General Model and Equivalent Circuit for the Chemical Noise Spectrum Associated to Surface Charge Fluctuation in Potentiometric Sensors

Abstract

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 staircase 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.

Sensitivity, Noise and Resolution in a BEOL-Modified Foundry-Made ISFET with Miniaturized Reference Electrode for Wearable Point-of-Care Applications

“…Changes of the pH buffer cause shifts of V TH , due to surface charge developed at the sensing layer surface. The pH-induced V TH modulation in ISFETs is usually described using the first order SB model, whose kinetic form is illustrated in Figure 6 [ 20 ]. The model considers at least two chained surface reactions involving the hydrogen ions at the surface (with concentration ) and the exposed surface hydroxyl groups in the complexation states MO − , MOH, and MOH 2 + .…”

“…The model in Figure 6 a is, thus, calibrated by comparison with the current waveforms extracted when switching the pH. From Reference [ 20 ], the master equation of the SB model, shown in Figure 6 a, reads whereas the net surface charge density for identical sites per unit of surface area is: …”

“…Fluctuations of the surface charge at the sensing layer can be calculated from the master equation, as presented in Reference [ 20 ]. In particular, it is possible to directly link the master equation to the surface charge density noise PSD or to an equivalent circuit of the surface reactions.…”

“…The latter method was chosen, since it can be included in the circuit representation of the entire electro-chemical system. The equivalent circuit of the SB-like model consists of a two-cells ladder network (see Figure 6 b), where each cell is the series of a resistor and a capacitor [ 19 , 20 ], and the chemical noise at the single port is given by the thermal noise of the resistive components, i.e., and . This network must be placed parallel to the double layer capacitance in the complete model, as shown in Figure 7 .…”

“…In this regard, it has often been reported that the electrical noise of the FET underlying any ISFET is much larger than the so-called chemical noise (i.e., the noise related to the stochastic binding/unbinding of the target ions), with the latter source of noise then being neglected [ 11 , 12 , 13 , 14 , 15 , 16 ]. However, recently published models [ 17 , 18 , 19 , 20 ] show that when the chemical noise can be observed on top of the FET intrinsic noise, then precious information on the biological transduction can be extracted from measurements. Furthermore, few works also claimed successful experimental evidence of chemical noise [ 19 , 21 , 22 ].…”