An impact ionization model including an explicit cold carrier population

Conventional macroscopic impact ionization models which use the average carrier energy as main parameter cannot accurately describe the phenomenon in modern miniaturized devices. Here we present a new 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 MOS 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.