Simulating Cl diffusion in polycrystalline CdTe

Most theoretical treatments of grain boundary (GB) diffusion start with the model developed by Fisher over sixty years ago, where a bulk material with a low diffusion constant is bisected by a narrow slab with high diffusivity (the GB). For this system, Fisher derived two coupled differential equations, the second involving a first order derivative. While Fisher's model can be applied to more general situations, it can be very cumbersome to implement in cases where the GBs are only piecewise linear and/or intersect at arbitrary angles. In this work, we develop an alternate model involving only second order derivatives that is more conducive to simulating arbitrary GB geometries, but yields results that are equivalent to those one would obtain from Fisher's. We apply our model to the problem of Cl diffusion in CdTe, using it to obtain Cl concentration profile data that is similar to those obtained in recent experiments.