Coplanar transmission lines on thin substrates for high-speed low-loss propagation

396 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 42, NO. 3, MARCH 1994

Coplanar Transmission Lines on Thin Substrates for High-speed Low-Loss Propagation

Michael Y. Frankel, Robert H. Voelker, and James N. Hilfiker

Abstruct- We investigate the attenuation and phase velocity characteristics of coplanar strip (CPS) transmission lines designed for high-speed, low-loss propagation at sub-THz frequencies. Photoconductor switches driven by femtosecond optical pulses were used to generate propagating picosecond electrical transients. External electrooptic sampling was used to measure the time-domain impulse-response characteristics with subpicosecond time resolution. The finite-difference transmission-line- matrix (FD-TLM) numerical method was used to model picosecond pulse propagation on identical transmission lines. The experiment and the numeric simulations have clarified nonquasistatic high-frequency effects and were shown to agree over a 500- GHz frequency range. Additionally, analytic quasi-static velocity and characteristic impedance formulas have been verified and their frequency range of validity established for the investigated CPS geometries. Radiation into the substrate is the dominant loss mechanism at frequencies above -100 GHz for the CPS lines on thick substrates. CPS transmission line fabrication on thin substrates has been proposed as a method for reducing high-frequency loss and increasing the microwave propagation velocity. CPS transmission lines fabricated on I-pm-thick Si membranes have been studied and demonstrated to possess the desired high-speed, low-loss properties.

I. INTRODUCTION IGH-speed, low-loss coplanar transmission lines are H important for a variety of applications, including mi-

crowave integrated circuits [ 11, ultrafast device characterization [2], and traveling-wave optical modulators [3]. Coplanar transmission lines are typically fabricated on relatively thick substrates with an air superstrate. Therefore, in the quasi- static limit, the microwave guided mode propagates with a phase velocity determined by the average of the air and substrate relative permittivities. Typical substrates have high permittivities resulting in a factor of 3 to 6 reduction in propagation velocity compared to that in vacuum.

In addition, the microwave guided mode experiences an inhomogeneous dielectric. The result is a highly non-”EM behavior at higher frequencies exhibited as phase velocity dispersion and attenuation, which severely limits the transmission line bandwidth.

Several methods have been proposed to improve the transmission line characteristics by increasing the propagation

Manuscript received March I , 1993; revised May 17, 1993.This work was supported in part by the Office of Chief of Naval Research, in part by the Center for Electro-Optics, and in part by the Research Council of the University of Nebraska-Lincoln.

M.Y. Frankel is with CODE 5670, Optical Sciences Division, Naval Research Laboratory, Washington, DC 20375-5338.

R.H. Voelker and J.N. Hilfiker are with the Department of Electrical Engineering and Center for Electro-Optics, University of Nebraska-Lincoln, Lincoln, NE 68588-05 1 1.

velocity and decreasing the attenuation. One of these relies on etching away most of the substrate material between the CPS electrodes, allowing the guided mode to experience mostly air dielectric [4]. However, such technique may not be applicable to all substrate materials of interest. Another method for increasing the propagation velocity is to use thick coplanar transmission line electrodes on a thick substrate [3]. The thick electrodes force the guided mode to experience an effectively lower permittivity dielectric and propagate with a higher velocity. However, the significant velocity mismatch between the microwave guided mode and possible substrate modes results in large radiative losses into the substrate at high frequencies [ 5 ] .

A method for reducing dispersion, which relies on fabricat- ing coplanar transmission lines on thin substrates, has been demonstrated [6]. The microwave guided mode field extends past the substrate material into the air, and the fraction of the guided mode volume occupied by the high permittivity material is reduced, which reduces the effective permittivity [ 7 ] , [SI and dispersion [9]. The use of a thin substrate also serves to suppress the radiative losses [ 5 ] . This technique can produce coplanar lines with good propagation characteristics and is applicable to a wide range of substrates. Furthermore, the geometry still allows for the interaction of microwave fields with the substrate as required for optical traveling-wave modulators [8].

Here, we investigate the propagation characteristics of CPS transmission lines fabricated on thick as well as thin- membrane substrates. We apply ultrafast optoelectronic microwave signal generation and measurement techniques, as described in Section 11, to experimentally obtain the phase velocity dispersion and attenuation characteristics over an 800 GHz frequency range. Quasi-static formulas and a finite-difference transmission-line-matrix numeric analysis technique, described in Section 111, are used to model the CPS characteristics. In Section IV, we demonstrate the quasi- static formulas to be accurate to within 6% at low frequencies for both phase velocity and impedance. The numeric analysis is demonstrated to be accurate over a 500 GHz bandwidth for the investigated transmission lines, reproducing the measured dispersion and attenuation effects.

