Ultrahigh-Bandwidth Vector Network Analyzer Based on External Electro-Optic Sampling

ULTRAHIGH-BANDWIDTH VECTOR NETWORK ANALYZER BASED ON EXTERNAL ELECTRO-OPTIC SAMPLING

M. Y. FRANKEL, J. F. WHITAKER, G. A. MOUROU and J. A. VALDMANIS Ultrafast Science Laboratory, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2099, U.S.A.

(Received 31 July 1991)

Abstract--We report the development of an ultrahigh-bandwidth vector network analyzer useful for small-signal characterization of high-speed semiconductor devices. It employs 100-fs optical pulses for making terahertz-bandwidth electro-optic measurements of electrical signals, as well as for sub-picosecond, photoconductive, electrical-stimulus-signalgeneration. High-bandwidth coplanar strip transmission lines are used for signal transmission. A 0.15 x 50gm gate A1GaAs/InGaAs/GaAs HFET has been characterized over a bandwidth of 100 GHz using this network analyzer. A comparison with conventional RF network analyzer measurements performed to 40 GHz demonstrated good agreement throughout this bandwidth. Such measurements of the actual device characteristics across their entire operating frequency range should improve device development and incorporation into active circuits.

NOTATION scopes are not effective at such high frequencies, the major limitation being imposed by the connectors ~t(f) frequency-dependent attenuation factor fl(f) frequency-dependent phase factor and waveguides needed for signal coupling between d substrate thickness the instrument and the device under test (DUT). This Esos sapphire relative permittivity lack of convenient and accurate high-bandwidth Esup effectivesuperstrate relative permittivity including device characterization methods imposes a serious the effect of an external electro-optic probe f~x transistor maximum frequency of oscillation obstacle to progress in semiconductor device S coplanar strip transmission line spacing between development and utilization. conductors The recent development of ultrafast optoelectronic tr coplanar strip transmission line conductor d.c. con- techniques has allowed novel high-bandwidth device ductivity characterization to be implemented[2-7]. These St1 forward reflection scattering parameter St2 reverse transmission scattering parameter techniques rely on the unrivaled high-speed electrical $21 forward transmission scattering parameter signal generation and measurement capabilities t coplanar strip transmission line conductor thickness provided by ultrashort optical pulses--50fs-10.ps V~ actual incident electrical signal duration--emitted by various lasers. The photocon- V~ measured incident electrical signal V~r measured reflected electrical signal ductive switching method[8] is used to generate pi- V~,t measured transmitted electrical signal cosecond-duration electrical stimulus signals which V r actual reflected electrical signal have bandwidths that extend for hundreds of giga- Vt actual transmitted electrical signal hertz. For electrical measurements over similar band- W coplanar strip transmission line conductor width widths, either photoconductive[8] or electro-optic[9] z electricalsignal propagation distance ZEEp perturbed transmission line characteristic impedance sampling may be used, where the ultimate response of Z0 unperturbed transmission line characteristic such techniques is limited by the duration of the impedance photoconductively generated electrical stimulus signal, the bandwidth of the interconnecting trans- 1. INTRODUCTION mission lines carrying the signals to be measured and the duration of the optoelectronic sampling gate. The continuing advances in the development of mod- There are two significant advantages that opto- ern semiconductor devices have pushed the response electronic techniques possess over conventional, of such devices to frequencies in excess of 400 GHz[1]. purely electronic ones. First, optoelectronic electrical Frequency-domain characterization across this entire signal generation and measurement bandwidths far bandwidth range would be one requirement for exceed those achievable electronically. Secondly, both facilitating further improvements and applications the stimulus-generation site and response-measure- for devices. However, conventional, purely electronic ment planes are physically close to the DUT, so measurement instruments such as vector network that it is possible to completely eliminate any inter- analyzers, spectrum analyzers and sampling oseillo- connection discontinuities (transitions), as well as the

