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Секция 3
References
1. Sabelfeld K.K. Stochastic simulation algorithms for solving narrow escape diffusion problems by introducing a drift to the target, Journal of Computational Physics, 410 (2020), Article ID 109406.
2. Sabelfeld K.K. Random walk on spheres algorithm for solving transient drift-diffusion-reaction problems Monte Carlo Methods Appl. 2017. Vol. 23 (3), P. 189-212.
3. Kaganer Vladimir M., Lahnemann Jonas, Pfuller Carsten, Sabelfeld Karl K., Kireeva Anastasya E., and Brandt Oliver. Determination of the Carrier Diffusion Length in GaN from Cathodoluminescence Maps Around Threading Dislocations: Fallacies and Opportunities, Physical Review Applied. 2019. Vol. 12, 054038.
4. K. Sabelfeld, A. Kireeva. A new Global Random Walk algorithm for calculation of the solution and its derivatives of elliptic equations with constant coefficients in an arbitrary set of points, Applied Mathematics Letters, vol. 107, 2020, 106466.
Monte Carlo methods for solving a system of nonlinear parabolic-elliptic equations of semiconductors
K. K. Sabelfeld1,2, A. E. Kireeva1
lInstitute of computational mathematics and mathematical geophysics, SB RAS
2Novosibirsk State University
Email: [email protected]
DOI: 10.24411/9999-017A-2020-10095
In this study we develop a Monte Carlo method for solving a system of nonlinear parabolic-elliptic equations governing the transport and recombination of electrons and holes in semiconductors. This field attracts considerable experimental and theoretical interest because the optoelectronic properties of technologically important semiconductor materials have been found to be controlled by the electron-hole recombination dynamics. A stochastic method for solving a nonlinear system of divergence free drift-diffusion-Poisson equations is developed in [1]. It is based on the global Random Walk algorithm [2] which calculates a gradient of the solution of the Poisson equation in arbitrary family of points of the domain. The drift-diffusion-Poisson system is solved by the iteration procedure including alternating simulation of the drift-diffusion processes and calculating the gradient of the solution to the Poisson equation. In the present study we extend the stochastic algorithm to solve the nonlinear system of drift-diffusion-Poisson equations in the general divergence form.
The support of the Russian Science Foundation under grant № 19-11-00019 is gratefully acknowledged. References
1. Sabelfeld K., Kireeva A. Stochastic simulation algorithms for solving a nonlinear system of drift-diffusion-Poisson equations // BIT Numerical Mathemaatics, submitted 2020.
2. Sabelfeld Karl K. A global random walk on spheres algorithm for transient heat equation and some extensions // Monte Carlo Methods and Applications. 2019. № 25(1). P. 85-96.
Stochastic simulation of transients of cathodoluminescence intensity: impact of randomly distributed dislocations
K. K. Sabelfeld^ A. E. Kireeva1
lInstitute of computational mathematics and mathematical geophysics, SB RAS
2Novosibirsk State University
Email: [email protected]
DOI: 10.24411/9999-017A-2020-10096
In this study a stochastic algorithm of simulation of exciton diffusion and drift in a semiconductor in vicinity of randomly distributed dislocations is developed. The Monte Carlo algorithm is based on the random walk on spheres method suggested for solving the transient drift-diffusion-reaction problems in [1]. The cathodoluminescence intensity is computed as a fraction of the radiatively recombined excitons. The cathodoluminescence method is employed for the analysis of a material structure. Threading dislocations are visible as dark spots in cathodoluminescence maps. The recent experiments [2] showed that the strain field in the vicinity of dislocations produces a piezoelectric field which affects the exciton life-time close to the dislocation edge and causes a drift of excitons. In our previous model [3] we simulate the threading dislocation as a semi-cylinder whose surface adsorbs excitons. In the present work, the dislocation is simulated with its piezoelectric field around which defines the life-time and the drift of excitons depending on the distance from