11. EXPERIMENT

The frequencies of interest in this work are consider- ably higher than those easily accessible with conventional electronic instrumentation. Therefore, ultrafast optoelectronic experimental techniques have to be utilized. We have used

0018-9480/94$04.00 0 1994 IEEE

PaANKBL er aL: COPLANAR TRANSMISSION LINES ON THIN SUBSTRATES 397

photoconductor switches and extemal electrooptic sampling to generate and measure the electrical transients with frequency content extending to near 1 THz [lo], [ll].

The optical source was a dispersion-compensated colliding- pulse mode-locked laser producing two optical pulse trains with a 100 M H z repetition rate. The 620 nm wavelength pulses had a -150 fs full width at half maximum (FWHM). The experimental measurement geometry is shown in Fig. 1. One of the optical pulse trains was focused between the dc- biased electrodes of the CPS line and generated an electrical transient which propagated along the transmission line. The other optical pulse train passed through an extemal electrooptic probe positioned on the CPS line. The induced birefringence change in the probe alters the beam polarization, which is demted by slow photodetectors after additional optical processing [12]. The propagating transients are measured by

I

~

scanning the time delay between the excitation and probe I optical pulses.

The probe was positioned at points 0.2, 0.7, 1.2, 2.2, and 3.2 mm from the transient generation site along the CPS to investigate the electrical pulse evolution as it propagates. The fresuency domain CPS characteristics can then be obtained by taking a ratio of the Fast Fourier Transforms (FFT) of any pair of measprements. The electrooptic transducer perturbation of the m a t i n g mode may be assumed to be linear, and its influence.on the frequency domain results will cancel out. The accuracy of the frequency-domain attenuation coeffi-

cient is -cult to asses. It is dominated primarily by the timedomaiu waveform tmmtion e m [MI, and these errors depend criticaUy on the shape and duration of the generated transient. AS will be discussed in Section lV, the mrs are more severe for the CPS on Si membranes. However, we estimate a maximum error of Q.2 Np/mm at 800 GHz and rapidly decreasing errors at lower frequencies.

The accuracy of the experimental low-frequency phase velocity extracted from the measurements is limited primarily by the knowledge of the separation distance between the signal " e n t points. The position measurement is estimated to be accurate to within 10 pm, giving a relative low- frequency velocity error of under 2%. At higher frequencies, the waveform truncation errors become important and lead to additional inaccuracies.

Four transmission line configurations were investigated to clarify the influence of the geometric parameters on the microwave propagation characteristics. CPS lines with 12.5 pm conductors and 26.5 pm gap (12.5126.5) and 12.5 pm conductors and 59 pm gap (12.5159) were fabricated on two different substrates. One of the substrates was a 430 pm-thick sapphk wafer with a 0.5 pm film of epitaxial Si (SOS). The CPS lines on this substrate represented the thick-substrate limit. The other substrate was an 8pm-thick commercially available Si membrane [ 131. Conventional photolithography process was used to define the electrodes after the membrane was grafted onto a thick Si support wafer with a layer of photomist. The CPS metalization was 300/2500 a TdAu film.

The frequency domain characteristics are best obtained from the impulse-like time-domain waveforms. Furthermore, time-limited signals allow us to window out the effects of

Probelaser Probelaser beam in beam out

Total intemal reflection LTa0,bansducer

Excitation laser beam

Ph sw switch

I substrate

Fig. 1. Typical excitation and electmoptic sampling geometry for a coplanar strip transmission line.

the transmission line terminations. The generation of required ultrashort electrical transients demands the use of a short-carrier-lifetime material for the photoconductor switch. Nitrogen implant at several energies was used to damage the material to a depth of w.06 pm and reduce the carrier lifetime in both the SOS and Si-membrane substrates.