ss~ 35/~-~ 325 326 M.Y. FRANKELet al. errors and uncertainties introduced by the device CPM laser is currently the best source of ultrashort de-embedding procedures. Optoelectronic techniques pulses in the visible region of the spectrum, this laser have been applied and demonstrated up to 100 GHz, has been used in this investigation. The first beam is and the measurement instruments based on these acousto-optically modulated at 3.5 MHz and used to techniques should provide a viable complement to periodically excite a photoconductive switch. The electronic ones. second beam goes through the external electro-optic In this paper we describe the application of the probe (Terametrics Model 200-TIR transducer) to external electro-optic sampling (EEOS) technique[9] gate the electric-field-induced birefringence which for the extraction of small-signal S-parameters of an creates a polarization change in the probe[9]. active device. When combined with a high-band- The beam polarization change is converted via a width, coplanar-strip-transmission-line (CPS) test Wollaston-prism analyzer to an intensity change fixture[10], this technique allows one to determine detectable by the photodiodes. A compensator intro- device small-signal, frequency-domain characteristics duces additional birefringence to bias the intensity over a range of 100 GHz, although it may also be transmission function of this modulator to its 50% extended to significantly higher frequencies. In point, thereby making the intensity change linearly Section 2, we discuss the parameters and the results proportional to the local microwave electric field affecting the selection of electrical signal generation, strength in the probe. The electro-optic probe and measurement and propagation methods. Based on probing beam can be positioned to interrogate electri- these results, we have developed a complete small- cal signals appearing anywhere in the test fixture. A signal device characterization procedure. In slowly varying time-delay is introduced between the Section 3, we demonstrate the implementation of this excitation and the probing laser pulses by passing the procedure to obtain device time-domain and fre- probing beam through an optical delay rail; hence, a quency-domain characteristics. time-domain sampling scheme is realized. A low-noise audio-frequency lock-in is used in 2. OPTOELECTRONIC SYSTEM conjunction with a front-end RF mixer to reduce the signal-to-noise threshold of the described system to Figure l shows the overall measurement system sub-millivolt levels[12]. schematic. The optical pulse source is a balanced The photoconductor switch, used to generate elec- colliding-pulse mode-locked (CPM) laser which pro- trical stimulus transients[8], consists of a gap within vides two 100-fs pulse-trains at a 100 MHz repetition one of the metal transmission-line electrodes de- rate and a wavelength of 620 nm[l 1]. Since the optical posited on a semiconductor substrate. The switch gap pulse duration places a fundamental limit on the typically has a very high dark resistance and is d.c. achievable measurement-system bandwidth, and the biased. The laser excitation pulse, with photon energy

Outputpulse CPM Laser J

Excitatior ~ beam I beam Delay Beam {~ ~--~ rail chopper ~'"~I ~ Polarizer

I I Sy,mulus Photoconductor I I signal switch Jr ~ "~ [ Device under test (DUT) dcu switch i "T"~ Electro-optic I bias _ . ~nsducer Compensatorc~_ X-axis Analyzer [~P-m~,,~ Lockin I Photoaioaes ~ ~ averager

