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A two‐dimensional finite element algorithm for the simultaneous solution of the semiconductor device equations with automatic convergence
Author(s) -
Armstrong G. A.,
Ferguson R. S.,
Flynn J.
Publication year - 1986
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620230409
Subject(s) - finite element method , nonlinear system , convergence (economics) , node (physics) , divergence (linguistics) , algorithm , mathematics , partial differential equation , iterative method , mathematical analysis , physics , engineering , structural engineering , linguistics , philosophy , quantum mechanics , economics , economic growth
The proposed algorithm solves equations governing the behaviour of semiconductor devices using a finite element technique. Electrostatic potential and the hole and electron quasi‐Fermi potentials are chosen as the solution variables. The equation set is written in a steady‐state form using these three variables and this gives rise to a system of three nonlinear partial differential equations. The equations, which are intimately coupled, are solved simultaneously using a weighted residual formulation. Convergence of the nonlinear solution procedure using any initial guess is guaranteed by employing ‘incremental loading’ coupled to a test for divergence that is applied at each iterative step. The triangular elements used in the program are automatically generated from a mesh of eight‐node isoparametric elements that is itself an automatically generated subdivision of a small number of eight‐node (super) elements. A novel method of generating an initialisation state using the boundary element method is also described.