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General Theory of Phosphorus and Arsenic Diffusions in Silicon

By solving the diffusion equations based on the pair-diffusion model, it is determined that the difference in excess vacancy generation between phosphorus and arsenic is caused by their intrinsic diffusion coefficients, that is, their E center diffusion coefficients, or the potential energies of a vacancy in the vicinity of their atoms. Assuming that (i) the vacancy formation energy decreases with increasing phosphorus or arsenic concentration, (ii) the binding energy between a vacancy and a phosphorus or an arsenic atom is constant, and (iii) the As2V complex is formed in the case of arsenic diffusion, not only the diffusion of phosphorus, whose profile has a kink, but also that of arsenic, whose profile has no kink, can be explained.