Internal resistance and carrier transit time in PIN photodetectors

The frequency response of PIN diodes was analyzed by Read (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 of thickness L (v is the effective carrier velocity). 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. In order to explain experimental results we must turn to a far simpler argument that relates the carrier transit time to the internal resistance of the photodiode. The elementary theory predicts the observed single-pole response of PIN detectors, it anticipates correctly the relationship between the bandwidth and the load resistance, and forces us to include in the detector equivalent circuit the resistance R_int=T/(2C), where C=εA/L is the diode capacitance; ε is the dielectric constant and A is the junction area