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^{1,a)}and Akira Fujiwara

^{1}

### Abstract

We demonstrate stochastic resonance (SR), which takes advantage of noise to detect a weak signal, using a field-effect transistor(FET). An FET's structure composed of a nanowire channel enables current characteristics to show strong nonlinearity, which overcomes thermal limitation, and dynamic bistability, both of which boost an effect of SR and silhouette noise from noise. Moreover, the dynamic bistability enables SR effect to be enhanced by adding common noise to multiple FETs. The FET providing such unique characteristics opens the way to use SR for practical applications.

We are grateful to Y. Ono, H. Kageshima, J. Noborisaka, G. Yamahata, T. Yamaguchi, K. Yamazaki, I. Mahboob, and H. Yamaguchi of NTT for various supports of fabrication, experiments, and discussions. This work was partly supported by the Funding Program for Next Generation World-Leading Researchers of JSPS (GR103).

### Key Topics

- Electrical properties
- 10.0
- Field effect transistors
- 7.0
- MOSFETs
- 5.0
- Nanowires
- 5.0
- Monte Carlo methods
- 4.0

## Figures

Device structure of an SRT. (a) A birds-eye view of an SRT with a double channel. Voltage applied to each electrical contact is also shown. (b) A cross-sectional views along the channel.

Device structure of an SRT. (a) A birds-eye view of an SRT with a double channel. Voltage applied to each electrical contact is also shown. (b) A cross-sectional views along the channel.

Current characteristics of an SRT. (a) *I* _{S1}-*V* _{LG} characteristics of an SRT when *V* _{D} is changed from 1 to 2.5 V in 0.25-V steps. The slope of the dotted line indicates the *SS* of 60 mV/dec, which is the minimum theoretically determined at room temperature in conventional MOSFETs. Cyclic measurements of *I* _{S1}-*V* _{LG} characteristics at *V* _{D} of (b) 2.0 and (c) 2.3 V. Triangle waveforms with amplitude of 0.6 V and center voltage of (b) −2.1 and (c) −2.3 V are applied to *V* _{LG}. Frequencies of triangle waveforms are 1, 10, 100, and 1000 Hz. For clarity, *I* _{S1}-*V* _{LG} characteristics during ten periods of triangle waveforms applied to *V* _{LG} are shown here. Voltages, *V* _{on} and *V* _{off}, at which current cut across 10^{−6} A in positive and negative sweeps of *V* _{LG}, respectively, are also shown. (d) Histograms of 50 samples of *V* _{on} and *V* _{off} at *V* _{D} of 2.3 V. Solid lines are fitting curves based on Gaussian distribution. Dotted lines indicate shifts of the peaks of Gaussian distributions.

Current characteristics of an SRT. (a) *I* _{S1}-*V* _{LG} characteristics of an SRT when *V* _{D} is changed from 1 to 2.5 V in 0.25-V steps. The slope of the dotted line indicates the *SS* of 60 mV/dec, which is the minimum theoretically determined at room temperature in conventional MOSFETs. Cyclic measurements of *I* _{S1}-*V* _{LG} characteristics at *V* _{D} of (b) 2.0 and (c) 2.3 V. Triangle waveforms with amplitude of 0.6 V and center voltage of (b) −2.1 and (c) −2.3 V are applied to *V* _{LG}. Frequencies of triangle waveforms are 1, 10, 100, and 1000 Hz. For clarity, *I* _{S1}-*V* _{LG} characteristics during ten periods of triangle waveforms applied to *V* _{LG} are shown here. Voltages, *V* _{on} and *V* _{off}, at which current cut across 10^{−6} A in positive and negative sweeps of *V* _{LG}, respectively, are also shown. (d) Histograms of 50 samples of *V* _{on} and *V* _{off} at *V* _{D} of 2.3 V. Solid lines are fitting curves based on Gaussian distribution. Dotted lines indicate shifts of the peaks of Gaussian distributions.

Signal detection using SR in an SRT. (a) A schematic view for SR demonstration. *V* _{offset} is the center of the square waveform. (b) Measured signals applied to the LG. Root mean squares of *S* _{noise} are 0.128 and 0.096 V_{rms}, respectively. *V* _{offset} is −2.6 V. For clarity, the top and middle lines are shifted vertically by 2 and 1 V, respectively. *I* _{S1}-*S* _{in} characteristics at *V* _{D} of (c) 2.0 and (d) 2.3 when *S* _{noise} superimposed on *S* _{in} is changed. For clarity, each line in (c) and (d) is shifted by 1 and 2.5 *μ*A, respectively. *S* _{in} is the same as that in (b). (e) *C* characteristics as a function of *S* _{noise} at various *V* _{D}'s. Solid lines are guides for the eyes. In the legend, *SS* at each *V* _{D} is also shown. Open plots at *V* _{D} of 2.0 and 2.1 V are theoretical plots^{8} fitted to the experimental results. Open squares at *V* _{D} of 2.35 V are fitted to experimental curves at *V* _{D} of 2.35 V by using MC simulation. (f) *C-S* _{noise} characteristics simulated by an MC method with the assumption that *V* _{off} is changed at constant *V* _{on} of −2.35 V. The dotted arrow indicates the shift of peak values of *C* when *V* _{off} is changed from −2.35 to −3.1 V. (g) A Schematic of energy diagram in a non-linear system when *S* _{in} is “High” value and *S* _{out} is still “Low” value. Schematics of energy diagrams in bistable systems (h) without and (i) with dynamic hysteresis loops. Closed circles and broken arrows represent *S* _{out}, and its transition caused by *S* _{noise}. Since *S* _{in} is “High,” energy diagrams are modulated. While slope of energy diagram between “Low” and “High” becomes gentle in a non-linear system, energy at “High” becomes the global minima at a bistable system corresponding to hysteresis current characteristics. The dotted curve in (i) represents fluctuation of barrier height in the case of hysteresis characteristics with fluctuation of *V* _{on} and *V* _{off}.

