Light-induced persistent resonance frequency shift of MoS₂ mechanical resonator

As semiconducting atomically thin materials, ^1,2) transition metal dichalcogenides are promising optoelectronic materials because of their large band gap, ^3,4) high mobility ^5,6) and superior mechanical properties. ^7–9) In particular, molybdenum disulfide (MoS₂) is a promising material for an optical sensor based on field-effect transistors (FETs) ^10–19) or mechanical resonators (MRs). ^5,6,20,21) For the MR application of MoS₂, they show a very high resonance frequency due to their extremely light weight and broad dynamic range at the linear oscillation regime. These features are important not only for sensing application, but other novel applications such as ultralow power information processing. Oscillators with a tunable resonance frequency ^21,22) are candidates for the base-clock element in digital circuits. In addition, non-volatile memory function is required to realize information processing using nano-electro-mechanical systems (NEMS). Persistent photocurrent (PPC), in which the photocurrent even under dark conditions is maintained after the termination of light irradiation, is a candidate for non-volatile memory function. In the case of photosensitive MoS₂-FET, PPC has been widely observed. ^10–19) PPC observed on MoS₂-FET mainly originates from the gradual release of the photogenerated charge accumulating around the channel on a substrate. Recently, we have reported that the photoresponse of the MoS₂-FET could be improved by inserting a thin Al₂O₃ buffer layer on a SiO₂ gate insulator. ¹⁹⁾ This improvement can be explained by the random localized potential fluctuation model ²³⁾ combined with the model based on the recombination of the bounded electrons around the trapped hole. In the case of MR, however, there are hardly any reports about PPC effects on the resonance, which is important for MR towards high performance in optically tuned nano-electro-mechanical systems with non-volatile memory function. In this study, we investigate the PPC effect on an electrically driven MoS₂ MR and explore the possibility of the optical non-volatile memory function.

Figure 1(a) shows a scanning electron microscope (SEM) image of a monolayer-MoS₂ MR prepared on n⁺-Si (<0.02 Ωcm)/SiO₂(300 nm) substrate, which is a drum-type resonator with a typical diameter of 6 μm. The fabrication process is similar to the case of a drum-type graphene-MR as follows. ²⁴⁾ The monolayer MoS₂ was transferred onto a pair of electrodes consisting of Cr/Au (5 nm/30 nm) using polymethyl methacrylate, where MoS₂ was synthesized by CVD. ²⁵⁾ To form the suspended structure, the SiO₂ layer underneath MoS₂ was etched using buffered HF. The heavily doped Si substrate acts as a back gate. Note that the monolayer MoS₂ supported by the metal electrodes was free from the SiO₂ region on the n⁺-Si substrate to eliminate the additional charging effect from the MoS₂/SiO₂ interface.

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All electrical measurements were performed in a vacuum (less than 10⁻³ Pa) at room temperature after annealing at 150 °C for 2 h. For the resonance property measurements, the AM down mixing method ²⁶⁾ was used, as shown in Fig. 1(b). The mechanical vibration was driven by applying AC drain source voltage V_ds ^AC = V_ds0cos(2πft) with a certain frequency f, where V_ds0 = ${{V}_{{\rm{ds}}0}}^{{\rm{AM}}}$(1 + acos(2πf_MOD t)) with t the time, f_MOD the modulation frequency and a the modulation depth. The resonance vibration is induced when the frequency f is close to the resonance frequency f₀ of the MR. As a result of the vibration, the current through the channel changes due to the modulation of the gate capacitance. Finally, the down mixed current was measured by a lock-in-amplifier as a mixed current I_mix modulated by f_MOD. The mechanical tension of MoS₂ can be changed electrostatically by the potential difference between the MoS₂ and back gate using the back-gate voltage, V_gs.

Figure 1(c) shows the Raman spectra for MoS₂ after the fabrication process. For the suspended MoS₂, first-order Raman active modes at 381.0 cm^{– 1} (${{{\rm{E}}}^{1}}_{2{\rm{g}}}$) and 400.6 cm⁻¹ (A_1g) are clearly observed. Thus, the MoS₂ was determined to be a single layer from the peak difference between ${{{\rm{E}}}^{1}}_{2{\rm{g}}}$ and A_1g. ²⁷⁾ Figure 1(d) shows the DC transfer characteristic of the MoS₂-MR with V_sd ^DC = 100 mV. The gate voltage V_gs successfully controls the drain current, I_dsDC even for the suspended MoS₂ after the sample preparation process. It is obvious that the MoS₂-FET exhibits n-type behavior as in other reports. ^5,19,28) The field-effect mobility of electrons determined from Fig. 1(d) is ∼9.2 cm² V⁻¹ s⁻¹. To prevent the MoS₂ membrane from sticking onto the substrate, the gate bias was limited to less than ±5 V.

We first investigated the PPC effects on the suspended MoS₂-FET. The laser with 660 nm wavelength was irradiated on the MoS₂ through a microscope to induce PPC. The beam radius of the laser is ∼11.5 μm. The laser power is ∼1 W cm⁻² and the laser exposure time is ∼10 s. Figure 2(a) shows the temporal variation of the source–drain current ΔI_ds = I_ds(t) − I_ds-dark under DC bias after 10 s laser irradiation, where I_ds-dark is the well-saturated source–drain current measured under dark conditions. The current was not recovered to I_ds-dark over 20 min, which is typical behavior of PPC. As schematically shown in Fig. 2(b), the origin of PPC is the trapped charge and the gradual decrease in trapped charge density gives rise to slow decay.

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It was reported that the main origin of the PPC observed at the MoS₂ on the SiO₂ substrate is trapped photogenerated holes at the interface between MoS₂ and SiO₂. ^6,19) The decay characteristic of PPC is explained by the gradual release and recombination of the trapped carriers at the trapping site. In our case, the PPC appeared even without the SiO₂ under the MoS₂. Therefore, the PPC on the suspended MoS₂-FET is most likely due to the trapped holes in defects of MoS₂ or contamination on MoS₂. Note that as the laser power is stronger than that of previous reports (a few μW cm⁻²), ¹⁹⁾ we hardly observed the PPC on the suspended samples when the light intensity was 1 mW cm⁻².

Figure 3(a) shows the typical frequency response curve, I_mix, of the monolayer-MoS₂ MR measured under V_gs = 3 V and ${{V}_{{\rm{ds}}0}}^{{\rm{AM}}}$ = 100 mV_rms with f_MOD = 1 kHz and a = 99% without a DC component (${{V}_{{\rm{ds}}}}^{{\rm{DC}}}$  = 0). The abrupt change in I_mix at f₀ = 9.26 MHz corresponds to the resonance of the monolayer-MoS₂ MR. The solid line represents the fitting curve with a Q factor of 350. Figure 3(b) shows the grayscale plot of the gate-voltage dependence of the frequency response curve. The resonance frequency indicated by the yellow dotted line shifts upwards when the gate voltage is increased. This is because the mechanical tension induced by the electrostatic attraction of the suspended MoS₂ is increased.

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We investigated the PPC effects on the MoS₂-MR. Note that the frequency resonance curve was measured every 33 s to obtain the temporal variation of the resonance frequency, where the measurement cycle time was limited by the time constant of the lock-in-amplifier to obtain a sufficient signal-to-noise ratio. Figure 4(a) shows the temporal variation of the resonance frequency shift Δf₀ after the termination of 10 s light irradiation with the intensity of 1 W cm⁻². The resonance frequency shift Δf₀ decreases ∼1.6% just after the termination of light irradiation and then the downshifted Δf₀ gradually recovers its initial frequency. The downshift was observed over more than 20 min. This is very similar to the PPC described in Fig. 2.

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The photothermal effect should be considered as one of the origins. However, the increased temperature is very low (∼0.1 K) estimated from the light intensity and the thermal conductivity of MoS₂. ²⁹⁾ In addition, the thermal relaxation time estimated from the heat capacity of the monolayer MoS₂ ³⁰⁾ is quite short (∼100 ns) in comparison to the time constant observed in this study. Therefore, the photothermal effect is not dominant in the downshift of the resonance frequency.

