devices as
special cases. The route we take is m otivated by th e observation th at, in the
equations for filters and modulators presented in Sec. 3.3, th e roles of tim e
and frequency are complementary, i.e., th e 1-D characterization functions
are along orthogonal axes in the complex plane. This leads to the realiza­
tion th a t a more general, 2-D characterization is possible by considering the
device’s response over the entire plane.
For the LTI model there is no time variation in th e coefficients of Eq. 3.1,
and it therefore simplifies to
Cij(p)Bi(t) = Aj(t).
Assuming
(3.2)
complex exponentials e±juJt for th e basis function solutions (which
simplifies the differential operator p to u;) and converting to 5-param eter
notation
= Cj^ip), we derive the frequency-domain filter transfer
function of Table 3.1, and the process is analogous for th e LFI model. The
use of complex exponential basis functions in th e transform integral leads
to the formalism of Fourier transform s [111]. Fourier transform s are useful
for microwave device characterization because they transform between a
system of differential equations and a system of algebraic equations; i.e.,
they are “compatible” integral transform operators [112]. Non-compatible
transforms result in relationships between th e input and output th a t are
neither algebraic nor a convolution.
In contrast to modulators and filters, for a general lin ear device a com­
patible integral transform operator depends on th e functional form of the
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 3. S w itch M odel
49
variable coefficients in Eq. 3.1. This m eans th a t th e basis functions are not,
in general, e±jult b u t are dependent on the p articu lar form of m odulation and
frequency response. The key to the characterization technique described in
this chapter is th a t to rem ain independent of th e specifics of th e tem poral
variations in device properties we choose a non-compatible transform th a t
will enable u s to continue to use e±Jtj£ basis functions [113]. Several impor­
ta n t implications of this choice will be m entioned during o u r derivation of
the properties of th e system function.
To define th e tran sfer function for any lin ear lumped- or distributedelement device from th e algebraic relationships in Table 3.1 we dropped the
assum ptions of tim e- and frequency-invariance. The resulting equation (in
the tim e domain) can be w ritten as
(3.3)
which differs from th e traditional S p aram eter definition in th a t it is now
a function of tim e as well as frequency [114, 115]. Also Sij(uj, t) = £JZ-L(p. t),
where as u su al the differential operator p simplifies to u; due to th e differentiation of eJu;£. Equation 3.3 quantifies th e la st p arag rap h of Sec. 3.3 in
the frequency domain, which states th a t th e output signal Bi(t) will have
time-varying am plitude and phase m odulation (as w ith a modulator), and
this m odulation will be frequency dependent (as w ith a filter).
Therefore Bl{t) — Sij(ui.t) ejuJt is the output of the device for an input
Aj(t) = ejuJt, given th a t the device is in a know n state a t every tim e t > tQ
(i.e., the variable coefficients evolve determ inistically from tim e t = tQ). By
virtue of th e linearity of the device, superposition applies and th e output
Bj(t) can be defined in term s of Aj(r) according to
(3.4)
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission.
50
Chapter 3. S w itch M odel
where th e lim its of the integral have been set by assum ing a) causality,
and b) th e signal is zero a t tim es less th a n t0. Eq. 3.4 is a generalization
of the tim e-invariant convolution in Table 3.1, w here th e impulse response
function h(r —t) is now the more general G reen’s function h(r. t), i.e., it now
depends separately on im pulse time r and observation t, and not m erely on
the difference [116].
S ubstituting Eq. 3.4 into Eq. 3.3 resu lts in a transform relationship
between th e system function S and the new generalized impulse response
h:
Sij (jJ. t )
=
f
J —OC
(3.5)
t ) e ~ :juJi't ~ T)d T .
Notice th a t S( uj, t) an d hL-j(r. t ) are related by a F ourier transform of th e first
axis; in addition to these transfer function definitions, two others resu lt
from transform ing S and h in their second variable. The resulting inputoutput relationship for these four system functions a re listed in Table 3.2.
Table 3.2: Input-output relationships for all four 2-D system functions
In p u t Time
In p u t Frequency
Bi(t) =
Bi{t) =
Jo hijir.tjAjir) dr
/ Sij(u:, t) dj(uj) eJUJtdoJ
Domain
O utput Time
bi(uj) =
O utput Frequency
f
uj)
Aj(t) e~^wtdt
bi(u) =
j? oai if(v ,e)A j (€)d f
An im p o rtan t distinction exists betw een these 2-D transfer functions
and tran sfer functions th a t are found by windowing signals: the form er
may have arb itrarily sharp features (peaks and valleys) on either (indepen­
dent) axis, w hereas the extent of the windowed function along each (de­
pendent) axis h as a n inverse relationship (i.e., a n increase in one m eans
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
51
C hapter 3. Switch Model
a decrease in th e other). This is due to the uncertainty principle: a n ar­
row windowing of a signal in tim e (necessary to prevent averaging the tim e
fluctuations of th e system) necessarily implies a widening of th e spectral
window (which forces averaging over spectral fluctuations) and vice versa.
T h is
lim itation is ultim ately due to the 1-D n atu re of the m easurem ent,
which is only capable of completely characterizing a 1-D transfer function.
It is necessary to apply m ultiple signals to characterize a 2-D tran sfer func­
tion. In other words, in the tim e
d o m a in ,
a series of delta functions m ust
be applied and m easured, w hereas for an LTI device a single delta function
suffices. Similarly, in th e frequency domain, the am plitude and phase of
each sine wave m ust be m easured a t each point in time, rath er th an only
once, at any time, as w ith a filter (e.g., a tuned receiver in a netw ork ana­
lyzer). Further, for conventional 1-D m easurem ents a fundam ental inverse
relationship between tem poral (spectral) range and spectral (temporal) res­
olution exists, related to the uncertainty principle. For 2-D m easurem ents,
the benefit of having to m easure m ultiple signals is th a t this fundam ental
trade-off doesn’t occur. M easurem ents are made along both the tem poral
and spectral axes, and no relationship between the range and resolution of
the two independent axes exists. However, this inverse relationship does
exist between r and u;, and betw een t and f in the transfer functions of Ta­
ble 3.2, because these variables are related by the Fourier transform . These
differences between 1-D and 2-D m easurem ents will be shown in Sec. 3.5
by applying windowed signals (via ambiguity functions and time-frequency
distributions) [117, 118, 119, 120, 121].
From Eq. 3.4, we get a relationship between in p u t and output by replac­
ing Aj (r) w ith its transform f aj (w) ejuJtdui, inverting th e order of integration,
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
52
C hapter 3. Switch M odel
and substituting from Eq. 3.5
Bi(t) =
t) aj(uj)} *
(3.6)
where th e transform operator T ~ l is sim ilar to the inverse Fourier tra n s ­
form b u t w ith th e variable t held as a constant param eter. Equation 3.6 is
analogous to th e frequency-domain filter relation in Table 3.1 in th a t th e
signal is the transform of the product of th e scattering p aram eter and th e
input spectral function. Unlike conventional Fourier transform s, however,
Eq. 3.4 is not a convolution. Therefore, th e argum ent inside th e braces of
Eq. 3.6 is not th e product of two 1-D functions. This m eans th a t, in general,
there is no algebraic relationship betw een the output signal an d the in p u t
signal:
bi{us) ^ Sij(uj. t ) aj(uj).
(3.7)
An im portant point is th at the complete function S(u;.t) cannot be found
by taking a quotient b{u)/a{uj), as can be done for S'(^’) of LTI devices. For
netw ork synthesis, where a model (differential equation) m u st be synthe­
sized from a given (measured) S{uj,t), th is consequence of noncompatible
transform s has no major negative im plications [122]; in fact, choosing th e
noncompatible (but Fourier-like) transform allows use of stan d ard Fourier
transform tables, m aking the synthesis easier. On the other h an d for n e t­
work analysis, where the output B(t) is to be found in term s of A(t), the sig­
nificance of Eq. 3.7 is th a t only simple linear time- and frequency-varying
device models (which can be solved directly, w ith first- or second- order dif­
ferential equations) can be created since signal flow graphs an d the combi­
nation of series and parallel devices are no longer algebraic or even analytic,
as explained in the next paragraph.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
53
Chapter 3. Sw itch M odel
For netw ork analysis of microwave system s w ith tim e- and frequencyvarying elem ents, th e network can be broken down into block diagrams
where the lin ear tim e- an d frequency-varying elem ent is isolated from the
re st of the LFI or LTI components. This approach th en requires operational
methods of com bining th e general linear elem ent w ith other components, in
cascade and parallel, to determine th e overall system function. All types of
linear devices in p arallel can be combined by adding either their impulse
response functions or (equivalently) th e ir tra n sfe r functions [123]. For de­
vices in series, however, determ ination of th e combined response is not triv­
ial unless the devices are shift-invariant. The overall transfer function of
LTI devices in series is accomplished by m ultiplying th e individual tran s­
fer functions together, or equivalently convolving th e ir impulse responses.
For LFI devices in series, the transfer (modulation) functions are multiplied
while the spectral transform of the m odulation is convolved.
To derive th e tra n sfe r function of general linear devices in series, we
will begin w ith th e repeated operation of th e tran sfer function (in opera­
tional form)
S(p, t) [a(<j)] = Sb(p, t) {Sa(p, t) [a(u;)]} ,
(3.8)
where Sa{p. t ) and Sb(p, t) are the transfer functions for the first and second
device, respectively. S a(p, t) operates on a(uj), giving th e product Sa{w, t)a(co),
and then by th e product rule Sb{p, t) will u ltim ately operate on both Sa{u. t)
and a(u;) th e resu lt being
S e ^ = Sb \e^l§-tSa + 5af e H =
L
1
(3.9)
SbeJu,t§-tSa + Sbjuje^Sa.
By simplifying we find th e transfer functional form of th e two linear devices
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
54
Chapter 3. Sw itch M odel
in series:
S(p, t)A(t) = Sb(p 4- u, t) [Sa(p. £)-4(£)] .
(3.10)
3.5 Analytical Example
To dem onstrate th e application of S{ui,t) to microwave device characteri­
zation, a simple lum ped-elem ent device model will be solved analytically.
The model, which is draw n in Fig. 3.5, is a single-pole low-pass filter with
a sinusoidally varying capacitive element C(t) = C0 + Cm sin(umt), where
for convenience we have chosen suitable values of th e variables: Co = 1
pF is the steady-state capacitance, ujrn = 2.3 Grad/s is th e Cm modulation
rate, Cm/ C0 = 0.2 is the modulation depth, and the device is assum ed to
be embedded in a transm ission line with characteristic impedance ZQ. A
device such as th is is very sim ilar to a photoconductive switch model, how­
ever a sinusoidal ra th e r th a n exponential modulation was chosen to keep
th e analysis results in closed-form expressions.
•----- -----AAAA------- ------------------R
b,(ca)
^C (t)
A,(t), 3,(0)
-
■#
---------- ►
Baft), ba(<D)
Aaft), a2(co)
Q40C
Figure 3.5: An example linear device with a tim e-varying capacitance rep­
resenting a tim e-vaiying pole location (bandwidth). The tim e-varying fre­
quency response cannot be completely characterized by either a filter or
modulator model.
The differential equation for this device w ritten in th e form of Eq. 3.1
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
55
Chapter 3. Switch M odel
IS
A(t) = [±C(f)(fl + Z„)] $B(t )+
[l + i R /Z 0 + 1(R + Z „)|C (t)] B(t).
From S param eter analysis the S2 i(u;) for a conventional LTI filter [where
C{t) = C0 in Fig. 3.5] is given by
S2l(uj) = 2Z0 + R + ju,CZ0(R + Z0)'
(3*12)
Applying Eq. 3.10 to th e cascaded elements of resistance and sh u n t capaci­
tance we get
*) = 2, Z7q ^+ R-\g J . ,[p +Y juZ\) )nC yZ q • \ R +
Z 0)
(3-13)
which coiold also have been found by the direct solution of the differential
equation in Eq. 3.11. The
6 2 1
(0 ;. t) plot for th e LTI version of th is device is
shown in Fig. 3.6, an d |S2 i(u:, £)| is shown in th e elevation plot of Fig. 3.7 for
one cycle of modulation. Observe in both figures the low-pass atten u atio n
along the frequency axis. Also, Fig. 3.7 shows sinusoidal modulation of the
frequency response along the temporal axis th a t shifts in phase for different
frequencies.
Fig. 3.8 is a cross-section of Fig. 3.7 along th e time axis,show ing the
modulating aspect of the device, which is dependent on frequency. Fig. 3.9,
a line-out along the frequency axis, shows th a t the low-pass filter shape
depends on time. Notice in both of these plots th a t the instantaneous m ag­
nitude of the tran sfer function can rise m om entarily above unity, im plying
the possibility of oscillation [124].
To further illu strate the properties of the. time-varying system function
we show a surface density plot of S2 i(uj, t) in Fig. 3.10, over several cycles
of modulation and from dc to 50 GHz. Figure 3.7 covers the lower left com er
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
56
C hapter 3. Switch Model
1.0
0.9
0.8
(0
0.7
3dB = 6.1 GHz
0.6
0.5
0.4
0
2
4
6
8
10
Frequency (GHz)
Figure 3.6: M agnitude of th e tran sfer function S2i(u;) of a low-pass, single­
pole filter, which is equivalent to the circuit in Fig. 3.5 b u t w ith a constant
(unmodulated) capacitance.
Figure 3.7: M agnitude of th e tran sfer function S 21 (iuj. t) of a low-pass, single­
pole filter w ith sinusoidally varying capacitance, plotted over one cycle of
modulation and 150% of th e bandwidth.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
57
C hapter 3. Switch Model
DC
1.0
i 08
Sf
0.6
10 GHz
0.4
0.0
0.4
0.1
oo.
Tlme(ns)
Figure 3.8: A series of cross-sections through Soi(u;, t) along th e tim e axis,
showing the change in the m agnitude and phase of th e m odulation for dif­
ferent signal frequencies.
1.0
3,
3f
0.3 ns
0.8
0.6
0.4
0
Z M It
2
4
6
8
10
Frequency (GHz)
Figure 3.9: A series of cross-sections through S2 1 (<■*->,t) along th e frequency
axis, showing the change in instantaneous bandw idth for different times.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
58
Chapter 3. Switch M odel
of this plot; Fig. 3.10 will be multiplied w ith a windowed signal to show th e
limitations of windowing. An aspect of S( uj, t) shown clearly in Fig. 3.10 is
the skew in th e p eak of th e temporal modulation along the 3-dB frequency of
6.1 GHz caused by th e phase shift in the transm ission function th a t occurs
around this frequency.
2.56
1.72
?
g ’ 1-28
P
0.64
0.0
0.0
es4s3
12.5
25.0
37.5
50.0
Frequency (GHz)
Figure 3.10: Surface density plot of |S2i (w,£)| w ith six cycles of m odula­
tion along the tim e axis an d dem onstrating low-pass filtering along th e fre­
quency axis.
Using Eqs. 3.6 and 3.13 we sim ulated th e propagation of the sum of
5.9- and 19.5-GHz sine waves through the device, shown in Fig. 3.5. The
attenuation and dispersion of each spectral component is dem onstrated in
Fig. 3.11, w here th e low-pass aspect is readily apparent. The influence of
the modulation can best be compared by looking at a plot of th e spectral
output in Fig. 3.12, w here th e sinusoidal modulation puts different, discrete
sidebands on each in p u t spectral component. Since this device not only
modulates each frequency differently but also filters the signals, standard
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
59
Chapter 3. Switch Model
network or spectrum analysis would not adequately characterize th e device.
1
V*—Input
Output
0
1
Time (100 ps/div)
22426
Figure 3.11: Plot of in p u t a n d output signals showing th e D U T s low-pass
filtering effect. Dashed line is in p u t signal; solid line is th e ou tp u t signal.
o
-1 0
-2 0
S
-3 0
-4 0
-5 0
aar
0
5
10
15
20
25
Frequency (GHz)
Figure 3.12: Magnitude-only plot of the output signal spectrum , as a spec­
tru m analyzer would display it. The two major frequencies are the input
signals, and the different side-lobes show the variations in m odulation char­
acteristics for different frequencies, which a m odulator model is unable to
account for.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 3. Switch M odel
3.5.1
6 0
Windowed M easurem ent Comparison
We will now use windowed signals to characterize our tim e-varying fil­
te r using conventional 5 -p aram eter analysis, and we will compare the re­
sults to our m easurem ent approach. For the windowing we will use timefrequency distributions because of th e ir appealing rep resen tatio n [125,126,
127]. They also dem onstrate more intuitively the fundam ental constraint
due to the uncertainty principle; a narrow windowing in tim e necessarily
leads to a broad frequency window and vice versa. This windowing depen­
dency between the axes is easily observed on a tim e-frequency representa­
tion by phenomenon of “m inim um area”: a tim e-frequency distribution of
a signal consists of areas (or regions) w here the signal exists a t a localized
tim e and frequency. These areas cannot be sm aller th a n a dimensionless
constant (the product of tim e an d frequency) determ ined by th e uncertainty
principle. This u n certainty is not a feature of tim e-frequency distributions
b u t of windowing in general; therefore, th e choice of tim e-frequency distri­
butions doesn’t detract from th e general dem onstration of th e uncertainty
lim itations of windowing.
