Embracing structural nonidealities and asymmetries in two-dimensional nanomechanical resonators

Identifying, Resolving, and Quantifying Anisotropy in ReS2 Nanomechanical Resonators

As an emerging two-dimensional semiconductor, rhenium disulfide (ReS₂ ) is renowned for its strong in-plane anisotropy in electrical, optical, and thermal properties. In contrast to the electrical, optical, optoelectrical, and thermal anisotropies that are extensively studied in ReS₂ , experimental characterization of mechanical properties has largely remained elusive. Here, it is demonstrated that the dynamic response in ReS₂ nanomechanical resonators can be leveraged to unambiguously resolve such disputes. Using anisotropic modal analysis, the parameter space for ReS₂ resonators in which mechanical anisotropy is best manifested in resonant responses is determined. By measuring their dynamic response in both spectral and spatial domains using resonant nanomechanical spectromicroscopy, it is clearly shown that ReS₂ crystal is mechanically anisotropic. Through fitting numerical models to experimental results, it is quantitatively determined that the in-plane Young's moduli are 127 and 201 GPa along the two orthogonal mechanical axes. In combination with polarized reflectance measurements, it is shown that the mechanical soft axis aligns with the Re-Re chain in the ReS₂ crystal. These results demonstrate that dynamic responses in nanomechanical devices can offer important insights into intrinsic properties in 2D crystals and provide design guidelines for future nanodevices with anisotropic resonant responses.

Nanomechanical Resonators: Toward Atomic Scale

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

Frequency Scaling, Elastic Transition, and Broad-Range Frequency Tuning in WSe2 Nanomechanical Resonators

Nanomechanical resonators based on atomic layers of tungsten diselenide (WSe₂) offer intriguing prospects for enabling novel sensing and signal processing functions. The frequency scaling law of such resonant devices is critical for designing and realizing these high-frequency circuit components. Here, we elucidate the frequency scaling law for WSe₂ nanomechanical resonators by studying devices of one-, two-, three-, to more than 100-layer thicknesses and different diameters. We observe resonant responses in both mechanical limits and clear elastic transition in between, revealing intrinsic material properties and devices parameters such as Young's modulus and pretension. We further demonstrate a broad frequency tuning range (up to 230%) with a high tuning efficiency (up to 23% V^-1). Such tuning efficiency is among the highest in resonators based on two-dimensional (2D) layered materials. Our findings can offer important guidelines for designing high-frequency WSe₂ resonant devices.

Imaging Off-Resonance Nanomechanical Motion as Modal Superposition

Observation of resonance modes is the most straightforward way of studying mechanical oscillations because these modes have maximum response to stimuli. However, a deeper understanding of mechanical motion can be obtained by also looking at modal responses at frequencies in between resonances. Here, an imaging of the modal responses for a nanomechanical drum driven off resonance is presented. By using the frequency modal analysis, these shapes are described as a superposition of resonance modes. It is found that the spatial distribution of the oscillating component of the driving force, which is affected by both the shape of the actuating electrode and inherent device properties such as asymmetry and initial slack, greatly influences the modal weight or participation. This modal superposition analysis elucidates the dynamics of any nanomechanical system through modal weights. This aids in optimizing mode-specific designs for force sensing and integration with other systems.

Soft Three-Dimensional Microscale Vibratory Platforms for Characterization of Nano-Thin Polymer Films

Vibrational resonances of microelectromechanical systems (MEMS) can serve as means for assessing physical properties of ultrathin coatings in sensors and analytical platforms. Most such technologies exist in largely two-dimensional configurations with a limited total number of accessible vibration modes and modal displacements, thereby placing constraints on design options and operational capabilities. This study presents a set of concepts in three-dimensional (3D) microscale platforms with vibrational resonances excited by Lorentz-force actuation for purposes of measuring properties of thin-film coatings. Nanoscale films including photodefinable epoxy, cresol novolak resin, and polymer brush with thicknesses as small as 270 nm serve as the test vehicles for demonstrating the advantages of these 3D MEMS for detection of multiple physical properties, such as modulus and density, within a single polymer sample. The stability and reusability of the structure are demonstrated through multiple measurements of polymer samples using a single platform, and via integration with thermal actuators, the temperature-dependent physical properties of polymer films are assessed. Numerical modeling also suggests the potential for characterization of anisotropic mechanical properties in single or multilayer films. The findings establish unusual opportunities for interrogation of the physical properties of polymers through advanced MEMS design.

