Monte Carlo Particle Simulation for Electrical and Thermal Analysis of a MESFET using the Finite-Element Approach

Particle simulations based on the Boltzmann Transport Equation (BTE) and the Monte Carlo method are a powerful tool for studying semiconductor devices in the nanometer to submicrometer regime. As with most numerical solvers, particle simulations require a mesh to solve for the fields within a semiconductor device. Traditionally, particle simulations use a finite-difference method (FDM) on a mesh with uniform step sizes. This work explores using a finite-element method (FEM) with a non-uniform triangular mesh. The FEM is validated by comparing results back to those obtained by using the FDM, for the simple example of a GaAs MESFET. And the FEM runs ten times faster than the FDM. Aside from electrical aspects of the device, heat flow within the device is also studied using the finite-element approach.