Spatial mapping of multimode Brownian motions in high-frequency silicon carbide microdisk resonators

Mapping of Vibrational Modes Revealing a Strong and Tunable Coupling in Two Juxtaposed 3R-WSe2 Nanodrums

Two-dimensional (2D) material resonators have emerged as promising platforms for advanced nanomechanical applications due to their exceptional mechanical properties, tunability, and nonlinearities. We explored the strong mechanical mode coupling between two adjacent 3R-WSe2 nanodrums at room temperature. Combining a piezoelectric material, as noncentrosymmetric 3R-WSe2, and vibration manipulation is the building block for phononic experiments with 2D materials. By strategically placing gate grids beneath each resonator and mapping the spatial distribution of these modes, we demonstrate the ability to transit between localized modes in individual membranes to delocalized, strongly coupled modes that span the entire suspended region. The coherent coupling is strongly tunable with simple gate voltage, and remarkable resonance splitting was achieved, corresponding to up to 5% of the vibration frequency. These results showcase the potential of 2D material resonators for efficient information exchange, paving the way for novel applications in quantum technologies and nanoscale sensing.

4H-Silicon Carbide as an Acoustic Material for MEMS

This article discusses the potential of 4H-silicon carbide (SiC) as a superior acoustic material for microelectromechanical systems (MEMS), particularly for high-performance resonator and extreme environments applications. Through a comparison of the crystalline structure along with the mechanical, acoustic, electrical, and thermal properties of 4H with respect to other SiC polytypes and silicon, it is shown that 4H-SiC possesses salient properties for MEMS applications, including its transverse isotropy and small phonon scattering dissipation. The utility and implementation of bonded SiC on insulator (4H-SiCOI) substrates as an emerging MEMS technology platform are presented. Additionally, this article reports on the temperature-dependent mechanical properties of 4H-SiC, including the temperature coefficient of frequency (TCF) and quality factor ( Q -factor) for Lamé mode resonators. Finally, the 4H-SiC MEMS fabrication including its deep reactive ion etching is discussed. This article provides valuable insights into the potential of 4H-SiC as a mechanoacoustic material and provides a foundation for future research in the field.

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.

Electrically Tunable MXene Nanomechanical Resonators Vibrating at Very High Frequencies

As an emerging class of two-dimensional (2D) layered nanomaterial, MXene exhibits a number of intriguing properties, such as good electrical conductivity and high elastic modulus, and has witnessed continued growth in related device research. However, nanoscale MXene devices which leverage both the intrinsic electrical and mechanical properties of these 2D crystals have not been experimentally studied. Here we demonstrate nanoelectromechanical resonators based on 2D MXene crystals, where Ti₃C₂T_x drumheads with a wide range of thickness, from more than 50 layers all the way down to a monolayer, exhibit robust nanomechanical vibrations with fundamental-mode frequency f₀ up to >70 MHz in the very high frequency (VHF) band, a displacement noise density down to 52 fm/Hz^1/2, and a fundamental-mode frequency-quality factor product up to f₀ × Q ≈ 6.85 × 10⁹ Hz. By combining experimental results with theoretical calculations, we independently derive the Young's modulus of 2D Ti₃C₂T_x crystals to be 270-360 GPa, in excellent agreement with nanoindentation measurements, based on which we elucidate frequency scaling pathways toward microwave frequencies. We further demonstrate electrical tuning of resonance frequency in MXene resonators and frequency-shift-based MXene vacuum gauges with responsivity of 736%/Torr and detection range down to 10^-4 Torr. Our study can lead to the design and creation of nanoscale vibratory devices that exploit the intrinsic electrical and mechanical properties in 2D MXene crystals.

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.

