[Back]

C. Heitzinger, L. Taghizadeh:
"Analysis of the drift-diffusion-Poisson-Boltzmann system for nanowire sensors in the alternating-current regime";
Communications in Mathematical Sciences, 15 (2017), 8; 2303 - 2325.

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.

drift-diffusion-Poisson-Boltzmann system, existence, local uniqueness, charge transport, alternating current, field-effect sensor, nanowire sensor, nanocapacitor, nanopore sensor, nanotechnology

http://dx.doi.org/10.4310/CMS.2017.v15.n8.a8