Fokker-Planck model for nonlocal impact ionization in semiconductors

The probability distribution function (PDF) for impact ionization path leng th is a crucial quantity for understanding and modeling the low noise behav ior of avalanche photodiodes with short multiplication regions. In such dev ices the ionization coefficient is no longer in equilibrium with the local electric field but depends on the carrier's history. The high electric fiel ds needed to produce avalanche gain narrow the PDF, thereby reducing the ra ndomness in ionization position and hence the noise in the multiplication. In this article we present a method for calculating PDFs using a Fokker-Pla nck model. The results are compared with those obtained from an equivalent Monte Carlo simulation employing a parabolic energy band, deformation poten tial optical phonon scattering, and a hard energy threshold for impact ioni zation. (C) 2001 American Institute of Physics.