The rich properties of atomic layer crystals enable researchers to design and fabricate micro/ nanoelectromechanical devices and systems towards signal processing and sensing applications. In particular, mechanical properties of two-dimensional (2D) materials play an increasingly important role in designing devices with predictable responses in order to achieve desired device performance, such as frequency and mode sequence in 2D nanoelectromechanical systems (NEMS) resonators.

Rhenium disulfide (ReS₂) crystal is a 2D semiconductor with weak interlayer coupling which can lead to relatively low Young’s modulus (E_Yz=0.4 GPa) along the out-of-plane direction of the layered crystal. Interestingly, it exhibits strong in-plane anisotropy. However, its mechanical anisotropy has not been experimentally demonstrated yet. Here, we experimentally demonstrate ReS₂ nanomechanical resonators, and elucidate their mechanical anisotropy using multi-mode spectromicroscopy measurements.

ReS₂ nanomechanical resonators are fabricated by mechanically exfoliating MoS₂ crystal onto Si/SiO₂ substrates with pre-patterned cavities and electrode. We measure the multi-modal resonance response using a customized scheme that incorporates electrical driving and optical detection. For each resonance peak, by using XY stage and spectromicroscopy measurement scheme, we can visualize the mode shape. We then perform extensive calculations to fit to the experimental results. Specifically, we sweep the input parameters (E_Yx and E_Yy) in an FEM model for an anisotropic circular drumhead resonator, and pinpoint the optimal input parameters by minimizing the collective difference between measurement and calculation for all modes.

The thickness t and diameter d of the ReS₂ resonator are t =106 nm and d =10 μm. The frequency response of first six vibrational modes are shown in the Figure, respectively. Using the spectromicroscopy technique [8], the mechanical vibration modes shapes are visualized. We then run numerical simulations (using both mechanically anisotropic and isotropic models) to predict multimode response and mode shape of the ReS₂ resonator, and optimize the input Young’s moduli to achieve the best agreement between measurement and simulation results. We find that the best result is produced by the mechanically anisotropic model, with E_Yx= 191 GPa and E_Yy=134 GPa for our ReS₂ device. We thus quantitatively determine the mechanical anisotropy in ReS₂.

In summary, we clearly prove that ReS₂ is mechanically anisotropic, and successfully obtain its Young’s moduli.

Figures and Refs in PDF.

Nanomechanical resonators based on atomic layers of tungsten diselenide (WSe₂)show good promises for ultralow-power signal processing and novel sensing functions. However, frequency scaling in WSe₂ NEMS resonators remains yet to be explored, which impedes the realization of 2D circuits involving WSe₂ resonators at large scale. Here, we elucidate frequency scaling law in such 2D semiconducting resonators, and determine that the Young’s modulus of WSe₂ is 130GPa. Further, by operating devices from the appropriate mechanical region, we demonstrate a broad frequency tuning range (up to 230%) with just 10V gate voltage, representing some of the highest gate tuning efficiency in 2D NEMS resonators reported to date.

We fabricate a total of 26 circular drumhead WSe₂ resonators of different diameters using mechanical exfoliation and dry transfer technique, with device thickness ranging from single layer to 127 layers. We measure the resonant response of WSe₂ resonators using a custom-built 2D resonator measurement system based on laser interferometry, in which the device’s vibratory motion is transduced into optical signal and detected by a photodetector.

From measured data of all the devices, we determine that the Young’s modulus E_Y of WSe₂ is 130GPa, in good agreement with theoretical predictionsand nanoindentation measurements, as well as the pre-tension to be 0.05-0.4N/m, in good agreement with other measurements.

We further analyze the frequency scaling and elastic transition of WSe₂ resonators. From the experimental data, we clearly observe the elastic transition from the “membrane” limit (left end) to “plate” limit (right end) in different devices, allowing us to fully explore resonant characteristics by leveraging the unique mechanical responses from each specific region. For example, we observe that devices with lower pre-tension see a greater relative change of total tension, and thus exhibit larger relative frequency shifts. We therefore choose the 8 μm-diameter, 18.4 nm-thickness device to demonstrate efficient gate tuning. This NEMS resonator exhibits clear and consistent gate tuning of frequency under three measurement schemes: electrical excitation, optothermal excitation, and thermomechanical resonance. We achieve an excellent tuning range Δf/f₀ reaching 230%, comparable to the best performance found in NEMS resonators, as well as a gate tuning efficiency of 23%V^-1, the highest among 2D NEMS resonators reported to date. Our resultsoffer important design guidelines for frequency tunable NEMS resonators based on these emerging 2D materials.

Fig & Ref in PDF

Resonant nanoelectromechanical systems (NEMS) based on two-dimensional (2D) materials such as molybdenum disulfide (MoS₂) are interesting for highly sensitive mass, force, photon, or inertial transducers, as well as for fundamental research approaching the quantum limit, by leveraging the mechanical degree of freedom in these atomically thin materials. For these mechanical resonators, the quality factor (Q) and signal transduction are essential, yet the mechanism for energy dissipation and accurate signal transduction model in 2D NEMS resonators have not been fully explored. Here, we present the accurate strain-modulated dissipation model and equivalent circuit model focusing on NEMS resonators based on a 2D semiconductor: MoS₂. We further show that for doubly-clamped resonators, the Q increases with larger DC gate voltage, while fully-clamped drumhead resonators show the opposite trend. Using DC gate voltages, we can tune the Q by ΔQ/Q = 120% for fully-clamped resonators, and by ΔQ/Q = 229% for doubly-clamped resonators. We develop the strain-modulated dissipation model for these 2D NEMS resonators, which is verified against our measurement data for a fully clamped resonator and a doubly clamped resonator. We find that static tensile strain decreases dissipation while vibration-induced strain increases dissipation, and the actual dependence of Q on DC gate voltage depends on the competition between these two effects, which is related to the device boundary condition. Furthermore, we find that strain also tunes the mobility and carrier density of MoS₂, and develop a strain-modulated equivalent circuit model for 2D MoS₂ NEMS resonators, to show the enhancement of signal transduction efficiency due to the strain effect. Such strain dependence is useful for optimizing the resonance linewidth and signal transduction efficiency in 2D NEMS resonators towards low-power, ultrasensitive, and frequency-selective devices for sensing and signal processing.

Nanomechanical resonators are chip scale implementations of a mechanical oscillator, which are of both practical and fundamental interest. In many applications, such as force sensing and quantum control of mechanical oscillators, it is typically advantageous to create lightweight, compliant mechanical elements with high quality factors Q. Recent years have seen a rapid development of devices with ever higher Q values, with current records approaching Q~10¹⁰ at room temperature. As a result, these devices become increasingly sensitive to smallest changes in certain environmental parameters, such as the pressure of the surrounding gas. In this work, we demonstrate the practical use of a mm-scale nanomechanical trampoline resonator with intrinsic resonance frequencies f ~ 100 kHz and Q ~ 10⁷ for gas pressure sensing. To this end, we place the trampoline inside an ultra-high-vacuum chamber and interferometrically measure resonance frequency and quality factor of its fundamental out-of-plane mode as a function of gas pressure, using air and helium. In the pressure (p) range from 10^-6 mbar to 10³ mbar (i.e., ambient pressure), the quality factor continuously decreases from 10⁷ to 15 (30) for air (helium). At ~ 10 mbar we observe a change from a Q~p^-1 to a Q~(1+a√p)^-1 dependency, with fit parameter a, related to a transition from the free molecular to the viscous flow regime. This transition is accompanied by the onset of a decrease in the trampoline’s resonance frequency towards higher pressures. Leading to a 10 % (3 %) reduction at ambient air (helium) pressure. We find excellent agreement within ~ 10 % between the measured data and a model, covering the investigated pressure range. Based on additional measurements for higher-order modes, we argue, that the estimated deviation might be mainly limited by a commercial reference pressure gauge. In this regard, we discuss prospects for nanomechanical-resonator-based pressure sensing with a precision on the order of few percent and the inherent benefit of self-calibration. In addition, we highlight the possibility for extending the measurement range with optimized devices by more than two orders of magnitude towards both lower and higher pressure ranges.

*This work was supported and partly financed (Hossein Masalehdan) by the DFG under Germany’s Excellence Strategy EXC 2121 ‘Quantum Universe’-390833306 and via a PIER Seed Project.