Construction of higher-moment terms in the hydrodynamic electron-transport model

Abstract

A critical step in the development of all hydrodynamic transport models (HTMs), derived from moments of the Boltzmann transport equation, is the introduction of accurate closure relations to terminate the resulting infinite set of macroscopic equations. In general, there are a number of resulting integral terms that are highly dependent on the form of the true electron distribution function. The so-called heat flux term is one very important higher-moment term that requires attention. Methods for the accurate construction of an improved heat-flux model are presented. In this construction, a higher-moments approach is combined with a unique definition of electron temperature (i.e., based upon an ansatz distribution) to investigate the effects of conduction-band nonparabolicity and distributional asymmetry. The Monte Carlo method has been used to evaluate the resulting model closures and to study microscopic electron dynamics. These investigations have identified an important relationship between a particular symmetric (i.e., thermal) component of the electron distribution function and the heat flow vector. This knowledge is important because all the parameters in the HTM must be closed (i.e., related to each other through a common set of system variables) before the technique can be accurately applied to the study of electron transport in semiconductor devices.