Stabilization of the Drift-Diffusion Model for Arbitrary Carrier Statistics

International Conference on Simulation of Semiconductor Processes and Devices, pp. 1–4

Abstract

Modern semiconductor simulation is still mostly based on the drift-diffusion model which is solved numerically using the finite volume method together with the ScharfetterGummel stabilization. Unfortunately, the Scharfetter-Gummel stabilization is only applicable if the charge carriers follow Maxwell-Boltzmann statistics. In this paper, we present a stabilization scheme generalizing the Scharfetter-Gummel scheme to arbitrary carrier statistics using no additional approximations. So far, no such scheme exists which is accurate and robust enough for a full-scale device simulation. In our method we solve an integral equation for the edge current using Tanh-Sinhquadrature. This approach works for general carrier statistics, is easily implemented and can be effectively parallelized. Practical use of this method is demonstrated with 2D transient and smallsignal simulation results for an exemplary MOSFET at 4 K using Fermi-Dirac statistics. Parallelizing over 64 CPU cores, the edge current calculation takes up less than 6 % of the total runtime.

Authors 3

1. Max Renner Aachen Chair of Electromagnetic Theory

   RWTH Aachen University

   Affiliation as printed

   Chair of Electromagnetic Theory RWTH Aachen University,Aachen,Germany

2. Tobias Linn Aachen Chair of Electromagnetic Theory

   RWTH Aachen University

   Affiliation as printed

   Chair of Electromagnetic Theory RWTH Aachen University,Aachen,Germany

3. Christoph Jungemann Aachen Chair of Electromagnetic Theory

   RWTH Aachen University

   Affiliation as printed

   Chair of Electromagnetic Theory RWTH Aachen University,Aachen,Germany