A physics-based analytical/numerical solution to the Boltzmann transport equation for use in device simulation

Abstract

A computationally very efficient technique for obtaining the electron velocity distribution function in silicon is presented. Analytical methods using Legendre polynomials are combined with numerical techniques using matrices to solve the Boltzmann transport equation. Results agree with Monte Carlo calculations, but are obtained in approx. 1 100 the CPU time. The method accounts for the effects of acoustic and intervalley phonon scattering, as well as silicon's nonparabolic, ellipsoidal band structure. Accurate expressions for electron average energy, drift velocity and mobility in terms of the distribution function are also provided. The method is appropriate for use in CAD tools for semiconductor devices. © 1991.