Statistical features of the avalanche multiplication build-up in semiconductors with different coefficients of impact ionization

The statistical fluctuations of the efficiency of the avalanche multiplication are studied for the Geiger- mode avalanche photodiodes. The resulting distribution function of the partial multiplication coefficients is characterized by an anomalously broad variance (on the order of the mean value). The expressions for the partial feedback coefficients are derived in terms of the mean gain, and the corresponding dependences on the over-voltage across the diode are calculated. An algorithm for the Monte-Carlo simulation of the avalanche process is presented, and the results of the statistical tests are compared with the theoretical dependence.