Stochastic resonance in MoS2 photodetector

Abstract

In this article, we adopt a radical approach for next generation ultra-low-power sensor design by embracing the evolutionary success of animals with extraordinary sensory information processing capabilities that allow them to survive in extreme and resource constrained environments. Stochastic resonance (SR) is one of those astounding phenomena, where noise, which is considered detrimental for electronic circuits and communication systems, plays a constructive role in the detection of weak signals. Here, we show SR in a photodetector based on monolayer MoS₂ for detecting ultra-low-intensity subthreshold optical signals from a distant light emitting diode (LED). We demonstrate that weak periodic LED signals, which are otherwise undetectable, can be detected by a MoS₂ photodetector in the presence of a finite and optimum amount of white Gaussian noise at a frugal energy expenditure of few tens of nano-Joules. The concept of SR is generic in nature and can be extended beyond photodetector to any other sensors.

Fig. 1. Monolayer MoS₂ synthesis, characterization, and device fabrication.

a Schematic of cold-wall horizontal reactor setup. b Coalesced monolayer MoS₂ film grown on a 2-inch sapphire substrate using MOCVD at 1000 °C with Mo(CO)₆ and H₂S as precursors. c AFM images at the center and edge of the wafer showing uniform surface coverage, film morphology, and thickness. d In-plane X-ray diffraction showing the epitaxial relation between MoS₂ and sapphire as (10$\overline{1}$0) MoS₂ ‖ (10$\overline{1}$0) α-Al₂O₃. The inset shows a narrow full-width half-maximum (FWHM) of 0.27°, which emphasizes the high crystalline quality of these monolayer films. Raman map of (e) ${\mathrm{E}}_{2g}^1$ and (f) A_1g peaks show <5% variation and the peak separation of 18 cm⁻¹ confirms monolayer MoS₂. g Photoluminescence (PL) map shows an intense peak at 1.84 eV, which is attributed to the indirect to direct bandgap transition in monolayers and is severely suppressed in multilayers of MoS₂. h Schematic and i SEM image of monolayer MoS₂ FET. j Logarithmic scale and k linear scale transfer characteristics of monolayer MoS₂ FET measured at different drain biases (V_D). l Mobility plot and m output characteristics measured at different back gate biases (V_BG).

Fig. 2. Demonstration of stochastic resonance (SR) in monolayer MoS₂ field-effect transistor (FET).

a Schematic showing the basic concept of SR with three essential components: a nonlinear thresholding device, a weak coherent input such as a periodic signal, and a source of noise. When the noise intensity reaches some finite and appropriate level, the system can detect the weak time-variant signal, which otherwise lies below the detection threshold of the sensor. b A 2.5 Hz square wave of amplitude 0.4 V is applied to the back-gate of the monolayer MoS₂ FET at different operating regimes: ON-state (V_BG = 3.5 V), subthreshold (V_BG = −1 V), and OFF-state (V_BG = −2.5 V). c Output current (I_DS) and d corresponding PSD plots obtained using the FFT. Current sampling was done at 20 Hz for ~100 s. In the ON-state and subthreshold regime the signal is detected, whereas, in the OFF-state, I_DS is obscured by the noise floor and corresponding peaks are absent in the PSD. e In order to detect the signal in the OFF-state, Gaussian noise of different standard deviations (σ) are superimposed on the square wave centered at V_BG = −2.5 V. f PSD of measured I_DS. The current sampling was done at 20 Hz for ~400 s. The signal is detected for an optimum amount of Gaussian noise, confirming SR in MoS₂ FET. g SNR as a function of σ for various total sampling time (T_P). h Color map of the correlation coefficient (CC) between I_DS and V_BG. i Energy consumption as a function of σ for various T_P. Clearly, optimum signal detection can be achieved with energy as frugal as 10–100 nJ corresponding to σ = 0.5 V.

