Full nonlinear closure for a hydrodynamic model of transport in silicon

Abstract

The increasing miniaturization of modern electronic devices requires an accurate modelization of transport in semiconductors. This is of great importance for describing phenomena such those due to hot electrons, i.e., the conditions very far from thermodynamic equilibrium caused by strong electric fields and field gradients. The most general approach to the simulation of charge transport in semiconductors employes the semiclassical Boltzmann transport equation ~BTE! coupled with Poisson equation. A numerical solution of such system of equations with traditional techniques is extremely complex, and then approximate methods based on kinetic and fluid dynamic ~FD! models are often preferred. The most accurate kinetic description is given by Monte Carlo ~MC! methods, which can take into account explicitly both the band structure and the various scattering phenomena. 1,2 This method permits us to compute directly all the quantities relative to transport ~such as the distribution function, density of carriers, velocity, mean energy, and so on! but at a cost of long computation times and stochastic noise in data. The results obtained from MC simulations permit us also to calculate transport coefficients , which are used as an input to more simplified FD models. Other kinetic approaches are based on the choice of particular forms of the nonequilibrium distribution function of carriers. Common examples are the simple shifted Maxwellian 3 or an expansion of the distribution in spherical harmonics. 4 The cylindrical symmetry constraint in momentum space and the reduced number of terms of the expansion that can be practically used do not permit, however, to describe transport properties of carriers in conditions very far from equilibrium. 5