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Basis adaptation for the stochastic nonlinear Poisson–Boltzmann equation

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Abstract

A basis-adaptation method based on polynomial chaos expansion is used for the stochastic nonlinear Poisson–Boltzmann equation. The uncertainty in this numerical approach is motivated by the quantification of noise and fluctuations in nanoscale field-effect sensors. The method used here takes advantage of the properties of the nonlinear Poisson–Boltzmann equation and shows an exact and efficient approximation of the real solution. Numerical examples are motivated by the quantification of noise and fluctuations in nanowire field-effect sensors as a concrete example. Basis adaptation is validated by comparison with the full solution, and it is compared to optimized multi-level Monte-Carlo method, and the model equations are validated by comparison with experiments. Finally, various design parameters of the field-effect sensors are investigated in order to maximize the signal-to-noise ratio.

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Acknowledgments

The authors acknowledge the support by FWF (Austrian Science Fund) START Project No. Y660 PDE Models for Nanotechnology. The authors also would like to appreciate Prof. Roger Ghanem (University of Southern California) for useful discussions about polynomial chaos expansion.

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Authors and Affiliations

  1. Institute for Analysis and Scientific Computing, Vienna University of Technology (TU Vienna), Vienna, Austria

    Amirreza Khodadadian & Clemens Heitzinger

  2. School of Mathematical and Statistical Sciences, Arizona State University (ASU), Tempe, AZ, USA

    Clemens Heitzinger

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  1. Amirreza Khodadadian
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  2. Clemens Heitzinger
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Correspondence to Amirreza Khodadadian.

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Khodadadian, A., Heitzinger, C. Basis adaptation for the stochastic nonlinear Poisson–Boltzmann equation. J Comput Electron 15, 1393–1406 (2016). https://doi.org/10.1007/s10825-016-0922-2

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  • DOI: https://doi.org/10.1007/s10825-016-0922-2

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