Efficient ohmic boundary conditions for the Monte Carlo simulation of electron transport

The development of macroscopic transport models, accurate for studying hot-electron transport in semiconductors, involves a direct consideration of higher-moment terms. All hydrodynamic transport models (HTM´s), derived from moments of the Boltzmann transport equation, require the introduction of closure relations to terminate the resulting infinite set of macroscopic equations. These closure relations are used as analytical approximations to distributional-dependent integral coefficients. The most popular theoretical approach employed for the construction and evaluation of these higher-moment transport-parameter closures is the Monte Carlo (MC) method. Since the MC method is computationally intensive, the discovery and implementation of efficient MC modeling techniques (either numerical or physical) is of significant value. This paper reports on a relationship between device boundary conditions and the convergence range of higher-moment terms in time-independent MC simulations. Specifically, a set of ohmic BC´s which offer computational advantages is presented. This particular mathematical approach, which allows for two degrees of freedom, is shown to be more efficient in generating the full electron distribution function than conventional BC methods (i.e., strictly equilibrium-based)