To dem onstrate th e lim itations of windowing, th e p articu lar choice of
algorithm
to generate a tim e-frequency representation is a m a tte r of conve­
nience: for this example we will use
(3.14)
where -4(u;: t) is th e tim e-frequency distribution of .4(2) and a semi-colon is
used between the jo in t tim e-frequency variables to em phasize th e dependence of the axes. This definition has the virtues of showing all th e essentia l features of tim e-frequency distributions, and being easily transform able
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
Chapter 3. Sw itch M odel
6 1
back into th e Fourier transform of the signal by integration:
/
CC
.4.(u;: t) dt.
(3.15)
•OO
Fig. 3.13 shows a n example time-frequency representation of a signal to
be propagated through our system: a 2-GHz sine wave th a t abruptly tr a n ­
sitions (with broadband noise) after 1.28 n s to a 20-GHz sine wave. I t is
easy to see the sm earing of the signal in tim e (for the low-frequency signal)
and frequency (for th e high-frequency signals) caused by fundam ental w in­
dowing trade-offs. The FFT algorithm used to generate the tim e-frequency
distribution assum es a continuous, periodic signal; this causes “leaking”
across th e tim e boundary (top and bottom) of each spectral component of
the signal; however, away from the edges th ese artifacts have no im pact on
th e results.
By m ultiplying th e input signal A(uj:t) of Fig. 3.13 w ith th e system
function S(u!. t) of Fig. 3.10 we get the tim e-frequency representation of th e
output signal shown in Fig. 3.14. Im portant features of the resulting out­
pu t signal are the low-pass filtering (shown clearly in the resulting spectral
content of the tran sitio n noise) and the differences in modulation of each
spectral component, both in amplitude an d phase.
Converting back to the time domain using Eq. 3.15 and th en inverse
Fourier transform ing to the temporal signal, we can compare the resu ltin g
output signal w ith our technique. The windowed technique gives th e solid
line in Fig. 3.15, an d our result is the th in line. It is evident th a t w hereas
windowing produced acceptable results for th e second half of th e signal,
when th e m odulation was much slower th a n th e signal (i.e., th e slowlyvarying envelope approxim ation is valid), for th e first half the m odulation
was comparable to th e signal frequency a n d th e windowing m ethod effec-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 3. Switch M odel
62
2.56
1.72
?
s ' 1-28
p
0.64
0.00
0.0
12.5
25.0
37.5
50.0
Frequency (GHz)
Figure 3.13: Time-frequency representation (ambiguity function) of a 2GHz sine wave th a t transitions abruptly to a 20-GHz sine wave. Due to
window trade-offs, low frequencies are sm eared vertically and high frequen­
cies are smeared out horizontally. In addition, some wrap-around from top
to bottom is caused by the FFT. Areas of greater signal energy are propor­
tionately lighter.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
63
C hapter 3. S w itch M odel
2.56
1.72
?
a 1>28
p
0.64
0.0
0.0
f
12.5
25.0
37.5
50.0
Frequency (GHz)
Figure 3.14: Time-frequency representation of the o u tput signal, after mul­
tiplication of th e input time-frequency distribution w ith th e system function
S-2 i(u;,t). The effect of the system function in shown by th e attenuation of
the high-frequency signals an d th e tem poral ripple in th e different spectral
components.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
64
Chapter 3. S w itch M odel
tively sm eared th e modulation in tim e. Choosing a narrow er tim e window
would not solve th e fundam ental problem, since doing so would necessar­
ily broaden th e spectral window, causing increased smearing of th e spectral
response.
1.5
Windowing gives
wrong output signal
Actual signal
1.0
cn
w
Windowing gives
similar results
'2 0.5
&
C3
3 0.0
<
-0.5
Windowed signal
-1.0
0.00
E9655
1.72
0.64
2.56
Tune (ns)
Figure 3.15: Time-domain comparison of output signals using th e technique
described in th is thesis (thin line), an d th e windowing m ethod (thick line).
Windowing can be applied successfully to th e high-frequency segm ent of
the signal w here the modulation is slow compared to the cycle; however, it
averages over th e system function for th e first segment.
3.6 Summary of Modeling Results
We provided some of th e im portant properties of the 5 param eter and showed
sim ilarities to conventional 5-param eter analysis th at preserve m ost fea­
tures of th e fam iliar Fourier transform tables. We use 5 to characterize the
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 3. Sw itch M odel
65
transfer function of a single-pole low-pass filter whose elem ents vary on the
time-scale of the in p u t signal. An example signal was propagated through
th e device using our S tran sfer function. To dem onstrate th e lim itations of
windowing, we applied the time-frequency representation of an input signal
to 5 and showed the lim ited ability of th e resulting output signal to follow
both time and spectral variations in the device.
When a linear device such as an optoelectronic photoconductive mi­
crowave switch has rapid changes in its tem poral and spectral responses,
and the tem poral variations cannot be controlled independently (i.e., can­
not be made separable for m easurem ent purposes), standard windowed 5
param eters cannot be applied accurately. To allow characterization of such
devices, we developed a linear system function S{ui,t). The system func­
tion S can be applied to device characterization by taking m easurem ents
in either th e “frequency domain” or the “tim e domain”. In the frequencydomain approach a series of single-frequency waves are applied to th e DUT
for the tim e duration of interest. Then one can record the tem poral evo­
lution of the resulting output signal’s am plitude and phase by comparison
w ith a reference. To m easure the analytic signal (thereby separating the
device’s effect on signal am plitude and phase) th e same input wave shifted
by 7r/4 is applied over the same time duration. This requires a determ in­
istic, triggerable device. By applying signals a t different frequencies over
th e time span relative to th e trigger, a m ap of S(u>, t) is constructed of tim e
slices at each successive frequency. In the time-domain approach a series of
impulse functions can be applied at suitable tim e-intervals over th e period
of interest. The im pulse response of the system to each successive im pulse
is then recorded. Although these descriptions are intuitively appealing, it
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Chapter 3. Switch Model
66
may not be readily ap p aren t how to extract an input-output relationship
such as S{uj. t) from the m easured signals, create a device model, and apply
it to the calculation of o u tput signals given an a rb itra ry input signal, while
avoiding th e lim itations of windowing. The following C hapter will clarify
the technique and the m ethod of calculation.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
67
Chapter 4
Experimental Characterization
In this chapter w e discuss our application of experim ental characterization
techniques to OMSS’s. We begin w ith th e conventional techniques and pro­
ceed to o u r novel m ethod as introduced in Ch. 3. The discussion is presented
in the context of th e param eters of prim ary interest to pulse-shaping (i.e.,
microwave signal transm ission S2i, not reflection 5 U). I t h a s been shown
[128] th a t th e high-frequency (>4-GHz) components of th e OMEGA pulseshaping system are attenuated by th e electrical pulse generator, limiting
the bandw idth of th e shaped optical pulse. To determ ine th e bandwidthlim iting effects of th e electrical pulse generator components, th e microwave
frequency response of each elem ent m u st be m easured. All other compo­
nents w ere easily characterized, however the OMSS’s p resen ted some dif­
ficulties. Therefore our attention focused on the OMSS, a n d th is chapter
presents th e resu lts of our exam ination of their frequency response.
We show in Sec. 4.1 the time-domain oscilloscope m easu rem en ts of the
microwave signals before and after th e OMSS, which can indirectly mea­
sure th e am plitude of the transfer function |S{ui) \ and therefore we can infer
the signal transm ission lim itations. We then present in Sec. 4.2 th e results
of windowed m easurem ents of the tran sfer function S( uj), an d describe the
capabilities an d lim itations of this technique. In Sec. 4.3, w e apply th e tech­
nique developed in Ch. 3 to m easure S( cj. t) . A lum ped-elem ent model of
the OMSS is th e n fitted to S in Sec. 4.4 by relating physical properties such
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
C hapter 4. Experim ental Characterization
68
as gap width, contact resistance, and capacitance to th e lumped elem ents
[129]. The best-fit model is given, and based on th a t model the OMSS fab­
rication param eters have been changed, for the purpose of optimization. In
Sec. 4.5 the expanded frequency response range of th e new OMSS is shown
and finally, in Sec. 4.6 we sum m arize the results.
4.1
Oscilloscope Measurements
Oscilloscope tim e-domain m easurem ents of microwave signals before and
after transm ission through an illum inated OMSS m ounted on a microstrip
transm ission line indicate significant degradation in signal rise- and falltim es [130], as shown in Fig. 4.1. From these m easurem ents, an approxi­
m ate bandwidth can be calculated by Fourier transform ing the signals to
the frequency domain and calculating the ratio of input to output spectrum,
as shown graphically in Fig. 4.2. By simple m easurem ents such as this we
ascertained th a t th e OMSS transm ission frequency response has a signifi­
cant (3-dB bandw idth reduced to approximately 3 GHz) im pact on th e input
signal amplitude and bandw idth.
To optimize th e signal transm ission of the OMSS, we need to construct
a lumped-element model th a t fits the observed transm ission function and
whose elements are related to param eters such as gap width, thickness
and optical wavelength [131, 132, 133]. Unfortunately, using only oscil­
loscope m easurem ents, th e lumped-elements and th e ir values cannot be
determined. The transm ission function of a microwave filter is typically
m easured w ith a netw ork analyzer in the form of an S param eter, however,
OMSS’s with pulsed illum ination do not operate in a steady-state ON con­
dition (unlike conventional diode or transistor microwave switches). There-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
69
C h apter 4. Experim ental Characterization
201 Spectrum
S p ectru m
0.8
0.8
04 -
•Before
switch
Design
Frequency
(GHz) /
0.4
#
Before
switch
Frequency
(G H z)
0.0
0.0
Time (ns)
Time (ns)
Figure 4.1: Oscilloscope m easurem ents of the shaped electrical signal before
and after reflection from th e variable-impedance line (left plot) and before
and after transm ission through th e switch (right plot) are shown. The sig­
n al attenuation in the spectral domain is also given as an inset, to indicate
bandwidth.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
70
C hapter 4. E xperim ental Characterization
Output
signal
(b) Input and output signal and spectra (inset)
0.8
Input
Input
-Output
0.4
Freq. (GHz)
Output
oo
35
0.0
0
1
3
2
4
Time (ns)
(c) PCS switch frequency response
0
Fitted filter response
-3
-6
Switch response
-1 2
1
3
5
7
Frequency (GHz)
Figure 4.2: The top plot graphically dem onstrates the incident an d tra n s­
m itted signals. The middle plot shows th e incident signal and th e signal af­
te r transm ission, w ith an inset of the spectral distribution. The frequency
response can be approxim ated by dividing th e spectrum of th e tra n sm it­
ted signal by th e spectrum of the incident signal, shown in th e bottom plot
w ith a linear fit, indicating the initial 3-dB bandw idth of the OMSS (before
optimization) was approximately 3 GHz.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C h apter 4. E xperim ental Characterization
71
fore th e next section presents a method of partially circumventing th e timevariations of th e device response by gating or windowing the signals.
4.2 Windowed Measurements
Performance requirem ents for OMSS’s are defined for ON- and O FF-state
transm ission and reflection properties (reflection coefficient, power-han dling,
insertion loss), as well as turn-on and turn-off times. OMSS’s are designed
so th a t in the OFF sta te conduction across th e gap is prevented by th e low
values of the uniH um inated bulk an d surface conductivity of the semicon­
ductor. On the other hand, for minimum reflection coefficient in th e ON
state, the (usually laser-illuminated) conductivity should be high enough
th a t th e conduction currents of th e signal are not significantly different
from the rest of th e transm ission line. T h at is, in th e ON state th e OMSS
should appear to th e microwave signal as a segm ent of transm ission line of
m atching characteristic impedance.
By m easuring th e microwave characteristics of OMSS’s as circuit ele­
m ents in a transm ission line, th eir high frequency lim itations can be di­
rectly observed [134].
However they violate th e LTI assum ption as de­
scribed in Ch. 3; therefore S-param eter m easurem ents performed w ith a
standard vector netw ork analyzer will be inaccurate. So, we im plem ented
a gated m easurem ent technique. Considering OMSS’s used for electrical
pulse generation, th ree regimes of operation m ay yield results by applying
gated 5-param eter m easurem ents. Before illum ination, it m ust hold off dc
voltage bias and minimize capacitive coupling; under illumination, it m ust
allow a charged line to discharge as quickly as possible; and shortly after
illum ination, it m u st allow microwave signals to propagate easily through
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 4. Experim ental Characterization
72
it, w ith very little frequency-dependent signal loss due to reflection, ab­
sorption, or radiation. The microwave bandw idth of the electrical pulse
generator will be lim ited if th e OMSS does n o t perform either of th e la st
two functions well. During illumination, the conductivity of the OMSS is
changing rapidly, an d so it cannot be considered an LTI device. Therefore
th e 5-param eter m easurem ent procedure described in this section cannot
be applied to OMSS’s in this regime.
After illumination, the conductivity of th e OMSS changes much m ore
slowly, allowing th e 5 param eters to be windowed and m easured a t m i­
crowave frequencies much faster th an th e conductivity changes. The rate
of change in OMSS conductivity is directly lim ited by the rate of decrease
in excess carrier density. C arrier trapping, A uger recombination tim e and
free-carrier recombination depth control the in itial temporal and sp atial
carrier-density change, but in a high-purity Si OMSS the decay tim e con­
sta n t will eventually settle out to be on the order of 10 \js. This tim e con­
sta n t is much slower th an the temporal duration of the shaped pulse. T here­
fore, if 5-param eter measurem ents are performed on a time scale m uch
shorter th an 10 /is, the conductivity will be constant and the LTI assum p­
tion will not be violated. Thus, within this restricted regime, an OMSS can
be considered a symmetric, LTI, two-port elem ent of the transm ission line
in the simple microwave circuit shown in Fig. 4.3.
The OMSS is symmetric because its two ports, or microwave connec­
tions, are electrically indistinguishable. The symm etric nature of the device
m eans th a t only th e two 5 param eters reflection (5 U) and transm ission (52i)
are necessary for complete characterization. These param eters are defined,
a t a single microwave frequency, as the complex ratios of the reflected and
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
73
Chapter 4. Experim ental Characterization
Q-switched
Nd: YAG laser
Delay
trigger
Reflecte d 1
Variable freq.
microwave
oscillator
Gated
integ rater/
averager
Computer
analysis
E76S0
Figure 4.3: T ransient microwave bandwidth m easurem ent system. The
gated integrator allows accurate m easurem ent of th e S param eters when
the OMSS conductance is constant.
transm itted electromagnetic waves at the reference plan es A and B, shown
in Fig. 4.3, respectively, divided by the incident wave a t reference plane A:
Sn =
AL
Ssi = X
Ai ■
(4-1}
where B0 is the microwave power propagating out of p o rt B, A/ is the power
propagating into port A, and -40 is the power out of p o rt .4. In general, the
S param eters are complex; however, in a conventional scalar experimented
arrangem ent, only th e m agnitude of the param eters a re recorded, allowing
bandwidth and insertion loss to be measured. Inform ation th a t depends on
phase information, such as group and phase dispersion an d device electrical
length, is therefore not m easured.
The microwave signals are all m easured a t the sam e, single microwave
frequency, and a t a fixed laser pulse intensity. The frequency dependence
of the S param eters for th e device is m easured by stepping the microwave
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 4. Experim ental Characterization
74
source frequency across the frequency range of interest for subsequent laser
pulses. To m aintain m easurem ent accuracy, the ports m u st be impedance
m atched to the transm ission line to prevent incorrect m easurem ents due
to m ism atch reflections. Also, these m easurem ents were predicated on the
fact th a t the time and frequency variations in th e OMSS response were
negligible over one cycle a t th e frequencies of interest.
4.2.1
Experimental Setup a n d Procedures
U sing microwave crystal detectors, scattering param eters can be determined
by m easuring the microwave power incident on, reflected from, and trans­
m itted through th e device to be tested [135]. Various m ethods were used
in this experiment to increase th e signal-to-noise ratio. To reduce the noise
floor of the m easurem ent system , we boxcar averaged th e gated detector sig­
nal over many shots. To reduce microwave source fluctuation an d capacitive
coupling noise, the shot-to-shot power m easurem ents w ere norm alized by
simultaneously m easuring shot-to-shot reference power. Finally, the mea­
surem ents were not sensitive to small laser intensity fluctuations because
th e OMSS was in saturation.
The voltage signal m easured by the detectors a t a fixed microwave fre­
quency was proportional to th e power incident on th e detectors. The signal
m easured in this way is given by
where P q is the power of the detected signal (either tra n sm itte d or reflected)
and Ps is the power of the microwave source incident on th e device. Ps is
m easured by sampling the microwave source incident pow er w ith a direc-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
75
Chapter 4. E xperim en tal Characterization
tional coupler, as shown in Fig. 4.3.
To determ ine th e response of the experim ental apparatus, the m ea­
surem ent procedure was first performed w ithout th e OMSS and tran sm is­
sion line b ut w ith a short length of low-loss, low-dispersion, high-frequency
coaxial
tr a n s m is s io n
line (the “th ru ” line) connecting the two ports of the
te st equipment. In th is arrangem ent, th e transm ission and reflection of the
apparatus can be defined as
Sn —Dr.
S 21 —Dt-
(4.3)
respectively, w here D t is th e normalized voltage signal transm itted through
the m easurem ent setup and the th ru line, and
Dr
is the norm alized re­
flected voltage signal through the same. The th r u line was assum ed to have
perfect t r a n s m i s s i o n and zero reflection w ith in th e frequency range of in ter­
est to us. This
was verified to w ithin 0.05 dB from 1 to 9 GHz
a s s u m p t io n
by using a stan d ard vector network analyzer.
