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Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors

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  • Sabelfeld, Karl K.
  • Kireeva, Anastasya

Abstract

Stochastic simulation algorithms for solving transient nonlinear drift diffusion recombination transport equations are developed. The governing system of equations includes two drift–diffusion equations coupled with a Poisson equation for the potential whose gradient forms the drift velocity. A stochastic algorithm for solving nonlinear drift–diffusion equations is proposed here for the first time. In each time step, the method calculates the solution on a cloud of points using a new global Monte Carlo random walk and Cellular Automata algorithms. The Poisson equation is solved by a global version of the Random Walk on Spheres method which calculates both the solutions and the derivatives without using finite difference approximations. The method is also able to calculate fluxes to any desired part of the boundary, from arbitrary sources. For transient drift–diffusion equations we suggest a stochastic expansion from cell to cell algorithm for calculating the whole solution field. All new global random walk algorithms developed in this paper are validated by comparing the simulation results with exact solutions. Application of the developed method to solve a system of 2D transport equations for electrons and holes in a semiconductor is given.

Suggested Citation

  • Sabelfeld, Karl K. & Kireeva, Anastasya, 2020. "Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    • Handle: RePEc:eee:phsmap:v:556:y:2020:i:c:s037843712030409x
    DOI: 10.1016/j.physa.2020.124800
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    References listed on IDEAS

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    1. Madalina Deaconu & Antoine Lejay, 2006. "A Random Walk on Rectangles Algorithm," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 135-151, March.
    2. Sabelfeld Karl K., 2016. "Random walk on spheres method for solving drift-diffusion problems," Monte Carlo Methods and Applications, De Gruyter, vol. 22(4), pages 265-275, December.
    3. Sabelfeld Karl K., 2019. "A global random walk on spheres algorithm for transient heat equation and some extensions," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 85-96, March.
    4. Sabelfeld, Karl K., 2017. "A mesh free floating random walk method for solving diffusion imaging problems," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 6-11.
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