1838 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 43, NO 11, NOVEMBER 1996

Transit-Time Limited. High-Frequency Response Characteristics of MSM Photodetectors

Jau-Wen Chen, Member, IEEE, Dae-Kaen Kim, and Mukunda B. Das, Senior Member, IEEE

Abstract-A simplified, but useful, one-dimensional transit-time limited frequency domain current response model of MSM pho- todetectors is presented. The model includes the effects of uinequal velocities and lifetimes governing the lateral transport of photo- generated holes and electrons in the absorption layer. Normalized frequency response curves depicting the amplitude and phase versus the frequency are presented using the transit-time ratio as a parameter. The usefulness of the analytical response amplitude curves for the extraction of hole and electron transit times has been demonstrated by regressively fitting them with the me:asured results obtained from practical MSM photodetectors.

I. INTRODUCTION

OR high-speed optoelectronic applications, the metal- F semiconductor-metal (MSM) photodetector has been rec- ognized as being more versatile than the p-i-n photodetector due to its low capacitance per unit area and relative ease of incorporation in optoelectronic integrated circuit (OEIC) receivers. High-speed 111 and ultra-high-speed [2] MSM pho- todetectors for 0.85 pm wavelength have been demonstrated using GaAs absorption layer, and similar high-speed perfor- mances are expected from comparable InAIAs/InGaAs/InP MSM photodetectors for 1.3-1.55 pm wavelengths. In the lat- ter structure, a thin InAlAs surface layer is often incorporated above the InGaAs absorption layer to enhance the Schottky barrier voltage 131, [4], and this in turn reduces the dark current of the MSM photodiode. For the same purpose others [5] have incorporated semi-insulating InP surface layer.

In interdigitated GaAs MSM photodiodes metallization, with finger spacing of 0.5 pm and width of 0.75 pm, a 3 dB frequency response bandwidth ( f 3 d ~ ) of 105 GHz has been reported Cl], and for 0.1 pm spacing and width the reported bandwidth is 300 GHz [2]. However, in the case of InAlAs/InGaAs/InP MSM photodiodes 151-1 101, reported spacing ranges from 3-1 pm, and the corresponding f j d B

ranges from 1.3-11 GHz. In several of the reported cases [I], [2], 161, [7] the f 3 d B ’ s were estimated from the full- width-at-half-maximum (FWHM) optical impulse response time (qT) using the relationship, f 3 d ~ = 2.8/2nr;,.. In other cases 151, [SI-[lo] the f 3 ~ B ’ S were determined from measured frequency response characteristics. The latter f 3 dB’S range

Manuscript received January 2, 1996; revised May 9, 1996. The review of’ this paper was arranged by Editor P. K. Bhattacharya. This work was supported in part by NSF Grant ECS-9202642, and by NSF International Cooperative Research Grant ECS-9541739 (INT-9412658).

J.-W. Chen and M. B. Das are with the Department of Electrical Engi- neering, and Electronic Materials and Processing Research Laboratory, The Pennsylvania State University, University Park, PA 16802 USA,

D.-K. Kim is with the Electronic Engineering Department, Seoul National University, Seoul, Korea.

Publisher Item Identifier S 0018-9383(96)07715-5.

from 1.3-11 GHz, and since they were obtained directly from frequency domain measurements, they can be regarded as more reliable and accurate than those estimated from optical impulse responses, particularly those above 100 GHz. However, even the accuracy of the experimental frequency response characteristics cannot be validated due to the non- availability of an analytical frequency response model for the MSM photodetector, similar to the one reported for the p-i-n photodetector [ I 11, 1121. In this paper, as a first attempt, we present a simplified “equivalent one-dimensional’’ transit-time limited frequency response model for the MSM photodetector under surface illumination condition, and examine the effects of unequal transit times of holes and electrons on the detailed amplitude and phase versus frequency behavior, and on f 3 <IB

itself.