The th ru line w as th e n replaced w ith th e microstrip transm ission line
having a copper strip in place of the OMSS, and th e m easurem ent was per­
formed again a t th e sam e frequency. T his procedure was carried out to
separate the response of the microstrip line from th e response of th e m ea­
surem ent apparatus. The reflection and transm ission of the m icrostrip line
with a copper sh o rt over th e OMSS gap a re th en
9
_
(D 'r - D r )
5 u - ~ ( i - D R)
9
—
D't
521 ~ D r
,A
^
(4A)
where D'T is th e norm alized voltage signal transm itted through th e m i­
crostrip an d m easurem ent setup, and D'R is th e normalized reflected voltage
signal through th e same.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 4. Experimented Characterization
76
The copper electrode over the gap was then, replaced w ith the illumi­
nated OMSS, and th e m easurem ent was performed a th ird tim e at the same
frequency. This procedure was developed to isolate, or de-embed, the re­
sponse of the OMSS from th e response of the m icrostrip line and the mea­
surem ent setup. The transm ission and reflection of the OMSS are then
{D"r - D'r ) „
D'±
S u ~ (i - d 'r ) ; 521 “
(4‘5)
w here D'-f is th e norm alized voltage signal tran sm itted through the OMSS,
microstrip, and m easurem ent setup, and D"R is th e normalized reflected
voltage signal through th e same. To determ ine Soi and Su as functions
of frequency, this series of steps was then repeated, stepping the microwave
source sequentially th ro u g h th e frequency range of interest. The measure­
m ents were triggered a t a fixed delay tim e after laser excitation of the
OMSS to ensure th a t th e conditions were identical betw een measurements.
The above procedure relates the results of OMSS transm ission and re­
flection, or S2i and Su- However, other properties of OMSS’s besides fre­
quency response can be m easured by this method. At a constant microwave
source frequency, th e delay tim e of the gated detectors can be swept through
th e duration of the conducting state of the OMSS, giving th e amount of re­
flection and transm ission for different frequencies as a function of the con­
duction state. At a fixed microwave frequency, th e laser pulse intensity can
be varied and gated detection performed a t a fixed tim e sifter laser excita­
tion, giving th e S p aram eters of the device as a function of deposited laser
energy.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Chapter 4. E xperim ental Characterization
77
4.2.2 M easurement Results
Figure 4.4 shows th e insertion, loss of th e device and m easurem ent system,
as measured by the microwave detectors. The system in sertio n loss is rep­
resented as a ratio of th e m easured power transm itted th ro u g h th e device
to the m easured power incident on th e device for each of th e three experi­
mental setups described in th e previous section.
The d ata points were connected by lines to clarify th e different data
sets. The first set of data, m arked by the line labeled “th ru ,” was taken
with the th ru line attached to the m easurem ent setup. The next two data
sets were tak en w ith th e microstrip line alone, and w ith th e m icrostrip line
and activated OMSS, respectively, attached to the m easurem ent setup. The
thru-connected d ata set did not indicate a constant, norm alized value of 1.0
because of loss due to multiple scatterers in th e microwave signal p ath be­
tween the directional coupler and th e crystal detector. The bandw idth limit
of the m easurem ent system was due to the transm ission line discontinu­
ities and, as seen by th e transm ission drop of the th ru line in Fig. 4.4, was
3 dB at 9 GHz. As expected, the sets of d ata w ith the m icrostrip and OMSS
show a transm ission attenuation, or insertion loss, g reater th a n the th ru
line. From th e above d ata we can derive the transm ission function of the
microstrip an d the OMSS.
The frequency-response calculations presented in Fig. 4.5 were derived
from Fig. 4.4 an d show the transm ission of the m icrostrip line w ith illu­
minated OMSS, (“both”) the transm ission of the m icrostrip line without
OMSS, and th e transm ission (521 ) of th e illum inated OMSS alone, as a func­
tion of frequency.
The lines shown in Fig. 4.5 are w eighted least-square fits to indicate
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
78
Chapter 4. E xperim en tal Characterization
0.8
c
■o
(3
C
0.6
w
0
Thru
1
#«
0.4
M icrostrip
£
E
w
1 0.2
M icrostrip and sw itch
0
5
o
CL
E7GS2
0.0
0
2
4
6
8
F re q u e n c y (GHz)
Figure 4.4: D a ta used to derive S param eters of OMSS and microstrip.
The “th ru ” connected m easurem ent calibrates th e m easurem ent system.
The “m icrostrip” an d “microstrip and switch” m easurem ents allow th e mi­
crostrip tran sm issio n and OMSS transm ission functions to be determ ined
separately.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
79
Chapter 4. E xperim ental Characterization
th e general tren d of the data. The d a ta were weighted by th e m easure­
m ents in Fig. 4.4 to reflect the increased error a t lower signal levels. The
linear fit of the d a ta marked by crosses shows th e transm ission of th e illu­
m inated OMSS together with the m icrostrip transm ission line on which it
was mounted. This line demonstrates a n increasing am ount of microwave
signal attenuation a t higher frequencies. The response of the m icrostrip
mount was th e n de-embedded from the combined response of the m icrostrip
and OMSS and m arked by triangles. The linear fit of th is d ata is nearly
parallel to the lin ear fit of the combined data. This reveals th a t, for this
m easurem ent setup in this frequency range, the attenuation is prim arily
due to the m icrostrip transm ission line an d not the OMSS. The linear fit of
the data m arked by diamonds shows a nearly constant insertion loss due
to the OMSS a t frequencies <9 GHz. The bandwidth lim it of th e OMSS,
which would be indicated by a decreasing
S o
i value as frequency increased,
m ust therefore be above the 9-GHz bandw idth of the windowed m easure­
m ent system.
To verify th e accuracy of some of th e presented results, other conven­
tional methods were used. Only the device configurations th a t involved
a n illum inated OMSS required the netw ork analysis procedure described
above. The thru-line configuration and th e microstrip line w ith copper foil
substituted for th e OMSS are both stan d ard LTI microwave devices and
can be m easured statically, without the need for pulsed laser illum ination.
This allowed u s to verify our m easurem ent process by using a commercial
20-GHz vector netw ork analyzer on th ese configurations. A linear fit to
th e magnitude of th e transm itted and reflected vector param eters (S2 1 and
5u ) as m easured by th e vector netw ork analyzer agreed w ith th e weighted
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
80
Chapter 4. E xperim ental Characterization
1.0
CM
CO
O
0 .8
CO
to
OMSS switch
E
CO
c
CO
Microstrip
Both
0.6
E7651
Frequency (GHz)
Figure 4.5: S2i p aram eters of activated OMSS an d microstrip. These d ata
were derived from th e d ata in Fig. 4.4 and dem onstrate that the m icrostrip
attenuation dom inates the illuminated OMSS attenuation.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C hapter 4. Experim ental C haracterization
81
linear fit to our d ata w ithin 1 dB. Another verification method utilized e n ­
ergy conservation. The sum of th e reflected and transm itted signal pow er
should be equal to the power incident on th e device m inus power absorbed
and radiated. Indeed, neglecting the absorbed and radiated power, our com­
bined transm itted and reflected power did equal th e power delivered from
the source to a high degree of accuracy.
4.3 General Linear Device Measurements
Based on th e theory developed in Ch. 3, we present a novel m easurem ent
technique to characterize lin ear microwave devices whose frequency depen­
dent transm ission properties rapidly change in time. This m easurem ent
technique uses the generalized 2-D S param eters S(cu\t) , and allows th e
device’s transm ission function to be determ ined even if th e changes sp a n a
microwave cycle or less. The device we characterized was an OMSS config­
ured as a series elem ent on a microstrip transm ission line.
After optical illum ination, th e carrier recombination mechanism causes
the free carrier density in th e bulk to decay approximately exponentially.
The carrier recombination drives the OMSS to its off state because th e b u lk
m aterial conductivity is proportional to th e carrier density. Even m aterial
w ith long carrier lifetimes, such as undoped Si whose carrier lifetim e is
on th e order of microseconds, decay much faster th a n the millisecond m ea­
surem ent tim es of conventional microwave te st equipm ent (e.g., th e tunedreceiver system of a vector netw ork analyzer) [136]. To m aintain a con­
sta n t on state, an initial consideration is th e use of a constant illum ination,
however, th is is difficult or even impossible to attain , and even if achieved,
detrim ental to performance for a t least two reasons: the typical process for
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
C hapter 4. E xperim ental Characterization
82
creating fast, high-contrast optical rise-tim es is incompatible w ith long opti­
cal pulses [137], and for long optical pulses the absorbed illum ination power
required to achieve adequate carrier densities would be excessive an d lead
to therm al problems [138]. Therefore th e illum ination is necessarily pulsed
and the OMSS’s on-state is tra n sie n t in nature.
4.3.1
Experim ental Setup
A system to m easure the tim e an d frequency variations of a microwave de­
vice’s tran sfer function using envelope-detection (asynchronous) m ethods
is shown in block-diagram form in Fig. 4.6. This method did not require
equipm ent capable of m easuring th e am plitude and phase of 10 GHz m i­
crowave signals, rath e r it only n eeded to m easure th e change in am plitude
and phase of th e signal. This h ad th e advantage of being compatible w ith
easily-available, inexpensive m easurem ent equipment, however th e m ea­
surem ent was indirect and therefore more prone to error, and it w as unable
to follow th e rap id signal change th a t occurred during the 30-ps OMSS tu rn ­
on. A photograph of the experim ental setup is shown in Fig. 4.7. The DUT
for which we m easure the two-dim ensional tran sfer function is shown a t
th e center of th e figure (in our case, a n OMSS). The OMSS is triggered by a
laser pulse, causing a single-frequency microwave signal of constant power
and known phase to propagate from th e microwave generator th ro u gh th e
DUT.
If equipm ent is available w ith th e bandw idth to m easure the tra n sm it­
ted and reference microwave signals directly, th en more direct m easu re­
m ents w ith less error contributions can be performed, as shown in Fig. 4.8.
Here the amplitude/power and p h ase detectors are eliminated, and th e two
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
83
Chapter 4. E xperim ental Characterization
Timing
system
Laser system
with SB S p u lse
com pression
38 MHz
10 MHz
M icrowave
generator
0.1
Directional
coupler
detecto
to 20
GHz
detector;
• Low frequency signal
■Laser pulse
■Microwave signal
iW SaO SS
P h a se
shifter
Figure 4.6: Block diagram of a test and m easurem ent system capable of
m easuring tim e- an d frequency-varying DUTs. The m easurem ent is asyn­
chronous, in th a t th e power (envelope) is detected rath er th an the m i­
crowave signal electric field. Thus the oscilloscope m ust only span the m od­
ulation bandwidth.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
C hapter 4. Experim ental Characterization
84
Z2308
Figure 4.7: Photograph of experim ental setup for m easuring the transfer
function of OMSS’s. In th e foreground on th e optical table is the test fixture
and the microwave cabling. In the background is the laser system th a t
creates the 200-ps fast risetim e optical pulse to trigger th e OMSS’s.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C h apter 4. Experim ental Characterization
85
signals can be directly m easured an d com pared either by th e oscilloscope (if
it is a two-channel unit) or post-processing can be performed on th e dataacquisition computer. This arrangem ent, w ith a 20-GHz sam pling oscillo­
scope, was th e one primarily used for th e m easurem ents shown in subse­
q uen t figures. An advantage to using a sam pling scope is th e increased
resolution and reduced noise from repetitive averaging, however a disad­
vantage is th a t the device optical trigger a n d the incident microwave signal
m u st be synchronous. If this is impossible or impractical, a single-shot tra n ­
sient digitizer m ust be used. E arlier experim ental m easurem ents for this
thesis did not have the trigger and signal synchronized, and for th a t reason
we used a 6-GHz single-shot scope. This allowed m easurem ents to be per­
formed, b u t the noise was significant due to th e lack of averaging, and the
device bandw idth was comparable to the scope which led to high-frequency
attenuation, fu rth er exacerbating th e noise problem.
W hen m easuring the S(uj.t) of an OMSS, the signal transm ission in­
creases in am plitude as the generated carriers increase the conduction cur­
re n t and th e phase of the tran sm itted signal shifts due to the change from
capacitive to conductive coupling. This is shown in Fig. 4.9. Since this is a
four-hour d a ta capture (sampling oscilloscope set to infinite persistence) of
a switched 1-GHz sine wave input, im p o rta n t operating p aram eters can be
observed. The combination of tim ing jitte r an d 4-hour drift causes th e hori­
zontal blurring of the sine wave of 100 ps. The combined OMSS tu rn -on rate
and drift and jitte r of the illum ination w ith respect to th e microwave sig­
nal/scope trigger results in the approxim ately 1-ns-wide tran sitio n region.
The ON/OFF-state isolation a t 1 GHz can be calculated by a ratio of the am ­
plitudes of th e signal before and after switching, and for this OMSS results
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 4. E xperim en tal Characterization
8 6
5 Hz
T im ing
s y s te m
L a ser s y ste m
with S B S p u lse
c o m p r e s s io n
38 M H z'
10 MHz
M icrow ave
g e n e r a to r
0.1
D irection al
c o u p le r
GHz
20-GH z
sa m p led or
7-GHz
s in g le -s h o t
o s c illo s c o p e
■Low frequency signal
■Laser pulse
i Microwave signal
TB SS-
Figure 4.8: Block diagram of a synchronous te st and m easurem ent sys­
tem capable of m easuring time- and frequency-varying DUTs. This sys­
tem is shown using either a sampling scope, requiring the trigger and m i­
crowave signal be in phase, or a single-shot digitizer, which doesn’t require
the phase-locked signal b u t has degraded noise values due to the lack of
averaging.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
87
C h apter 4. Experimental Characterization
in 5 dB isolation at 1 GHz. A ratio of the amplitude of the sine wave incident
on th e OMSS (inferred from th e reference signal) and th e sine wave after
th e OMSS can give an approxim ate value of the series resistance in the
lumped-element model, relative to the transm ission line impedance. From
the d a ta shown here it can be concluded th a t the series resistance was much
less th a n the transm ission line characteristic impedance Z0 = 50ft. Finally,
the complex impedance of th e OMSS gap is calculable from the signal ratios
and relative phase shift before and after illumination and the switch resis­
tance before and after iUumination. From these d ata the switch impedance
is approximately 1 ft, due prim arily to the large series contact resistance.
1.5
1.0
a
0.5
I
0.0
• PK
■fi
< -0.5
-
1.0
-1.5
0.0
E9652
0.5
1.0
1.5
2.0
T im e (ns)
v
'
Figure 4.9: Signal transm ission during triggering of the OMSS. Notice the
nearly 7r/4 phase shift as th e transm itted signal transitions from capacitive
to conductive coupling.
A fter illumination stops, carrier generation ceases and the carrier tem ­
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 4. E xperim en tal Characterization
88
poral dynam ics are th en a strong function of the energy band diagram a t the
m etal sem iconductor contacts. The electric field of the incident microwave
signal will sw eep carriers from one (possibly blocking) contact to th e other
while a t th e sam e tim e carriers will recombine. As carrier density falls, less
carrier screening of th e built-in m etal-sem iconductor contact potential will
occur and band-bending will begin to re-establish itself. These and other
effects occur on picosecond to nanosecond time-scales m aking th e OMSS
an interesting device to which we can apply this linear tim e-vaiying m ea­
surem ent technique. The signal from th e generator also travels through
a separate, p arallel reference arm consisting of an amplifier and a phase
shifter. The tw o arm s split a t th e directional coupler and can be recom­
bined and com pared to one another in am plitude (at the diode detectors)
and phase (at th e m ixer/phase detector). Alternatively, each microwave sig­
nal can be first m easured directly by a scope of sufficiently high bandw idth
(see Fig. 4.8) a n d subsequently compared.
The tim in g system synchronizes th e triggering of the DUT w ith the
phase of th e microwave signal incident on it, so th a t each trig g er occurs at
the same p h ase of th e microwave signal. This allows sam pling oscilloscope
m easurem ents, which improves the m easurem ent resolution over single­
shot digitizing oscilloscopes. The synchronization was done by designing a
phase-locked loop th a t locked th e 10 M Hz ± 10 Hz microwave signal refer­
ence to the 37.998932 MHz ± 2 Hz of th e m aster laser oscillator.
The signal-m easurem ent process proceeds in the following step-anddwell m anner: The microwave generator is set to a single, given frequency
of known p h ase and amplitude. T hen th e DUT is triggered, an d the tempo­
ral evolution of th e transm itted signal’s am plitude and phase is m easured
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Chapter 4. E xperim en tal Characterization
89
and compared w ith th e reference arm signal for th e tim e duration of in te r­
est. The microwave generator then steps to th e next microwave frequency,
and the process rep eats for the appropriate range of frequencies. The d a ta
are then reduced to a complex (amplitude and phase), two-dimensional
transfer function S(u>, £), which can th en be analyzed for bandw idth a n d
modulation features. For an OMSS, th e tran sfer function would be expected
to show an exponentially decaying m odulation due to carrier recom bination
and a (possibly changing) bandwidth. The S( uj, t) function can th en be m od­
eled by a lum ped-elem ent circuit consisting of a (possibly time-changing)
reactance an d a tim e-changing resistance. The values of these elem ents can
then be associated w ith such physical OMSS properties as non-ohmic con­
tacts, thickness, gap length, and width. By appropriately modifying th ese
param eters, th e values of the model elem ents can be controlled and th e
bandwidth of th e OMSS optimized.