After the implantation, the membrane was detached from its Si wafer support by soaking in acetone and was mounted on an aerogel support substrate [ 141. The aemgel support with an index of qdraction of N 1 .Of5 provided mechanical stability while at the same h e preserving a ne=-perfect membrane-air interface.

m. SIMULATION

halytic formulas have been developed that allow us to calculate the quasi-static characteristic impedance and phase velocity for the CPS lines on substrates of varying thickness as [7]:

1207rK(k) & X ( k ' ) ' Zcps =

cP - 1 K(k')K(kl) &,tf = 1 + -

2 K(k)K(k{) '

C vph = -

where c is the speed of light in vacuum,

(3)

s, w: and h are interelectrode gap, electrode width and substrate height respectively, K is the complete elliptic integral of the first kind, and k' = d m .

Nthough (1H3) are approximations, they have been numerically shown to be reasonably accurate for a wide range of geometrical parameters [7]. However, their frequency range of validity has not been experimentally tested. If experhen- tally verified, these equations will provide a convenient tool for the synthesis of CPS transmission lines with specified characteristics.


X Fig. 2. perfectly-conducting rectangular shielding box.

Layout of half of the 12.5/59-pm CPS on 8-pm silicon inside of a

To further develop the tools for the analysis of the thin-substrate transmission lines, we have implemented a finite-difference transmission-line-matrix (FD-TLM) numeric technique. The full-wave time-domain FD-TLM numerical method solves Maxwell’s curl equations for the electric and magnetic fields at discrete points in space [15]. By selectively modifying the parameters at these points, or nodes, material properties such as permittivity, permeability, and conductance are represented. In the FD-TLM method, space is discretized in three dimensions with a variable mesh to allow closely spaced nodes in areas where the fields are intense and rapidly varying, and widely spaced nodes where the fields are weak and slowly varying in space. The variable mesh provides good accuracy and uses much less computer time and memory than would a closely spaced uniform mesh.

The procedure used to perform the FD-TLM simulations is explained for the 12.5159 CPS fabricated on the Si membrane. Fig. 2 shows half the CPS housed in a perfectly conducting rectangular shielding box with 2, y. z dimensions of 1.0245, 1.964, and 1.615 mm, respectively. The Si membrane is located 0.96 mm from the bottom. Since the CPS structure is symmetrical, only one line is simulated with the left box boundary acting as an electric wall to provide the image representing the other conductor. Utilizing symmetry reduces the computer memory and time requirements by half. Perfectly conducting boundary conditions are readily implemented in the program and require no cumbersome special code, unlike free-space boundary conditions.

Table I describes the variable mesh spacing along the three coordinates starting at the origin. The mesh is specified as multiples of the 2pm unit spacing. The mesh is fine near the conductors and is smoothly graded to a coarse mesh at the metal walls. There are two constraints on the choice of mesh size. First, to avoid excessive dispersion caused by the discretization of space in the FD-TLM method, the largest mesh spacing must be much smaller than the wavelength of the highest frequency component expected to propagate [16]. Thus, l l p m is used as the largest mesh spacing in

TABLE I VARIABLE-MESH DISCRETIZATION OF THE

12.5/59-j~m CPS ON &pm-THICK SI MEMBRANE

x-axis y-axis z-axis

1-87 5.5 1-24 18.0 1-8 5.5 88-90 3.0 25-27 9.0 9-11 2.5 9 1-94 1.25 28-30 4.0 12-17 1.0

95-112 1 .0 31-33 2.0 18-20 2.5 113-113 1.75 34-43 1.0 21-155 5.5

4446 2.0 47-49 4.0 50-52 9.0 53-77 18.0

cell No. space cell No. space cell No. space

the Si substrate, which is one-tenth of a wavelength at 800 GHz. Likewise, in air the largest mesh spacing is 36 ym, which is one-tenth of a wavelength at 800 GHz. Although using a smaller maximum mesh spacing would provide better accuracy, it would also require more nodes and thus more computer memory and time.

Second, the width of the conductors also must be adequately represented. This requirement forced the choice of the mini- mum mesh spacing to be 2pm, which provides six mesh cells across the conductor width. Better accuracy could be obtained by using a smaller unit mesh spacing, but this would consume additional computer resources in two ways. Using more nodes to describe the conductor width increases the amount of memory required and the number of computations. Additionally, the time step is proportional to the unit mesh spacing. Thus, for a given simulation duration, more computations are needed for a smaller unit mesh spacing.

The CPS transmission lines on a thick substrate are similarly simulated, but with the bottom half of the box filled by sapphire dielectric. For simulation purposes, we assume that the epilayer of Si on top of the thick sapphire substrate is negligibly thin and can be ignored.

