Robust thresholdlike effect of internal noise on stochastic resonance in an organic field-effect transistor

The application of noise to a nonlinear system can have the effect of increasing the signal transmission of the system through the phenomenon of stochastic resonance (SR). This paper presents an analytical characterization of the dependence of the signal transmission performance of an organic field-effect transistor (OFET) on external noise. Similarly to the threshold of a nonlinear system, the additive internal noise of the system can be used to control the emergence of SR. Internal noise or the addition of random numbers to the system enables one to observe the SR phenomenon in an OFET under an intrinsically nonresonant condition. Internal noise plays a thresholdlike role, but it functions in a different manner. The fluctuations in performance due to external noise become smaller when the effect of internal noise becomes dominant compared with that of the threshold. In conclusion, it is found that internal noise plays a robust thresholdlike role with respect to variations in external noise intensity.

Figure 1

Variation of the correlation coefficient between input and output signals as a function of external noise intensity for various thresholds. Symbols represent the averaged value of the correlation coefficient calculated from experimental data from four trials under identical conditions using the fabricated OFET, and solid lines represent the analytical value from Eqs. (3) and (4). In the experiments, the threshold was changed by an input dc bias at the input signal voltage $x=\pm 4\mathrm{V}$ and a duty ratio $D=80\%$. Parameters, normalized by the input signal intensity, are an internal noise intensity ${\sigma }_{\eta }=1.25\times {10}^{-5}$ and a fitting parameter $A=1.2\times {10}^{-5}$.

Figure 2

Correlation coefficient between input and output signals (three-dimensional surface) and the square of its first derivative with respect to external noise intensity (contour map) as functions of external noise intensity and threshold at ${\sigma }_{\eta }=0$ (a) and of external noise intensity and internal noise intensity at $\theta =0$ (b) for the OFET model. Here, the duty ratio of the input signal $D=80\%$ and the fitting parameter $A=1$.

Figure 3

Variation of the correlation coefficient between input and output signals as a function of external noise intensity for various values of threshold at internal noise intensity ${\sigma }_{\eta }=0$ (a), and for various amplitudes of internal noise at threshold $\theta =0$ (b). Here, duty ratio of input signal $D=80\%$ and fitting parameter $A=1$.

Figure 4

Variation of the correlation coefficient between input and output signals as a function of external noise intensity when random numbers with a Gaussian distribution were added to the output signal. Symbols represent the averaged value of the correlation coefficient calculated from experimental data from four trials under identical conditions using the fabricated OFET (open circles) and with random numbers with different standard deviations added to the output signal (filled circles, squares, and diamonds). The normalized dimensionless parameters of the input signal intensity are threshold $\theta =0.235$, internal noise intensity ${\sigma }_{\eta }=1.25\times {10}^{-5}$, and fitting parameter $A=1.2\times {10}^{-5}$.

Figure 5

Variation of the correlation coefficient between input and output signals (a) and the magnitude of its derivative with respect to external noise intensity (b) as functions of external noise intensity under the condition that the system shows identical signal transmission performance at ${\sigma }_{\xi }=0$. Here, the duty ratio of input signal $D=80\%$, the fitting parameter $A=1$, and the constant $c=1$ in Eq. (6).

Figure 6

Variation of the correlation coefficient between input and output signals (a) and a magnitude of its derivative of external noise intensity (b) as a function of external noise intensity for various constant values $c$ in Eq. (6). Here, duty ratio of input signal $D=80\%$ and fitting parameter $A=1$.

Figure 7

Time courses of output value (b), (d) to input signal (a) calculated using Eq. (1) and output distribution (c), (e). A total of 5000 dots (100 dots $\times$ 50 trials) are plotted per a period of input as output of OFET (b), (d). Output distribution is normalized and horizontal lines indicate the average value of output to each input signal value (c), (e). Here, external noise intensity ${\sigma }_{\xi }=4$, duty ratio of input signal $D=80\%$, and fitting parameter $A=1$.

Figure 8

Drain current vs drain voltage (a) and vs gate voltage (b) of the fabricated OFET.