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Exact representations for the probability density of the life time and survival probability for a sphere and a disc are derived for a general drift-diffusion-reaction process. Based on these new formulas, we suggest an extremely efficient stochastic simulation algorithm for solving transient cathodoluminescence (CL) problems without any mesh in space and time. The method can be applied to a broad class of drift-diffusion-reaction problems where the time behavior of the absorbed material is of interest. The important advantage of the method suggested is the ability to incorporate local inclusions like dislocations, point defects and other singular folds and complicated structures. General Robin boundary conditions on the boundary are treated in a probabilistic way. The method is tested against exact solutions for a series of examples with bounded and unbounded domains. An application to the dislocation imaging problem, which includes thousand threading dislocations, is given.

monte carlo methods and applications

Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging