Poisson–Nernst–Planck model for an ionic transistor based on a semiconductor membrane

In this paper we developed a Poisson–Nernst–Planck model of an ionic current flowing through a nanopore in a layered solid-state membrane made of a single highly-doped n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-Si layer sandwiched between two thick oxide layers which we call the ionic transistor. We studied this layered membrane for a range of source-drain voltages while keeping the gate (the semiconductor membrane) voltage fixed at a certain value, which was later varied too. We find that for this ionic transistor to be effective in controling the ion fluxes through the nanopore, the gate voltage must be kept relatively large. Another solution could be to increase the surface negative charge on the membrane or to replace the outer oxide layers with the semiconductor material, such as the p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Si material. The developed model can be applied to study ionic filtering and separation properties of membranes of different composition and nanopore geometries.