A three-dimensional process simulator in which both the standard nonlinear diffusion model and a five-species kinetic model are implemented to model phosphorus diffusion in silicon is described. The reaction-diffusion equations are discretized using finite differences in space and the numerical method of lines. The resulting ordinary differential equations are solved using the system integrator LSODP. LSODP uses a backward difference formula for time integration and a Krylov projection method to solve the linear system in the inner Newton loop. Comparisons of the two diffusion models are run on several test problems. Results show that the Krylov approach works well for the mildly asymmetric system of the single species, but requires a large dimension (K/sub m/ approximately=20) subspace for the five-species model.>

PEPPER is a computer program that simulates in one dimension the ion implantation, diffusion, oxidation, epitaxy, deposition, and etch processes used in VLSI technology. The program contains an efficient Monte Carlo ion implantation algorithm that includes explicit calculation of ion channeling and damage. The key feature of the diffusion calculation is a general partial differential equation solver for rapid prototyping of physical models. The solver has been used to develop several unique diffusion models. A novel model for impurity diffusion in polysilicon treats the problem as a two-stream process, with relatively slow standard diffusion within the grain and a much more rapid component of diffusion along the grain boundaries. The two components are coupled at each point by a segregation term. Two other models for impurity diffusion in silicon include explicit calculation of the coupling of point defects with impurities. One of the point-defect models is a general and detailed formulation from a chemical kinetics viewpoint, while the other makes further assumptions to simplify the model for engineering analysis.>