Fig. I. Optoelectronic device characterization system schematic. Ultrahigh-bandwidth vector network analyzer 327 above that of the bandgap of the photoconductor, arrangement have been investigated[15], and it has illuminates the gap, is absorbed, and creates an been shown that a properly designed external probe electron-hole plasma, thereby electrically shorting allows accurate measurements to be made with the gap. Thus, an electrical transient signal which terahertz bandwidth. propagates along the transmission line is generated. Several perturbations in a propagating electrical Three parameters affect the electrical bandwidth of waveform can result from the interaction of the this transient signal--electron-hole pair generation electrical signal with the probe tip. First, reflections rate, electron-hole pair lifetime and switch RC time at the points where the guided waveform enter and constant. The generation of the electron-hole pairs in exit the EEP input and output discontinuities are the semiconductor follows the incident optical pulse linear and cancel out in the frequency domain, where envelope to within the limitations imposed by the only the relative difference in the signals detected at uncertainty principle, assuming the optical pulse two different measurement points is typically desired. spectrum to be within the semiconductor absorption However, perturbations have to be accounted for in band[13]. Hence, for 100-fs optical pulses, the electri- situations where their influence on signals being cal signal bandwidth is determined by the switch measured is not identical. This occurs when a signal geometry and by the carrier lifetime in the semicon- which has traveled through the tip, reflected from a ductor. Proper design of the photoconductor switch discontinuity farther down the line, and returned to geometry to minimize its RC time constant makes the the tip is being measured. The perturbation intro- carrier lifetime the limiting mechanism. So, the rise- duced by the EEP itself can be modeled as a small time of the generated electrical signal is determined reduction of the transmission line characteristic by the optical pulse duration and the falltime by the impedance over the distance the footprint of the carrier lifetime in the semiconductor. To maximize probe overlaps the transmission line. Although the the electrical signal bandwidth, the transmission relative dielectric permittivity of the LiTaO3 EEP lines are fabricated on an ion-implant damaged material is ~ 43, the effective superstrate permittivity Si-on-sapphire (SOS) substrate with a picosecond introduced by the EEP is substantially reduced to carrier lifetime[14]. Thus, the generated electrical esup ~ 5 due to the unavoidable presence of a small signal has a single picosecond duration correspond- air gap between the circuit substrate and the ing to a ~ 35 GHz bandwidth. EEP. The E,up is even lower than the substrate The external electro-optic sampling technique, relative permittivity, e,os ~ 10.4 and thus its influence because of its unsurpassed bandwidth, is used to on the effective permittivity and the characteristic measure the picosecond and subpicosecond electrical impedance of the CPS is small, although not signals generated for device excitation in this work. negligible. Also, it does not require on-circuit, photoconductive As mentioned previously, the electro-optic sampling gate structures, and it is independent of the measurement is sensitive to the electric field. To obtain circuit substrate material. Figure 2 shows the a voltage calibration, an electrical signal of 1.0 V is measurement position of an external electro-optic applied to the transmission line at the modulation probe (EEP) fabricated from an Li tantalate frequency of 3.5 MHz. The induced birefringence of (LiTaO3) crystal relative to a signal-carrying trans- the electro-optic probe is detected and the resulting mission line and the optical probing team. The accu- lock-in offset signal provides the calibration infor- racy and invasiveness of such a measurement mation necessary to determine any transient electrical

Probe Probe beam beam Excitation beam \ ~ica~Fused\ LiTa~O3

~ c-axis

K(-~H.-,-,'A rh'.'H.'/A I Side view End view Fig. 2. Schematic of the external electro-optic probe, the coplanar strip transmission line and the probing beam alignment. 328 M.Y. FRAr4KELet al.

