Existence analysis for a simplified transient energy-transport model for semiconductors
Abstract
A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing momentum relaxation limit. It consists of a drift-diffusion-type equation for the electron density, involving temperature gradients, a nonlinear heat equation for the electron temperature, and the Poisson equation for the electric potential. The global-in-time existence of bounded weak solutions is proved. The proof is based on the Stampacchia truncation method and a careful use of the temperature equation. Under some regularity assumptions on the gradients of the variables, the uniqueness of solutions is shown. Finally, numerical simulations for a ballistic diode in one space dimension illustrate the behavior of the solutions.
Keywords
Cite
@article{arxiv.1206.5722,
title = {Existence analysis for a simplified transient energy-transport model for semiconductors},
author = {Ansgar Jüngel and René Pinnau and Elisa Röhrig},
journal= {arXiv preprint arXiv:1206.5722},
year = {2012}
}