Asymptotic Representation of Solutions of the Basic Semiconductor Device Equations.

Abstract

In this paper the basic semiconductor device equations modelling a symmetric one-dimensional voltage-controlled diode are formulated as a singularly perturbed two point boundary value problem. The perturbation parameter is the normed Debye-length of the device. The authors derive the zeroth and first order terms of the matched asymptotic expansion of the solutions, which are the sums of uniformly smooth outer terms (reduced solutions) and the exponentially varying inner terms (layer solutions). The main result of the paper is that, if the perturbation parameter is sufficiently small then there exists a solution of the semiconductor device problem which is approximated uniformly by the zeroth order term of the expansion, even for large applied voltages. This result shows the validity of the asymptotic expansions of the solutions of the semiconductor device problem in physically relevant high-injection conditions.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1984
Accession Number
ADA149040

Entities

People

  • C. Schmeiser
  • P. A. Markowich

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Abstracts
  • Asymptotic Series
  • Boundary Layer
  • Boundary Value Problems
  • Christianity
  • Current Density
  • Differential Equations
  • Electrons
  • Equations
  • Intervals
  • Materials
  • Mathematics
  • Metal-Semiconductor Junctions
  • P-N Junctions
  • Semiconductor Devices
  • Semiconductors
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Semiconductor Device Technology

Technology Areas

  • Microelectronics