signal amplitude on the transmission line. Since the .... , . ~, . , . . , .... calibration signal is applied externally, care must be (11 "~ 0.8 taken to determine its actual amplitude at the point where the short-pulse measurements are to be made. E 0.6 The selection of microstrip or coplanar strip transmission line for the device test fixture is dictated by .N 0.4 the considerations of high-bandwidth electrical- E signal generation and propagation properties. The 0,2 Z microstrip bandwidth is primarily determined by the ./ thickness of the dielectric substrate, and mechanical 5 10 15 20 25 limits on this dimension impose an upper boundary Time(ps) on its bandwidth. However, the CPS is photolitho- Fig. 4. Comparison of modeled and measured picosecond graphically defined and can be scaled to much higher pulse propagation on a CPS with S = 5 #m, W = 50 #m, bandwidths. t = 1.2#m, tr =2 x 107Sm -t, d=430#m, E~os= 10.4. Figure 3 shows the electrical waveforms generated by photoconductor switches embedded into ~ 50 £~ impedance microstrip (90#m wide top electrode, that may last for tens or even hundreds of picosec- 100 #m thick sapphire substrate) and ~ 60 £~ onds. To investigate this parasitic effect, a CPS impedance CPS transmission lines (for dimensions analysis procedure has been implemented following see Section 3), as measured ~ 300 #m from the gap. the work of Gupta et al.[17] for a coplanar wave- The microstrip signal is longer in time indicating guide. To verify the accuracy of this procedure, we lower bandwidth. The electrical signal round-trip have measured and modeled picosecond electrical time between the top electrode and the ground plane pulse propagation with the dimensions specified in (~ 2 ps) is greater than the switch response time Fig. 4. The excellent agreement between the measured ( ~ 1 ps), resulting in the substantial ringing evident and the modeled risetime, amplitude, falltime and in the microstrip signal. Thus, the CPS geometry was trailing shoulder evident in this figure justifies the found to be a better choice for high-bandwidth assumption that the model behaves adequately at electrical signal generation and propagation. Ad- both low- and high-frequency extremes. ditionally, the planar nature of the CPS potentially The shoulder formation is attributed to the ohmic allows for a parasitic-less integration with the planar contribution of the conductor in the dispersion and devices under test (i.e. connections through via holes the attenuation. Most of the geometric parameters of to the microstrip ground plane are not necessary). the CPS are fixed, as they are dictated by the require- The propagation properties of the CPS have been ments on characteristic impedance, minimum attenu- investigated with terahertz bandwidth to determine ation and dispersion, coupling to the device and the geometry most suitable for the vector network physical realizability. The parameter that can be analyzer application[10]. The obtained analytic for- varied and that is shown to strongly influence the mulas allow for an accurate and convenient compu- low-frequency CPS characteristics is the conductor tation of the CPS high-frequency attenuation ~t(f) thickness. Figure 5 shows the effects of 5 mm of CPS propagation on a 1 ps FWHM 1 V amplitude Gaus- and dispersion fl(f) characteristics. The low-frequency propagation characteristics are sian pulse. The modeled pulses have been normalized equally important for a truly broadband characteriz- to a unity peak amplitude which is off the scale of the ation. In particular, the low-frequency dispersion and graph to emphasize the shoulder formation (the actual peak amplitudes are indicated on the figure). attenuation effects have been shown by Paulter et al.[16] to cause a propagating picosecond electrical The thinnest, 0.5 #m conductor clearly shows a very pulse to develop a low-amplitude, trailing shoulder 0.2 2.5 0.15 0.1 2 Q. Microstrip E 0.05 .~ .Z..z.: ...... 1.5 -~ 0

"C} 1 ._N -0.05 -0.1 -- 0.5 .~~an ar strip 0 Z -0.15 0 °'285' go 9s i00 ios i~o i~S i20 i25 -05 . .~ .... i , ,i .... i .... i .... p 0 5 10 15 20 25 30 Time(ps) Time (ps) Fig. 5. Modeled 1 ps FWHM 1V Oaussian pulse after Fig. 3. Comparison of photoconductively generated electri- 5 mm of propagation on a CPS with S = 5 #m, W = 50 #m, cal transients on microstrip and coplanar strip transmission tr =2 x 107Sm -l, d =430#m, ~,os= 10.4 and with thick- lines. ness t as parameter. Ultrahigh-bandwidth vector network analyzer 329

