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# Single-trap phenomena in nanoscale biosensors. (a) Schematic illustration of a liquid-gated Si NW FET with a single trap that induces (b) two-level RTS fluctuations of the drain current. (c) Schematic interpretation of SR: an optimal amount of white noise is added to a system to detect weak signals under the system threshold. (d) DP noise suppression due to single-trap phenomena considering a single trap as a nonlinear bistable system that can amplify the signal in the regime of SR. (e) Trap occupancy probability (g-factor) and its derivative plotted as a function of gate voltage for simulated RTS noise. (f) Schematic illustration of the conversion of RTS voltage fluctuations into the fluctuations of trap occupancy probability (g-factor noise).

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Transistor biosensors are mass-fabrication-compatible devices of interest for point of care diagnosis as well as molecular interaction studies. While the actual transistor gates in processors reach the sub-10 nm range for optimum integration and power consumption, studies on design rules for the signal-to-noise ratio (S/N) optimization in transisto...

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... phenomena as a stochastic resonance effect. The third noise suppression effect, as introduced in 21,22 , aims to exploit the presence of a single active trap in a gate dielectric layer of a nanotransistor, where RTS noise is observed (see Fig. 3a,b). Such an RTS effect is usually avoided as it increases the noise level (see Fig. 2b,c), but if RTS parameters (i.e. trap occupancy probability, time constants) are monitored (see Fig. 3b), then RTS noise becomes a signal. Intuitively, one could expect that the use of RTS as a signal would provide a gain corresponding to the difference ...
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... as introduced in 21,22 , aims to exploit the presence of a single active trap in a gate dielectric layer of a nanotransistor, where RTS noise is observed (see Fig. 3a,b). Such an RTS effect is usually avoided as it increases the noise level (see Fig. 2b,c), but if RTS parameters (i.e. trap occupancy probability, time constants) are monitored (see Fig. 3b), then RTS noise becomes a signal. Intuitively, one could expect that the use of RTS as a signal would provide a gain corresponding to the difference between a single-trap and a trap-free device, e.g. between one and two orders of magnitude (see Fig. 2a,b). Below, we show that the potential of single-trap phenomena for the noise ...
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... that the potential of single-trap phenomena for the noise suppression is even larger and that it is similar to the SR effect observed in biology 31 , enabling here to overpass the thermal DP noise limit. The idea beyond this is that the addition of white noise to a signal that is nonmeasurable below a given threshold can become measurable (see Fig. 3c). As RTS is nothing but a white noise below a cut-off frequency that is added to the signal of interest, there are obviously some similarities (Fig. 3d). However, a technical difference comes from the fact that RTS time constants are related to the signal of interest (surface potential), which is usually not the case for the white ...
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... , enabling here to overpass the thermal DP noise limit. The idea beyond this is that the addition of white noise to a signal that is nonmeasurable below a given threshold can become measurable (see Fig. 3c). As RTS is nothing but a white noise below a cut-off frequency that is added to the signal of interest, there are obviously some similarities (Fig. 3d). However, a technical difference comes from the fact that RTS time constants are related to the signal of interest (surface potential), which is usually not the case for the white noise. Below, we combine theory and experiments to push the limits of noise suppression with single-trap ...
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... this section, the aim is to propose a theoretical framework for the signal-to-noise ratio in the case of the singletrap phenomena approach. We consider the trap occupancy probability as the signal and evaluate the noise of g to determine the S/N ratio (see Fig. 3e,f). We demonstrate experimentally, numerically, and analytically that under optimized conditions, the S/N ratio can be beyond that of the thermal noise in trap-free ...
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... and current fluctuations are noise. In contrast, we define the signal in singletrap-based biosensors 21,22,32 as trap occupancy probability g . To calculate the g-factor noise (fluctuations in time) considering two-level RTS time trace, one can extract g(t) over a given window directly from the distribution of the voltage fluctuations (see Fig. 3f). Then, by sliding the window along with the RTS time trace one can obtain a new time trace with the trap occupancy factor fluctuations in time. The time-domain g-factor data can be then translated into frequency spectrum resulting in the power spectral density S g . experimental results. Figure 4a shows the two-level drain current ...
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... can be seen from Fig. 4c, the g-factor noise decreases with increasing the time window . The dependence of g-factor noise against the time window can be explained by considering the fact that the larger time window contains more transition events enabling g-factor to be estimated with higher accuracy, as illustrated in Fig. 3f. g-factor noise analytical model. Let's consider a two-level RTS signal X t that jumps between states 0 and 1. The transition probabilities P for an RTS with states (0, 1) and rates (, µ) to jump from states 0 to 1, and 1 to 0, respectively, are given by Kolmogorov´s forward equation: www.nature.com/scientificreports/ Then, we consider ...
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... ω = 2πf and is a duration of a sliding time window (see Fig. 3(f)). input-referred g-factor noise S gg . To compare the performance and efficiency of the nanotransistor sensors exploiting single-trap phenomena, one should first introduce and calculate an equivalent input-referred noise caused by the variation of the g-factor. This can be done similarly as for the voltage noise (see Eq. (1b)) defining ...

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... A time trace of the 4-nanowire one and its amplitude evolution versus Vds and Vg are shown in Figure 2. The relative amplitude was as high as 15% of the overall current (Ids vs. Vg in the inset of Figure 3a), i.e., as high as 60% of the current flowing in the nanowire holding the defect. This RTS amplitude was extremely large when compared to 6 the RTS usually obtained in nanotransistors 33,34 . The evolution of the time spent in the up state (up) or down state (down) showed no correlation with Vg ( Figure S5) but demonstrated a clear ...
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