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.
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Acknowledgements
The authors acknowledge support by the FWF (Austrian Science Fund) START project no. Y660 PDE Models for Nanotechnology.
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Taghizadeh, L., Khodadadian, A., Heitzinger, C. (2017). The Stochastic Drift-Diffusion-Poisson System for Modeling Nanowire and Nanopore Sensors. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_48
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DOI: https://doi.org/10.1007/978-3-319-63082-3_48
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