Notice th a t for th is 2-D m easurem ent system , signals are repeatedly
applied a t different tim es and frequencies, as opposed to 1-D m easurem ents
(single frequency for modulator m easurem ents, single time delta functions
for filter m easurem ents), as described in the previous chapter. As for im por­
ta n t m easurem ent figures of merit: dynamic range and noise level consid­
erations are identical between 1-D an d 2-D m easurem ents on a signal-bysignal basis (th a t is, sampling directly improves noise level by th e square
root of the n u m b er of samples n, and dynamic range is proportional to th e
equivalent n u m b er of bits per sample) however for 2-D m easurem ents, in ­
creasing the sam pling rate or the bits per sam ple adds to the m easurem ent
time and storage by th e square of these two param eters, instead of linearly
as with the 1-D case. Thus for a given m easurem ent tim e or storage capac­
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
C h apter 4. Experimental Characterization
90
ity, the dynamic range and noise level will be worse for 2-D measurements.
As d ata acquisition speeds up, and storage capacity grows, these factors will
decrease in importance. However, as a point of interest, th e data required
to adequately model the OMEGA switches and to generate the plots for this
thesis was compressed to approxim ately 10% to fit unto a single 650 Mb
CD-ROM. The amount of personal (desktop) processing power and storage
capacity required to calibrate the m easurem ents and to calculate th e cor­
rected transm ission functions w ith th is d ata would have been unheard of
ju st 20 years ago.
4.3.2
System Calibration
F irst, th e measurement system shown in Fig. 4.8 is calibrated by m easur­
ing the transfer function w ith no DUT, this allows th e DUT response to be
de-embedded from the system [139]. Then a comparison between S ampli­
tude m easurements taken by our system (on the tim e-invariant test fixture)
and S{ uj) measurements on a commercial 20-GHz netw ork analyzer is per­
formed. Since the te st fixture is a tim e-invariant device, th is m easurem ent
can be compared with stan d ard netw ork analysis. The transfer function
of the microstrip fixture th a t holds th e OMSS is m easured by replacing an
actual OMSS with something approaching an ideal OMSS, called a “th ru ”.
This th ru is created by placing a m icrostrip line w ith no gap in the fixture,
or holding a small copper b u tto n having the same dimensions as the OMSS
across th e microstrip line gap in th e fixture, either by soldering or by me­
chanical pressure.
The transfer function m agnitude of this fixture w ith a thru, comparing
a commercial network analyzer and our test system, is shown in Fig. 4.10.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
91
Chapter 4. Experim ental Characterization
The absolute value of the relative error between th e two m easurem ents is
also shown, and indicates good agreem ent to frequencies above 10 GHz,
past w hich th e frequency response of the test fixture is significantly re­
duced.
©
©
E
2
to
Q.
ch
o
©
■D
IS(cato)l parameter
IS(C0)l parameter
Error (relative)
C
O)
co
JWVU WAj
-
0.2
5
E9650
10
15
20
Frequency (GHz)
Figure 4.10: Comparison of th e m agnitude of the frequency response, be­
tween a commercial 20-GHz netw ork analyzer and our m easurem ent sys­
tem.
The phase of th e tran sfer function was also calibrated, as shown in
Fig. 4.11. The phase m easurem ents show excellent agreem ent (within 5°)
w ithin th e same frequency ran g e th a t the m agnitude m easurem ents also
agree.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
92
Chapter 4. E xperim ental Characterization
30
20
o
10
T"“
CM
CO
o
©
CO
CO
£
-10
S(Qto) parameter
S(o)) parameter
-20
-30
0
E96S1
5
10
15
20
Frequency (GHz)
Figure 4.11: Comparison of th e phase of th e frequency response, betw een a
commercial 20-GHz network analyzer an d our m easurem ent system.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C h apter 4. Experim ental Characterization
4.3.3
93
Experimental Procedure
All m easurem ents were perform ed by placing th e device in the system an d
m atching
the impedance of th e ports of the device w ith th e ports of th e te s t
system so as to minimize th e am plitude of th e reflections. Then relative to
th e trigger for the DUT, th e incident microwave signal was stepped through
a range of frequencies and on one channel of th e scope th e output signal was
m easured over a range of tim e delays by setting th e microwave frequency
generator reference and th e sam pling oscilloscope delay. On the other chan­
nel a reference signal from th e generator was m easured, isolated from th e
signal arm.
To calculate the m agnitude of S(u. t), the am plitude ratio of the device
signal and reference arm signal was divided by th e am plitude ratio of th e
calibration (“th ru ” or fixture) signal and reference arm signal. To calculate
th e phase of S(u:, t) we subtracted the difference between the calibration
phase from the difference betw een the signal and reference phases. This
results in a phase difference calculated between th e reference planes of th e
calibration fixture. In our case th e reference planes were further ap art th a n
th e OMSS. To shift the m easurem ents of S( uj, t) to th e OMSS we m ultiplied
each frequency by
w here
o = L/up.
(4.6)
L is the difference betw een th e m easured reference plane and the OMSS
contact, and up is the phase velocity of the given frequency. We assumed th e
te st fixture was lossless an d did not account for the change in m agnitude
caused by the shift in th e m easurem ent plane.
In calculating S{ui,t) from th e m easured data, interpolation betw een
m easurem ent points was sometim es required. To accomplish this, the am -
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 4. Experim ental Characterization
94
plitude and phase a t each point of th e m easurem ents were fit to a linearlychirped sine wave with linear atten u atio n ram p. For variations in the signed
th a t were more swift than the sam pling rate, this provided a sufficiently ac­
curate determ ination of the system function S(uj, t) to allow calculation of
a lumped-elem ent fit with a large degree of confidence. If th e variations in
frequency and/or phase were swift enough to prevent an obvious distinction
betw een am plitude and phase changes, th e analytic signal was m easured
w ith the
sa m p lin g
scope (by taking two sequential m easurem ents of a sig­
nal, tt/4 radians out of phase w ith each other). Following this, S{uj,t) was ob­
tain ed by comparing the partial overlap of th e low-frequency signals and by
smoothing. This procedure required significantly more com putational tim e
and interm ediate data storage th a n th e fitting procedure, and resulted in
a transfer function th at often did n o t fit a simple lumped-element model
w ith a high degree of confidence. However, it allowed determ ination of
S(u,\ t) near the tum -on (trigger) point of th e OMSS, allowing characteri­
zation near this rapid change in th e tran sfer function.
4.3.4
Characterization Results
W ith these calibration and test m easurem ents it was th en possible to deter­
m ine the S{ uj. t) of the OMSS’s. Fig. 4.12 shows the S a t S{ uj. 5 ns ), th a t is,
after sufficient tim e delay (5 ns) to allow initial transient carrier dynamics
to disappear, leaving only carrier drift and recombination. The plot shows
th a t the new er (L981029) switches have slightly improved ohmic contacts
(increased transm ission at frequencies below 4 GHz compared to the older
(L980214B) switches. The am plitude of th e frequency response of the newer
OMSS’s also rem ained higher th a n th e older switches a t high frequencies,
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
95
Chapter 4. E xperim ental Characterization
representing g reater bandwidth. The dip in th e transm ission a t 5.5 GHz
and 11 GHz is due to a parasitic resonant mode in the test fixture. T he top
curve is th e S( uj) of th e te st fixture alone, an d is th e best possible tran sm is­
sion the OMSS’s could achieve.
System reference
1.0
0.9
0.8
October —
1998 switch
0.7
February
1998 switch
0.6
0.5
0.4
E9671
0
2
4
6
8
10
12
Frequency (GHz)
Figure 4.12: Frequency response of th e m icrostrip test fixture alone (solid)
and with old (gray) an d new (dashed) OMSS’s.
As m entioned in C hapter 2, it w as suspected th a t the band-bending
due to the non-ohmic contacts between the Si an d the m etal would cause a
depletion region to reform after illum ination h ad ceased, during electrical
signal transm ission, causing a strong phase slew between different spectral
components of th e signal due to the tran sitio n from capacitive to conduc­
tive “coupling” across the cap [140]. The following plot, Fig. 4.13, graphs
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C h apter 4. E xperim ental Characterization
96
line-outs of the m agnitude of S( uj. t ) along th e frequency axis a t successive
points in tim e after th e trigger. The reforming of the depletion region a t
th e OMSS metal-semiconductor contacts is apparent. This changing tran s­
m ission response causes signal dispersion, lengthening th e risetim e of the
shaped electrical pulse transm ission. Fig. 4.13 shows clearly th a t the band­
w idth of the device, defined as th e range of frequencies w ithin which the
m agnitude of the tran sfer function is within 3 dB of the peak, can stay con­
sta n t or even increase over time. This can occur although the amplitude
an d phase of the tran sfer function are changing rapidly. This dispersion re­
sults in detrim ental changes to th e low-frequency as well as high-frequency
components of the signal, which m ay not be observable by time-windowed
or other conventional characterization techniques th a t provide bandwidth
m easurem ents only.
As expected the phase of S( uj. t) shown (again by tim e slices) in Fig. 4.14
also shows the change in time, due to the opening up of th e depletion region.
For th is m easurem ent only one point per 0.25 GHz was acquired, so the line
is fit to three points. However th e points are an average of 256 samples, the
goodness-of-fit p aram eter R2 for these lines averaged 0.88 and the vertical
erro r bars for each point are approximately ±0.5°. This plot in conjunction
w ith Fig. 4.13 completely defines the S(ui, t) of th e OMSS as a tim e changing
filter, over the tim e span and frequency range th a t was m easured.
To indicate th e ability of th e m easurem ent technique to operate during
optical illumination, th e full S was measured during optical illumination, as
shown in Fig. 4.15. The capacitive coupling before triggering is followed by
th e typical satu rated conductive transfer function after illumination. How­
ever for this particular set of switches, the m easurem ent revealed some
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
97
C hapter 4. E xperim ental Characterization
1.0
47 ns time delay
57J
<D
-a
3
"cL 0.9
E
cB
cq
97107,
117.
C/3
127
0.8
E9707
0
4
8
12
Frequency (GHz)
Figure 4.13: The decrease in th e am plitude of the low-frequency tran sfer
function as shown here is consistent w ith the reformation of a depletion
region.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission .
98
Chapter 4. Experim ental Characterization
-113
-1 1 4
127 ns
-115
Time delay after trigger
£ - 116
£C8 -1 1 7
a.
117-
JS
-1 1 8
107.
-1 1 9
•47-
-120
1.00
E968I
1.25
1.50
Frequency (GHz)
Figure 4.14: Temporal evolution of the phase o f S shown by line-outs along
the tim e axis, dem onstrating the reformation of the metal-semiconductor
depletion region capacitance.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
99
C hapter 4. Experim ental Characterization
rem nant capacitance after illum ination, indicated by th e dip in the transfer
function along the low frequency (0.5 GHz) line. This indicates poor qual­
ity m etal contact evaporation, w hich was confirm ed by subsequent m ea­
surem ents of contact resistances w ith large values an d highly nonlinear
current-voltage curves [141, 142, 143].
A fter
illumination
Before
illumination
Frequency (GHz)
E9949
Figure 4.15: Full
t) m agnitude plot of an OMSS before and after optical
illumination.
The 5 m agnitude plot in Fig. 4.16 is characteristic of a n OMSS th a t
is under-illum inated. In th is case, th e pulse energy was 10 n J which was
significantly lower th a n th e u su al minimum of 1 m J. The increased series
resistance creates an impedance m ism atch along th e transm ission line be­
tw een signal generator an d oscilloscope, leading to a standing wave. The
standing wave causes the m easured signal to fluctuate as the distance be­
tw een generator and OMSS changes in units of w avelengths, creating con­
structive and destructive interference.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
100
C hapter 4. E xperim ental Characterization
IS21(w,t)l
0 Time Delay (ns)
Frequency (GHz)
Figure 4.16: Full S( uj. t) magnitude plot of a n under-illum inated OMSS,
showing am plitude variations consistent w ith a n increased on-state resis­
tance an d consequently increased reflection coefficient.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 4. Experim ental Characterization
101
4.4 Model Synthesis
A device model is necessary, both in the optical regime an d the microwave
regime, as a method for improving the OMSS properties an d performance.
From the m easurem ents of Sec. 4.3 it is possible to generate a time-varying
low-pass filter model th a t aids in optimizing th e transm ission performance.
The model will indicate w hat aspect limits performance (e.g., transm ission
bandwidth) via its lum ped-elem ent equivalent in the model. For exam­
ple contact resistance betw een the m etal contact and th e semiconductor
would evidence itself as a series resistance from electrode to electrode. Also,
th e microwave skin depth is very large in th e semiconductor, compared to
th e m etal because the carrier density is a t least two orders of m agnitude
smaller. This creates a n inductive effect in th e OMSS th a t is approximately
equivalent to a series inductance element in the model. The complex per­
m ittivity of th e carrier plasm a is also a frequency-dependent contributor to
th e series impedance of th e device. Energy-band differences between the
bulk semiconductor and th e m etal interface create depletion regions th a t
mimic lumped-element capacitors in shunt w ith th e series inductance. The
physical dimensions of the OMSS differ som ewhat from th e transm ission
line leading to field and cu rren t disturbances th a t can be modeled as par­
asitic reactances. M isalignm ent when m ounting to the m icrostrip line can
contribute to this effect as well.
The complete m easurem ent of S(u, t) perm its us to determ ine the val­
ues of the lumped-elem ents and how those values evolve with time. A
lumped-element model th a t fits our observed d ata very well is shown in
Fig. 4.17. Based on these m easurem ents, th e depletion region capacitance
was found to exponentially decay from an in itial value of approximately 100
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C h apter 4. Experimental C haracterization
102
pF to around 100 fF. This decrease is caused by the optically-generated car­
riers being swept from th e depletion region, enlarging the separation of car­
riers. This increase in sep aratio n will decrease th e capacitance. The contact
resistance was also calculated to be around 1 Q and to be tim e-invariant.
^contact
-J
L
Rbulk
L P'asma
—
o
Rcontact
o
■
o
Figure 4.17: Lumped elem ent m odel of an OMSS, compatible w ith the m ea­
sured S . The resistance RtiUk initially drops upon application of the optical
trigger, an d subsequently re tu rn s to the intrinsic, unillum inated value. The
contact capacitance
C c o n ta c t
drops immediately after th e trigger. The other
two elements remain approxim ately tim e-invariant over the m easurem ent
range.
4.5 Frequency Response Improvement
Based on the m easurem ent of S(cj.t) and the development of a suitable and
accurate time-varying lum ped-elem ent model, the fabrication process was
altered w ith a view tow ard improving performance. A figure of m erit for
th e OMSS performance is bandw idth, calculated a t the 3-dB point. The
bandw idth was improved from 3 GHz (see Fig. 4.2)to over 5 GHz, w ith more
improvem ents possible.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
Chapter 4. E xperim en tal Characterization
103
The OMSS’s 3-dB bandw idth of approxim ately 5 GHz agrees well with
the observed bandw idth loss of shaped pulses in th e OMEGA pulse-shaping
system (Fig. 4.18). M easurem ent of optical an d electrical tem poral pulse
shapes a t different stages in our pulse-shaping system indicate th a t the
primary bandw idth lim itations occur during transm ission of our electrical
pulse shapes through the OMSS’s. W hen pulse shaping was first imple­
mented on OMEGA, the m easured atten u atio n a t 6 GHz (corresponding to
30-ps pulse rise- and fall-times) was more th a n 12 dB through th e OMSS.
This is much g reater th an the atten u atio n of th e other components in the
pulse-shaping system: e.g., microstrip transm ission line, microwave tran ­
sition from m icrostrip to coaxial line, and electro-optic modulator. By im­
proving th e OMSS’s physical properties, th e 3-dB bandw idth of the OMEGA
pulse-shaping OMSS’s as implemented h as been increased to over 5 GHz.
The full bandw idth is currently as broad as th e next-m ost-lim iting device
in the pulse-shaping system (believed to be th e electro-optic modulator).
Modeling [144, 145] indicates th a t a m uch larg er bandw idth is theoretically
possible; thus, efforts were taken to isolate an d comprehensively m easure
their microwave transm ission bandw idth. This characterization m ade pos­
sible the system atic optimization of the m any param eters of th e OMSS,
such as gap w idth, microwave skin depth versus optical absorption depth,
and metalsemiconductor contact preparation.
4.6 Summary o f Characterization Results
We described a novel m easurem ent technique and te st system to obtain
the vector (am plitude and phase) tra n sie n t frequency response of a mi­
crowave device based on the theory of generalized S(uj.t) p aram eters from
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
104
C h apter 4. Experim ental Characterization
(a)
(b)
Switch frequency response
1/3
1
Switch frequency response
1
Fit
3a
e
3
e
a zjr
3C ®
T3
.