The CPS conductors are modeled as having infinite con- ductivity, since the purpose of the simulations is to evaluate the radiative loss and dispersion properties rather than the resistive skin-effect loss. Also, the conductors are modeled as being infinitely thin-a reasonable approximation of the actual lines, because they are only 0.28ym thick and their width and separation are much larger.

The simulation proceeds by applying an x-directed electric field between the left edge of the conductor and the left box wall, indicated by “Ez” in Fig. 2. Temporally, this odd-mode excitation is in the form of a 1.7 ps FWHM Gaussian pulse with a delay of 3 ps. As the Gaussian pulse propagates along the CPS toward the rear wall of the box, the higher-frequency components will travel more slowly and will be attenuated more than the lower-frequency components. The voltage is calculated every 0.1 ps in the simulation by integrating the z-directed electric field from the edge of the conductor to the left wall while the current is calculated by integrating the transverse magnetic field along a rectangular path surrounding the conductor, indicated by “I” in Fig. 2. Frequency-domain dispersion and attenuation are found by calculating the ratio of the FFT’s of voltage samples at two widely spaced points along the CPS, indicated by “VI” and “VZ” in Fig. 2. The

PRANKBL n d: COPLANAR TRANSMISSION LINES ON THIN SUBSTRATFS

"."

A 1.4 --measured E . m&eM

0

1-

2.0 10'

2 1.2 ioa ir" 1.6 10' -%

>

Ei 0

8.0 io7 3 > W

4.0 io7 u) 4[

FREQUENCY (GHZ)

(b)

Fig. 3. Frequencydomain characteristics of a 12326.5 pm CPS on 430-pm-thick SOS. (a) Phase velocity and attenuation; @) characteristic impedance from numeric simulations and (1).

CPS impedance is found as the ratio of the FTT's of voltage and current at a single point. Before calculating the frequency response, the time-domain samples were time windowed to remove the reflections of the initial pulse from the walls of the rectangular box.

IV. RESULTS AND DISCUSSION Figs. 3 and 4 show the measured and simulated frequency-

domain results for the CPS lines on the thick SOS substrate. These measurements allow us to validate the simulation and the experiment based on a known transmission line behavior [ 111. The sapphire substrate is birefringent, with the ordinary and extraordinafy permittivities being 9.4 and 11.6, respectively. In the calculations, the substrate permittivity of 10.44 was used as computed from the geometric mean of these two values [17].

Fig. 3(a) shows the phase velocity and attenuation for the 12326.5 CPS on SOS. For fresuencies up to 100 GHz, the phase velocity is nearly constant and is indistinguishable from the quasi-static value obtained from (3) with h + 00.

For fresuencies above 100 GHz, modal dispersion appears as a decrease in the phase velocity due to the preferential confinement of the guided mode to the substrate material. lEe resistive losses m poorly resolved in the experimental

results. However, the primary objective was the elimination of high-frequency losses dominated by radiation into the substrate. Such radiative loss appears as a rapid increase

10 100 1 FREQUENCY (GHz)

W x 4 gg n r g No E K

399

2.0 I O 8

2 1.6 10' -'

g 1.2 10'

8.0 107 3 4.0 io7 3 E

W >

0 10

180 , 1

160 140

120 100

80 60

40 20

0

2,. quasi-static I====+ L 4

FREQUENCY (GHz) (b)

Fig. 4. Fquency-domain characteristics of a 12.5159-pm CPSon 430-pm-thick SOS. (a) Phase velocity and attenuation; (b) characteristic impedance from numeric simulations and (1).

in the attenuation coefficient above 100 GHz. As has been shown before [ 113, this loss increases as a near-cubic power of frequency. The agreement between the measurements and the FD-TLM simulation is good to 500 GHz.

Fig. 3(b) shows the characteristic impedance computed from the FD-TLM simulation results, as well as (1) results with h + 00. The analytic formulas are seen to agree to within 3% with the numeric simulations, again indicating the validity of the analytic quasi-static formulas in the thick-substrate limit at low frequencies.

As expected for the thick substrate limit, the 12.5159 CPS on SOS shows the same low-frequency phase velocity as the 12326.5 CPS, as seen from Fig. 4(a). However, the modal dispersion effects are more severe than those for the narrower CPS. Also, the radiative loss is seen to be much larger for the wider line as compared to the narrower one, as expected from its dependence on the CPS transverse dimensions. Thus, increased dispersion and attenuation effects of the wider line indicate that it has significantly poorer propagation characteristics.