Intrinsic Properties of Suspended MoS2 on SiO2/Si Pillar Arrays for Nanomechanics and Optics

Semiconducting two-dimensional (2D) materials, such as transition-metal dichalcogenides (TMDs), are emerging in nanomechanics, optoelectronics, and thermal transport. In each of these fields, perfect control over 2D material properties including strain, doping, and heating is necessary, especially on the nanoscale. Here, we study clean devices consisting of membranes of single-layer MoS₂ suspended on pillar arrays. Using Raman and photoluminescence spectroscopy, we have been able to extract, separate, and simulate the different contributions on the nanoscale and to correlate these to the pillar array design. This control has been used to design a periodic MoS₂ mechanical membrane with a high reproducibility and to perform optomechanical measurements on arrays of similar resonators with a high-quality factor of 600 at ambient temperature, hence opening the way to multiresonator applications with 2D materials. At the same time, this study constitutes a reference for the future development of well-controlled optical emissions within 2D materials on periodic arrays with reproducible behavior. We measured a strong reduction of the MoS₂ band gap induced by the strain generated from the pillars. A transition from direct to indirect band gap was observed in isolated tent structures made of MoS₂ and pinched by a pillar. In fully suspended devices, simulations were performed allowing both the extraction of the thermal conductance and doping of the layer. Using the correlation between the influences of strain and doping on the MoS₂ Raman spectrum, we have developed a simple, elegant method to extract the local strain in suspended and nonsuspended parts of a membrane. This opens the way to experimenting with tunable coupling between light emission and vibration.

Strain and defect engineering on phase transition of monolayer black phosphorene

Under biaxial strain, SW-2 defect can move inward the phase boundary of α-P and β-P remarkably and promote the phase transition from α-P to β-P, serving as an excellent ‘phase transition catalyzer’.

Hexagonal boron nitride nanomechanical resonators with spatially visualized motion

Atomic layers of hexagonal boron nitride (h-BN) crystal are excellent candidates for structural materials as enabling ultrathin, two-dimensional (2D) nanoelectromechanical systems (NEMS) due to the outstanding mechanical properties and very wide bandgap (5.9 eV) of h-BN. In this work, we report the experimental demonstration of h-BN 2D nanomechanical resonators vibrating at high and very high frequencies (from ~5 to ~70 MHz), and investigations of the elastic properties of h-BN by measuring the multimode resonant behavior of these devices. First, we demonstrate a dry-transferred doubly clamped h-BN membrane with ~6.7 nm thickness, the thinnest h-BN resonator known to date. In addition, we fabricate circular drumhead h-BN resonators with thicknesses ranging from ~9 to 292 nm, from which we measure up to eight resonance modes in the range of ~18 to 35 MHz. Combining measurements and modeling of the rich multimode resonances, we resolve h-BN's elastic behavior, including the transition from membrane to disk regime, with built-in tension ranging from 0.02 to 2 N m^-1. The Young's modulus of h-BN is determined to be E _Y≈392 GPa from the measured resonances. The ultrasensitive measurements further reveal subtle structural characteristics and mechanical properties of the suspended h-BN diaphragms, including anisotropic built-in tension and bulging, thus suggesting guidelines on how these effects can be exploited for engineering multimode resonant functions in 2D NEMS transducers.