To clarify the relation between the PPC and the downshifted Δf₀, we plotted the frequency shift Δf₀ (t) versus the PPC current ΔI_ds(t) at t after the termination of light, as shown in Fig. 4(b). The frequency shift Δf₀ (t) shows the linear dependence of the PPC current ΔI_ds(t). Therefore, we can conclude that the downshift of the resonance frequency is mainly induced by the trapped holes on MoS₂. As mentioned before, the tension of the MoS₂ is determined by the potential difference between the back gate and MoS₂. The most dominant part of the potential difference is induced by V_gs. In addition, the work function difference between the MoS₂ and bottom gate electrode should be considered. After the light irradiation, the mobile carrier density (electrons) was increased to compensate the immobile trapped holes, so that the quasi-Fermi level would be shifted upwards. However, the shift of the quasi-Fermi level induced by the PPC is estimated from k_B Tln[(ΔI_ds + I_ds-dark)/I_ds-dark] to be ∼10 meV at t = 0, ³¹⁾ which gives rise to the frequency shift of only 350 ppm, where k_B and T are the Boltzmann constant and temperature, respectively. This value is much smaller than that shown in Fig. 4(a).

Another scenario of the downshift of the resonance frequency based on the trapped holes is screening of the gate voltage by the trapped holes, as schematically shown in Fig. 4(c), which is similar to the case of the carbon nanotube ³²⁾ or graphene ³³⁾ MRs with single-electron tunneling. At steady state, the trapped holes would be fully compensated by the mobile electrons supplied from the source electrode. In the case of the vibrating channel at the resonance, the gate capacitance is also vibrated. To compensate the trapped holes on the MoS₂ within one cycle of the vibration, the time constant τ_c given by C_g δV_gs/δI_ds = δC_g g_m at V_gs, which is comparable to the cutoff frequency of the FET, is sufficiently shorter than (2πf₀)⁻¹, where C_g, δV_gs, δI_ds and g_m are the gate capacitance, small change in gate voltage, corresponding drain current change and the transconductance, respectively. In this experiment, the time constant τ_c ∼ 0.45 μs at V_gs = 3 V is longer than the 17 ns estimated from f₀, which is insufficient to compensate the positive charge caused by the trapped holes. As a result, the tension is reduced, which results in the downshift of the resonance frequency.

It is very important to eliminate the PPC-like behavior for practical application such as an MR with optical memory function. To overcome this issue, we just apply the excess current for Joule heating to the channel, which enhances the detrapping of the trapped holes. The additional voltage pulse with ${{V}_{{\rm{sd}}}}^{{\rm{DC}}}$  = 5 V for Joule heating was applied for 3 s, which gives rise to I_ds = 3.5 μA. The temperature rise is estimated from the power consumption to be ∼10 K. As shown in Fig. 5(a), the PPC current slightly decreased from 16 to 11 nA after the application of the voltage pulse. This indicated that the trapped holes were partially detrapped by applying the excess current. Figure 5(b) shows the temporal variation of the resonance frequency shift after the application of the excess voltage with ${{V}_{{\rm{sd}}}}^{{\rm{DC}}}$  = 5 V for 3 s. The downshifted frequency was recovered to its original frequency just after the application of the voltage pulse. We found the gradual downshift, as observed in Fig. 5(b), after the recovery. This implies that the residual holes appeared as a result of the separation process of the bounded electrons induced by the excess current around the trapped holes like excitons. In addition, the temperature rise (∼10 K) may cause thermal stress at the supported region, which affects the resonance frequency shift with a longer time constant. The detailed mechanism for this phenomenon is still unclear, making this a subject for further study. Further repeated application of the voltage pulse results in the successful reduction of the PPC effect on the mechanical resonance.

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We investigated the PPC effects on the monolayer-MoS₂ MR towards optically tunable nano-electro-mechanical systems with memory function. After the termination of light irradiation, we found that the resonance frequency of the resonator shifted downwards and the downshift was maintained over 20 min, where the origin of the persistent behavior was most likely due to the trapped photogenerated holes at defects or contamination on MoS₂. The trapped holes induced the screening effects to the back-gate potential, which resulted in the reduction of the electrostatic force acting on the MoS₂. The downshift of the resonance frequency could be eliminated by applying the excess voltage pulse to induce Joule heating. The present results suggest that the PPC-like behavior of the monolayer-MoS₂ MR can pave the way to realizing NEMRs with optical memory function without external memory devices.

Acknowledgments