Sabelfeld K.   Киреева А.Е.  

Mesh free stochastic algorithm for anisotropic transient diffusion imaging of dislocations and defects in semiconductors.

Reporter: Sabelfeld K.

Mesh free stochastic algorithm for anisotropic transient diffusion imaging of dislocations and defects in semiconductors
K. K. Sabelfeld, A. Е. Kireeva

In this presentation we implement and apply to practically relevant imaging problems in semiconductors a stochastic algorithm suggested in [1] for solving anisotropic transient diffusion equations where the random walk is carried out on arbitrary cubes or parallelepipeds inside the domain. The method is mesh free both in space and time, and is well applied to solve high-dimensional problems with complicated domains. The algorithm is based on tracking the trajectories of the diffusing particles exactly in accordance with the probabilistic distributions derived from the explicit representation of the relevant Green functions for a cube and parallelepiped. It can be conveniently used not only for the solutions, but also for a direct calculation of fluxes to any part of the boundary without calculating the whole solution in the domain. Applications in exciton transport in semiconductors and cathodoluminescence imaging methods are discussed. In particular, we calculate  the time resolved cathodoluminescence intensity for a set of dislocations in semiconductors considered in our recent study [2]. The transients of the cathodoluminescence are used to solve the inverse problem of recovering the diffusion length of excitons and the dislocations density.

Support of Russian Science Foundation under Grant 14-11-00083  is kindly acknowledged. 

1. Sabelfeld K.K. Stochastic simulation methods for solving isotropic and anisotropic drift-diffusion equations in cathodoluminescence imaging, submitted to Mathematical Models and Methods in Applied Sciences, 2018.
2. Sabelfeld K.K., Kireeva A. A. Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging, Monte Carlo Methods and Applications, v.24 (2018), N2, 79 – 92.

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