Photoconductor Sampling External electro-optic switch spot probe

Fig. 6. Ultrahigh-bandwidth vector network analyzer device holder. long, low-amplitude shoulder due to the high resistive superimposed and a distinct time window was defined attenuation and dispersion at low frequencies. The for each signal. Similarly, the 6 mm input CPS is low-frequency dispersion is highest for the 1.5-/am- sufficiently long so that one can separate in time the thick conductor and produces the highest initial reflected DUT signal from signals arising at other shoulder amplitude. However, the shoulder decay discontinuities. time is also faster due to the reduced attenuation. A measurement 200/am from the output of the Finally, although low-frequency dispersion is still DUT (C on Fig. 6) was used to obtain the forward present for the 3.0/am conductor, the reduced attenu- transmission signal. Again, the CPS was long enough ation leads to the disappearance of the shoulder in to time-window the transmitted DUT signal from preference of increased ringing caused by the domi- reflections due to discontinuities further down the nance of high-frequency dispersion. CPS. After the forward time-domain signals have been 3. DEVICE CHARACTERIZATION measured, the switch bias is applied to the other end of the test fixture, and an identical procedure is The results from the previous section were used to followed to determine the time-domain character- develop a CPS based vector network analyzer (VNA), istics while exciting the output port (device drain). as shown in Fig. 6. The symmetric design of the VNA The DUT employed for this experiment was a allows a complete two-port characterization of a General Electric 0.15 x 50/am gate pseudomorphic DUT wirebonded into this test fixture. The CPS had heterojunction field-effect transistor (HFET), devel- 50/~m wide conductors separated by 5/am, and it was oped and described by Smith et al.[18]. Its design was fabricated on an ion-implant-damaged, SOS sub- different from conventional high-electron-mobility strate, resulting in a characteristic impedance transistors in that a planar doped layer was incorpor- Z0~ 60f~ (including finite metalization thickness ated into the strained channel. It improves the con- effects). duction channel carrier density, which more than As discussed previously, the optical excitation of a compensates for any degradation in the mobility. An d.c.-based, ion-implanted SOS photoconductor AIGaAs/GaAs superlattice is used below the channel switch results in the generation of picosecond electri- to improve the carrier confinement. This device was cal pulses. Photoconductor switches are embedded chosen for its high-speed, large breakdown voltages, into the CPS and the d.c.-bias voltages are brought and lack of detrimental low-frequency effects due to to the DUT along the same lines as the broadband DX-centers in the A1GaAs buffer layer. electrical stimulus pulses. Figure 7 shows the signal measured on the DUT Two spatially separated measurement points on the gate input and drain output transmission lines. It input CPS (A and B on Fig. 6) were used to exper- should be noted that the resistive shoulder effects imentally obtain waveforms which were compared described earlier have already been subtracted out for with each other to determine the broadband attenu- clarity. The distinct incident and reflected waveforms ation ~(f) and dispersion/~(f) characteristics of the demonstrate the benefits of removing the measure- line. One measurement point on the input CPS (B on ment plane from the DUT, allowing the signals to be Fig. 6) was used to obtain both the incident and time-windowed. As can be seen, the input signal reflected gate signals. It was separated by 1.2 mm recovers to its baseline before the reflected signal from the DUT to allow the incident signal to recover arrives from the DUT. The 6-mm-long input CPS to its baseline before the reflected signal was detected. assumes that the DUT reflected response itself recov- The incident and reflected pulses were thus not ers to its baseline before any other discontinuity 330 M.Y. FRANKELet al.

0.005 i i i i i i i i i i

Gate incident,Vmi Gate reflected, Vmr 0.003

R 0.001 3 -8

~" -0.001 7 <

-0.003 Drain transmitted, Mint

-0005 i I I I I I I I I I 0 10 20 30 40 50 Time (ps ) Fig. 7. Measured time-domain signals on the gate and drain transmission lines in the forward measurement mode.