11. A SIMPLIFIED ANALYTICAL APPROACH

In an MSM photodetector, a complete analytical modeling of the simultaneous two-dimensional transport of spatially distributed photo-generated holes and electrons in opposite directions with different carrier velocities is a difficult task. The electric field responsible for carrier transport is high and nonuniform near the edges of the metal contacts. Based on the fact that the carriers are mostly generated within the absorption layer up to a depth of lln, where n: is the absorption coefficient of the material, the MSM photodetector is usually designed to have the absorption layer thickness W E l / a , and the metal finger spacings sf 2 W . When sf >> W the effect of vertical (y-direction) current flow on the carrier transit-time can be neglected. However, when sf is comparable to W , the effect of y-direction current flow can have significant impact on the carrier transit-time. A schematic representation of the current and carrier flow paths within the photo-absorption region is depicted in Fig. l(a). For analytical simplicity, in this two dimensional system we have assumed an “equivalent one-dimensional” structure with an effective carrier transit path-length, L, as shown schematically in Fig. I(b). The effective path-length is shown to be greater than the separation between the MSM electrodes ( s f ) since it has to represent the effects of carrier transport near the surface as well as deeper in the absorption region. The effective path-length L is dependent on both sf and W , and when sf E W , it can be approximated as L E 7r(sf/2). Note that in this simplified one-dimensional model the carriers are collected at the “virtual“ vertical planes shown as dotted lines separated by the effective length L. The vertically incident optical power is absorbed uniformly in the lateral 2-direction at a given depth y such that the ac

0018-9383/96$05.00 0 1996 IEEE

1839 CHEN et ul.: TRANSIT-TIME LIMITED HIGH-FREQUENCY RESPONSE CHARACTERISTICS

s.1.m (a)

- Wf + *+ sf +-spsI,

’ Ax , ! A Y - undoped InGaAs

Tx 1 ; Y w - -

SPSL :- L -: s. I. InP

(b)

Fig. 1. (a) Schematic representation of current flow paths which correspond to both hole and electron transport paths in opposite directions. (b) Equivalent one-dimensional representation of the carrier transport paths of equal length ( L ) at different depths. Electrons and holes are collected at the “virtual” planes through the vertical dotted lines under the anode and the cathode, respectively.

component of the carrier generation rate can be written as

Go<: = ~ e ~ ~ ~ & n (1 ejwt (1)

where w is the angular signal frequency, is the incident photon flux related to the ac component of the incident optical power (Po,,), the reflection coefficient (On), the effective illuminated surface area (A) , and the photon energy (hv), i.e.,

We assume that the electric field is high and both holes and electrons are transported with their effective constant velocities ur, and uIL, respectively, and the current flow is essentially one- dimensional in our assumed model, i.e., a J / 3 y = 0. Thus, J p = qpvp and J , = qfivlL, where JP and @, and JTl and ii represent the ac components of hole and electron current densities and carrier concentrations, respectively, and q stands for the electronic charge. Using the per-unit-length ac electron current (,?,Ay) flowing in the layer of thickness, Ay, the following continuity equation can be written

6cLc = Poopt(l - 0~) /Ahr / .

where r, is the electron lifetime, and current flow due to diffusion is neglected. A similar equation holds good for the ac hole current (j,Ay) with lifetime rp and carrier velocity wp. By integrating (2), the current j,,Ay, at any position z, can be obtained as

where I’ = ( l /rr l + j w ) / w n . Integration of (3) and a corre- sponding equation for & a y from y = o to y = W , where w is the absorption layer thickness, will yield the total current

density [&(z) + &(.)I crossing the zz plane at any point z. The b_oundary conditions being, at x = 0, j,, = 0, and1 at z = L , J p = 0, since electrons travel toward the anode while holes travel toward the cathode as schematically shown in Fig. 1 (a). The total ac short-circuit terminal conduction current due to the transport of all generated carriers distributed within the zz plane at z = 0 to z = L, can be obtained by taking the average of the integrated currents, i.e.,

&w) = ; .il” { j n ( z ) + &(.)} dz. (4)

It is assumed that the ac short-circuit condition between the anode and the cathode does not alter the dc electric field.

Due to the MSM capacitance (c,) a displacement current will also flow whenever an alternating voltage is present be- tween the anode and the cathode. The leakage conductance of the MSM diode is usually insignificant. Finally, the expression for the frequency response of J”( jw) can be written in terms of the effective electron and hole transit times (r,, = L/un , and ~~f~ = L/v,), and the respective transit-time to lifetime ratios (aTL = r,,/rn, and a, = r,h/rp), namely,

where

J ( 0 ) = -

and Q = [cxp (a7,) - 1]/u: - l/a, + [exp (arl) - 1]/a5 - l / a p . It follows that T~~ >> IT,, and rr, >> 7-&, O S 1.

