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Bayesian inversion for nanowire field-effect sensors

  • Amirreza KhodadadianEmail author
  • Benjamin Stadlbauer
  • Clemens Heitzinger
Article
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Abstract

Nanowire field-effect sensors have recently been developed for label-free detection of biomolecules. In this work, we introduce a computational technique based on Bayesian estimation to determine the physical parameters of the sensor and, more importantly, the properties of the analyte molecules. To that end, we first propose a PDE-based model to simulate the device charge transport and electrochemical behavior. Then, the adaptive Metropolis algorithm with delayed rejection is applied to estimate the posterior distribution of unknown parameters, namely molecule charge density, molecule density, doping concentration, and electron and hole mobilities. We determine the device and molecules properties simultaneously, and we also calculate the molecule density as the only parameter after having determined the device parameters. This approach makes it possible not only to determine unknown parameters, but it also shows how well each parameter can be determined by yielding the probability density function (pdf).

Keywords

Silicon nanowire sensors Markov chain Monte Carlo Adaptive Metropolis–Hastings algorithm Stochastic drift–diffusion–Poisson–Boltzmann system 

Notes

Acknowledgements

The authors acknowledge support by the FWF (Austrian Science Fund) START project No. Y660 PDE Models for Nanotechnology. The authors also acknowledge the helpful comments by the anonymous reviewers.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Amirreza Khodadadian
    • 1
    • 2
    Email author
  • Benjamin Stadlbauer
    • 1
  • Clemens Heitzinger
    • 1
    • 3
  1. 1.Institute for Analysis and Scientific ComputingVienna University of Technology (TU Wien)ViennaAustria
  2. 2.Institute of Applied MathematicsLeibniz University HannoverHanoverGermany
  3. 3.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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