reflections arrive at the measurement plane. Similarly, is then employed to normalize this, and subsequent the drain output is seen to recover to the baseline S-parameters, to a standard 50 f~ impedance[19]. completely within the measurement time-window. Additionally, at this time the absolute voltage level The forward reflection scattering parameter (S- calibration of our electro-optic measurements is only parameter) Sn is computed from the ratio of the accurate to ~ 10-15%. The VNA data has thus been Fourier transform of the reflected and the incident scaled by a constant to exactly match the HP8510 time-domain signals. Since the EEP perturbs the data at low frequency (2 GHz), where confidence is signals slightly, as described in Section 2, we have to highest that the results should overlap. The VNA correct for its effects on the incident and reflected phase reference calibration can be obtained from the signals. As a first approximation, we take into reflectance and transmission measurements of an account only single reflections at the EEP interfaces unbiased (i.e. cold) transistor. This technique is and ignore any resonant (multiple reflection) effects. analogous to the one in which a through-line is used Then, the ratio of the actual reflected and incident as a reference standard. The advantage is that no signals V,/V~ is given in terms of the measured ones actual through-line has to be wirebonded into the Vmr/Vmi as: fixture, minimizing uncertainties due to unavoidable v~ Zo Vm~ wirebond differences. Figure 8a shows the comparison between the SH Vi ZEEpVmi (I) amplitude and phase obtained from the electro-optic where the CPS characteristic impedance, perturbed measurements up to 100 GHz, with the conventional due to the EEP over its footprint overlap, is given as: HP8510 network analyzer data acquired to 40 GHz. The forward transmission scattering parameter $21 ~/~o, + 1 ZEEP = Zo Eso, + Esup " (2) is computed from the ratio of the Fourier transforms of the transmitted and the incident time-domain Combining eqns (1) and (2), the gate reflection signals as: S-parameter is computed as: S2~ = F{{V::lexp[(~ +jfl)z ]. (4) = ,~o~+. _.,~,, F{ V,.,,r} 311 ~/ Esos--~ I F{gmi } exp[(a +jfl)z], (3) No correction due to the EEP is necessary in this case where F{ } denotes a Fourier transform operation. since the transmitted signal is measured with the EEP The addition of the exponential term corrects for the removed from the input line and Vmt/Vmi = Vt/Vi. small attenuation and dispersion introduced by the Figure 8b shows the 50 f~ normalized S:l amplitude CPS and allows the effective measurement planes to and phase data from the electro-optic and conven- be moved up to the device wirebonds. tional HP8510 network analyzer measurements. However, the S-parameter obtained from eqn (3) is Similarly, the reverse scattering parameters can be referenced to a 60 f~ CPS transmission line used in the obtained from measurements at the other port. The VNA. A straightforward impedance transformation reverse transmission parameter, Sl2, in particular Ultrahigh-bandwidth vector network analyzer 331

(a) ~ 3O 5 50 [-- Electro-optic to 100 GHz i 0 E 25 .%7'ol ~n -50 ~ ¢~ v "O ~ 20 0 "O -.s -150 ~ ='~ e~ E -2oo~ E lo

.300 v o -10 -350 10 100 20 40 60 80 100 Freq(GHz) Freq(GHz) Fig. 9. Maximum unilateral gain computed from measured S-parameters. (b) 10 200

I-- Electro-opticto 100 GHz [ 150 CO • • . . . .. " the variation in the tested devices, which were not