The FD-TLM simulation shows good agreement with the measurements up to 400 GHz. The characteristic impedance from (1) is within 5% of the value computed from the numeric simulations at low frequencies, as can be seen in Fig. 4(b).

The dispersion and loss levels observed for the CPS lines on thick substrates ate unacceptable for high-speed low-loss signal transmission and must be reduced. As suggested in


a

pp , , , , 2.0 - measured

-

V , quasi-static

h - I -

2 0.8 P i 8.0

0.0 - 10 100

FREQUENCY (GHz)

(a)

108 *- t 0

w > 107 S

107 2 a n r

1.2 1.6

5 1.2 -measured

1 8.0 1 4.0

r + - 1,. . I 0

O . O l b - - - - - - 100 1000 Freq (GHz)

(a)

IO8 +”

10’

t 0 0

> 107 2 a

n I

(b) (b) Fig. 5. Frequency-domain characteristics of a 12.5/26.5 pm CPS on Fig. 6. Frequency-domain characteristics of a 12.5159-pm CPS on 8-pm-thick Si membrane.(a) Phase velocity andattenuation; (b) characteristic 3-pm-thick Si membrane. (a) Phase velocity and attenuation: (b) characteristic impedance from numericsimulations and (1). impedance from numeric simulations and (1).

the introduction, a possible way of reducing both the CPS attenuation as well as the propagation delays is to reduce the substrate thickness.

Figs. 5 and 6 show the frequency-domain data obtained for the CPS transmission lines with identical transverse dimensions as before, but fabricated on 8pm-thick Si membranes.

The ripple apparent in the frequency-domain data extracted from the time-domain measurements is due to the signal waveform extending beyond the measurement time window [18]. The Nitrogen implant used to reduce the carrier lifetime in the material had a penetration depth of -0.6pm. However, the absorption depth of 620nm light in Si is -2.2 pm, and a large number of carriers were photogenerated below the implanted region. These. carriers have long lifetimes, and it is speculated that they contribute a substantial long-lived shoulder to the generated electrical transient. Thus, clean and unambiguous time windowing is precluded.

The phase velocity, shown in Fig. 5(a) for 12326.5 CPS, is increased 23% as compared to one that would be obtained for the semi-infinite substrate. The quasi-static value computed from (3) is in reasonable agreement with both the measurements and the numeric calculations. The high-frequency dispersion is still present in this transmission line, but the attenuation has been reduced to a level below one that can be accurately resolved in our measurements. We can, however, assign a maximum value of -0.2 Np/mm to attenuation at the

highest frequency of 800 GHz as compared to 1.2 Np/mm for the thick-substrate CPS at the same frequency. The FD- TLM simulation did not show any losses up to 600 GHz, and the phase velocity matches the measured one fairly accurately. This indicates the effectiveness of the FD-TLM method for modeling thin-substrate CPS lines.

The characteristic impedance, shown in Fig. 5(b), is larger than that for the thick-substrate case. This is expected due to the decreased effective permittivity. Equation (1) agrees with the numerically computed impedance to within 6% for frequencies up to 100 GHz.

The phase velocity for the 1 2 3 5 9 CPS on the membrane, shown in Fig. 6(a), is higher than that for the 12.Y26.5 CPS on the membrane. This is expected from (2) and (3) and is in contrast to the identical phase velocities for two CPS lines on the thick substrate. The wider conductor separation forces a larger fraction of the guided-mode energy to propagate in air outside the membrane substrate. The phase velocity is increased 41% compared to the thick-substrate case. The attenuation is nearly unresolvable but an upper limit of -0.2 Np/mm can be set at 800 GHz as compared to the - 1.4 Np/mm for the thick-substrate case at the same frequency. Also, the FD-TLM results did not show any losses up to 600 GHz.

The characteristic impedance computed from numeric simulations, shown in Fig. 6(b), is within 5% of one computed from (1).

FRANKEL et al.: COPLANAR TRANSMISSION LINES ON THIN SUBSTRATES 401

The close agreement between the experimental results and the ones computed from the FD-TLM simulations validates the modeling procedure for the investigated CPS lines. Fur- thermore, the analytic formulas given in (1) and (2) for the quasi-static characteristic impedance and phase velocity are shown to be in reasonable agreement with the experiments and simulations up to 100 GHz frequencies for the tested CPS lines. These formulas provide a fast and convenient method for the initial design of high-speed, low-loss CPS transmission lines for particular goals.

