3.6 Energy Relaxation Time

In this section the models for the energy relaxation times of electrons and holes, in Si, Ge, SiGe, and III-V materials are presented. The energy relaxation times are used in the HD mobility models, in the energy balance equations of the hydrodynamic transport model, and in the lattice heat flow equation.

A constant energy relaxation time ( $\tau_{\epsilon,n}$), or a quadratic dependence on the electron temperature [183,184], are usually assumed. A precise simulation needs to include the dependence of $\tau_{\epsilon,n}$ on the lattice and carrier temperatures.

An empirical model for the electron energy relaxation time has been suggested in [185]. It is based on Monte-Carlo simulation results [94], and is applicable to all relevant diamond and zinc-blende structure semiconductors. The energy relaxation times are expressed as functions of the carrier and lattice temperatures, and in the case of semiconductor alloys of the material composition. The influence of doping concentration is not taken into account.