Gettering simulator: physical basis and algorithm

The basic physical principles and mechanisms of gettering of metal impurities in silicon are well established. However, a predictive model of gettering that would enable one to determine what fraction of contaminants will be gettered in a particular process and how the existing process should be modified to optimize gettering is lacking. Predictive gettering of transition metals in silicon requires development of a robust algorithm to model diffusion and precipitation of transition metals in silicon, and material parameters to describe the kinetics of defect reactions and the stable equilibrium state of the formed complexes. This paper describes the algorithm of a gettering simulator, capable of modelling relaxation and segregation gettering of interstitially diffusing transition metal impurities in silicon wafers. The basic physical equations used to model gettering are differential equations for diffusion, precipitation and segregation. These equations are solved using the implicit finite-difference algorithm, based on the underlying physics of the problem. The material parameters required as input for the gettering simulator such as segregation coefficient, precipitation site density and precipitation radius, which need to be obtained experimentally, are briefly discussed.