1310 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 45, NO. 8, AUGUST 1997 Traveling-Wave Photodetector Theory Kirk S. Giboney, Member, IEEE, Mark J. W. Rodwell, Member, IEEE, and John E. Bowers, Fellow, IEEE Abstract—Photodetector efficiency decreases as bandwidth in- creases. Bandwidth-efficiency limitations of traveling-wave pho- todetectors (TWPD’s) are substantially greater than those of lumped-element photodetectors because the velocity-mismatch bandwidth limitation is independent of device length. TWPD’s can be long for high efficiency without significantly compro- mising bandwidth. The TWPD is modeled by a terminated section of transmission line with a position-dependent photocur- rent source propagating on it at the optical group velocity. A wave model for the transmission line confirms the accuracy of an equivalent-circuit model for electrical wave propagation. The velocity-mismatch impulse and frequency response are de- termined by absorption coefficient and wave velocities rather than junction capacitance and load resistance. The velocity- mismatch bandwidth limitations can be written in a simple form which elucidates the factors affecting device response. A discretized periodic TWPD is described by the same equations as the fully distributed version. This more complicated device offers additional degrees of freedom in design and potentially improved performance. Index Terms— High-speed circuits/devices, photodiodes, pho- todetectors, optical waveguides, optoelectronic devices, slow-wave structures, traveling-wave devices, ultrafast optoelectronics. I. INTRODUCTION T HE bandwidth-efficiency product of a photodetector im- poses a bound on the speed and sensitivity of the pho- toreceiver in which it is used. Bandwidth-efficiency products of conventional vertically illuminated photodetectors (VPD’s) are limited to about 40 GHz (in GaAs) [1]. The bandwidth- efficiency product can be improved by guiding the light per- pendicular to the collection field, as in a waveguide photode- tector (WGPD) or a traveling-wave photodetector (TWPD), so that absorption and carrier drift are orthogonal. The TWPD is based on the WGPD, an in-plane illuminated photodetector in which transparent dielectric cladding layers about the absorbing core form a dielectric optical waveguide [1]–[6]. However, the TWPD is a distributed structure that overcomes the RC bandwidth limitation of the lumped-element WGPD. This is accomplished by implementing an electrode arrangement designed to support traveling electrical waves with characteristic impedance matched to that of the external circuit [7]. Manuscript received June 18, 1996; revised April 28, 1997. This work was supported by the DARPA Optoelectronics Technology Center and Ultra Program, and Rome Laboratories. K. S. Giboney was with the Department of Electrical and Computer Engineering, University of California at Santa Barbara, CA 93106 USA. He is now with Hewlett-Packard Laboratories, Palo Alto, CA 94304 USA. M. J. W. Rodwell and J. E. Bowers are with the Department of Electrical and Computer Engineering, University of California at Santa Barbara, CA 93106 USA. Publisher Item Identifier S 0018-9480(97)05999-1. TWPD bandwidth is limited by the optical absorption coef- ficient and the velocity mismatches between the optical wave and the forward- and reverse-traveling electrical (photocurrent) waves rather than an RC bandwidth limitation determined by the total junction area. For devices significantly longer than the absorption length, this bandwidth limitation is roughly independent of device length. This is why TWPD’s can have larger bandwidth-efficiency products than are possible in lumped-element photodetectors. The concept of the TWPD was first proposed in 1990 as a means to overcome the bandwidth-efficiency limits of con- ventional photodetectors [8]. Both p-n and Schottky junctions were briefly mentioned, although the several designs listed in the proposal were of the metal–semiconductor type. No detailed theory or experimental results from these designs have been reported. In 1991, a velocity-matched p-i-n TWPD was proposed [9], although a quantitative theory of the effects of velocity matching on device response was not included in this report. Electrical waves generally propagate in a slow-wave mode on a p-i-n waveguide. Experiments derived from this proposal and directed toward high-power applications have recently been reported together with a frequency-domain analysis based on an equivalent-circuit model [10]. The theory of TWPD’s, based on an equivalent-circuit model and quantifying the velocity-mismatch impulse re- sponse and associated bandwidth limitations was initially detailed in 1992 [7], and the first experimental demonstration of TWPD’s followed in 1994 [11]. The TWPD’s had signifi- cantly higher bandwidth-efficiency products than comparable WGPD’s and VPD’s on the same wafer, breaking records by large margins [12], [13]. The velocity-mismatch bandwidth limitation has been cast in a simpler form which affords physical insight and allows the use of standard design methods for TWPD’s [7], [14]. TWPD’s can be fabricated in many different configurations. The photodetector element can be a semiconductor p-i-n, Schottky, or metal–semiconductor–metal (MSM) diode. It can have gain, as in a photoconductor or avalanche photodetector. The geometry can be of any form in which the photodetector function is incorporated over the length of a simultaneous optical and electrical waveguide. The photodetector could be continuous over the length of the waveguides, as in a fully distributed TWPD. Alternatively, a passive or active optical waveguide periodically loaded by discrete photodetector el- ements is called a periodic TWPD. All TWPD’s share the fundamental velocity-mismatch bandwidth limitation. In this paper, a wave model for a fully distributed, parallel- plate, p-i-n TWPD provides the basis for the theory of dis- 0018–9480/97$10.00  1997 IEEE Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on March 09,2010 at 12:01:49 EST from IEEE Xplore. Restrictions apply.