Diffusion Equation Model for Kilovolt Electron Transport at X-Irradiated Interfaces

A simple energy-dependent diffusion model for kilovolt electron transport is derived and applied to the problem of predicting the charge and energy deposition profiles near x-irradiated material interfaces. Some simplifying approximations and a transformation of variable permit the problem to be transformed into the form of the conventional time-dependent heat conduction equation. Closed-form analytical solutions are obtained. Using these solutions, dose profiles in silicon next to gold at photon energies from 10 to 200 keV are evaluated and compared with those calculated from the POEM Monte Carlo code and the semi-empirical model of Burke and Garth. At all photon energies in this energy range, the agreement between the models is within a factor 2 or better, the diffusion model energy deposition profiles lying between the profiles predicted by the other two models. Application of this model to predicting dose profiles in multilayered and even three-dimensional device structures is readily possible as an alternative to Monte Carlo calculations.