Analysis of the drift-diffusion-Poisson–Boltzmann system for nanowire and nanopore sensors in the alternating-current regime

The basic analytical properties of the drift-diffusion-Poisson-Boltzmann system in the alternating-current (AC) regime are shown. The analysis of the AC case differs from the direct-current (DC) case and is based on extending the transport model to the frequency domain and writing the variables as periodic functions of the frequency in a small-signal approximation. We first present the DC and AC model equations to describe the three types of material in nanowire field-effect sensors: The drift-diffusion-Poisson system holds in the semiconductor, the Poisson-Boltzmann equation holds in the electrolyte, and the Poisson equation provides self-consistency. Then the AC model equations are derived. Finally, existence and local uniqueness of the solution of the AC model equations are shown. Real-world applications include nanowire field-effect bio- and gas sensors operating in the AC regime, which were only demonstrated experimentally recently. Furthermore, nanopore sensors are governed by the system of model equations and the analysis as well.