Fig. 3. Detection limit of monolayer MoS₂ photodetector.

a Experimental setup showing the photodetector chip based on monolayer MoS₂ FET placed at a distance of ~1 cm from a blue LED. b Current (I_LED) versus voltage (V_LED) characteristics of the LED. c Transfer characteristics of the MoS₂ FET under dark and illumination corresponding to different V_LEG. d The extracted photocurrents (I_PH). e 2.5 Hz periodic signals of different amplitudes applied to the LED and f corresponding snapshots of the glowing LED. The LED intensity drops linearly for 5 V > V_LED > 2.8 V and exponentially for V_LED < 2.8 V in accordance with the output characteristics of the LED, as indicated using the colored circles in (b). g PSD plots obtained from FFT of I_DS for a total duration of T_P = 51.2 s in different operation regimes in response to periodic LED signals in (e). Peaks observed in the PSD at 2.5 Hz are indications of successful detection of the LED signal. h Extracted SNR in different detection regimes for various LED illuminations. For comparison, we have also included the results obtained from the same experiments performed on a commercial Si photodiode in Supplementary Note 6. i Table summarizing the detection limit for the blue light by MoS₂ photodetector and Si photodiode. j Sensitivity of the MoS₂ photodetector in different detection regimes. The sensitivity (S) of a photodetector is defined as the ratio of photocurrent (I_PH) to the luminous flux (L_ϕ). The rated sensitivity of the Si photodiode (S = 9 nA/lx) and its photoresponse to different V_LED were used for calibrating L_ϕ, which were subsequently used to calculate the sensitivity of MoS₂ photodetector. k Comparison of energy expenditure for the Si photodiode and MoS₂ photodetector for detection of above threshold signals. The MoS₂ photodetector offers orders of magnitude higher energy efficiency when operated in the subthreshold regime, owing to significantly lower dark current.

Fig. 4. Demonstration of SR in monolayer MoS₂ photodetector.

a White Gaussian noise of different standard deviations (σ) superimposed on 2.5 Hz periodic and subthreshold LED signal of amplitude V_LED = 2.4 V and b corresponding histogram of the LED voltage distribution. Each histogram shows two Gaussian curves of the same variance but different means, one centered at V_LED = 1 V (LED OFF) and the other one centered at V_LED = 2.4 V (Dim LED), marking the level difference between the two states of the LED signal. c PSD plots obtained from the FFT of the output current (I_DS) measured in the monolayer MoS₂ photodetector for a total duration of T_P = 204.8 s in response to the LED signals in (a). The MoS₂ photodetector was biased in the OFF-state (V_BG = −2 V). In the presence of a finite and appropriate amount of noise, the subthreshold LED signal is detected. (see Supplementary video files 1–3 for real-time observation of SR in the MoS₂ photodetector). d SNR as a function of σ for different sampling time T_P. For very low variance Gaussian noise (σ < 0.2 V), the signal hardly crosses the detection threshold of the MoS₂ photodetector, i.e., V_LED = 2.6 V. As σ increases, a larger fraction of the LED signal corresponding to the 2.4 V level crosses the detection threshold of the MoS₂ photodetector, increasing the SNR. For even larger variances, the SNR starts to decrease since the tail of the Gaussian distribution centered at V_LED = 1 V will also start to cross the detection threshold of the MoS₂ photodetector, obscuring the periodicity of the V_LED = 2.4 V signal. The SNR curves in this instance show the typical SR response found in biological species such as paddlefish, crayfish, etc. e Energy consumption by the MoS₂ photodetector is plotted as a function of σ for different T_P. Since the MoS₂ photodetector was operated in the deep OFF-state (V_BG = −2 V) to minimize the dark current, the operating power budget is drastically reduced, making the signal detection extremely energy efficient. For comparison, refer to Supplementary Note 9 for the exploitation  of SR using the Si photodiode (see Supplementary video files 4–6 for real-time observation of SR in the Si photodiode). f The energy consumption by the Si photodiode for detecting subthreshold optical signal, exploiting SR, is found to be in the range of a few micro-Joules, which is 1000X higher compared to the MoS₂ photodetector for sampling time T_P = 100 s.