As an example, an important application of such transmission lines is in traveling-wave electrooptic light modulators. The modulators are typically fabricated on LiNbO3 substrates having an optical ordinary and extraordinary indices of refrac- tion of nb = 2.286 and n’, = 2.2 respectively. However, the corresponding microwave-frequency indices of LiNb03 are significantly higher with no = 6.56 and ne = 5.3. Thus, the microwave mode velocity for a thick-substrate CPS is much lower than the velocity of the optical signal, with a concomitant modulator bandwidth limitation,

Using (1) and (2), we can design a transmission line to simultaneously obtain a conventional 50R line impedance and a microwave propagation velocity matching that of the optical mode. Since the material is birefringent, as an approximation we use a geometric mean of the ordinary and extraordinary permittivities for substrate relative permittivity in the equations [8]. Also, the thickness for the anisotropic substrate can be easily related to an equivalent isotropic one [8]. We calculate that a CPS transmission line on a 10pm E, = 34.7 substrate with 130pm conductors and a 7pm gap would have a -500 impedance and a microwave velocity matched to an optical one given by Vph = c/nb.

The geometry obtained with the aid of the analytic formulas provides only an approximate design starting point. The FD-TLM numeric simulations may then be used to refine the geometry and to investigate the detailed frequency domain characteristics. Also, the constraint on the maximum substrate thickness may be relaxed by combining the proposed thin-substrate geometry with the commonly-used thick-electrode one.

Resistive losses are expected to be the dominant bandwidth- limiting mechanism in such a transmission line at the frequencies of interest. It, therefore, may be beneficial to consider the use of superconducting electrodes to alleviate this constraint 1191. Such investigations are currently being pursued in our laboratory.

V. CONCLUSION We have investigated the characteristics of high-speed,

low-loss coplanar strip transmission lines. Time-domain, subpicosecond-resolution, electrooptic sampling measurements of the transmission-line impulse response have been performed. Such time resolution allows us to obtain quantitative frequency domain data over a range of 800 GHz. A numeric model based on the finite-difference transmission- line-matrix method has been developed to explore the frequency-dependent characteristics. The model has been

experimentally verified to give accurate results over a -500 GHz frequency range. The results were used to verify the accuracy and valid frequency range of analytic formulas for calculating the quasi-static transmission line characteristics. Two fundamental parameters-the characteristic impedance and the phase velocity-were shown to be accurate to within 6% at frequencies as high as 100 GHz. Several transmission line geometries have been investigated. A high- speed, low-loss CPS transmission line using a thin substrate has been proposed and demonstrated. Its applicability to high- bandwidth traveling-wave electrooptic light modulators has been indicated.

ACKNOWLEDGMENT

The authors wish to thank M.R. Martin of Thermalux for providing aerogel samples, H. Dietrich, and E. West for assistance with sample preparation, G. Gopalakrishnan for stimulating discussions, and J. Weller for encouragement. .

REFERENCES

M. Riaziat, R. Majidi-Aby, and 1.-J. Feng, “Propagation modes and dispersion characteristics of coplanar waveguides,” IEEE Trans. Microwave Theory Tech., vol. 38, pp. 245-251, Mar. 1990. M. Y. Frankel, J. F. %taker, and G. A. Mourou, “Optoelectronic transient characterization of ultrafast devices,” IEEE J. Quunt. Electron.,

G.K. Gopalakrishnan, C.H. Bulmer, R.W. McElhanon, and A.S. Greenblatt, “40 GHz, low half-wave voltage Ti: LiNb03 intensity modulator,” Electron. Lett., vol. 28, pp. 826827, Apr. 1992. U. D. Keil, D. R. Dykaar, A. F. J. Levi, R.F. Kopf, L.N. Pfeiffer, et al., “High-speed coplanar transmission lines,’’ IEEE .I. Quant. Electron.,

