CONSTRUCTION OF HIGHER-MOMENT TERMS IN THE HYDRODYNAMIC ELECTRON-TRANSPORT MODEL

A critical step in the development of all hydrodynamic transport model s (HTMs), derived from moments of the Boltzmann transport equation, is the introduction of accurate closure relations to terminate the resul ting infinite set of macroscopic equations. In general, there are a nu mber of resulting integral terms that are highly dependent on the form of the true electron distribution function. The so-called heat flux t erm is one very important higher-moment term that requires attention. Methods for the accurate construction of an improved heat-flux model a re presented. In this construction, a higher-moments approach is combi ned 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 mi croscopic electron dynamics. These investigations have identified an i mportant relationship between a particular symmetric (i.e., thermal) c omponent of the electron distribution function and the heat flow vecto r. This knowledge is important because all the parameters in the HTM m ust be closed (i.e., related to each other through a common set of sys tem variables) before the technique can be accurately applied to the s tudy of electron transport in semiconductor devices.