Elsevier

Solid-State Electronics

Volume 27, Issue 12, December 1984, Pages 1043-1054
Solid-State Electronics

An interactive two-dimensinal finite element process modelling package for a single user mini-computer

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Abstract

The algorithms and models of an accurate finite element based simulation of th eprocessing steps of semiconductor wafer fabrication are described. Properties of the latest generation of single user mini-computers allow the process engineer to use the computer package in an interactive mode. The process steps modelled are, implantation, oxidation/diffusion and annealing. Implantation models are based on the well-tested one-dimensional statistical distributions. Interaction between impurity atoms is assumed to be mainly through the built-in field. To obtain an accurate estimate of the built-in field, the non-linear Poisson equation is solved at the same nodes and in the same elements used for the simulation of the diffusion process. On making the assumption that small time steps are taken in the numerical formulation of the diffusion problem, the finite element equation system becomes linear and can be rapidly solved. Each impurity is assumed to diffuse independently in a non-uniform electric field, enhanced by a component due to the other impurities. Coupling between oxidation and diffusion is accounted for by a simple algorithm that deforms the solution mesh after the oxidising agent reacts with silicon to create a larger volume of SiO2.

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