A novel parallel adaptive Monte Carlo method for nonlinear Poisson equation in semiconductor devices

We present a parallel adaptive Monte Carlo (MC) algorithm for the numerical solution of the nonlinear Poisson equation in semiconductor devices. Based on a fixed random walk MC method, 1-irregular unstructured mesh technique, monotone iterative method, a posterior error estimation method, and dynamic domain decomposition algorithm, this approach is developed and successfully implemented on a 16-processors (16-PCs) Linux-cluster with message-passing interface (MPI) library. To solve the nonlinear problem with MC method, monotone iterative method is applied in each adaptive loop to obtain the final convergent solution. This approach fully exploits the inherent parallelism of the monotone iterative as well as MC methods. Numerical results for p–n diode and MOSFET devices are demonstrated to show the robustness of the method. Furthermore, achieved parallel speedup and related parallel performances are also reported in this work.