~ fi 100 ~- identical, but diced from the same wafer. "O Conventional figures of merit, such as the unity current gain frequency and the maximum frequency E ~ 0 0 ~ of oscillation (/max) can be determined from the CO measured S-parameters without need for extrapolation. -5o ~ Figure 9 shows the maximum unilateral gain curve -5 ...... 100 computed from both the electro-optic and HP8510 20 40 60 80 100 measured S-parameters. The electro-optically, directly Freq(GHz) measuredfmax is seen to be ~ 94 GHz. This is slightly (c) lower than that obtained from the extrapolated -10 100 HP8510 measurements, although this could be due to -15 the sources of error previously mentioned. Work is in O~ -2o so ~ progress to apply this technique to the characteriz- .~ -25 ation of much faster devices. .= ~ -30 o $ 4. CONCLUSION ~ -35 e~ -40 -50 ~ A vector network analyzer that utilizes photocon- GO -45 ductor switches for picosecond electrical signal gener- -50 -100 ation, the external electro-optic sampling technique 20 40 60 80 100 for measurement, and coplanar strip interconnecting Freq(GHz) lines for electrical signal transmission has been devel- Fig. 8. S-Parameters measured electro-optically (up to oped and demonstrated. The vector network analyzer 100 GHz) and with HP8510 (up to 40 GHz). (a) Sl~; (b) $2=; has been applied to the small-signal time and (c) Si2. frequency-domain characterization of modern ultrafast transistors. A characterization bandwidth of indicates the degree to which the transistor is unilat- 100 GHz has been experimentally demonstrated (i.e. eral. A good device would exhibit a very small reverse without need for extrapolation). Work is in progress transmission, ideally tending to zero at d.c. and hence to extend this bandwidth by several times, while this parameter tests the limits of the dynamic range characterizing devices with cutoff frequencies greater of the measurement system. This property for the than those reported here. electro-optic technique is indeed demonstrated by the Acknowledgements--M. Y. Frankel would like to thank reverse transmission ($12) measurements. Figure 8c Siemens, Munich for financial support. This work was shows the 50 f~ normalized S12 amplitude and phase supported by the Air Force Otfice of Scientific Research, data from the electro-optic VNA and HP8510 net- University Research Initiative under Contract No. AFOSR- work analyzer. As can be seen, the match between the 90-0214. electro-optic measurement and the HP8510 measurement is good over the common frequency span within REFERENCES a range of ~ 25 db. In general, the agreement between 1. P. Ho, M. Y. Kao, P. C. Chao, K. H. G. Duh, J. M. the two methods is good over a range of ~ 40 db. Ballingall, S. T. Allen, A. J. Tessmer and P. M. Smith, The disagreements can be attributed to the differ- Electron. Lett. 27, 325 (1991). 2. P. R. Smith, D. H. Auston and W. M. Augustyniak, ences in the DUT wirebonds, which are not de- Appl. Phys. Lett. 39, 731 (1981). embedded in either the RF or electro-optic measure- 3. D. E. Cooper and S. C. Moss, IEEE J. Quant. Electron. ments. Additional differences could be introduced by QE-22, 94 (1986). 332 M. Y. FRANKEL et al.

4. M. Matloubian, H. Fetterman, M. Kim, A. Oki, J. 12. J. M. Chwalek and D. R. Dykaar, Rev. Sci. Inst. 61, 1273 Camou, S. Moss and D. Smith, IEEE Trans. Microwave (1990). Theory Tech. 38, 683 (1990). 13. P. P. Vasil'ev, Soy. J. Quant. Electron. 20, 209, (1990). 5. C. Rauscher, IEEE Trans. Microwave Theory Tech. 39, 14. F. E. Doany, D. Gfischkowsky and C.-C. Chi, Appl. 1179 (1991). Phys. Lett. 50, 460 (1987). 6. M. Y. Frankel, J. F. Whitaker, G. A. Mourou and J. A. 15. M. Y. Frankel, J. F. Whitaker, G. A. Mourou and J. A. Valdmanis, Picosecond Electronics and Optoelectronics Valdmanis, IEEE Microwave Guided Wave Lett. 1, 60 Conf., Salt Lake City, UT (1991). (1991). 7. C. H. Lee, IEEE Trans. Microwave Theory Tech. 38, 596 16. N. G. Paulter, D. N. Sinha, A. J. Gibbs and W. R. (1990). Eisenstadt, IEEE Trans. Microwave Theory Tech. 37, 8. D.H. Auston, IEEE J. Quant. Electron. QE-19, 639 1612 (1989). (1983). 17. S. Gupta, J. F. Whitaker and G. A. Mourou, IEEE 9. J. A. Valdmanis, Electron. Lett. 23, 1308 (1987). Microwave Guided Wave Lett. 1, 161 (1991). 10. M. Y. Frankel, S. Gupta, J. A. Valdmanis and G. A. 18. P. M. Smith, L. F. Lester, P.-C. Chao, P. Ho, R. P. Mourou, IEEE Trans. Microwave Theory Tech. 39, 910 Smith, J. M. Ballingall and M.-Y Kao, IEEE Electron (1991). Dev. Lett. 10, 437 (1989). 11. J. A. Valdmanis and R. L. Fork, IEEE J. Quant. 19. G. Gonzalez, Microwave Transistor Amplifiers Analysis Electron. QE-22, 112 (1986). and Design. Prentice-Hall, Englewood Cliffs, NJ (1984).