
Accession Number : ADA136368
Title : A Nonlinear Eigenvalue Problem Modelling the Avalanche Effect in Semiconductor Diodes.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Markowich,P A
PDF Url : ADA136368
Report Date : Nov 1983
Pagination or Media Count : 26
Abstract : This paper is concerned with the analysis of the solution set of the twopoint boundary value problems modelling the avalanche effect in semiconductor diodes for negative applied voltage. We interpret the avalanchemodel as a nonlinear eigenvalue problem (with the current as eigen parameter) and show (using a priori estimates and a well known theorem on the structure of solution sets of nonlinear eigenvalue problems for compact operators) that there exists an unbounded continuum of solutions which contains a solution corresponding to every negative voltage. This effect (also called avalanche generation) is characterized by a sudden increase of the current flowing through the device starting at a certain negative voltage. Physically, the diode breaks down shortly after the onset of avalanche generation. Therefore, it was conjectured that there is a threshold voltage beyond which no solutions of the avalanche model exists. We show that this conjecture is false; more precisely a continuous branch of solution along which every negative voltage and every negative bias is assumed (at least once) exists. Mathematically, the avalancheeffect only becomes apparent through an exponential increase of the absolute value of the current starting at a certain negative voltage.
Descriptors : *Boundary value problems, *Eigenvalues, Nonlinear analysis, Semiconductor diodes, Avalanche effect(Electronics), Mathematical models, Theorems, Ionization
Subject Categories : Electrical and Electronic Equipment
Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE