Impact of surface charge density modulation on ion transport in heterogeneous nanochannels

The PNP nanotransistor, consisting of emitter, base, and collector regions, exhibits distinct behavior based on surface charge densities and various electrolyte concentrations. In this study, we investigated the impact of surface charge density on ion transport behavior within PNP nanotransistors at different electrolyte concentrations and applied voltages. We employed a finite-element method to obtain steady-state solutions for the Poisson-Nernst-Planck and Navier-Stokes equations. The ions form a depletion region, influencing the ionic current, and we analyze the influence of surface charge density on the depth of this depletion region. Our findings demonstrate that an increase in surface charge density results in a deeper depletion zone, leading to a reduction in ionic current. However, at very low electrolyte concentrations, an optimal surface charge density causes the ion current to reach its lowest value, subsequently increasing with further increments in surface charge density. As such, at Vapp=+1V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{app}=+1 \text{V}$$\end{document} and C0=1mM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{0}=1 \text{mM}$$\end{document}, the ionic current increases by 25% when the surface charge density rises from 5 to 20 mC.m-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{mC}.{\text{m}}<^>{-2}$$\end{document}, whereas at C0=10mM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{0}=10 \text{mM}$$\end{document}, the ionic current decreases by 65% with the same increase in surface charge density. This study provides valuable insights into the behavior of PNP nanotransistors and their potential applications in nanoelectronic devices.