Subsonic Solutions to a One-Dimensional Non-isentropic Hydrodynamic Model for Semiconductors

P Amster,M.P Beccar Varela,A Jüngel,M.C Mariani

doi:10.1006/jmaa.2000.7359

Abstract

The one-dimensional stationary full hydrodynamic model for semiconductor devices with non-isentropic pressure is studied. This model consists of the equations for the electron density, electron temperature, and electric field in a bounded domain supplemented with boundary conditions. The existence of a classical subsonic solution with positive particle density and positive temperature is shown in two situations: non-constant and constant heat conductivities. Moreover, we prove uniqueness of a classical solution in the latter case. The existence proofs are based on elliptic estimates, Stampacchia truncation methods, and fixed-point arguments.

Highlights

For the simulation of semiconductor devices usually drift-diffusion models are used
The one-dimensional stationary full hydrodynamic model for semiconductor devices with non-isentropic pressure is studied. This model consists of the equations for the electron density, electron temperature, and electric field in a bounded domain supplemented with boundary conditions
The existence of a classical subsonic solution with positive particle density and positive temperature is shown in two situations: non-constant and constant heat conductivities

Summary

Jungel

Fakultat fur Mathematik und Informatik, Uniersitat Konstanz, 78457 Konstanz, Germany and. The one-dimensional stationary full hydrodynamic model for semiconductor devices with non-isentropic pressure is studied. This model consists of the equations for the electron density, electron temperature, and electric field in a bounded domain supplemented with boundary conditions. The existence of a classical subsonic solution with positive particle density and positive temperature is shown in two situations: non-constant and constant heat conductivities. We prove uniqueness of a classical solution in the latter case. The existence proofs are based on elliptic estimates, Stampacchia truncation methods, and fixed-point arguments. Copyright ᮊ 2001 by Academic Press All rights of reproduction in any form reserved

INTRODUCTION

ASSUMPTIONS AND PROOF OF THEOREM 1

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PROOF OF THEOREM 2