Internal Resistance and Carrier Transit Time in PIN Photodetectors

The frequency response of PIN diodes was analyzed by Read in 1958. Starting with one of Maxwell's equations it was shown that the small-signal frequency response of the diode should exhibit a phase delay and amplitude roll-off due to the time T=L/v required for charge carriers to drift across the "intrinsic" layer if thickness L. Here "v" is the effective carrier velocity. Read's analysis was cited by Emmons and Lucovsky and adapted to their theory of avalanche photodiode (APD) bandwidths. The presentation by Sze is essentially the same as Read's original calculation. The small-signal amplitude is expected to roll-off as sin(omega T/2), where omega=2 pi f and f is the frequency. This so-called "transit time effect" implies a two-pole frequency response: one pole for the transit time and a second for the RC time constant. In reality, this analysis has little to do with the bandwidth of high speed PIN photodetectors.