Carrier Diffusion in Semiconductor Avalanches

The effect of carrier diffusion has been evaluated in a large-signal analysis of semiconductor avalanches in the quasistatic approximation. It is shown that diffusion tends to smooth out the carrier distributions by upstream diffusion against the drift velocities, which causes a change in the carrier induced electric field. The dc solutions of the carrier and current distributions can be used in evaluating the effects of diffusion on the current response of the avalanche. The main effect is to increase the intrinsic response time with the ratio between the characteristic diffusion length D/v and the width of the avalanche region w as a critical parameter. In the effective avalanche width approximation a correction factor for the intrinsic response time due to diffusion is calculated. The results are also presented in curves with α/β and D/wv as parameters. The correction factor is found to increase linearly with D/vw for small values and saturate for large values. A criterion is given for the maximum multiplication factor possible in avalanche photodetectors without significantly reducing the bandwidth. Previously found discrepancies between experimental and theoretical values for the intrinsic response time can be removed by estimating a high-field diffusion constant of 600 cm2/sec for an electric field of 3×105 V/cm in silicon. Diffusion corrections to the carrier transport in the drift regions adjacent to the avalanche region have been considered for a time-harmonic component of the current. As a result, modifications to the usual transport factors (1−cosθ)/θ and sinθ/θ are established.