Fit
GHz
GHz
Input
es
Input
Output
0
1
— Output
\
0
2
3
4
5
1
2
3
4
5
Figure 4.18: Improvement of OMSS frequency response from a 3-dB band­
w idth of 3 GHz to over 5 GHz. The graph on th e left shows input and
output signals a t the beginning of the pulse-shaping campaign, in 1995. By
dividing the spectrum of the signals, th e approxim ate bandwidth can be
indirectly measured. The graphs to the rig h t show a more recent m easure­
m ent, showing the improved bandwidth.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
C h apter 4. Experim ental Characterization
105
Ch. 3. We also dem onstrated th a t the method was capable of observing the
tem poral modulation as well as th e bandwidth lim itations of time-varying
bandwidth-limited devices such as optoelectronic OMSS’s. W ith this sys­
tem , microwave devices whose tran sien t bandwidths were only approxi­
m ated can now be characterized and th u s optimized. This m easurem ent
technique is compatible w ith microwave devices th a t are e ith e r triggerable
and/or have a deterministic tim e evolution [146].
The measurem ent and fitted model in Fig. 4.19 are representative of the
resu lts of measuring the S of photoconductive OMSS’s. A m plitude m easure­
m ents such as this, along w ith phase m easurements, show th e establish­
m en t of capacitive coupling and the requisite am plitude an d phase changes
th a t will occur in the transfer function. These phenom ena a re difficult or
impossible to observe directly using conventional, windowed characteriza­
tion techniques. This technique allows unprecedented observation of tra n ­
sien t OMSS transmission function changes, which lead to m uch greater
possibilities in optimization and perm it deeper understanding' of device dy­
namics.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
Chapter 4. E xperim ental Characterization
106
M easured
100
S 21
ns
Model
a—t/X
100
S 21
ns
Z2319
G Hz
Figure 4.19: M easured and fit S( uj. t) , a n d a lumped-element model corre­
sponding to th e fit. The variable resistance h a s an exponential decay.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
107
Chapter 5
Summary and Conclusions
In th is Chapter we sum m arize the achievements, resu lts and conclusions
presented in th e thesis. We discuss research topics th a t hold promise for
yielding farth er OMSS performance improvements, and suggest alternative
area s of focus to which our m easurem ent technique m ay be easily applied.
5.1 Advancement o f Microwave Measurement Technique
O ur m easurem ents show th a t th e transm ission properties of OMSS’s change
a t least on th e order of picoseconds after optical triggering, m eaning the de­
vice is not tim e-invariant for microwave signals. Any microwave device like
th is th a t rapidly changes its temporal m odulation and frequency response
over time-periods comparable to the microwave signal cannot be fully char­
acterized w ith conventional windowed S p aram eter techniques. They can,
however, be characterized w ith the technique of tim e-varying S param eters
S(co,t) th a t we have described in Ch. 3. We provide some of the impor­
ta n t properties of th e S param eter and show sim ilarities to conventional
S-param eter analysis th a t preserve most features of the fam iliar Fourier
transform tables. U sing the S technique, the tra n sfe r function of an simple
lin ear time-varying device is calculated and an example signal is propa­
gated through the device. To dem onstrate th e lim itations of windowing, we
apply the time-frequency representation of an in p u t signal to S and show
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 5. S u m m a ry and Conclusions
108
the lim ited ability of the resulting output signal to follow both tim e and
spectral variations in the device.
5.2 Construction of Measurement System
A system to m easure the tim e an d frequency variations of a microwave
device’s tran sfer function S(u;, t) was designed, constructed and employed
for bandw idth m easurem ents of polysilicon switches, OMEGA OMSS’s, and
integrated-optic modulators. The system was calibrated an d compared with
conventional S-param eter m easurem ent tools such as netw ork and spec­
trum analyzers.
The m easurem ents on OMEGA OMSS’s revealed poor
(non-ohmic) metal-semiconductor contact conditions causing the reforma­
tion of a depletion region capacitance, which has a large and detrim ental
effect on th e am plitude and phase of th e frequency response. O ther effects
on the frequency response were identified and related to physical switch
param eters such as switch thickness and illum ination energy.
5.3 Complete OMSS Transmission Measurement
In Ch. 4 we describe in detail th e application of S to m easuring OMSS
transm ission functions, including th e arrangem ent and requirem ents of the
m easurem ent equipment. The m easurem ents are compared w ith conven­
tional windowed results, and it is shown th a t the conventional m easure­
ments have limitations th a t ours do not have, such as th e ability to measure
devices whose transm ission response (attenuation and dispersion) changes
during th e transm ission of only a single cycle of the signal. Standard filters
were m easured, both to verify w ith conventional m easurem ents th a t the
m easurem ents are accurate, and to calibrate the m easurem ent system for
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 5. S u m m ary and Conclusions
109
repeatability and th e determ ination of system resolution. M easurem ents of
OMSS transm ission functions were given an d comprehensively discussed,
with relevant features a n d im portant implications highlighted. A lumpedelement microwave model of an OMSS w as developed based on th e mea­
surements. The elem ents were correlated w ith physical switch param eters,
allowing the OMSS to be optimized more completely for the first tim e.
5.4 OMSS Optimization
Using a simple figure of merit, the microwave transm ission band w idths of
OMEGA’s OMSS’s have been improved from 3 to 6 GHz. This is m ainly
due to im provem ents in turn-on time, due to optimizing the stru ctu re ge­
ometry and im proving operating conditions (reduced gap length to 0.5 mm,
thinned switches to 0.5 mm, improved repeatability and uniform ity of il­
lumination by propagating through 400 fim-core fiber). However another
significant factor in device performance was found by improving th e m etalsemiconductor contact to create ohmic-like contacts, thereby reducing the
effect the re-establishm ent of the depletion region had on the switch tra n s­
mission bandw idth via a time-changing capacitance. The re-establishm ent
of the depletion region immediately after illum ination ceased led to a con­
tinuous variation in th e phase of the microwave signal, causing a timevarying phase chirp of th e different frequency components, resu ltin g in a
smearing of the tran sm itted pulse. These conclusions would be difficult or
impossible to reach w ithout the characterization technique described in this
thesis.
As of the end of 1998, due to im provem ents in OMSS bandw idth, the
frequency response of th e OMSS’s is no longer the prim ary limiting factor in
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter S. S u m m ary an d Conclusions
110
the optical pulse envelope bandwidth. Frequency response m easurem ents
performed on th e m icrostrip t r ansm ission lines, th e microwave connector
transitions from p la n a r to coaxial microwave propagation, and the electro­
optic modulator reveal th a t each of these devices contribute to th e lim ita­
tions on the final achievable optical pulse bandw idth, which is presently
approximately 6 GHz.
5.5 Further OMEGA. Switch Improvements
Based on the research presented in this thesis, some areas of the OMSS’s
performance have been identified as showing room for fu rth er im provem ent
by additional changes to th e ir design.
An increase in th e bias voltage would in general enhance switch perfor­
mance. The bias voltage is lim ited by th e critical breakdown electric field
across the gap [147]. Presently the voltage across the 0.5 mm gap is 75
volts. With a ten-fold increase in bias, it would still be less th a n h alf of th e
breakdown field an d device properties such as risetim e would improve. To
m aintain the m axim um voltage incident on th e integrated-optic m odulator
a t the half-wave voltage, the maximum reflection coefficient of the variableimpedance m icrostrip lines can be reduced. The reflection coefficient can
be reduced until th e unintended impedance deviations due to m anufactur­
ing processing (m illing or photolithography) are comparable to the desired
reflection impedances. A reduction in gap length on th e initially-triggered
OMSS would also improve risetime. To protect th e m odulator from large
transients, the gap of the second OMSS (closest to th e modulator) could
then be increased.
The m etal-sem iconductor interface u n d er th e m etal contacts has been
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 5. S u m m ary and Conclusions
111
identified as a major source of frequency-response limitations. By suit­
able design of th e energy bands and Fermi surfaces a t the interface, better
ohmic-like contacts can be achieved, even in nearly-intrinsic silicon. P re­
cise control of th e properties of this interface are difficult, however there
are many processes beyond those mentioned in Ch. 2 Sec. 2.10 and App. A
which can be employed to improve the I-V characteristics of the contacts,
such as high-energy ion im plantation, heavy doping of the surface of the Si
substrate ju st beneath th e contacts so as to increase the num ber of deeplevel defects, surface etching, passivation and possibly high-vacuum cleav­
ing and in situ m etal contact evaporation. Also, narrowing of the OMSS
w idth relative to th e m icrostrip line (using for example microstrip line ta ­
pers) allows an additional range of freedom to modify the trade-offs of width,
length, resistance and capacitance.
The overhead of having to m aintain a separate and physically-extensive
laser system ju s t to illum in ate th e OMSS’s has been a barrier to th eir wide­
spread use in industry, despite their promising an d unique operating p a­
ram eters. For OMEGA pulse shaping this has been less of an issue since th e
optical expertise was already in-house, b ut it is still undesirable, and is one
of the reasons for the c u rren t plans to replace the OMSS pulse-shaping sys­
tem with an all-electrical one. Presently the only way to create rapid (<30
ps) tum -on of a 1-micron-wavelength optical pulse w ith 100 microjoule-level
optical energy an d high co n trast (> 107) is to use a solid-state oscillator and
a regenerative am plifier followed by an SBS cell. The SBS nonlinear pro­
cess contributes significant jitte r to the trigger/tim ing system. However,
recently compact turn-key sources of (separately) femtosecond, nanojoulelevel IR laser pulses have been developed and are being improved in the ar­
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C hapter 5. S u m m ary and Conclusions
112
eas of reliability, cost, and performance. These sources, which include laser
diode arrays, fiber lasers, microchip lasers, integrated-optic lasers and op­
tical param etric devices, are still being actively researched and show great
promise as eventual photoconductive switch illum ination sources. Some of
these also hold out promise of monolithic fabrication of the pulse-shaping
system, from th e modulator to th e shaped-pulse generator, including the il­
lum ination source and optical pulse source to be shaped. This is perhaps the
greatest area of improvement, and such optoelectronic/photonic integrated
circuits are already being aggressively explored in other applications.
5.6 Application of S(uj, t) Measurement to Other Devices
The ability to follow the transient behavior of linear devices, for character­
ization purposes, opens up opportunities for more thorough understanding
of other devices besides OMSS’s. The current measurem ent system as de­
scribed was applied only to the transm ission of guided microwave signals.
However it is n atu ral to consider extending the measurem ent capabilities
to other frequencies, in fact this is routinely done at lower frequencies, e.g.,
speaker design, switched filter banks for communications, and for changing
sampling rates [148, 149].
At higher frequencies, photoconductive devices w ith faster carrier re­
combination tim es comparable to THz (submillimeter) frequencies would
be analogous in concept to the m easurem ents performed in this thesis. At
these higher frequencies the system would m ost likely operate in free-space
propagation mode, and would m easure transm ission and reflection. The
device to be m easured would be considered a distributed-element device,
and device physical param eters would be associated w ith features of the
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Chapter 5. Su m m ary and Conclusions
113
2-D tran sfer function, ra th e r th a n using th e interm ediate step of fitting
a lumped-element model. Besides photoconductivity, other non-electrical
tim e-varying processes (e.g., heat, pressure, m echanical change or m otion
[150]) would also induce th e device to behave as a linear, tim e-varying de­
vice, and characterization over th e tim e scale of those processes w ould be
aided by m easuring S . For devices w ith sm all duty cycles such as covert
radar, w here the device is only on very briefly and operation d u ring the
turn-on and turn-off tran sien ts is desirable [151, 152, 153], conventional
characterization is difficult and applying S m ay be useful.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
114
Bibliography
[1] C. Clark, E. Chauchard, K. Webb, K. Zaki, C. Lee, P. Polak-Dingles,
H. Hung, and H. Huang, “Investigation of a new optoelectronic cw m i­
crowave source,” Journal o f Lightwave Technology, vol. LT-5, pp. 388—
397, Mar. 1987.
[2] A. Rim, M. Weiner, R. Zeto, R. Youmans, L. Jasper, and B. Lalevic,
“Photoconductive nanosecond pulse generation utilizing radial tra n s­
mission lines,” IE E E Transactions on Electron Devices, vol. ED-37,
pp. 2506-2510, Dec. 1990.
[3] W. Nunnally, “High-power microwave generation using optically ac­
tivated semiconductor switches,” IE E E Transactions on Electron De­
vices, vol. ED-37, pp. 2439—2447, Dec. 1990.
[4] J. Thaxter and R. Bell, “Experim ental 6-GHz frozen wave generator
with fiber-optic feed,” IE E E Transactions on Microwave Theory and
Techniques, vol. MTT-43, pp. 1798—1804, Aug. 1995.
[5] C. F raser and M. Lancaster, “Microwave filtering realized through in ­
coherent optical processing,” IEEE Microwave and Guided Wave L et­
ters, vol. 7, pp. 225—226, Aug. 1997.
[6] B. Saleh and M. Teich, Fundam entals o f Photonics. New York: John
Wiley and Sons, Inc., 1991.
[7] R. H. Bube, Photoconductivity o f solids. N ew York: Wiley, 1960.
[8] A. Rose, Concepts in photoconductivity a n d allied problems, rev. ed.,
with corrections and new m aterial ed. H untington, NY: Krieger, 1978.
Includes bibliographies an d index.
[9] R. Simons, Optical Control of Microwave Devices.
Artech House, 1990.
Norwood, MA:
[10] W. Platte, “Optoelectronic microwave switching,” IE E Proceedings-J
Optoelectronics, vol. 132, pp. 126-132, Apr. 1985.
[11] I. Andersson, “Photoconductive devices for optical control of m i­
crowave signals,” Ph.D. dissertation, C halm ers University of Tech­
nology, Goteborg, Sweden, 1989.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
BIBLIOGRAPHY
115
[12] C. Lee, “Picosecond optics an d microwave technology” IE E E Transac­
tions on Microwave Theory a n d Techniques, vol. MTT-38, pp. 596—607,
May 1990.
[13] D. Chadha, S. Aditya, M. Ambe, an d G. Bamra, “Optically controlled
microwave attenuator,” Journal o f the Institution o f Electronics and
Telecommunications Engineers, vol. 41, pp. 151—155, Mar. 1995.
[14] A. Smirl, T. Boggess, S. Moss, an d I. Boyd, “Pulsewidth-dependence
of nonlinear energy deposition an d redistribution in Si, GaAs and Ge
during 1 p m picosecond irradiation,” Journal o f Luminescence, vol. 30,
pp. 272-289, 1985.
[15] K. Luke and L. Cheng, “Analysis of the interaction of a laser pulse
w ith a silicon wafer: D eterm ination of bulk lifetime an d surface re­
combination velocity” Journal o f A pplied Physics, vol. 61, pp. 2282—
2293, Mar. 1987.
[16] D. Sm ith, J. Knudsen, and S. Moss, “Nonlinear optoelectronic effects
in u ltrafast photoconductive switches,” in SP IE Interconnection o f
H igh Speed and High Frequency Devices and System s, vol. 947, SPIE,
1988, pp. 146-161.
[17] E. Sano and T. Shibata, “M echanism of subpicosecond eletrical pulse
generation by asymmetric excitation,” Appl. Phys. Lett., vol. 55,
no. 26, pp. 2748-2750, 1989.
[18] S. Alexandrou, C. Wang, R. Sobolewski, and T. H siang, “Genera­
tion of subpicosecond electrical pulses by nonuniform illum ination of
GaAs transmission-line gaps,” IE E E J. Quantum Electron., vol. 30,
pp. 1332-1338, May 1994.
[19] C. Wang, M. Curry, R. Sobolewski, and T. Hsiang, “Subpicosecond
electrical pulse generation by edge illumination of silicon and indium
phosphide photoconductive switches,” Appl. Phys. L ett., vol. 67, no. 1,
pp. 79—81, 1995.
[20] C. Lee, P. Mak, and A. De Fonzo, “Optical control of millimeter-wave
propagation in dielectric waveguides,” IEEE Journal o f Quantum
Electronics, vol. QE-16, pp. 277—288, Mar. 1980.
[21] N. Weber, “Two dimensional carrier-distribution of CW-controlled op­
toelectronic switches,” Archiv fu r Elektrotechnik, vol. 73, pp. 91-96,
1990.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
BIBLIOGRAPHY
116
[22] L. Mu an d W. Donaldson, “Sim ulating photoconductive switches in
a microwave transm ission line,” in 9th IE E E International Pulsed
Power Conference, IEEE, 1993, pp. 629—632.
[23] W. Donaldson, L. Kingsley, M. Weiner, A. Kim, and R. Zeto, “Electro­
optic im aging of the internal fields in a GaAs photoconductive switch,”
J. Appl. Phys., vol. 68, no. 12, pp. 6453-6457, 1990.
[24] Y. Horii, T. Matsuyoshi, T. N akagaw a, an d S. Kurazono, “Consider­
ation of th e effectiveness of the quasi-TEM approximation on m i­
crostrip lines w ith optically induced plasm a layer,” IEIC E Trans. F un­
damentals, vol. E76-A, pp. 1158—1160, Ju ly 1993.
[25] E. Sano and T. Shibata, “Fullwave analysis of picosecond photocon­
ductive switches,” IEEE Journal o f Q uantum Electronics, vol. QE-26,
pp. 372-377, Feb. 1990.
[26] E. Rhoderick, Metal-semiconductor contacts. Monographs in electrical
and electronic engineering, Oxford: Clarendon Press, 1980. Includes
index.
[27] P. Chattopadhyay, ‘Effect of localized states on the current-voltage
characteristics of metal-semiconductor contacts with thin interfacial
layer” Solid-State Electronics, vol. 37, no. 10, pp. 1759—1762, 1994.
