Simulation of silicon semiconductor devices by means of a direct Boltzmann-Poisson solver
Purpose - The purpose of this paper is to present a new deterministic solution method to the coupled Boltzmann-Poisson system for simulating semiconductor devices. Design/methodology/approach - A non-parabolic six-valley model allows for the investigation of anisotropy effects. The solution method is based on a discontinuous piecewise polynomial approximation of the carrier distribution function. Integrating the Boltzmann equation over tiny cells of the phase space leads to a system of ordinary differential equations. The Poisson equation is selfconsistently solved by applying a finite element Galerkin approach. Findings - Good agreement with shock-capturing "WENO solutions" is obtained for n(+)-n-n(+) silicon diodes. The anisotropy due to the six-valley model affects considerably macroscopic quantities at the beginning of the transients. The method is also applicable to spatially two-dimensional problems. Research limitations/implications - The presented method is extendable by including full band structure data, although the method is much easier applicable when analytical band structure models can be used. Practical implications - The new model is an efficient tool to acquire transport coefficients for device simulations or to directly simulate one- or two-dimensional submicron devices on a kinetic level. Originality/value - New grounds are broken by introducing a fast finite volume method for solving the Boltzmann equation in the spirit of finding a weak solution. The presented model is a good choice for the simulation of anisotropy effects in silicon semiconductor devices.
simulation silicon semiconductor devices