Diffusion-limited Reactions in Nanoscale Electronics
Abstract
A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor surface (or biochemical gate) located at the bottom of a solution-well, which result in a time-dependent change in the FET 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 was constructed by applying the method of lines. The need for specialized quadrature techniques was obviated and numerical evidence strongly suggests 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.
Cite
@article{arxiv.1710.07211,
title = {Diffusion-limited Reactions in Nanoscale Electronics},
author = {Ryan M. Evans and Arvind Balijepalli and Anthony J. Kearsley},
journal= {arXiv preprint arXiv:1710.07211},
year = {2017}
}