Rational Design of Field-Effect Sensors Using Partial Differential Equations, Bayesian Inversion, and Artificial Neural Networks

Amirreza Khodadadian; Maryam Parvizi; Mohammad Teshnehlab; Clemens Heitzinger

doi:10.3390/s22134785

Rational Design of Field-Effect Sensors Using Partial Differential Equations, Bayesian Inversion, and Artificial Neural Networks

Sensors (Basel). 2022 Jun 24;22(13):4785. doi: 10.3390/s22134785.

Authors

Amirreza Khodadadian¹, Maryam Parvizi^{1

2}, Mohammad Teshnehlab³, Clemens Heitzinger^{4

5}

Affiliations

¹ Institute of Applied Mathematics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany.
² Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines), Leibniz University Hannover, 30167 Hannover, Germany.
³ Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran 19697, Iran.
⁴ Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria.
⁵ Center for Artificial Intelligence and Machine Learning (CAIML), TU Wien, 1040 Vienna, Austria.

Abstract

Silicon nanowire field-effect transistors are promising devices used to detect minute amounts of different biological species. We introduce the theoretical and computational aspects of forward and backward modeling of biosensitive sensors. Firstly, we introduce a forward system of partial differential equations to model the electrical behavior, and secondly, a backward Bayesian Markov-chain Monte-Carlo method is used to identify the unknown parameters such as the concentration of target molecules. Furthermore, we introduce a machine learning algorithm according to multilayer feed-forward neural networks. The trained model makes it possible to predict the sensor behavior based on the given parameters.

Keywords: Bayesian inversion; biosensors; charge transport; field-effect sensors; inverse modeling; neural networks.

MeSH terms

Algorithms
Bayes Theorem
Monte Carlo Method
Nanowires*
Neural Networks, Computer*

Grants and funding

C. Heitzinger and A. Khodadadian acknowledge support by FWF START project no. Y660 PDE Models for Nanotechnology. M. Parvizi acknowledges the financial support of the Alexander von Humbold Foundation project named ℋ–matrix approximability of the inverses for FEM, BEM and FEM–BEM coupling of the electromagnetic problems. She is affiliated to the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453).