MSM 98
MSM 98
Technical Proceedings of the 1998 International Conference on Modeling and Simulation of Microsystems

Modeling Chapter 3

Adaptive Hierarchical Finite Element Modeling of Dopant Diffusion

Authors: A. Bose and C.S. Rafferty

Affilation: Bell Laboratories, United States

Pages: 100 - 104

Keywords: TED. h-p finite element, numerical modeling

We present a finite element formulation based on a hóp refinement strategy for the coupled dopant-defect diffusion problem in semiconductor process modeling. The algorithm involves increasing the degree p of the element basis as well as mesh refinement (h', and redistribution as an optimal u ay of generating more accurate approximate solutions to the diffusion problem. A hierarchic famil~ of nested basis functions based on integrated Legendre polynomials is employed in the present study. The lower-degree monomial functions are explicitly embedded in successively higher order bases and therefore. the element matrices and vectors need not be recomputed corresponding to the lower-order bases for each p-refinement. Nlore specifically, an element matrix corresponding to a degree p = k is a nested sub-matrix of the neu- element matrix corresponding to p = k 1. An important characteristic of the hierarchic monomials is that the coefficients corresponding to the mid-side and interior element nodes are tangential derivatives of the solution field and not necessarily the function values. Numerical examples demonstrate the optimal convergence rate and accuracy of the present formulation.

ISBN: 0-96661-35-0-3
Pages: 678