
Accession Number : ADA136322
Title : A Singular Perturbation Analysis of the Fundamental Semiconductor Device Equations.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Markowich,P A
PDF Url : ADA136322
Report Date : Oct 1983
Pagination or Media Count : 60
Abstract : In this paper the author presents a singular perturbation analysis of the fundamental semiconductor device equations which form a system of three second order elliptic differential equations subject to mixed NeumannDirichlet boundary conditions. The system consists of Poisson's equation and the continuity equations and describes potential and carrier distributions in an arbitrary semiconductor device. The singular perturbation parameter is the minimal Debyelength of the device under consideration. Using matched asymptotic expansions they demonstrate the occurrence of internal layers at surfaces across which the impurity distribution which appears as an inhomogeneity of Poisson's equation has a jump discontinuity (these surfaces are called 'junctions') and the occurrence of boundary layers at semiconductoroxide interfaces. The author derives the layerequations and the reduced problem (chargeneutralapproximation) and give existence proofs for these problems. They layer solutions which characterize the solution of the singularly perturbed problem close to junctions and interfaces resp. are shown to decay exponentially away from the junctions and interfaces resp. It is shown that, if the device is in thermal equilibrium, then the solution of the semiconductor problem is close to the sum of the reduced solution and the layer solution assuming that the singular perturbation parameter is small. Numerical results for a twodimensional diode are presented. (Author)
Descriptors : *Partial differential equations, *Perturbation theory, *Semiconductor devices, Boundary layer, Boundary value problems, Asymptotic series, Two dimensional, Semiconductor diodes, Poisson equation
Subject Categories : Electrical and Electronic Equipment
Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE