Monte-Carlo Simulation of Particle Diffusion in Various Geometries and Application to Chemistry and Biology

Abstract

Different techniques of event biasing have been implemented in the particle-based Monte Carlo simulations of a 15nm n-channel MOSFET. The primary goal is to achieve enhancement in the channel statistics and faster convergence in the calculation of terminal current. Enhancement algorithms are especially useful when the device behavior is governed by rare events in the carrier transport process. After presenting a brief overview on the Monte Carlo technique for solving the Boltzmann transport equation, the basic steps of deriving the approach in presence of both the initial and the boundary conditions have been discussed. In the derivation, the linearity of the transport problem has been utilized first, where Coulomb forces between the carriers are initially neglected. The generalization of the approach for Hartree carriers has been established in the iterative procedure of coupling with the Poisson equation. It is shown that the weight of the particles, as obtained by biasing of the Boltzmann equation, survives between the successive steps of solving the Poisson equation.