Modeling of very high concentration effects on impurity diffusion in semiconductors

The standard theory of dopant diffusion in semiconductors based on the reaction–diffusion equations is generalized to include ‘many body effects’ due to the presence of a very high concentration of immobile dopants. This new formulation makes it possible to calculate the concentration profiles of donors/acceptors, clusters, and precipitates, if any, both in silicon and semiconducting compounds in good agreement with the experiment. Moreover, it is possible to calculate the effective diffusion coefficient within the steady-state approximation. This approach has been used to calculate the explicit form of the effective diffusion coefficient in predoped semiconductors. Furthermore, simple analytical formulae are given for, respectively, dopant in-diffusion profiles and the maximum penetration depth.