Gettering simulator: physical basis and algorithm

Abstract

The basic physical principles and mechanisms ofgettering of metal impurities in silicon are well established.However, a predictive model of gettering that would enable oneto determine what fraction of contaminants will be gettered ina particular process and how the existing process should bemodified to optimize gettering is lacking. Predictive getteringof transition metals in silicon requires development of arobust algorithm to model diffusion and precipitation oftransition metals in silicon, and material parameters todescribe the kinetics of defect reactions and the stableequilibrium state of the formed complexes. This paperdescribes the algorithm of a gettering simulator, capable ofmodelling relaxation and segregation gettering of interstitially diffusingtransitionmetal impurities in silicon wafers. The basic physicalequations used to model gettering are differential equationsfor diffusion, precipitation and segregation. These equationsare solved using the implicit finite-difference algorithm,based on the underlying physics of the problem. The material parameters required as input for the getteringsimulator such as segregation coefficient, precipitation sitedensity and precipitation radius, which need to be obtainedexperimentally, are briefly discussed.