# Gating Hysteresis as an Indicator for Silicon Nanowire FET Biosensors
## 3 Results and Discussion
### Hysteresis of the Transfer Curve Versus Subthreshold Shift \(dV_{T}\) for thrombin Detection
Figure 3e summarizes the \(dV_{T}\) measurements and displays the calibration curve where the mean \(dV_{T}\) is represented as a function of the thrombin concentration trapped by the specific TBA at the sensor surface (red line). Note that \(dV_{T}\) is found to be significantly higher for the aptamer decorated surface compared to the negative control surface with RDM (red and black curves, respectively), indicating a primary specific interaction of TBA with thrombin, whereas the signal increase for the RDM functionalized surface is caused mainly by unspecific protein adsorption. In summary, the presented method enables the detection of the thrombin concentrations as low as 200 pM, which is within the range presented by other aptamer based FET sensors for thrombin detection [25; 47]. The achieved sensitivity reaches approximately 10 mV/dec, which is also comparable to recently published SiNW-based FET biosensing using antibodies [52]. _Hysteresis of the transfer curve_: In contrast to the saturating threshold voltage, the measured hysteresis shows a distinct response on the thrombin concentration that is only slightly impeded by the fluid flow and, most importantly, is reversibly changing with thrombin concentration (see Figure 3a, black line). Instabilities in the real time signal might be explained by a reference potential drift. A stable Ag/AgCl reference electrode should be immersed in a solution with constant chloride concentration, while here it is in direct contact with buffer and sample solutions [53]. The estimated magnitude of the \(V_{hyst}\) shift is by a factor of five lower than that of the threshold voltage shift \(dV_{T}\). We analyzed the magnitude of the hysteresis shift and plotted the result as a function of thrombin concentration in Figure 3c. We fit the hysteresis and thrombin concentration data with a model describing the change of hysteresis with the square root of thrombin concentration. Fit inputs were the averaged data for constant thrombin concentration and the respective standard deviation. The fitted sensitivity was 2.15 nM/mV\({}^{2}\), with a hysteresis offset for a zero thrombin concentration of \(-\)32.1 mV. Below 2 nM thrombin concentration the hysteresis is almost constant, while above that point the square root dependence is very clear. We can explain the experimental evidence of a square root dependence of hysteresis and thrombin concentration with the dipole moment of thrombin molecules that is potentially changing with thrombin concentration in a square root dependence. We derive an explanation of this hypothesis starting on the description of hysteresis itself. Generally the initial hysteresis in the transfer cure is attributed to charge traps along the Si NW/SiO\({}_{2}\) interface, with a trap filling and emptying process that requires time for equilibrium [54; 55]. However, it can also be a result of time-dependent capacitive gating, producing variations in the effective \(V_{T}\) and therefore in the hysteresis if the capacitance is changed at the dielectric layer and the ambient [56; 57]. Altogether, measurable differences will be found for increasing and decreasing \(V_{G}\). While the Si NW/SiO\({}_{2}\) traps are constant in our system, the explanation to hysteresis variations must be found on the thrombin itself in relation to capacitance changes. Since thrombin is positively charged in the hereby tested conditions, the binding due to the biorecognition process leaves a positively charged biomolecular layer on the FET surface, with the subsequent layer of attracted negative ions from the buffer solution. This results in a specific double-layer capacitance value. On the other hand, it is known that thrombin is a molecule that tends to be highly polarizable. [58]. An increasing dipole moment density at the surface leads to a diminishing double-layer and surface capacitance, as well as a modification of the hysteresis width. The dipole moment of surface bound molecules is therefore expected to have an influence on the hysteresis.