111. FREQUENCY RESPONSE CHARACTERISTICS

The normalized magnitudes of the detected short-circuit photocurrent versus frequency are graphically presented in Fig. 2(a) with the transit-time ratio, r,h/r,,, as a parameter assuming that Q = 1. These curves clearly indicate a “staircase- like” response roll-off with increasing frequency, particularly for higher values of rrfL/r,, or However, all response curves are seen to be free of this effect at frequencies below their respective 3-dB bandwidth frequency, f3 d~ = q/2n,rr,, where the factor Q decreases with increasing rrtr/r7., as depicted in Fig. 2(b). The phase versus frequency curves clearly indicate that except for a small oscillatory behavior at higher frequencies all curves converge to 90”, and the 3 dB phase angle varies between 53.5” and 32.6” as r,h/r,,

increases from 2 to 8, as shown in Fig. 2(b). Because of the linear phase shift below f 3 f i ~ the phase (4) can be written as 4 = K ~ w T , . ~ , and the variation of K~ with rTh , / r , , is noted in Fig. 2(a). The effects of the ratio of transit-time to lifetime on , f 3 d ~ are quantified in Table I.

Measured frequency responses of two MSM photodetectors are presented in Fig. 3 together with their theoretically fitted response curves based on (5). The RC time constant associated with the MSM capacitance and the measurement termination

1840 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 43, NO. 1 1, NOVEMBER 1996

+" z W fY E 3 0 n IO-' W t- o w !- W n

1 02

10'

I I

10-2 IO-' 1 00 101

2.5

2.0

!!! Pm 1.5

3" U

1 .o II

F

50

45

-

-

0.5 - 125

0.0 2 4 6 8 10

TRANSIT TIME RATIO, z,.~,/T,.~

(b)

Fig. 2. (a) The frequency response curves for the detected short-circuit current of MSM photodetectors depicting normalized magnitude and phase versus normalized frequency, UT,,, with r r h / T r e as a parameter. (b) Dependence of the normalized 3-dB frequency, w3 d B T r e . and the corresponding phase angle, 4 3 d B . on the transit time ratio, T ~ ~ / T $ . ~ .

TABLE I THE EFFECT OF TRANSIT-TIME TO LIFETIME RATIO ON f3 dB

current response. The detailed match between the theoret- ical and experimental data is indicative of the usefulness of the "effective one-dimensional" high-frequency response model proposed. Although the matching procedure yields r,, and T,h, the corresponding carrier velocities cannot be determined without a knowledge of the effective length, L. However, as a rough approximation, assuming that L is the semi-circumference of an ellipse with radiuses of s f /2 and

w/a, = 1.08 x

lo7 c d s , and up = 0.15 x lo7 c d s for device a; and resistance (50 0) as employed in the HP lightwave test- set, in both cases had negligible impact on the short-circuit

7 i ~ ~ / 2 d % One Obtains

CHEN et al.: TRANSIT-TIME LIMITED HIGH-FREQUENCY RESPONSE CHARACTERISTICS

(GHz) 1.7631 5.6425 U I I

1841

1 00 I I

Bias Voltage = 10 V

IO- ’ a w cn z 0 cn W OL

v

n IO-^

P 10-3

FREQUENCY (GHz)

Fig. 3 . used for the extraction of f:i d ~ . TTh , and T,‘,,

The measured and theoretically fitted frequency response curvcs representing the magnitude of’ the photocurrent for two MSM photodetectors,

h

Y 9. 102 T

n 5 n

2i 2

I I-

z I O ’ ?

I I I

0.1 1

FINGER SPACING, % (Fm)

Fig. 4. of the associated RC time constants based on parameters given in Table 11.

Dependence of the calculated 3-dB bandwidth ( i j d R ) on the h g e r spacing of MSM photodetectors, showing intrinsic behavior and the effect

7lTL = 0.68 x lo7 cm/s, and wp = 0.24 x lo7 cm/s for device b as shown in Fig. 3. The approximate average electric fields are 18 and 35 kV/cm for devices a and b, respectively. At these

value (-0.5 107 cm/s) at fields above 50 kV ~131. ~~~i~~~ a and b were interdigitated structures with 4 and

6 fingers, each finger being 35 and 21 pm long, respectively. They were fabricated using MBE-grown lattice-matched In- AlAs/InGaAs heterostructure layers on semi-insulating InP substrate. The layer structure, from the top, consisted of a 300 A undoped InAlAs layer, a 270 A InAlAs/InGaAs

undoped short period superlattice (SPSL) grading, the main 1 pm-thick undoped InGaAs absorption layer, a 270 8, SPSL grading, and a 3000 8, undoped I n A k buffer layer on the SI

and details of the measurements and interpretation of device HF characteristics can be found elsewhere [14].

electric fields remains considerably below its saturation InP. Further details of these and other MSM photodetectors,

