A Monte Carlo calibrated hydrodynamic model of hot electron transport in silicon

The hydrodynamic approach of modeling the high-field electron transport in silicon is pursued in this study. The major problems associated with the formulation of hydrodynamic equations are (i) the representation of collision moments and (ii) the closure of moments of the Boltzmann transport equation. A Monte Carlo experiment is performed to study the nonstationary transport characteristics of electrons in a highly inhomogeneous electric field. All terms of the moment equations, as functions of position, are carefully calculated. They provide the basis for construction of the transport coefficients. The major results obtained are: (1) a mobility model that depends on the ratio between the average energy flow and the average velocity, (2) an energy relaxation time model that depends only on the average energy, (3) an approximation of the longitudinal component of the average energy tensor by two-thirds of the average energy, and (4) an average heat flow that consists of a convective component and a diffusive component. The proposed hydrodynamic model is then applied to the simulation of three different silicon devices. The calculated results are compared to the Monte Carlo data and very good agreement between the data from the two approaches are obtained for all the calculations. The energy-dependent mobility model is demonstrated to be inaccurate in the high field-gradient regions. The nonparabolicity of the band structure is also shown to be important in the high field regime