Electron-hole transport in semiconductors: Stochastic dynamics simulation

A random walk based stochastic simulation algorithm for solving a nonlinear system of transient drift-diffusion-Poisson equations for semiconductors with random doping profile is developed. The method is then applied to simulate and analyze the stochastic dynamics of the transport of electrons and holes in doped semiconductor material. This analysis has a theoretical but also a practical interest since an addition even of a small concentration of foreign atoms to the regular semiconductor material produces dramatic changes in the electrical properties. The nonlinear drift-diffusion-Poisson system is solved by the iteration procedure including alternating simulation of the drift-diffusion processes and solving the Poisson equation. Here, we extend the iteration algorithm to solve the drift-diffusion-Poisson system with additional term governing the random inputs in the system like the stochastic doping, random distribution of quantum dots, and an irregular family of defects. Impact of these random entries on the stochastic dynamics of the drift velocity and electron and hole concentrations is studied.