IV. FREQUENCY LIMITS OF MSM PHOTODIODES WITH SUBMICRON SPACINGS

For future high-speed photodetector and OEIC designs., it is of interest to apply the proposed MSM frequency response

I842

TABLE I1 THE ASSUMED STRUCTURAL AND MATERIAL

PARAMETERS OF MSM PHOTODETECTORS

IEEE

0 2 5 127)1325~13751039121451 1 0 0 11021 1 5 I 0 5 0 1 0 1291 57x59 1 0 1 6 1 9 9 1 1 2 5 0 11021 2 0 I 0 5 Assumed: W = sf= wf ; L=~sd2 ; R, = 2r0!/N ; e : finger length

model to devices with micron and submicron spacings and finger widths. Since series resistance of a metallization finger strongly depends on its thickness and width, the resistance per-unit-length (T,) and its impact on the effective series resistance (R,) must be carefully determined for a given design. We considered the designs of MSM photodetectors with equal spacings and widths ranging from 1-0.1 pm, and used metallization resistance as determined previously [2]. The assumed dimensions and the relevant material and device electrical parameters for these designs are given in Table 11. It is also assumed that the carrier velocities are saturated, and for ultrasubmicron finger spacings the electron saturation velocity becomes enhanced due to carrier overshoot effects, although the same does not occur for the hole saturation velocity. The results of our simple model-based calculations are presented in Fig. 4, indicating the dependence of transit-time limited f3dB of the intrinsic MSM photodetector. Due to the RC time constant effect, c p ( R ~ + R,), where RL = 5 0 0 , f 3 d ~

becomes reduced as indicated on the same figure. It should be noted, however, that when the MSM photodetector i s incorporated at the front end of a high input impedance OEIC receiver, the effect of 50 62 load resistor disappears, and that due to R, becomes considerably less significant. In this situation it is the product of the transimpedance (12~ 1 ) and the detected short-circuit photocurrent, I J(.jw)/J(O) 1 , responses that determines the overall bandwidth of the OEIC receiver. Assuming that the intrinsic MSM photodetector bandwidth i s at least twice that of IZTI, when the latter includes the effect of the capacitance of the photodetector, it can be shown that for a 30 GHz bandwidth of the OEIC receiver, the bandwidth of 12~1 must be 2 34 GHz, and the MSM photodetector must have an approximate finger spacing of 0.25 pm (see Fig. 4). However, in order to maintain a high responsivity in such detectors, suitable Bragg reflectors need to be incorporated as considered previously [15]. It should also be noted that reduction of metal finger width ( w f ) below 0.25 pm greatly reduces the area of the photodetector. A small device area provides a low capacitance ( c p ) which i s essential for preserving the high bandwidth.

V. CONCLUSIONS Using an effective one-dimensional transit-time limited car-

rier transport concept, the frequency response of the short- circuit detected current of MSM photodetectors has been modeled. Using this model hole and electron transit times have been determined from frequency response data of test MSM

rRANSACTIONS ON ELECTRON DEVICES, VOL. 43, NO. 11, NOVEMBER 1996

photodetectors. Because of the lower saturation carrier velocity for holes compared to that of electrons, the f 3 d ~ of photo- response of submicron MSM photodiodes become primarily limited due to the former.

By applying the frequency domain model presented in this work to devices with 0.1 pm finger spacing, we predict an intrinsic f 3 d B of -210 GHz (see Fig. 4). This result is con- siderably lower than the previously predicted [2] bandwidth of 300 GHz for a similar structure, estimated from optical pulse response data. We believe that the results presented in Fig. 4 are more realistic and accurate, compared to those predicted previously based on optical pulse response, although the validity of all these results are yet to be tested by direct frequency domain measurements on practical devices.

ACKNOWLEDGMENT

The authors are thankful to Dr. S. Chandrasekhar, Dr. L. Lunardi, and Dr. J. M. M. Rios of AT&T Bell Labs (Crawford Hills), Holmdel, NJ, for their help concerning HF measurements.

