Diffusion of ion beam created vacancies and their effect on intermixing: A gambler’s ruin approach

Ion implantation has frequently been shown to modify the shape of quantum wells following thermal annealing by enhancing the interdiffusion. We have shown that, independent of chemical effects on the interdiffusion, there is a contribution from the vacancies created by the implant. The effects of the diffusion of these vacancies can be modeled using a very simple expression that does not rely on any knowledge of the diffusion coefficients for the vacancies in the material. By comparing the problem to the classic problem of the gambler’s ruin, we have shown that implantation into a surface should produce even intermixing of layers at different depths below it, ignoring the effects of vacancy trapping and other depth dependent diffusion processes.