Methods and Applications of Analysis

Volume 26 (2019)

Number 2

Special Issue in Honor of Roland Glowinski (Part 1 of 2)

Guest Editors: Xiaoping Wang (Hong Kong University of Science and Technology) and Xiaoming Yuan (The University of Hong Kong)

Diffusion-limited reactions in nanoscale electronics

Pages: 149 – 166

DOI: https://dx.doi.org/10.4310/MAA.2019.v26.n2.a4

Authors

Ryan M. Evans (Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, Maryland, U.S.A.)

Arvind Balijepalli (Engineering Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland, U.S.A.)

Anthony J. Kearsley (Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, Maryland, U.S.A.)

Abstract

A partial differential equation (PDE) is developed to describe time-dependent receptor-ligand interactions for applications in biosensing with biological field-effect transistors (Bio-FETs). This model describes biochemical interactions on a biochemical gate at the sensor surface, which results in a time-dependent change in the Bio-FET’s conductance. It was shown that one can exploit the disparate length scales of the solution-well and biochemical gate to reduce the coupled PDE model to a single nonlinear integrodifferential equation (IDE) that describes the concentration of reacting species. Although this equation has a convolution integral with a singular kernel, a numerical approximation is constructed by applying the method of lines. The need for specialized quadrature techniques is obviated and numerical evidence shows that this method achieves first-order accuracy. Results reveal a depletion region on the biochemical gate, which non-uniformly alters the surface potential of the semiconductor.

Keywords

biological field effect transistor, integrodifferential equation, method of lines

2010 Mathematics Subject Classification

35Q92, 41A60, 65R20, 92C40

Full Text (PDF format)

Received 8 November 2017

Accepted 2 August 2019

Published 2 April 2020