Photothermal Responsivity of van der Waals Material-Based Nanomechanical Resonators

Nanomechanical resonators made from van der Waals materials (vdW NMRs) provide a new tool for sensing absorbed laser power. The photothermal response of vdW NMRs, quantified from the resonant frequency shifts induced by optical absorption, is enhanced when incorporated in a Fabry-Pérot (FP) interferometer. Along with the enhancement comes the dependence of the photothermal response on NMR displacement, which lacks investigation. Here, we address the knowledge gap by studying electromotively driven niobium diselenide drumheads fabricated on highly reflective substrates. We use a FP-mediated absorptive heating model to explain the measured variations of the photothermal response. The model predicts a higher magnitude and tuning range of photothermal responses on few-layer and monolayer NbSe2 drumheads, which outperform other clamped vdW drum-type NMRs at a laser wavelength of 532 nm. Further analysis of the model shows that both the magnitude and tuning range of NbSe2 drumheads scale with thickness, establishing a displacement-based framework for building bolometers using FP-mediated vdW NMRs.

Monolayer MXene Nanoelectromechanical Piezo-Resonators with 0.2 Zeptogram Mass Resolution

2D materials-based nanoelectromechanical resonant systems with high sensitivity can precisely trace quantities of ultra-small mass molecules and therefore are broadly applied in biological analysis, chemical sensing, and physical detection. However, conventional optical and capacitive transconductance schemes struggle to measure high-order mode resonant effectively, which is the scientific key to further achieving higher accuracy and lower noise. In the present study, the different vibrations of monolayer Ti3 C2 Tx MXene piezo-resonators are investigated, and achieve a high-order f2,3 resonant mode with a ≈234.59 ± 0.05 MHz characteristic peak due to the special piezoelectrical structure of the Ti3 C2 Tx MXene layer. The effective measurements of signals have a low thermomechanical motion spectral density (9.66 ± 0.01  f m H z $\frac{{fm}}{{\sqrt {Hz} }}$ ) and an extensive dynamic range (118.49 ± 0.42 dB) with sub-zeptograms resolution (0.22 ± 0.01 zg) at 300 K temperature and 1 atm. Furthermore, the functional groups of the Ti3 C2 Tx MXene with unique adsorption properties enable a high working range ratio of ≈3100 and excellent repeatability. This Ti3 C2 Tx MXene device demonstrates encouraging performance advancements over other nano-resonators and will lead the related engineering applications including high-sensitivity mass detectors.

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.

A Novel High-Speed and High-Accuracy Mathematical Modeling Method of Complex MEMS Resonator Structures Based on the Multilayer Perceptron Neural Network

MEMS resonators have become core devices in a large number of fields; however, due to their complex structures, the finite element analysis (FEA) method is still the main method for their theoretical analysis. The traditional finite element analysis method faces the disadvantages of large calculation amount and long simulation time, which limits the development of high-performance MEMS resonators. This paper demonstrates a high-speed and high-accuracy simulation tool based on the artificial neural network, where a multilayer perceptron (MLP) neural network model is constructed. The typical structural parameters of MEMS resonator are used as the input layer, and its performance indicators produced by the finite element analysis method are the output layer. After iteratively trained with 4000 samples, the cumulative error of the neural network decreases to 0.0017 and a prediction network model is obtained. Compared with the finite element analysis results, the structural accuracy error predicted by the neural network model can be controlled within 6%, but its runtime is shortened by 15,000 times. This high-speed and high-accuracy mathematical modeling method can effectively improve the analyzing efficiency and provide a promising tool for the design and optimization of different complex MEMS resonators, which exhibit remarkable accuracy and speed.

The Recent Progress of MEMS/NEMS Resonators

MEMS/NEMS resonators are widely studied in biological detection, physical sensing, and quantum coupling. This paper reviews the latest research progress of MEMS/NEMS resonators with different structures. The resonance performance, new test method, and manufacturing process of single or double-clamped resonators, and their applications in mass sensing, micromechanical thermal analysis, quantum detection, and oscillators are introduced in detail. The material properties, resonance mode, and application in different fields such as gyroscope of the hemispherical structure, microdisk structure, drum resonator are reviewed. Furthermore, the working principles and sensing methods of the surface acoustic wave and bulk acoustic wave resonators and their new applications such as humidity sensing and fast spin control are discussed. The structure and resonance performance of tuning forks are summarized. This article aims to classify resonators according to different structures and summarize the working principles, resonance performance, and applications.