D. B. Rutledge, D. P. Neikirk, and D. P. Kasilingam, “Integrated-circuit antennas,” in K. J. Button, Ed., Infrared and Millimeter Waves. Orlando, FL: Academic, 1983. W.H. Knox, J.E. Henry, K.W. Goosen, K.D. Li, B. Tell et nl., “Femtosecond excitonic optoelectronics,” IEEE J. Quunt. Electron., vol. 25, pp. 25862595, Dec. 1989. G. Ghione and C. Naldi, “Analytical formulas for coplanar lines in hybrid and monolithic MICs,” Electron. Lett., vol. 20, pp. 179-181, Feb. 1984. K. Atsuki and E. Yamashita, “Transmission line aspects of the design of broadband electrooptic travelling-wave modulators,” J. Lightwave Tech., vol. 5 , pp. 316-319, Mar. 1987. G. Hasnain, K. W. Goosen, and W. H. Knox, “Effect of optical phonons on femtosecond pulse propagation in coplanar striplines,” Appl. Phys. Lett., vol. 56, pp. 515-517, Feb. 1990. M. Y. Frankel, J. F. Whitaker, G. A. Mourou, and J. A. Valdmanis, “Experimental characterization of external electrooptic probes,” IEEE Microwave Guided Wave Lett., vol. 1, pp. 60-62, Mar. 1991. M. Y. Frankel, S. Gupta, J. A. Valdmanis and G. A. Mourou, “Tera- hertz attenuation and dispersion characteristics of coplanar transmission lines,” IEEE Trans. Microwave Theory Tech., vol. 39, pp. 910-916, June 1991. J. A. Valdmanis and G. Mourou, “Subpicosecond electrooptic sampling: Principles and applications,” IEEE J. Quant. Electron., vol. QE-22, pp.

Virginia Semiconductor, Inc., Fredericksburg, VA. Thermalux, Richmond, CA. R. H. Voelker and R. J. Lomax, “A finite-difference transmission line matrix method incorporating a nonlinear device model,” IEEE Trans. Microwave Theory Tec., vol. 38, pp. 302-312, Mar. 1990. L. N. Trefethen, “Group velocity in finite difference schemes,” SIAM Rev., vol. 24, pp. 113-136, Apr. 1982. K. C. Gupta, R. Garg, and I. J. Bahl, Microstrip Lines and Slotlines. Norwood, MA: Artech House, 1979. S. L. Huang, L. P. Golob, E. A. Chauchard, C. H. Lee, T. Smith, et al., “Time window limited dynamic range of photoconductive sampling,”

VOI. 28, pp. 2313-2324, Oct. 1992.

VOI. 28, pp. 2333-2343, Oct. 1992.

69-78, Jan. 1986.

402

~ 9 1

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 42, NO. 3, MARCH 1994

in Proc.LEOS 1991 Summer Topical Meet. Dig., Newport Beach, CA,

M.C. Nuss, K.W. Goosen, P.M. Mankiewich, R.E. Howard, B.L. Straughn, et al., ‘‘YBazCu307 superconductors for high-speed inter- connects,” IEEE Electron. Device Lett., vol. 11, pp. 200-202, May 1990.

pp. 7-8. Robert H. Voelker (S’81-M’90) was born in Mid- land, MI. He received the B.S.E., M.S.E., and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1982, 1983, and 1989, respectively.

Since 1990, he has been an Assistant Profes- sor of Electrical Engineering at the University of Nebraska-Lincoln, where he teaches courses in ana- log and digital VLSI design, active filters, electro- magnetics, and electronics. His research interests

Michael Y. Frankel was born in St. Petersburg, Russia in 1964, He received the B.S. degree from the University of Maryland, College Park, the M.S. degree from the University of Rochester, Rochester, NY, and the Ph.D from the Universitv of Michigan.

incrude computer-aided design of high-speedhigh frequency integrated circuits and their interConneCtiOnS, and SUperCOmpUting.

Ann Arbor, all in electrical engineering, in 1986, 1988, and 1991, respectively.

He is curmetly at the Optical Sciences Divi- sion, Naval Research Laboratory, Washington, D.C. His research interests are in ultrafast optoelectronic studies and modeling of semiconductor materials,

high-speed transmission lines, photodetectors, and transistors. He is involved in developing optical control methods for phased-array radars. He has over 20 publications and conference presentations in these areas and holds two patents.

James N. Hilfiker (S’90) was born in Bloomfield, NE, in 1970. He received the B.S. degree in electrical engineering from the University of Nebraska-Lincoln in 1993. Currently, he is working toward the M.S.E.E. degree at the same university.

His research interests include the area of computer-aided design and modeling of high- speedihigh frequency integrated circuits.

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Coplanar transmission lines on thin substrates for high-speed low-loss propagation