Quasistatic Approximation for Semiconductor Avalanches

A time‐dependent differential equation for the average conduction current density in a semiconductor avalanche has been derived in the quasistatic approximation. For generality, unequal ionization rates and drift velocities have been assumed. The functional form of the resulting differential equation is simplified by introducing macroscopic quantities like the multiplication and the intrinsic response time. It is shown that in obtaining the correct quasistatic limit the carrier‐induced displacement current must be included, since this current modifies the intrinsic response time and also gives rise to a reactive term. Simplified analytical expressions are obtained for correction factors due to these effects in special cases, e.g., like assuming the ratio between the ionization rates to be independent of the electric field. The modification of the intrinsic response time is shown to be of special importance in the design of avalanche photodiodes. Analytical design criteria for such diodes are given. The sm...