Monocrystalline Silicon Carbide Disk Resonators on Phononic Crystals with Ultra-Low Dissipation Bulk Acoustic Wave Modes

Micromechanical resonators with ultra-low energy dissipation are essential for a wide range of applications, such as navigation in GPS-denied environments. Routinely implemented in silicon (Si), their energy dissipation often reaches the quantum limits of Si, which can be surpassed by using materials with lower intrinsic loss. This paper explores dissipation limits in 4H monocrystalline silicon carbide-on-insulator (4H-SiCOI) mechanical resonators fabricated at wafer-level, and reports on ultra-high quality-factors (Q) in gyroscopic-mode disk resonators. The SiC disk resonators are anchored upon an acoustically-engineered Si substrate containing a phononic crystal which suppresses anchor loss and promises Q_ANCHOR near 1 Billion by design. Operating deep in the adiabatic regime, the bulk acoustic wave (BAW) modes of solid SiC disks are mostly free of bulk thermoelastic damping. Capacitively-transduced SiC BAW disk resonators consistently display gyroscopic m = 3 modes with Q-factors above 2 Million (M) at 6.29 MHz, limited by surface TED due to microscale roughness along the disk sidewalls. The surface TED limit is revealed by optical measurements on a SiC disk, with nanoscale smooth sidewalls, exhibiting Q = 18 M at 5.3 MHz, corresponding to f · Q = 9 · 10¹³ Hz, a 5-fold improvement over the Akhiezer limit of Si. Our results pave the path for integrated SiC resonators and resonant gyroscopes with Q-factors beyond the reach of Si.

Anisotropic Thermal Conductivity of Suspended Black Phosphorus Probed by Opto-Thermomechanical Resonance Spectromicroscopy

Atomic layer semiconducting black phosphorus (P) exfoliated from its bulk crystals offers excellent properties and promises for emerging two-dimensional (2D) electronics, photonics, and transducers. It also possesses unique strong in-plane anisotropy among many 2D semiconductors, stemming from its corrugated crystal structure. As an important thermophysical aspect, probing the anisotropic thermal conductivity of black P is essential for device engineering, especially for energy dissipation and thermal management. Here, we report on measurement and analysis of anisotropic in-plane thermal conductivity of black P crystal, in a mechanically suspended device platform, by exploiting a novel opto-thermomechanical resonance spectromicroscopy (OTMRS) technique. With spatially resolved heating effects and thermomechanical resonance motions of suspended structures, anisotropic in-plane thermal conductivity (κ_AC and κ_ZZ) is determined for black P crystals of 10-100 nm thick. This study validates a new noninvasive approach to determining anisotropic thermal conductivity without any requirement of preknowledge of crystal orientation or specific configurations of structure and electrodes according to the anisotropy.

Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range

Atomically thin semiconducting crystals [such as molybdenum disulfide (MoS₂)] have outstanding electrical, optical, and mechanical properties, thus making them excellent constitutive materials for innovating new two-dimensional (2D) nanoelectromechanical systems (NEMS). Although prototype structures have recently been demonstrated toward functional devices such as ultralow-power, high-frequency tunable oscillators and ultrasensitive resonant transducers, both electrical tunability and large dynamic range (DR) are critical and desirable. We report the first experimental demonstration of clearly defined single-, bi-, and trilayer MoS₂ 2D resonant NEMS operating in the very high frequency band (up to ~120 MHz) with outstanding electrical tunability and DR. Through deterministic measurement and calibration, we discover that these 2D atomic layer devices have remarkably broad DR (up to ~70 to 110 dB), in contrast to their 1D NEMS counterparts that are expected to have limited DR. These 2D devices, therefore, open avenues for efficiently tuning and strongly coupling the electronic, mechanical, and optical properties in atomic layer semiconducting devices and systems.

