Improved hydrodynamical model for carrier transport in semiconductors

High-Order Entropy-Based Closures for Linear Transport in Slab Geometry II: A Computational Study of the Optimization Problem

“…Hence, near the boundary, the quadrature must depend on u and, in addition, it must be locally adaptive so that it can track the support of G α k during the course of the optimization process. (3) In doing so, the quadrature routine must carefully select and deselect points in order to maintain a practical bound on n Q and still guarantee convergence of the optimization algorithm. We have yet to design such a quadrature.…”

“…In transport and kinetic theory, entropy-based closures are used to derive moment models which retain fundamental properties of the underlying kinetic equations such as hyperbolicity, entropy dissipation, and positivity. The resulting models have been studied extensively in the areas of extended thermodynamics [18,48], gas dynamics [24,29,32,33,40,42,57], semiconductors [2][3][4][5]26,31,34,41,56], quantum fluids [16,19], radiative transport [9-12, 20-22, 28, 30, 46, 47, 59, 62], and phonon transport in solids [19]. In spite of their attractive mathematical properties and wide application, entropy methods still suffer from several short-comings.…”

2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

“…Hydrodynamical models are obtained from the infinite hierarchy of the moment equations of the Boltzmann transport equation using a suitable truncation procedure. However, most hydrodynamical models suffer from serious theoretical drawbacks due to the ad hoc treatment of the closure problem [19]. Recently in [1,2] a moment approach has been introduced in which the closure procedure is based on the maximum entropy principle, while the energy bands are described by the Kane dispersion relation.…”

Numerical study of the systematic error in Monte Carlo schemes for semiconductors

“…In contrast to other simulation tools, like drift-diffusion or hydrodynamic models [1], which involve the solution of coupled systems of partial differential equations, the Boltzmann equation is treated by replacing the distribution function with a representative set of particles. The Monte Carlo approach is a useful tool, since it permits particular physical simulations unattainable in experiments, or even investigations of nonexistent materials in order to emphasize special features of the phenomenon under study.…”