Tunable phonon-cavity coupling in graphene membranes

A major achievement of the past decade has been the realization of macroscopic quantum systems by exploiting the interactions between optical cavities and mechanical resonators. In these systems, phonons are coherently annihilated or created in exchange for photons. Similar phenomena have recently been observed through phonon-cavity coupling-energy exchange between the modes of a single system mediated by intrinsic material nonlinearity. This has so far been demonstrated primarily for bulk crystalline, high-quality-factor (Q > 10(5)) mechanical systems operated at cryogenic temperatures. Here, we propose graphene as an ideal candidate for the study of such nonlinear mechanics. The large elastic modulus of this material and capability for spatial symmetry breaking via electrostatic forces is expected to generate a wealth of nonlinear phenomena, including tunable intermodal coupling. We have fabricated circular graphene membranes and report strong phonon-cavity effects at room temperature, despite the modest Q factor (∼100) of this system. We observe both amplification into parametric instability (mechanical lasing) and the cooling of Brownian motion in the fundamental mode through excitation of cavity sidebands. Furthermore, we characterize the quenching of these parametric effects at large vibrational amplitudes, offering a window on the all-mechanical analogue of cavity optomechanics, where the observation of such effects has proven elusive.

Visualizing the Motion of Graphene Nanodrums

Membranes of suspended two-dimensional materials show a large variability in mechanical properties, in part due to static and dynamic wrinkles. As a consequence, experiments typically show a multitude of nanomechanical resonance peaks, which make an unambiguous identification of the vibrational modes difficult. Here, we probe the motion of graphene nanodrum resonators with spatial resolution using a phase-sensitive interferometer. By simultaneously visualizing the local phase and amplitude of the driven motion, we show that unexplained spectral features represent split degenerate modes. When taking these into account, the resonance frequencies up to the eighth vibrational mode agree with theory. The corresponding displacement profiles, however, are remarkably different from theory, as small imperfections increasingly deform the nodal lines for the higher modes. The Brownian motion, which is used to calibrate the local displacement, exhibits a similar mode pattern. The experiments clarify the complicated dynamic behavior of suspended two-dimensional materials, which is crucial for reproducible fabrication and applications.

Electromechanical coupling and design considerations in single-layer MoS2 suspended-channel transistors and resonators

We report on the analysis of electromechanical coupling effects in suspended doubly-clamped single-layer MoS2 structures, and the designs of suspended-channel field-effect transistors (FETs) and vibrating-channel nanoelectromechanical resonators. In DC gating scenario, signal transduction processes including electrostatic actuation, deflection, straining on bandgap, mobility, carrier density and their intricate cross-interactions, have been analyzed considering strain-enhanced mobility (by up to 4 times), to determine the transfer characteristics. In AC gating scenario and resonant operations (using 100 MHz and 1 GHz devices as relevant targets), we demonstrate that the vibrating-channel MoS2 devices can offer enhanced signals (than the zero-bandgap graphene counterparts), thanks to the resonant straining effects on electron transport of the semiconducting channel. We also show dependence of signal intensity and signal-to-background ratio (SBR) on device geometries and scaling effects, with SBR enhancement by a factor of ∼8 for resonance signal, which provide guidelines toward designing future devices with desirable parameters.

Tunable micro- and nanomechanical resonators

Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.

Black phosphorus nanoelectromechanical resonators vibrating at very high frequencies

We report on the experimental demonstration of a new type of nanoelectromechanical resonator based on black phosphorus crystals. Facilitated by a highly efficient dry transfer technique, crystalline black phosphorus flakes are harnessed to enable drumhead resonators vibrating at high and very high frequencies (HF and VHF bands, up to ∼100 MHz). We investigate the resonant vibrational responses from the black phosphorus crystals by devising both electrical and optical excitation schemes, in addition to measuring the undriven thermomechanical motions in these suspended nanostructures. Flakes with thicknesses from ∼200 nm down to ∼20 nm clearly exhibit elastic characteristics transitioning from the plate to the membrane regime. Both frequency- and time-domain measurements of the nanomechanical resonances show that very thin black phosphorus crystals hold interesting potential for moveable and vibratory devices and for semiconductor transducers where high-speed mechanical motions could be coupled to the attractive electronic and optoelectronic properties of black phosphorus.