The Stochastic Drift-Diffusion-Poisson System for Modeling Nanowire and Nanopore Sensors

Abstract

We use the stochastic drift-diffusion-Poisson system to model charge transport in nanoscale devices. This stochastic transport equation makes it possible to describe device variability, noise, and fluctuations. We present-as theoretical results-an existence and local uniqueness theorem for the weak solution of the stochastic drift-diffusion-Poisson system based on a fixed-point argument in appropriate function spaces. We also show how to quantify random-dopant effects in this formulation. Additionally, we have developed an optimal multi-level Monte-Carlo method for the approximation of the solution. The method is optimal in the sense that the computational work is minimal for a given error tolerance.