Diffusion-limited Reactions in Nanoscale Electronics

TL;DR

This paper develops a PDE-based model for ligand-receptor interactions in biosensing FETs, simplifying it to an IDE, and demonstrates numerical methods to analyze biochemical effects on sensor surface potential.

Contribution

It introduces a reduced nonlinear integrodifferential equation model for biochemical interactions in nanoscale FET biosensors, enabling efficient numerical analysis.

Findings

Identification of a depletion region affecting surface potential

Numerical method achieves first-order accuracy

Model captures time-dependent biochemical interactions

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.