Simulation of silicon semiconductor devices by means of a direct Boltzmann‐Poisson solver

Abstract

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.

Citation

Ertler, C. and Schürrer, F. (2006), "Simulation of silicon semiconductor devices by means of a direct Boltzmann‐Poisson solver", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 25 No. 4, pp. 979-994. https://doi.org/10.1108/03321640610684114