Numerical integral method for diffusion modeling

The authors present a numerically efficient mathematical approach, the numerical integral method, for diffusion modeling. This method extends the boundary integral methods to solve linear and nonlinear diffusion problems with physically based diffusivity models to account for concentration-dependent effects, oxidizing ambient effects, electric field effects, etc. The algorithm for solving nonlinear diffusion problems and its implementation in a computer program are described. Results from example problems are shown. This new numerical method provides the potential for achieving a diffusion simulation which is computationally efficient, numerically stable, and sufficiently accurate in an engineering environment. Such an efficient and yet accurate diffusion simulation is especially important in statistical simulation of VLSI processes