The efficient simulation of coupled point defect and impurity diffusion

A program has been developed which efficiently solves the coupled diffusion of interstitials, vacancies, and multiple impurity species in two dimensions. Due to the vast differences in diffusivities of the point defects and impurities, two separate spatial grids are used. A coarse grid is sufficient to represent the rapidly diffusing point defects, whereas a much finer grid is necessary to resolve the details of the impurity profile. Independent time steps are automatically selected for each species, permitting this extremely stiff system of diffusion equations to be solved in acceptable CPU time on a minicomputer. The simulation results are used to study the coupled diffusion of point defects and impurities under local oxidation conditions. Comparison with lap and stain measurements on structures with various widths of oxidizing and nitride-masked regions allows accurate values for numerous point defect diffusion parameters to be extracted