Statistics of a General Class of Avalanche Detectors With Applications to Optical Communication
Stewart D. Personick · Bell System Technical Journal · 1971
Previous results on the statistics of avalanche detectors are generalized to the case where electrons and holes suffer collision ionizations with unequal probability. It is assumed here that the ratio of collision ionization probabilities per unit length of weaker-to-stronger carrier is a constant k independent of position in the high-field region. The moment-generating function of the random avalanche gain G is obtained as a function of k and the average gain G, and is used to obtain Chernov bounds on error rates of digital optical receivers employing avalanche detectors. It is shown the required energy per pulse to achieve a given error rate decreases as k decreases for fixed G. For each k > 0, there is an optimal mean gain Goptresulting in minimum required energy per pulse. At k = 0.1 Gopt≈ 100 and the required energy is within 10 dB of that required with very high gains (a few thousand) at k = 0.