[28] S. Sze, Semiconductor Devices: Physics and Technology. N ew York:
John Wiley and Sons, 1985.
[29] M. V. Sullivan and J. H. Eigler, “Electroless nickel plating for m aking
ohmic contacts to silicon,” J. Electrochemical Soc., vol. 104, pp. 226—
230, Apr. 1957.
[30] S. E. Thompson and F. A. Lindholm, “Influence of heavily doped con­
tacts on photoconductive switch properties,” IEEE Trans. Elect. De­
vices, vol. 37, pp. 2542—2553, Dec. 1990.
[31] Y. Lou and C. Wu, “The effects of im purity bands on th e electrical
characteristics of metal-semiconductor ohmic contacts,” Solid-State
Electronics, vol. 38, no. 1, pp. 163—169, 1995.
[32] J. Sze and H. Cheng, “A new analytical expression for th e interface in­
dex of metal-Schottky contacts on semiconductors,” Solid-State Elec­
tronics, vol. 38, no. 5, pp. 1059—1063, 1995.
[33] J. Meyer and F. Bartoli, “Dynamic dielectric response to electronhole and electron-electron interactions,” Physical Review B , vol. 28,
pp. 915—926, July 1983.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
BIBLIOGRAPHY
117
[34] M. van Exeter and D. Grischkowsky, “C arrier dynamics of electrons
and holes in m oderately doped silicon,” Physical Review B, vol. 41,
pp. 12140-12149, June 1990.
[35] C. Lee, “Optical control of semiconductor closing an d opening
switches,” IE E E Transactions on Electron Devices, vol. ED-37,
pp. 2426-2437, Dec. 1990.
[36] U. Keil and D. Dykaar, “U ltrafast pulse generation in photoconduc­
tive switches,” IE E E Journal o f Q uantum Electronics, vol. QE-32,
pp. 1664-1671, Sept. 1996.
[37] D. Khalil and A. Safwat, “On th e im provem ent of the perform ance of
the optically controlled microwave switch,” IE E E Microwave Theory
and Techniques, vol. 45, pp. 1358—1361, Aug. 1997.
[38] D. Auston, “Picosecond optoelectronic sw itching and gating in silicon,”
Applied Physics Letters, vol. 26, pp. 101—103, Feb. 1975.
[39] A. Johnson an d D. Auston, “Microwave switching by picosecond pho­
toconductivity,” IEE E Journal o f Q uantum Electronics, vol. QE-11,
pp. 283-287, Ju n e 1975.
[40] W. Platte, “High-speed optoelectronic switching in silicon gap-shunt
microstrip structures,” Electronics Letters, vol. 12, pp. 427—438, Aug.
1976.
[41] J. Buck, K. Li, and J. Whinnery, “Optoelectronic switching in a stub
transm ission line,” Journal o f A pplied Physics, vol. 51, pp. 769—771,
Jan. 1980.
[42] W. Platte, “Optoelectronic microwave switching via laser-induced
plasm a tapers in GaAs microstrip sections,” IEEE Transactions on
Microwave Theory and Techniques, vol. MTT-29, pp. 1010—1018, Oct.
1981.
[43] P. Cheung, D. Neikirk, and T. Itoh, “Optically controlled coplanar
wave-guide phase shifters,” IE E E Transactions on Microwave Theory
and Techniques, vol. MTT-38, pp. 586—595, M ay 1990.
[44] S. Gevorgian, “Microwave conductivity of optically excited gap in a
semiconductor microstrip,” Electronics Letters, vol. 26, pp. 1921—1922,
Oct. 1990.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
BIBLIOGRAPHY
118
[45] G. Lin, T. Hwang, Y. Chuang, S. Wang, an d C. Pan, “Broad-band
(>20 GHz) laser-diode-based optoelectronic microwave phase shifter,”
IE E E Transactions on Microwave Theory a n d Techniques, vol. MTT46, pp. 1419-1426, Oct. 1998.
[46] H. Hasegawa, M. Furukaw a, and H. Yanai, “Properties of m icrostrip
line on Si-Si02 system ,” IE E E Trans. Microwave Theory Techn.,
vol. MTT-19, pp. 869-881, Nov. 1971.
[47] E. Tuncer and D. N eikirk, “Highly accurate quasistatic modeling of
microstrip lines over lossy substrates,” IE E E Microwave Guided Wave
Lett., vol. 2, pp. 409-^411, Oct. 1992.
[48] A. M. Johnson, “C a rrie r transport in am orphous silicon utilizing p i­
cosecond photoconductivity” Ph.D. dissertation, City University of
New York, New York, New York, 1981. Includes bibliographical refer­
ences.
[49] S. Alexandrou, C. Wang, T. Hsiang, Y. Liu, and S. Chou, “A 75 GHz
silicon metal-semiconductor-metal schottky photodiode,” Appl. Phys.
Letters, vol. 62, pp. 2507—2509, May 1993.
[50] C. Wang, S. A lexandrou, D. Jacobs-Perkins, and T. Hsiang, “Compar­
ison of the picosecond characteristics of silicon and silicon-on-saphire
metal-semiconductor-m etal photodiodes,” Appl. Phys. Lett., vol. 64,
no. 26, pp. 3578-3580, 1994.
[51] R. Westbrook, Ed., Lifetim e factors in silicon: a symposium, ASTM
special technical publication, (Philadelphia, PA), ASTM, The Society,
1980.
[52] G. Schlichthodrl, G. Beck, J. Lilie, and H. Tributsch, “Microwave pho­
toconductivity scanning microscope studies of silicon surfaces,” Rev.
Sci. Instrum ., vol. 60, pp. 2992—3003, Sept. 1989.
[53] A. Cutolo, S. D aliento, A. Sanseverino, G. Vitale, and L. Zeni, “A n
optical technique to m easure the bulk lifetim e and the surface re ­
combination velocity in silicon samples based on a laser diode probe
system,” Solid-State Electronics, vol. 42, no. 6, pp. 1035—1038, 1998.
[54] E. H am m erstad a n d O. Jensen, “Accurate models for m icrostrip
computer-aided design,” in MTT-S International Sym posium Digest,
(Washingto, D.C.), IEE E , May 1980, pp. 407—409.
[55] S. Rosloniec, A lgorithm s for computer-aided design o f linear m i­
crowave circuits. A rtech House, 1990.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
BIBLIOGRAPHY
119
[56] E. Fooks and R. Zakarevicius, Microwave engineering using mi­
crostrip circuits. Prentice-H all, 1990.
[57] P. Benedek and P. Silvester, “Equivalent capacitances for microstrip
gaps and steps,” IE E E Transactions on Microwave Theory and Tech­
niques, vol. MTT-20, pp. 729—733, Nov. 1972.
[58] P. Silvester and P. Benedek, “Equivalent capacitances of microstrip
open circuits,” IE E E Transactions on Microwave Theory and Tech­
niques, vol. MTT-20, pp. 511—516, Aug. 1972.
[59] A. Gersho, “C haracterization of time-varying linear systems,” Ph.D.
dissertation, Cornell University, Ithaca, N.Y., 1963.
[60] L. A. Zadeh and C. A. Desoer, Linear system theory; the state space
approach. McGraw-Hill series in system science, New York: McGrawHill, 1963. Includes bibliographies.
[61] W. J. Rugh, Linear system theory, 2nd ed. ed. Prentice-H all informa­
tion and system sciences series, Upper Saddle River, N.J.: PrenticeHall, 1996. Includes bibliographical references and indices.
[62] R. Achar and M. N akhla, “Efficient tran sien t sim ulation of embed­
ded subnetworks characterized by S-param eters in th e presence on
nonlinear elements,” IE E E Transactions on Microwave Theory and
Techniques, vol. MTT-46, pp. 2356—363, Dec. 1998.
[63] C. Hsue and C. H echtm an, “Transient responses of an exponential
tr ansmission line an d its applications to high-speed backdriving in
in-circuit test,” IE E E Transactions on Microwave Theory and Tech­
niques, vol. MTT-42, pp. 458—462, Mar. 1994.
[64] L. Hayden and V. T ripathi, “Nonuniformly coupled microstrip
transversal filters for analog signal-processing,” IE E E Transactions
on Microwave Theory and Techniques, vol. 39, pp. 47—53, Jan . 1991.
[65] A. M ohammadian an d C. Tai, “A general m ethod of tran sien t analy­
sis for lossless transm ission lines and its analytical solution to timevarying resistive term inations,” IEEE Transactions on Antennas and
Propagation, vol. AP-32, pp. 309—312, Mar. 1984.
[66] A. Djordjevic, T. Sarkar, and R. H arrington, “Analysis of lossy
transmission-lines w ith arbitrary nonlinear term inal networks,”
IEEE Transactions on Microwave Theory and Techniques, vol. 34,
pp. 660—666, June 1986.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
BIBLIOGRAPHY
120
[67] J. Schutt-Aine and R. M ittra, “Scattering param eter tra n sie n t a n a l­
ysis of transm ission lines loaded w ith nonlinear term inations,” IE E E
Transactions on Microwave Theory and Techniques, vol. MTT-36,
pp. 529—536, Mar. 1988.
[68] J. Schutt-Aine, “Transient analysis of nonuniform transm ission
lines,” IE E E Transactions on Circuits and Systems—1: F undam ental
Theory a n d Applications, vol. 39, pp. 378—385, May 1992.
[69] T. D haene, L. M artens, and D. Dezutter, “T ransient sim ulation of ar­
b itrary nonuniform interconnection structures characterized by scat­
tering param eters,” IE E E Transactions on Circuits and System s—1:
F undam ental Theory and Applications, vol. 39, pp. 928—937, Nov.
1992.
[70] K. Oh an d J. Schutt-Aine, “T ran sien t analysis of coupled, tap ered
transm ission lines with arb itrary nonlinear term inations,” IE E E
Transactions on Microwave Theory and Techniques, vol. MTT-41,
pp. 268-273, Feb. 1993.
[71] J. Bracken, D. Sim, and Z. Cendes, “S-domain m ethods for simulataneous tim e and frequency characterization of electrom agnetic
devices,” IE E E Transactions on Microwave Theory and Techniques,
vol. MTT-46, pp. 1277-1290, Sept. 1998.
[72] W. E isenstadt, R. Hammond, D. Bowman, and R. D utton, “Timedomain m easurem ents for silicon integrated circuit testing using pho­
toconductors,” in Picosecond electronics and optoelectronics: proceed­
ings o f the topical meeting, vol. 21 of Springer series in electrophysics,
(Lake Tahoe, Nevada), Springer-Verlag, Mar. 1985, pp. 66—69.
[73] S. Saddow an d C. Lee, “Optical control of m icrowave-integrated cir­
cuits using high-speed GaAs an d Si photoconductive switches,” IE E E
Transactions on Microwave Theory and Techniques, vol. MTT-43,
pp. 2414—2420, Sept. 1995.
[74] B. Boyer, J. Haidar, A. Vilcot, an d M. Bouthinon, “Tunable microwave
load based on biased photoinduced plasm a in silicon,” IE E E Transac­
tions on Microwave Theory a n d Techniques, vol. MTT-45, pp. 1362—
1367, Aug. 1997.
[75] A. De Salles, “Optical control of GaAs M ESFETs,” IE E E Transactions
on Microwave Theory and Techniques, vol. MTT-31, pp. 812—820, Oct.
1983.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
BIBLIOGRAPHY
121
[76] J. Gautier, D. P asquet, and P. Pouvil, “O ptical effects on the static and
dynamic characteristics of a GaAs M ESFET,” IE E E Transactions on
Microwave Theory a n d Techniques, vol. MTT-33, pp. 819—822, Sept.
1985.
[77] I. Andersson an d S. Eng, “Phase an d am plitude characteristics
of InP:Fe modified interdigitated gap photoconductive microwave
switches,” IE E E Transactions on Microwave Theory and Techniques,
vol. MTT-37, pp. 729-733, Apr. 1989.
[78] L. de Barros, Jr., A. Paolella, M. F rankel, M. Romero, P. Herczfeld,
and A. Madjar, “Photoresponse of microwave transistors to highfrequency m odulated lightwave carrier signal,” IE E E Transactions on
Microwave Theory a n d Techniques, vol. MTT-45, pp. 1368—1374, Aug.
1997.
[79] G. Gambardella, “A contribution to th e theory of short-tim e spectral
analysis w ith nonuniform bandw idth filters,” IE E E Transactions on
Circuit Theory, vol. CT-18, pp. 455—460, Ju ly 1971.
[80] M. Portnofif, “Time-frequency representation of digital signals and
systems based on short-tim e Fourier analysis,” IE E E Transactions
on Acoustics, Speech, and Signal Processing, vol. ASSP-18, pp. 55—69,
Feb. 1980.
[81] I. Sodagar, K. Nayebi, T. Barnwell, an d M. Smith, “Time-varying
analysis-synthesis system s based on filter banks and post filtering,”
IEEE Transactions on Signal Processing, vol. SP-43, pp. 2512—2524,
Nov. 1995.
[82] L. Weiss, “Tim e-varying system characterization for wideband input
signals,” Signal Processing, vol. 55, pp. 295—304, 1996.
[83] G. Womell, “E m erging applications of m u ltirate signal processing
and wavelets in digital communications,” in Proceedings o f the IEEE,
vol. 84 of 4, IEE E , USA, Apr. 1996, pp. 586—603.
[84] C. Bor-Sen, C. Yue-Chiech, and H. Der-Feng, “Optim al time-frequency
deconvolution filter design for nonstationary signal transm ission
through a fading channel: Af filter b an k approach,” IE E E Transac­
tions on Sig n a l Processing, vol. SP-46, pp. 3220—3224, Dec. 1998.
[85] D. Gindin, “T ransform ation of ’bandpass’ linear tim e-variant system
into equivalent ’lowpass’ system,” Electronics Letters, vol. 7, pp. 645—
646, Oct. 1971.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
BIBLIOGRAPHY
122
[86] R. E. Crochiere a n d L. R. Rabiner, Multirate digital signal process­
ing. Prentice-H all Signal Processing Series, Englewood Cliffs, N.J.:
Prentice-Hall, 1983. Includes bibliographical references and index.
[87] L. Heung-No an d G. Pottie, “Fast adaptive equalization/diversity com­
bining for tim e-varying dispersive channels,” IE E E Trans. Comm.,
vol. 46, pp. 1146—1162, Sept. 1998.
[88] L. Silverman, “R ealization of linear dynamical systems,” IEEE Trans­
actions on A utom atic Control, vol. AC-16, pp. —, Dec. 1971.
[89] L. Pipes, “Four m ethods for the analysis of tim e-variable circuits,”
IR E Transactions—Circuit Theory, pp. 4—12, Mar. 1955.
[90] L. Pipes, “A m athem atical analysis of a series circuit containing
periodically varying resistance,” IR E Transactions-Circuit Theory,
pp. 67—73, Mar. 1955.
[91] J. Adam s and B. Leon, “Steady-state analysis of linear networks con­
taining a single sinusoidally varying capacitor,” IE E E Transactions
on Circuit Theory, vol. CT-14, pp. 313—319, Sept. 1967.
[92] D. Thornburg an d B. Leon, “Noise figure and gain of linear systems
containing a single sinusoidally varying elem ent,” IE E E Trans. Cir­
cuit Theory, vol. CT-19, pp. 162—167, Mar. 1972.
[93] B. Bardalg'ian a n d M. Sablatash, “Spectral analysis o f periodically
time-varying lin e ar networks,” IEEE Trans. Circuit Theory, vol. CT19, pp. 297-299, M ay 1972.
[94] C. K urth, “S teady-state analysis of sinusoidal tim e-variant networks
applied to equivalent circuits for transm ission networks,” IE E E
Trans. Circuits a n d System s, vol. CAS-24, pp. 610-624, Nov. 1977.
[95] J. Richards, A nalysis o f periodically time-varying systems. Commu­
nications and control engineering series, New York: Springer-Verlag,
1983. Includes bibliographical references and index.
[96] T. R. Bashkow, “The A m atrix, new netw ork description,” IR E
Transactions-Circuit Theory, pp. 117—119, Sept. 1957.
[97] B. Kinariwala, “Analysis of time-varying networks,” in I.R.E. Conven­
tion Record, I.R.E., 1961, pp. 268—276.
[98] C. Desoer, “S teady-state transm ission through a network containing
a single tim e-varying element,” IR E Transactions on Circuit Theory,
pp. 244-252, Sept. 1959.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
BIBLIOGRAPHY
123
[99] EL Liu and M. K ujath, “Response of slowly tim e-varying systems
to harmonic excitation,” Journal o f Sound a n d 'Vibration, vol. 177,
pp. 423—432, Mar. 1994.
[100] A. Levi and H. Stark, Image Recovery: Theory and Applications,
p. 277. San Diego, California: Academic, 1987.
[101] L. Zadeh, “Correlation functions and power sp e ctra in variable n et­
works,” in Proceedings o f The I.R .E ., vol. 38, Nov. 1950, pp. 1342—
1345.
[102] L. Zadeh, “Band-pass low-pass transform ation in variable networks,”
in. Proceedings o f The I.R .E ., vol. 38, Nov. 1950, pp. 1339—1341.
[103] L. Zadeh, “Frequency analysis of variable netw orks,” in Proceedings
o f The I.R.E., Mar. 1950, pp. 291—299.
