Geodesic
Discrete stochastic simulation of the electrons and holes recombination in the $\mathrm{2D}$ and $\mathrm{3D}$ inhomogeneous semiconductor
Prikladnaâ diskretnaâ matematika, no. 4 (2016), pp. 110-127

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Stochastic models of electron-hole recombination in $\mathrm{2D}$ and $\mathrm{3D}$ inhomogeneous semiconductors based on a discrete cellular automata approach are presented in the paper. These models are derived from a Monte Carlo algorithm based on spatially inhomogeneous nonlinear Smoluchowski equations with the random initial distribution density used to simulate the annihilation of spatially separate electrons and holes in a disordered semiconductor characterized by the heterogeneous properties of the material. Recombination kinetics in different regimes such as a pure diffusion, diffusion in vicinity of tunneling and diffusion in the presence of recombination centers are investigated by a cellular automata simulation. Statistical characteristics of the recombination process (particle concentrations and the radiative intensity) obtained by the cellular automaton models are compared with the theoretically known asymptotics derived for a pure diffusion case. The results obtained for a two-dimensional domain correspond to the theoretical asymptotics, whereas in three-dimensional case, they differ from the exact asymptotics. It is found out by simulations that a spatial electron and hole separation (segregation) occurs under certain conditions on the diffusion and tunneling rates. The electron-hole spatial segregation in $\mathrm{2D}$ and $\mathrm{3D}$ semiconductors is analyzed by using the probability density of the electron-hole separation. In addition, the execution time of the codes implementing the cellular automaton model of the recombination in $\mathrm{2D}$ and $\mathrm{3D}$ semiconductors is studied in dependence on the number of simulated electron-hole pairs and the size of the semiconductor domain. It is shown that the execution time for semiconductors of dimension $d$ is proportional to a polynomial of order $d$.
Keywords: recombination, semiconductor, tunnelling, stochastic simulation, cellular automata.
Mots-clés : diffusion 
@article{PDM_2016_4_a8,
     author = {K. K. Sabelfeld and A. E. Kireeva},
     title = {Discrete stochastic simulation of the electrons and holes recombination in the $\mathrm{2D}$ and $\mathrm{3D}$ inhomogeneous semiconductor},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {110--127},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2016_4_a8/}
}
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K. K. Sabelfeld; A. E. Kireeva. Discrete stochastic simulation of the electrons and holes recombination in the $\mathrm{2D}$ and $\mathrm{3D}$ inhomogeneous semiconductor. Prikladnaâ diskretnaâ matematika, no. 4 (2016), pp. 110-127. http://geodesic.mathdoc.fr/item/PDM_2016_4_a8/