REFERENCES

B. J. Vanzeghbroeck, W. Patrik, J.-M. Halbout, and P. Vettiger, “105 GHz bandwidth metal-semiconductor-metal photodiode,” IEEE Electron Device Lett., vol. 9, no. 10, pp. 527-529, 1988. S. Y. Chou and M. Y. Liu, “Nanoscale tera-hertz metal-semiconductor- metal photodetector,” IEEE J. Quantum Electron., vol. 28, no. 10, pp. 2358-2368, 1992. J. B. Soole, H. Schumacher, H. P. Lehlanc, R. Bhat, and M. A. Koza, “High frequency performance of AIInAdGaInAs metal-semiconductor- metal photodetectors at 1 .55 and 1.33 pm wavelengths,” IEEE Photon. Technol. Lett., vol. 1, pp. 250-252, 1989. 0. Wada, H. Nobuhara, H. Hamaguchi, T. Mikawa. A. Tacheuchi, and T. Fujii, “Very high speed GaInAs metal-semiconductor-metal photodiodes incorporating an AlInAsiGaInAs graded superlattice,” Appl. Phys. Lett., vol. 54, pp. 16-17, 1989. E. H. Bottcher, D. Kuhl, F. Hieronymi, E. Droge, T. Wolf, and D. Bimberg, “Ultrafast semi-insulating InP: Fe-InGaAs: Fe-InP MSM pho- todetectors: Modeling and performance,” IEEE J. Quantum Electron., vol. 28, no. IO , pp. 2343-2357, 1992. D. L. Rogers, J. M. Woodal, G. D. Pettit, and D. Mclnturff, “High speed 1.3 pm GaInAs detectors fabricated on GaAs substrates,” IEEE Electron Device Lett., vol. 9, no. 10, pp. 515-517, 1988. H. Schumacher, H. P. Leblanc, J . Soole, and R. Bhat, “An investigation of optoelectronic response of GaAdInGaAs MSM photodetectors,” IEEE Electron Device Lett., vol. 9, no. 11, pp. 607-609, 1988. C. Jagannath, A. N. M. Chaudhury, A. Negri, B. Elman, and P. Hangsjaa, “High-speed 1.3 pm InCaAdGaAs metal-semiconductor- metal photodetector,” Appl. Phys. Lett., vol. 58 , no. 4, pp. 325-327, 1991. J. H. Burroughes, M. S. Milshtein, G. D. Pattit, N. Pakdaman, H. Henrich, and J . M. Woodell, “The frequency behavior of InGaAs/AlInAs metal-semiconductor-metal photodetectors at low bias voltages for data communications applications,” IEEE Photon. Technol. Lett.. vol. 4. no. 2, pp. 163-165, icj92. J. M. Kim, H. T. Griem, R. A. Friedman, E. Y. Chan, and S. Ray, “High- performance hack-illuminated InGaAs/InAlAs MSM photodetector with a record responsisivity OF 0.96 A N , ” IEEE Photon. Technol. Lett., vol. 4, no. 11 , pp. 1241-1243, 1992. G. Lucovsky, R. F. Schwara, and R. B. Emmons, “Transit-time consid- erations in p-i-n diodes,” J . Appl. Phy~. , vol. 35, no. 3, pp. 622-628, 1964. G. George and J. P. Krusius, “Dynamic response of high-speed p-i-n and Schottky-barrier photodiode layers to nonuniform illuminations,” J . Lightwave Technol., vol. 12, no. 8, pp. 1387-1393, 1994. K. Brennan, “Theory of the steady-state hole drift velocity in InGaAs,” Appl. Phys. Lett, vol. 51, no. 13, pp. 995-997, 1987. A. Mitra, J. W. Chen, M. Mirovic, W. H. Hwang, T. S. Mayer, D. L. Miller, and M. B. Das, “Measurement and interpretation of high-

CHEN et ul.: TRANSIT-TIME LIMITED HIGH-FREQUENCY RESPONSE CHARACTERISTICS 1843

frequency characteristics of InAIAs/ InCaAsLnP MSM photodetectors,” in Conj Lasers and Electro-optics (CLEO), June 2-7, 1996.

1151 J. Burm, K. L. Litvin, W. J. Schaff, and L. F. Eastman, “Optimization of high-speed metal-semiconductor-metal photodetectors,” ZEEE Photon. Technol. Lett., vol. 6 , pp. 722-724, 1994.

Dae-Kaen Kim photograph and biography not available at the timi: of publication.

Mukunda B. Das (S’57-M’62-SM’70), for a photograph and biography, see p. 791 of the May 1996 issue of this TRANSACTIONS.

Jau-Wen Chen (S’90-M’92) received the B.S.E.E. degree from Tamkang University, Tdmshui, Taiwan, in 1985, and the M.S.E.E. degree from Pennsylvania State University, University Park, in 1991. He is currently pursuing the Ph.D. degree in the Department of Electrical Engineering at Pennsylvania State University.

His current research interests include design and characterization of HEMT’s and HBT’s, noise in semiconductor devices, and optoelectronic integrated circuits.