On the Dependence of the Convergence of Gummel's Algorithm on the Regularity of the Solution.

Abstract

The convergence of a typical example from the class of highly successful decoupling algorithms for steady state semiconductor simulation, collectively known as Gummel's method, is considered for one, two, and three dimensional models. Because a nonlinear equation is solved for the potential u at every step, the considered version corresponds closely to the algorithms used for numerical computation in practice. As opposed to most earlier publications, the dependence of the regularity of the solution on the device geometry and the nature of the boundary conditions for the system of mixed boundary value problems is considered. From a detailed analysis of the boundary conditions for a typical two dimensional model we conclude that for a physically realistic device geometry the solution may be expected to be sufficiently regular for the algorithm to converge. Additional keywords: partial differential equations; functions(mathematical); inequalities. (Author).

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1985
Accession Number
ADA154628

Entities

People

  • T. Kerkhoven

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Computational Science
  • Differential Equations
  • Equations
  • Functional Analysis
  • Geometry
  • Mathematical Analysis
  • Numerical Analysis
  • Partial Differential Equations
  • Semiconductor Devices
  • Semiconductors
  • Simulations
  • Solid State Electronics
  • Steady State
  • Theorems
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.

Technology Areas

  • Microelectronics