[104] L. Zadeh, “The determ ination of the impulsive response of variable
networks,” Journal o f Applied Physics, vol. 21, pp. 642—645, July
1950.
[105] L. Zadeh, “Circuit analysis of linear varying-param eter networks,”
Journal o f Applied Physics, vol. 21, pp. 1171—1177, Nov. 1950.
[106] H. Davis, “The analysis and synthesis of a class of lin e a r tim e varying
networks,” U niversity of California, Los Angeles, Tech. Rep. 7, June
1953.
[107] L. Zadeh, “Time-varying networks, I,” in Proceedings o f The I.R.E.,
Oct. 1961, pp. 1488-1503.
[108] R. Collin, Foundations For Microwave Engineering, second ed.
McGraw-Hill Electrical and Computer E ngineering Series, New York:
McGraw-Hill, Inc., 1992.
[109] G. Owyang, Foundations for Microwave Circuits. N ew York: SpringerVerlag, 1989.
[110] E. Kamen, “The poles and zeros of a linear tim e-varying system,”
in Linear algebra and its applications, A. Hoffman, A. Householder,
A. Ostrowski, and O. T. Todd, Eds., vol. 98, New York, N.Y.: Elsevier
Science Publishing, 1988, pp. 263—289.
[111] K. Narendra, “Integral transform s for a class of tim e varying linear
systems,” H arvard University, Cambridge, M assachusetts, Tech. Rep.
330, Oct. 1960.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
BIBLIOGRAPHY
124
[112] H. D’Angelo, Linear tim e-varying systems: analysis a n d synthesis.
The Allyn and Bacon series in electrical engineering, Boston: Allyn
and Bacon, 1970. Includes bibliographies.
[113] A. Jan ssen , “Private comm uni cation,” Aug. 1996. Time-varying sys­
tems.
[114] L. Zadeh, “On the theory of filtration of signals,” Z. angew. Math. P.,
vol. 3, pp. 149-156, 1952.
[115] L. Zadeh and K. Miller, “G eneralized idealized filters,” Journal o f A p ­
plied Physics, vol. 23, pp. 223—228, Feb. 1952.
[116] K. Miller, “Properties of im pulsive responses an d Green’s functions,”
I.R.E. Transactions-Circuit Theory, pp. 26—31, Mar. 1955.
[117] A. Gerlach, “A tim e-variable transform and its application to spectral
analysis,” IR E Transactions-Circuit Theory, pp. 22—25, Mar. 1955.
[118] B. Boashash, “E stim atin g an d interpreting th e instantaneous fre­
quency of a signal 1. Fundam entals,” in Proceedings o f the IEEE,
vol. 80, IEEE, Apr. 1992, pp. 520—538.
[119] H. Ling, J. Moore, D. Bouche, an d V. Saavedra, “Time-frequency anal­
ysis of backscattered d a ta from a coated strip w ith a gap,” IE E E
Trans. A nt. Prop., vol. 41, pp. 1147—1150, Aug. 1993.
[120] H. Kritikos and J. Teti, “A time-frequency analysis m ethod for rad ar
scattering,” IEEE Transactions on Microwave Theory and Techniques,
vol. MTT-46, pp. 257—260, Mar. 1998.
[121] S. K unasani and C. Nguyenj, “Distortion of pulsed signals in mi­
crostrip transm ission lines using short-time fourier transform ,” IE E E
Microwave and G uided Wave Letters, vol. 6, pp. 1—3, Jan . 1996.
[122] B. Rudnitskii, “The synthesis of systems w ith variable param eters,”
Avtom atika i Telemekhanika, vol. 26, pp. 208—215, Feb. 1965.
[123] W. Kaplan, Operational methods for linear system s. Addison-Wesley
Series in M athematics, Reading, M assachusetts: Addison-Wesley
Publishing Co., Inc., 1962.
[124] J. Chao, K. Sakaniwa, an d S. Tsujii, “Stability of tim e-varying sys­
tem s w ith adaptively estim ated transfer function,” Electronics Let­
ters, vol. 25, pp. 481—482, Mar. 1989.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
BIBLIOGRAPHY
125
[125] S. Darlington, “An introduction to time-variable netw orks,” in Pro­
ceedings o f the Sym posium on Circuit Analysis, (U rbana, Illinois),
1955, pp. 5.1-5.25.
[126] A. Gersho and N. DeClaris, “D uality concepts in tim e-varying lin­
ear systems,” in IE E E International Covention Record, vol. 12, IEEE,
1964, pp. 344-356.
[127] W. Kim and H. Meadows, Jr., M odem Network A nalysis. New York:
John Wiley and Sons, Inc., 1971.
[128] M. Skeldon, A. Okishev, S. Letzring, W. Donaldson, K. Green, and
W. Seka, “Optically activated switches for the generation of com­
plex electrical waveforms w ith m ultigigahertz bandw idth,” in Solid
State Lasers for Application to Inertial Confinement Fusion, vol. 2343,
(Bellingham, WA), Ja n . 1994.
[129] D. Pozar, Microwave Engineering, second ed. John Wiley and Sons,
Inc., 1998.
[130] K. Green, W. Seka, M. Skeldon, R. Keck, A. Okishev, and
R. Sobolewski, “Improving th e microwave bandw idth of photoconduc­
tive switches used in th e omega pulse-shaping system,” in Solid State
Lasers for Application to Inertial Confinement Fusion, (Bellingham ,
WA), Jan . 1998.
[131] W. P latte, “An o p t i m i z a t io n of semiconductor film thickness in lightcontrolled microstrip devices,” Solid-State Electronics, vol. 20, pp. 57—
60, Ja n . 1977.
[132] W. P latte, “Spectral dependence of microwave power transm ission
in laser-controlled solid-state m icrostrip switches,” LEE Journal on
Solid-State and Electronic Devices, vol. 2, pp. 97—103, Ju ly 1978.
[133] W. P latte, “Effective photoconductivity and plasm a dep th in optically
quasi-cw controlled microwave switching devices,” LEE Proceedings-J
Optoelectronics, vol. 135, pp. 251—254, June 1988.
[134] J. Hwang, H. Cheng, and J. W hitaker, “Photoconductive sam pling
w ith a n integrated source follower/amplifier,” Applied Physics Letters,
vol. 68, pp. 1464—1466, Mar. 1996.
[135] K. Green, W. Donaldson, R. Sobolewski, A. Okishev, M. Skeldon,
S. Letzring, , and W. Seka, “T ran sien t microwave bandw idth m ea­
surem ents of illum inated silicon switches for optical pulse-shape con­
trol of laser-fusion drivers,” in Solid State Lasers for Application to
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
BIBLIOGRAPHY
126
Inertial Confinement Fusion, vol. 2633 of 615, (Bellingham, WA), Jan.
1995.
[136] G. Loubriel, F. Z utavem , G. Denison, W. Helgeson, D. McLaugh­
lin, M. O’Malley, C. SifFord, L. Beavis, C. Seager, A. Rosen, and
R. Madonna, “Long lifetime silicon photoconductive semiconductor
switches,” in S P IE Optically Activated Sw itching III, vol. 1873, SPUE,
1993, pp. 27-38.
[137] R. Wilcox, W. Behrendt, D. Browning, D. Speck, and B. Van Wonterghem, “Fusion laser oscillator and pulse-forming system using in­
tegrated optics,” in Laser Coherence Control: Technology and Appli­
cations, H. Powell and T. Kessler, Eds., vol. 1870, (Bellingham, WA),
SPIE, 1993, pp. 53-63.
[138] S. B urckhart and R. Wilcox, “A rbitrary pulse shape synthesis via
nonuniform transm ission lines,” IE E E Transactions on Microwave
Theory and Techniques, vol. 38, pp. 1514-1518, Oct. 1990.
[139] R. B auer and J. P. Penfield, “De-embedding and unterm inating,”
IEE E Trans. M TT , vol. MTT-22, pp. 282-288, Mar. 1974.
[140] S. Pandey and S. Kal, “A simple approach to the capacitance
technique for determ ination of interface sta te density of a metalsemiconductor contact,” Solid-State Electronics, vol. 42, no. 6,
pp. 943-949, 1998.
[141] W. Runyan, Semiconductor measurements and instrum entation. New
York: McGraw-Hill, 1975. Ch. 3.
[142] G. Reeves and H. H arrison, “O btaining th e specific contact resistance
from transm ission line model m easurem ents,” IE E E Electron Device
Letters, vol. EDL-3, pp. 111—113, May 1982.
[143] J. H. Zhao, K. Tone, S. R. Weiner, M. A. Caleca, H. Du, and S. P.
Winthrow, “Evaluation of ohmic contacts to P-Type 6H-SiC created
by C and A1 coim plantation,” IE E E Electron Device Letters, vol. 18,
pp. 375-377, Aug. 1997.
[144] S. Gevorgian, “Optics control microwaves: the next step,” in Proceed­
ings o f the 20th European Conference on Microwave Circuits, vol. 2,
(Budapest), 1990, pp. 1603—1608.
[145] S. Gevorgian, “Design considerations for a n optically excited semicon­
ductor microstrip gap a t microwave frequencies,” TEE Proceedings-J
Optoelectronics, vol. 139, pp. 153—157, Apr. 1992.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
BIBLIOGRAPHY
127
[146] T. Claasen and W. Mecklenbrauker, “On statio n ary lin ear timevarying systems,” IE E E Transactions on Circuits and Systems,
vol. CAS-29, pp. 169-184, Mar. 1982.
[147] G. Loubriel, M. O’Malley, F. Zutavem , B. McKenzie, and W. Conley,
“Surface flashover threshold and switched fields of photoconductive
semiconductor switches,” in Conference on Electrical Insulation and
Dielectric Phenomena, (Ottawa, Canada), IEEE Dielectrics and Elec­
trical Insulation Society, Oct. 1988, pp. 430—441.
[148] A. Jerri, “Application of th e sampling theorem to tim e-varying sys­
tems,” Journal o f The Franklin Institute, vol. 293, pp. 53—58, Jan.
1972.
[149] T. Claasen and W. M ecklenbrauker, “On the transposition of linear
time-varying discrete-tim e networks and its application to m ultirate
digital systems,” Philips J. Res. Vol., vol. 33, no. 1,2, pp. 78—102, 1978.
[150] H. Hashemi, “The indoor radio propagation channel,” in Proceedings
o f the IEEE, vol. 81 of 7, IEEE, July 1993, pp. 943—968.
[151] H. Zmuda and E. N. Toughlian, Photonic aspects o f m odem radar.
Boston: Artech House, 1994. Includes bibliographical references and
index.
[152] K. Horikawa, M. Shimizu, and H. Ogawa, “Optically controlled mul­
tiple beam forming,” in Proceedings o fS P IE -th e International Society
o f Optical Engineering, vol. 2155, (Los Angeles, CA, USA), Ja n . 1994,
pp. 325—334.
[153] E. Funk and C. Lee, “Free-space power combining and beam steer­
ing of ultra-w ideband radiation using an array of laser-triggered an­
tennas,” IEE E Transactions on Microwave Theory and Techniques,
vol. MTT-44, pp. 2039-2044, Nov. 1996.
[154] K Green, M. Lindgren, T. Hsiang, W. Seka, L. Fuller, and
R. Sobolewski, “O bservation of picosecond photoresponse in polycrys­
talline silicon,” in O SA TO PS on Ultrafast Electronics a n d Optoelec­
tronics, vol. 13, (Washington, DC), Jan. 1997, p. 106.
[155] A. Johnson, D. Auston, P. Smith, J. Bean, J. H arbison, and D. Ka­
plan, “Picosecond photoconductivity in am orphous silicon,” in Pi­
cosecond Phenomena II. Proa 2nd Int. Conf. Picosecond Phenomena,
R. Hochstrasser, W. Kaiser, and C. Shank, Eds., (Berlin, West Ger­
many), Springer-Verlag, 1980, pp. 285—289.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
BIBLIOGRAPHY
128
[156] D. Bowman, R. Dutton, and R. H am m ond, “New in teg rated polysili­
con photoconductor for u ltrafast m easurem ents on silicon,” Interna­
tional Electron Devices Meeting. Technical Digest, pp. 117—120, 1985.
[157] D. Bowman, R. Hammond, and R. D utton, “Polycrystalline-silicon in­
tegrated photoconductors for picosecond pulsing and gating,” IE E E
Electron Device Letters, vol. EDL-6, pp. 502—504, Oct. 1985.
[158] H. Beneking, “On the response behavior of fast photoconductive op­
tical p la n a r and coaxial sem iconductor detectors,” IE E E Trans. Elec­
tronic Devices, vol. ED-29, pp. 1431—1441, Sept. 1982.
[159] R. Ham m ond and N. Johnson, “Im p u lse photoconductance of thin-film
polycrystalline silicon,” Journal o f A p p lied Physics, vol. 59, pp. 3155—
3159, M ay 1986.
[160] R. H aw kins II, M. Jones, S. Pepper, an d J. Goll, “Com parison of
fast photodetector response m easu rem en ts by optical heterodyne and
pulse response techniques,” Journal o f Lightwave Technology, vol. LT9, pp. 1289-1294, Oct. 1991.
[161] L. A rm engaud, M. Lalande, B. Jecko, N. Breuil, A. Barthelemy, and
M. Cuzin, “Electromagnetic analysis of optoelectronic devices applied
to th e stu d y of a sampler and a n autocorrelator” IE E E Transactions
on M icrowave Theory and Techniques, vol. MTT-44, pp. 1017—1023,
Ju ly 1996.
[162] M. Kubinyi, A. Grofcsik, W. Jones, T. Tyer, and J. M arshall, “Picosec­
ond delay of photoinduced absorption in undoped am orphous and
polycrystalline silicon thin films,” T h in Solid Films, vol. 263, pp. 99—
104, Ju ly 1995.
[163] S. Alexandrou, R. Sobolewski, a n d T. Hsiang, “Time-domain charac­
terization of bent coplanar wave-guides,” IEEE J. Q uantum Elect.,
vol. 28, pp. 2325-2332, Oct. 1992.
[164] G. D. Roberts, “The m easurem ent of m inority carrier lifetim e near
grain boundaries in polyciystalline silicon,” M.S. thesis, U niversity of
Waterloo, O ttaw a, 1982.
[165] R. G hayour and A. Bakhtazad, “Trade-off between speed and ef­
ficiency of silicon metal-i-n photodetectors,” Solid-state electronics,
vol. 42, no. 5, pp. 715—720, 1998.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
129
A ppendix A
Material Characterization
In th is appendix we exam ine the silicon m aterial properties and fabrication
in g reater detail. In Sec. A.1 we document th e fabrication process th a t we
have developed. This process has evolved over 5 years of continuous im ­
provements, based on iteratio n and feedback from operational benchm arks.
For example we have fabricated OMSS’s from 0.25 mm thick to 1 m m thick,
we have experimented w ith a variety of m etal contact layers, passivation
techniques, anne aling and im plantation steps. In Sec. A.2 we explore in
g reater depth th e tim e-dom ain performance of one variety of OMSS, the
polycrystalline silicon, or polySi OMSS. The purpose of the exploration of
this m aterial was to exam ine the possibility of generating faster risetim es
and of using OMSS’s w ith m uch shorter lifetime.
A.1
OMEGA Single-Crystalline OMSS Fabrication
The OMSS fabrication process is shown in Fig. A.1. We use this sam e gen­
eral process for single-ciystal, polycrystalline an d amorphous OMSS’s. The
single-crystal OMSS’s are used in OMEGA, while the others were used for
m aterial characterization.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
130
Appendix A. M aterial Characterization
|
Undoped Si
Slice into wafers,
polish both sides
Photoresist
Pre-dean with
O2 ion etcher
')
n
Substrate
CoatAZ 5214 E
|
Deposit antireflective coating
Mount on 4 inch
wafer, AR side down
I . A )
1
\
Evaporate Alutrmntim
3000 A
n r i Tn Tr
Reversal process
Expose through
mask for contacts
Post exposure reversal
bake & flood expose
After development
Ida impsant boron
BH, 100 keV, 10U cm- 2
Evaporate chrome
Spotter nickel
1000 A
Evaporate copper
3000 A
Lift oft in acetone
1000A
Plate witti dectroless
gold 8 OC, 1 0 min
Etch aluminum
Pre-dean with
Ar ion etcher
Deposit highreflectance coating
Photoresist for
opening contacts to
metal thra HRC
Etch i s HF and
strip resist
Figure A.1: Step-by-step procedures for OMSS fabrication as performed a t
RIT.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
A ppendix A. M aterial Characterization
131
A.2 Polycrystalline Silicon Detectors
A s p a rt of our m easurem ent and optimization of OMSS’s, other designs
were considered. For exam ple inter-electrode designs, photoconductive tra n s­
mission line substrates, an d polySi m aterial were some of th e alternatives
considered [154]. This section will discuss the resu lts of our m easurem ents
of these devices, in p articu lar the polySi devices.
In th is section we explore the optimization of electrical pulse genera­
tion by probing the intrinsic lim its of polySi m aterial. In th e 1980s Auston
[155, 156, 157] and others studied processing m ethods to reduce the Si in­
trinsic photoresponse tim e far below the microsecond lim it set by its freecarrier lifetime. Although very fast responses were generated, the tem poral
resolution of the m easurem ent equipment a t th a t tim e w as not sufficient to
directly resolve the rise an d fall tim es of the resulting photoresponse [158].
