Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors - Sabelfeld, Karl K.; Kireeva, Anastasya (Physica A, 2020)
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. •A new Monte Carlo algorithm for nonlinear drift–diffusion-Poisson systems is developed.•The algorithm for drift calculation is meshless in space and time.•The accuracy and the cost of the algorithm are estimated and analyzed.•The performance of the algorithm is shown by solving transport problems in semiconductors.