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

  • Leila Taghizadeh
  • Amirreza Khodadadian
  • Clemens Heitzinger
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


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.



The authors acknowledge support by the FWF (Austrian Science Fund) START project no. Y660 PDE Models for Nanotechnology.


  1. 1.
    Baumgartner, S., Heitzinger, C., Vacic, A., Reed, M.A.: Predictive simulations and optimization of nanowire field-effect PSA sensors including screening. Nanotechnology 24, 225503 (2013)CrossRefGoogle Scholar
  2. 2.
    Bulyha, A., Heitzinger, C.: An algorithm for three-dimensional Monte-Carlo simulation of charge distribution at biofunctionalized surfaces. Nanoscale 3, 1608–1617 (2011)CrossRefGoogle Scholar
  3. 3.
    Fort, A., Rocchi, S., Serrano-Santos, M.B., Spinicci, R., Vignoli, V.: Surface state model for conductance responses during thermal-modulation of SnO-based thick film sensors: part I–model derivation. IEEE Trans. Instrum. Meas. 55, 2102–2106 (2006)CrossRefGoogle Scholar
  4. 4.
    Heitzinger, C., Taghizadeh, L.: Existence and local uniqueness for the stochastic drift-diffusion-Poisson system. Submitted for publication.Google Scholar
  5. 5.
    Heitzinger, C., Liu, Y., Mauser, N.J., Ringhofer, C., Dutton, R.W.: Calculation of fluctuations in boundary layers of nanowire field-effect biosensors. J. Comput. Theor. Nanosci. 7, 2574–2580 (2010)CrossRefGoogle Scholar
  6. 6.
    Heitzinger, C., Mauser, N.J., Ringhofer, C.: Multiscale modeling of planar and nanowire field-effect biosensors. SIAM J. Appl. Math. 70, 1634–1654 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Tulzer, G., Baumgartner, S., Brunet, E., Mutinati, G.C., Steinhauer, S., Köck, A., Barbano, P.E., Heitzinger, C.: Kinetic parameter estimation and fluctuation analysis of CO at SnO2 single nanowires. Nanotechnology 24, 315501 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Leila Taghizadeh
    • 1
  • Amirreza Khodadadian
    • 1
  • Clemens Heitzinger
    • 1
  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria

Personalised recommendations