To circumvent this m easurem ent bandwidth lim itation, optoelectronic cor­
relation methods were developed [159, 160, 161]. C orrelation takes advan­
tage of th e switch itself by using another, sim ilarly fast photoconductive
switch in a pulser/sam pler configuration. The m easured response from the
sam pler is then a correlation of th e two switch responses. This procedure,
however, does not allow direct reconstruction of a n individual switch re­
sponse because, even if th e switch geometries are identical, the m easured
response is not equivalent to a true autocorrelation since th e electric fields
across th e gaps have different evolution times. This is im portant because
m any param eters of the photoconductive switches, such as carrier mobil­
ity and trapping, vary w ith the applied electric field strength. Therefore,
detailed knowledge of th e photoresponse and how it depends on the switch
bias and illumination for different process conditions could not be deter-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
A ppen dix A. Material C haracterization
132
m ined [162].
We have m easured th e Si sw itch response a t 800 run a n d a t th e typ­
ical communication w avelength of 1.55 mm, using a 34-GHz sam pling os­
cilloscope to quickly and easily m easure properties d ependent on charge
(current integral) effects, such as quantum efficiency a n d satu ratio n. We
have also used an electro-optic (EO) sampling system capable of m easur­
ing submillivolt and subpicosecond responses [163]. See App. B for details.
This system allowed direct observation of th e Si photoresponse rise and fall
times.
A. 2.1
Sam ple Preparation a n d Characterization
The tested samples were 2.3-mm-thick, 2x2-mm, low -pressure chemicalvapordeposited (LPCVD) films of polySi grown at a su b stra te tem perature
of 600°C in 200 mTorr of silane. A 1-mm-thick m ultilayer of m e ta l was evap­
orated onto the polySi in an interdigitated fashion. The top layer was Au
for solderability, while the bottom layer was A1 for good adhesion to Si and
to promote ohmic-like contacts. The samples were not annealed, and no im­
plantation or etching was perform ed. Instead of growing th e film on a Si
substrate with an oxide in su latin g layer, we used a fused silica substrate to
facilitate switch illumination. T his optimized the oscilloscope te st fixture
bandw idth because th e sample could be directly soldered in a flip-chip man­
n er across a microstrip gap, elim inating bandw idth-lim iting discontinuities
such as inductive wire-bond leads. Illum inating th e sam ple from th e back
side (through the silica) also leads to reflection of the in cid en t laser illu­
m ination from the top m etal contacts, increasing the n u m b e r of photons
absorbed. With front-side illum ination, the m etal contacts would have de­
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
Appendix A. M aterial Characterization
133
creased the absorbed optical energy.
For characterization purposes, the polySi surface was etched preferen­
tially at the grain boundaries, and a scanning electron microscope (SEM)
image taken of th e surface (see Fig. A.2) revealed a grain size of approxi­
mately 30 nm. We h a d fabricated the switches w ith the idea of using sm aller
grains to decrease th e lifetime, without having too much of an effect on car­
rier mobility [164]. A sample was cleaved, and a 4-nm conductive silver
layer was evaporated onto the exposed face, allowing a high-resolution SEM
photograph of the sw itch cross section to be taken, as shown in Fig. A. 3.
LPCVD 2.3-p.m-thick polySi
growth at 22 Torr in Silane at
600°C.
Surface preferentially etched
to reveal grain boundaries.
Scanning electron microscope
shows grain size less than
500 A.
Figure A.2: An SEM image of the polySi surface taken after preferential
etching a t grain boundaries reveals grain sizes of the order of 30 nm .
The image shows the silica substrate b en eath the 2.3-^m layer of polySi;
on the top is a m ultilayer of m etal th a t allows a robust, repeatable lowtem perature-solder contact between the polySi and the m icrostrip tra n s ­
mission line. Close inspection of the grown polySi layer reveals some ev-
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Appendix A. M aterial Characterization
134
Multilayer metal contacts
for solderability and
ohmic-like metalsemiconductor contact.
Thick 2.3-pm polySi layer
shows evidence of some
columnarity in vertical
(growth) direction.
Fused silica substrate for
backside illumination.
Figure A.3: An SEM cross-section image showing the m etal m ultilayer on
the 2.3-^m polySi layer.
idence of columnarity in th e grow th direction of th e Si grains, which is
not unexpected; however, th e m easurem ents w ere not significantly affected
since the current flow was prim arily in the direction norm al to the Si growth.
To independently confirm th e polySi grain size an d obtain prelim inary d ata
on absorption depth, a PerkinE lm er Lambda 9 spectrophotom eter was used
to measure the transm ission of the polySi-on-quartz sample (see Fig. A.4).
The data, corrected for thin-film etalon fringes, show a broadened absorp­
tion band edge and a sm all b u t m easurable am ount of absorption in the
energy bandgap, which is consistent with the sm all-grain microcrystalline
film morphology observed in th e SEM.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
135
A ppen dix A . M aterial Characterization
1.0
c
o
8
£
0.8
0.6
ca 0.4
0.2
0.0
400
600
800 1000 1200 1400
Wavelength (nm)
1600
Figure A.4: Transmission spectra of the polySi sam ple (solid line), corrected
for thin-film etalon effects (dashed line).
A.3 Summary of Material Characterization Results
A 34-GHz (10-ps intrinsic rise time) sampling oscilloscope m easurem ent
setup, shown in Fig. A.5, allowed convenient m easu rem en t of relative quan­
tu m efficiencies for various la se r wavelengths, since o u r EO sampling sys­
tem operated up to only near-infrared wavelengths an d did not extend into
th e fiber optic communication wavelengths. The oscilloscope m easurem ents
also perm itted convenient te stin g of th e switch signal’s dependence on volt­
age bias (Fig. A.6) and illum ination power (Fig. A.7). T hese two plots, taken
a t a laser wavelength of 800 nm , show th a t the sw itch response is linear
w ith both the voltage bias a n d incident laser fluence, indicating th a t the
switch was not saturated. Additionally, the pulse-w idth w as independent of
bias voltage, indicating th a t th e photoresponse tim e w as not due to carrier
sweep-out b ut limited by e ith er the free-carrier lifetim e or the capacitanceresistance (RC) tim e constant of the switch. Since, as we will dem onstrate
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
136
Appendix A. M aterial Characterization
later, EO sam pling m easurem ents show th a t the m aterial response is in the
3-ps range, we can conclude th a t the observed photoresponse of our polySi
switch is lim ited by th e switch interdigitated geometry and th e switch fix­
tu re RC tim e constant.
34-GHz sampling
oscilloscope
100-fs-wide
laser
pulse
Trigger
-- - <
+
f:
mJLm
Z2 1 9 9
S w i t c h ____________
-
Microstrip transmission line
Figure A. 5: Experim ental setup for both optoelectronic and oscilloscope
m easurem ents of polySi interdigitated switches discharging a microstrip
transm ission line.
Our switch configuration was not designed for EO m easurem ents. Nev­
ertheless, we m anaged to get prelim inary results by connecting th e switch
as a meander-type slot line. The signal was generated and m easured en­
tirely on the face of th e switch stru ctu re. It propagated in a m eander line
fashion along th e gap from one end of th e switch to the other. The transient
measured before entering the first b end is shown in Fig. A. 8. We note a sub­
picosecond (system-limited) rise time, followed by a decay w ith an initial fall
tim e of approxim ately 3 ps.
A standard fabrication technique was implemented to design small-
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
137
Appendix A. M aterial Characterization
6
5
3
Bias
20 V'
16 V
12 V
2
8V
4
OO
■5.
Bias (V)
4V
1
0
1
Time (20 ps/div)
Z2196
Figure A.6: Im pulse response m easurem ents of polySi as a function of bias
voltage. The lin ear relationship of th e peak response to bias indicates an
ohmic-like contact.
Average
power
>
s
800 nm
210 mW
<0
C/3
180 mW-
C/3
125 mW" 60 mW-
eo
Q,
<D
-1
Fluence (nJ/cm2)
Time (20 ps/div)
Z 2195
Figure A. 7: Im pulse response m easurem ents of polySi as a function of opti­
cal power. The linear relationship of th e peak response to power also indi­
cates an ohmic-like contact.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
138
A ppendix A . M aterial Characterization
1.00
0.50
0.00
-0.25
Time (1 ps/div)
Figure A.8: EO sam pling of polySi.
grain polySi photoconductive switches fully compatible w ith Si VLSI pro­
cessing. By m eans of EO sampling, a m aterial photoresponse of 3-ps FWHM
was observed. The sw itch responded to 800-nm femtosecond laser illum ina­
tion w ith switch-geometry limited photocurrent pulses shorter th a n 40-ps
FWHM. The far-infrared response tim e was generated in nonim planted Si
with ohmic-like metal-semiconductor contacts, indicating th e response was
limited by the relaxation tim e of the extended-state (free) carriers into lo­
calized (immobile) states. Our prelim inary m easurem ents of response tim e
and efficiency can be optimized using sim ple process changes such as an ­
nealing a t m oderate tem peratures, sputter-etching for surface dam age, or
Fe and Au deep-level defect doping, while still allowing th e switch to be
integrated w ith Si IC’s [165].
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
139
Appendix B
Laser System Details
The accuracy and repeatability of our experim ental resu lts rely heavily on
knowledge of the optical illum ination’s w avelength, energy, average and
peak power, fluence, sp atial beam quality an d mode, an d temporal pulse
shape. The laser system s we used to take the d a ta in th is thesis were in
a continuous state of adjustm ent, repair and upgrade and therefore careful
attention was paid to determ ining and recording th e details of the illum i­
nation conditions for each experiment. This appendix documents the laser
systems th a t supplied th e optical illumination an d th e sta te of their opera­
tion at th e tim e of the experim ents. In addition, for completeness we indi­
cate some facts about the la ser system in which th e optoelectronic switches
were installed (LLE’s OMEGA laser fusion system), especially as it relates
to switch operation.
B.l
OMEGA Laser System.
The Laboratory for L aser Energetic’s fusion la ser system consists of two
different b ut synchronized lasers, the fusion laser system (called OMEGA)
and the OMSS activation la se r system. A block diagram of these two lasers
and how they in teract is show n in Fig. B.l. OMEGA is used for high energy
physics experiments, prim arily inertially-confined fusion. To encourage fa­
vorable conditions for fusion as well as increase th e ran g e of potential uses
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
140
Appendix B. L aser System D etails
for this laser to other areas of high-energy physics, the laser pulses are
shaped to account for nonlinear laser system effects such as frequency con­
version and amplifier saturation. This allows a desired tem poral output
pulse shape to be determ ined a priori. The following two subsections dis­
cuss the two laser systems, as they effect the operation of th e optoelectronic
switches.
cw mode-locked
timing laser
High-power,
single-mode
PM fiber
distribution
Single-mode
, PM fibers ,
L aser system with
SBS pulse compression
Multimode
fibers
Electrical waveform
generator
Shaped pulse
to be amplified
OMEGA
master oscillator
High-power,
single-mode
PM fiber
distribution
Modulator bias and
control electronics
E9229
Figure B.l: Block diagram of the front end of LLE’s fusion laser system,
including the Nd:YLF monomode Q-switched OMEGA ring-oscillator and
the Nd:YLF mode-locked oscillator and OMSS activation system.
jB .l.I
N d:YLF Ring-oscillator OMEGA Front-end
The optical pulses to be shaped originate with a diode-pumped, self-seeded
Nd:YLF unidirectional ring-cavity laser oscillator. I t operates a t 1053 nm
for compatibility w ith the NdrPhosphate glass amplifiers used fu rth er down­
stream in OMEGA, which have peak gain at 1054 nm. It produces 0.1 W in
cw (for diagnostic operations) or 1 p J p er 50-ns pulse a t 10 kHz in its usual,
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited without p erm ission.
141
Appendix B. L aser S ystem D etails
Q-switched operating state. It is operated in single-longitudinal mode to
prevent mode-beating, which leads to tem poral modulation and potentially
damaging high peak powers. To gen erate enough pulse energy to seed a re­
generative pre-amplifier, th e laser is Q-switched. A diagram of the oscillator
is shown in Fig. B.2. This laser effects the design of the OMSS by dictat­
ing the shaped electrical pulse envelope and am plitude (via th e m odulator’s
frequency response and half-wave voltage).
Temperature
control
Brewster
Prism
diode
Nd:YLF
rod
AOM
CCD
cam era
Cavity-length
control
E talon
O utput
coupler
RF
Amplitude
control
Side view
Figure B.2: Top and side views of th e diode-pumped Nd:YLF ring-oscillator
laser system. This laser can produce 3 W in CW mode and 10 m J in pulsed
mode, up to 300 Hz.
B. 1.2 OMSS Activation Laser System
The laser system used to illum inate th e OMSS’s is shown in Fig. B.3. The
system accepts 10-ps, 0.2 W average, 76-MHz pulses from a commercial cw
mode-locked Nd:YLF laser and uses th e m to seed a regenerative amplifier.
The 600-ps, 3-m J amplifier output p ulse is amplified and th en focused into
a cell filled w ith CC/4. A Brillouin signal is scattered in the backward di­
rection, with a steepened leading edge o f approximately 30 ps, a shortened
length of less th a n 150 ps, and a c o n trast ratio of 107 : 1. The high contrast
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited without p erm ission.
142
A ppendix B. L aser S ystem D etails
and fast rise-tim e promote rap id OMSS tum -on, w hich is otherwise difficult
to produce in long-life-time devices, due to th e long optical integration tim e
(carrier lifetime).
1.0
600-ps
FWHM
From
mode-locked
tuning laser
Switch-out]— ^
| FR]
0.0
Contrast =
Time (ns)
lO’:!
120-ps
FR
Prism for SRS
v separation
FWHM
0.0
E9605
0.5
Time (ns)
1.0
Multimode step-index
400-tun fibers to Si switches
Figure B.3: D etailed block diagram of pulse-shaping laser system from afte r
th e oscillator, to OMSS’s. A 10-mJ, 150-ps, 5-Hz pulse is split among m any
OMSS’s using a large-diam eter core fiber optical pow er distribution scheme.
6.2 Nd:YAG Laser System
The system shown in Fig. B.4 is a modified commercial mode-locked Nd:YAG
laser oscillator and Q-switched regenerative am plifier followed by a m u lti­
pass amplifier and was th e OMSS illum ination source for the cw currentvoltage m easurem ents an d for th e acquisition of gated microwave tr a n s ­
mission m easurem ents. I t can deliver 12 0 - / j J , 120-ps pulses a t 1064 nm
and 5 Hz. The oscillator can be operated in CW to supply 4 W, and th e re ­
generative amplifier can be used as an oscillator (w ithout injection) w hen
higher-power, nanosecond pulses are desired.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
143
A ppendix B. Laser S ystem D etails
Polarizer
100-MHz mode-locked NdrYAG optical oscillator
UI
Cavity-dumped Nd:YAG regenerative amplifier
Pulse selector
Pockels
cell
Pulse cleaner
Wedge
Pockels
cell
HI
Polarizer
Polarizer
Double-pass
amplifier
Beam splitter
7J4
H2
Beam
expander
Shutter
Laser pulse
Microwave
r~ i
Detector
Delay
Trigger
Microwave signal
generator
E9647
Splitter
Optoelectronic
Signal
microwave switch
Reference
Box-car
integrator
Figure B.4: Block diagram of th e NdrYAG laser system.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Appendix B. L aser S ystem D etails
144
B.3 Laser User’s Facility
A laser system centered around a commercial TirSapphire was used to ac­
quire m aterial characterization d ata on silicon, in the configuration shown
in Fig. B.5. I t illum inated the single-ciystalline and polycrystalline OMSS’s
w ith 90-fs, 24-nJ pulses a t 80 MHz, essentially an optical delta function
relative to the response of the OMSS. The Ti:S laser is pumped by a com­
mercial Argon ion laser a t 29 W. To increase th e accessible spectral range
beyond the 700-1070 nm Ti:S window, th e system also has a commercial op­
tical param etric oscillator th at provides 5 n J pulses from 1200 to 2500 nm.
For greater pulse energy levels, a commercial Ti:S regenerative chirpedpulse amplifier (CPA) pum ped by a commercial, intra-cavity doubled Nd:YLF
oscillator operates a t kH z repetition rates an d provides 1 m J pulses a t ap­
proximately 9 GW peak power. These u ltra fa st pulses from the CPA can be
used to access fa rth e r frequency bands via a n optical param etric amplifier
and difference-frequency generation (120 fs, 100 nJ, 3-12 ^m), or doubling
in BBO, or focusing into a glycol spray or unto a sapphire window for whitelight continuum generation from 400 to 1000 nm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
145
Appendix B. L aser S ystem D etails
Ti:S
70 fs
700-1000 nm
b —
A'— Y
Polarizer
Delay
iiline
C o m p u ter
7!
Acousto-optic
n n modulator
Lock-in
amplifier
Signal
generator
Mixer
/
Compensator
¥ *
Quartz
LiTa03 crystal
■§
IZ o
Figure B.5: Block diagram of th e experimental setu p used for electro-optic
sampling and m aterial characterization. The laser show n is but one p a rt of
a complete system capable of sub-picosecond, 1-nJ pulses from 400 nm to
12 //m.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Документ
Категория
Без категории
Просмотров
0
Размер файла
7 313 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа