Fokker–Planck model for nonlocal impact ionization in semiconductors

Abstract

The probability distribution function (PDF) for impact ionization path length is a crucial quantity for understanding and modeling the low noise behavior of avalanche photodiodes with short multiplication regions. In such devices the ionization coefficient is no longer in equilibrium with the local electric field but depends on the carrier’s history. The high electric fields needed to produce avalanche gain narrow the PDF, thereby reducing the randomness in ionization position and hence the noise in the multiplication. In this article we present a method for calculating PDFs using a Fokker–Planck model. The results are compared with those obtained from an equivalent Monte Carlo simulation employing a parabolic energy band, deformation potential optical phonon scattering, and a hard energy threshold for impact ionization.