Signal detection using SR in an SRT. (a) A schematic view for SR demonstration. *V* _{offset} is the center of the square waveform. (b) Measured signals applied to the LG. Root mean squares of *S* _{noise} are 0.128 and 0.096 V_{rms}, respectively. *V* _{offset} is −2.6 V. For clarity, the top and middle lines are shifted vertically by 2 and 1 V, respectively. *I* _{S1}-*S* _{in} characteristics at *V* _{D} of (c) 2.0 and (d) 2.3 when *S* _{noise} superimposed on *S* _{in} is changed. For clarity, each line in (c) and (d) is shifted by 1 and 2.5 *μ*A, respectively. *S* _{in} is the same as that in (b). (e) *C* characteristics as a function of *S* _{noise} at various *V* _{D}'s. Solid lines are guides for the eyes. In the legend, *SS* at each *V* _{D} is also shown. Open plots at *V* _{D} of 2.0 and 2.1 V are theoretical plots^{8} fitted to the experimental results. Open squares at *V* _{D} of 2.35 V are fitted to experimental curves at *V* _{D} of 2.35 V by using MC simulation. (f) *C-S* _{noise} characteristics simulated by an MC method with the assumption that *V* _{off} is changed at constant *V* _{on} of −2.35 V. The dotted arrow indicates the shift of peak values of *C* when *V* _{off} is changed from −2.35 to −3.1 V. (g) A Schematic of energy diagram in a non-linear system when *S* _{in} is “High” value and *S* _{out} is still “Low” value. Schematics of energy diagrams in bistable systems (h) without and (i) with dynamic hysteresis loops. Closed circles and broken arrows represent *S* _{out}, and its transition caused by *S* _{noise}. Since *S* _{in} is “High,” energy diagrams are modulated. While slope of energy diagram between “Low” and “High” becomes gentle in a non-linear system, energy at “High” becomes the global minima at a bistable system corresponding to hysteresis current characteristics. The dotted curve in (i) represents fluctuation of barrier height in the case of hysteresis characteristics with fluctuation of *V* _{on} and *V* _{off}.

Enhancement of SR in a SRT. (a) Simulated *C-S* _{noise} characteristics of the multiple SRTs. We assume that each SRT has the same *I* _{S1} characteristics and that V_{on} and V_{off} are without (lower figure) and with (upper figure) fluctuation of 0.06 V rms. The numbers of SRTs are 1, 2, 4, 8, 20, and 40. (b) Change in *I* _{D}, *I* _{S1}, and *I* _{S2} when *S* _{in} superimposed on *S* _{noise} is applied to the LG and *S* _{noise} is changed. *V* _{D} is 2.35 V. Each line is shifted by 0.25 *μ*A. *S* _{in} is the same as that in Fig. 3. (c) Change in *C* of *I* _{D}, *I* _{S1}, and *I* _{S2} when *S* _{noise} is changed at *V* _{D} of 2.35 V. The solid curves are guides for eyes. (d) Simulated *C-S* _{noise} characteristics of *I* _{D}, *I* _{S1}, and *I* _{S2}, with the assumption that *V* _{on} and *V* _{off} are without (lower graph) and with (upper graph) fluctuation of 0.04 V rms.

Enhancement of SR in a SRT. (a) Simulated *C-S* _{noise} characteristics of the multiple SRTs. We assume that each SRT has the same *I* _{S1} characteristics and that V_{on} and V_{off} are without (lower figure) and with (upper figure) fluctuation of 0.06 V rms. The numbers of SRTs are 1, 2, 4, 8, 20, and 40. (b) Change in *I* _{D}, *I* _{S1}, and *I* _{S2} when *S* _{in} superimposed on *S* _{noise} is applied to the LG and *S* _{noise} is changed. *V* _{D} is 2.35 V. Each line is shifted by 0.25 *μ*A. *S* _{in} is the same as that in Fig. 3. (c) Change in *C* of *I* _{D}, *I* _{S1}, and *I* _{S2} when *S* _{noise} is changed at *V* _{D} of 2.35 V. The solid curves are guides for eyes. (d) Simulated *C-S* _{noise} characteristics of *I* _{D}, *I* _{S1}, and *I* _{S2}, with the assumption that *V* _{on} and *V* _{off} are without (lower graph) and with (upper graph) fluctuation of 0.04 V rms.

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