The linear stage of evolution of electron-hole avalanches in semiconductors

Abstract

A complete analytical solution of the problem of the linear stage of evolution of electron-hole ava- lanches in the uniform time-independent electric field E ext is derived. The theory accounts for the drift, diffu- sion, and impact ionization of electrons and holes, thus providing a means for calculating the space-time dis- tributions of fields and charges as well as all the basic parameters of the avalanches up to the onset of nonlinear effects at the time t a . Formulas for the group velocity of the avalanches and for the velocity of its leading fronts are derived. It is shown that the time t a must be determined from the condition that the impact ionization coef- ficient α in the center of the avalanche be reduced by a specified small quantity η . A transcendent equation is derived, which allows the calculation of the time t a as a function of the quantity η , the unperturbed coefficient α ( E ext ), and other parameters of the semiconductor. It is found that, when α ( E ext ) is increased by two orders of magnitude, the total number of electron-hole pairs generated up to the point t a decreases by nearly three orders of magnitude.