Taghizadeh, L., Khodadadian, A., & Heitzinger, C. (2018). The Stochastic Drift-Diffusion-Poisson System for Modeling Nanowire and Nanopore Sensors. In Progress in Industrial Mathematics at ECMI 2016 (pp. 309–317). Progress in Industrial Mathematics, Springer. https://doi.org/10.1007/978-3-319-63082-3_48
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.
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Project title:
Partielle Differentialgleichungen für Nanotechnologie: Y660-N25 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
