General model and equivalent circuit for the chemical noise spectrum associated to surface charge fluctuation in potentiometric sensors

This paper firstly reports a general and powerful approach to evaluate the power spectral density (PSD) of the surface charge fluctuations, so-called ``chemical noise'', from a generic set of reactions at the sensing surface of potentiometric sensors such as, for instance, Ion-Sensitive Field Effect Transistors (ISFETs). Starting from the master equation, the spectral noise signature of a reaction set is derived as a function of the reaction kinetic parameters and of the interface concentration of the ionic species. Secondly, we derive an equivalent surface admittance, whose thermal noise PSD produces a noise PSD equal to that of the surface charge fluctuations. We also show how to expand this surface admittance into stair-case RC networks, with a number of elementary cells equal to the number of surface reactions involved. This admittance can be included in circuit simulations coupled with a SPICE compact model of the underlying FET, to enable the physically based modelling of frequency dispersion and noise of the sensing layer when simulating the sensor and the read-out. Validation with existing models and literature results as well as new application examples are provided. The proposed methodology to compute the PSD from rate equations is amenable to use in different contexts where fluctuations are generated by random transitions between discrete states with given exchange rates.