Accurate impact ionization model which accounts for hot and cold carrier populations

Conventional macroscopic impact ionization models which use the average carrier energy as a main parameter can not accurately describe the phenomenon in modern miniaturized devices. Here, we present a model which is based on an analytic expression for the distribution function. In particular, the distribution function model accounts explicitly for a hot and a cold carrier population in the drain region of metal-oxide-semiconductor transistors. The parameters are determined by three-even moments obtained from a solution of a six-moments transport model. Together with a nonparabolic description of the density of states, accurate closed form macroscopic impact ionization models can be derived based on familiar microscopic descriptions.