Stabilization of the Time-Dependent Drift-Diffusion Model for Fermi-Dirac Statistics

International Conference on Simulation of Semiconductor Processes and Devices, pp. 265–268

Abstract

The Scharfetter-Gummel scheme is a widely used stabilization method for solving the drift-diffusion model. However, it is only applicable when using Maxwell-Boltzmann carrier statistics and does not yield thermodynamically consistent results in other cases, such as Fermi-Dirac statistics. Several modifications to the scheme have been proposed as improvements in this case such as Diffusion enhanced schemes. These are usually based on approximations which are not always accurate. Using similar assumptions as Scharfetter and Gummel, we develop a new scheme where the boundary value problem for each edge is solved with the shooting method and a high-order solver for ordinary differential equations. Even though the computational cost is much larger than for the original scheme, it can be effectively parallelized and a significantly negative impact on the total runtime is avoided. The scheme is applied to an NMOSFET device and stationary, transient and small-signal solutions at cryogenic temperatures are presented.

Authors 3

1. Tobias Linn Aachen Chair of Electromagnetic Theory

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Chair of Electromagnetic Theory,Aachen,Germany

   Chair of Electromagnetic Theory, RWTH Aachen University, Aachen, Germany

2. Jan Flasskamp Aachen Chair of Electromagnetic Theory

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Chair of Electromagnetic Theory,Aachen,Germany

   Chair of Electromagnetic Theory, RWTH Aachen University, Aachen, Germany

3. Christoph Jungemann Aachen Chair of Electromagnetic Theory

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Chair of Electromagnetic Theory,Aachen,Germany

   Chair of Electromagnetic Theory, RWTH Aachen University, Aachen, Germany