A new approach to the simulation of the coupled point defects and impurity diffusion

A program, named FINDPRO, has been developed which efficiently solves the coupled diffusion of point defects and multiple impurity species in two dimensions, using the finite difference method for space discretization. The program simulates an oxidation process step by interfacing with a boundary element oxidation program. It accounts for the effect of point defect recombination by subtracting the vacancy continuity equation from that of the interstitials and then using the point defect equilibrium relationship. The resulting equation is easier to handle numerically because the recombination term has been eliminated. Further, the point-defect-dopant interactions are essentially based on a steady-state approximation, but the correct defect gradients and concentrations in two or three dimensions relative to equilibrium are efficiently generated at a great saving in computational resources. The essential feature of the model used in this program is a realistic coupling between point defects and impurity species. The point defect fluxes depend on the concentrations of impurities and their gradients. Similarly, the impurity fluxes depend on the concentration and gradients of the point defects. This approach allows successful two-dimensional simulation of all major point-defect-mediated diffusion phenomena