Kinetic simulation tools for nano-scale semiconductor devices

Abstract

Kinetic simulation tools for design of nano devices based on deterministic solution of the classical Boltzmann equation with quantum corrections are described. We used two-term spherical harmonic expansion in velocity space, reducing the Boltzmann equation for electrons to a Fokker–Planck equation in a four-dimensional space (three spatial coordinates and energy). Details of the numerical implementation of the four-dimensional Fokker–Planck solver using kinetic and total energy domains are presented. The effect of quantum corrections on spatial distribution of carriers is taken into account. Simulation results for the nonlocal nonequilibrium electron transport, short submicron n+nn+ Si diode, quantum single barrier problem, and ultra-small “well tempered NMOSFET” are presented and compared with drift-diffusion, experimental and other author results. The numerical method employed is the finite volume technique with time-splitting factorization of spatial and energy space transport.