Time Dependence of Avalanche Processes in Silicon

Abstract

An analysis of the time dependence of avalanche processes encountered in silicon junctions, including the effects of different ionization rates and velocities of the two charge carriers, is presented. An earlier analysis of Read was restricted to equal ionization rates and velocities; that restriction has been removed but the frequency limitation of his analysis has been retained here. Various solutions of the generalized differential equation are obtained, including a steady‐state solution to a sinusoidal perturbation of the avalanche‐field maximum. The important features of this steady‐state solution are that it describes the avalanche current for all explicit values of the multiplication M≥1, is valid for highly nonlinear responses to the sinusoidal perturbation, and contains both the in‐phase and out‐of‐phase parts of the fundamental‐frequency component of the avalanche response. The analysis is applied to solid‐state photomultipliers, is used to explain an anomalous rectification observed in operating Read structures, and, lastly, the small‐signal limit of the avalanche response is compared with susceptance measurements of a uniformly avalanching junction as a function of the multiplication and saturation current over a frequency range of 20 to 200 MHz.