Modeling Non-Equilibrium Ion-Transport in Ion-Selective-Membrane/Electrolyte Interfaces for Electrochemical Potentiometric Sensors

We present an approach to simulate ion's drift and diffusion in chemical sensors based on ion-selective-membranes (ISMs) in either ion-selective electrode structures or coupled to field-effect transistors. The model is used to analyze the sensitivity, selectivity, and transient response of ISMs in non-equilibrium conditions upon real-time concentration changes. Our simple implementation combines advanced features from semiconductor theory and analytical electrochemistry, such as the Schafetter-Gummel discretization scheme and Chang-Jaffé boundary conditions for ions at the interfaces, thus allowing to perform simulations beyond sensing. The results are in agreement with experimental transient responses reported in the literature. As relevant case studies, we examine the ISM preconditioning in miniaturized sensors and the electrostatic interaction between the FET channel and ISMs. In the first case, simulations reveal that calibration curves performed on incomplete ISM conditioning can lead to hysteretical responses when the ion affinity in the electrolyte and ISM is similar (e.g., with organic ions). In the second case, we find that the gate oxide field in contact with the ISM affects the device characteristics such that the ion concentrations not only change the FET threshold voltage but also the slope of its IV curve. This effect can be minimized by working in the subthreshold regime or using extended gates.