# Characterization of time and frequency -varying optoelectronic microwave silicon switches

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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. 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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.

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