Ultrawide Band Gap β-Ga2O3 Nanomechanical Resonators with Spatially Visualized Multimode Motion

Beta gallium oxide (β-Ga₂O₃) is an emerging ultrawide band gap (4.5 eV-4.9 eV) semiconductor with attractive properties for future power electronics, optoelectronics, and sensors for detecting gases and ultraviolet radiation. β-Ga₂O₃ thin films made by various methods are being actively studied toward such devices. Here, we report on the experimental demonstration of single-crystal β-Ga₂O₃ nanomechanical resonators using β-Ga₂O₃ nanoflakes grown via low-pressure chemical vapor deposition (LPCVD). By investigating β-Ga₂O₃ circular drumhead structures, we demonstrate multimode nanoresonators up to the sixth mode in high and very high frequency (HF/VHF) bands, and also realize spatial mapping and visualization of the multimode motion. These measurements reveal a Young's modulus of E_Y = 261 GPa and anisotropic biaxial built-in tension of 37.5 MPa and 107.5 MPa. We find that thermal annealing can considerably improve the resonance characteristics, including ∼40% upshift in frequency and ∼90% enhancement in quality (Q) factor. This study lays a foundation for future exploration and development of mechanically coupled and tunable β-Ga₂O₃ electronic, optoelectronic, and physical sensing devices.

Phase sensitive imaging of 10 GHz vibrations in an AlN microdisk resonator

We demonstrate a high frequency phase-sensitive heterodyne vibrometer, operating up to 10 GHz. Using this heterodyne vibrometer, the amplitude and phase fields of the fundamental thickness mode, the radial fundamental, and the 2nd-order modes of an AlN optomechanical microdisk resonator are mapped with a displacement sensitivity of around 0.36pm/Hz. The simultaneous amplitude and phase measurement allow precise mode identification and characterization. The recorded modal frequencies and profiles are consistent with numerical simulations. This vibrometer will be of great significance for the development of high frequency mechanical devices.

Carbon nanofiber high frequency nanomechanical resonators

Carbon nanofibers (CNFs) synthesized using a plasma-enhanced chemical vapor deposition (PECVD) process are investigated as a new class of building blocks for high-frequency vibrating nanomechanical resonators. The CNF resonators are prototyped by using vertically oriented few-μm-long cantilever-structured CNFs grown by PECVD. Undriven thermomechanical motions and photothermally driven resonances are measured in the frequency range of ∼3-10 MHz, which exhibit quality (Q) factors of ∼140-350 in moderate vacuum (milliTorr) at room temperature. Further, characteristics of CNF resonators after platinum deposition and intensive electron beam exposure are investigated, and resonance frequency shifts due to mass loading on the CNFs are clearly observed. In addition, extensive material characterization of the CNFs using techniques such as X-ray electron dispersive spectroscopy (XEDS) with spatial element-mapping reveals the structure and growth mechanism of the CNFs.

Single-Crystalline 3C-SiC anodically Bonded onto Glass: An Excellent Platform for High-Temperature Electronics and Bioapplications

Single-crystal cubic silicon carbide has attracted great attention for MEMS and electronic devices. However, current leakage at the SiC/Si junction at high temperatures and visible-light absorption of the Si substrate are main obstacles hindering the use of the platform in a broad range of applications. To solve these bottlenecks, we present a new platform of single crystal SiC on an electrically insulating and transparent substrate using an anodic bonding process. The SiC thin film was prepared on a 150 mm Si with a surface roughness of 7 nm using LPCVD. The SiC/Si wafer was bonded to a glass substrate and then the Si layer was completely removed through wafer polishing and wet etching. The bonded SiC/glass samples show a sharp bonding interface of less than 15 nm characterized using deep profile X-ray photoelectron spectroscopy, a strong bonding strength of approximately 20 MPa measured from the pulling test, and relatively high optical transparency in the visible range. The transferred SiC film also exhibited good conductivity and a relatively high temperature coefficient of resistance varying from -12 000 to -20 000 ppm/K, which is desirable for thermal sensors. The biocompatibility of SiC/glass was also confirmed through mouse 3T3 fibroblasts cell-culturing experiments. Taking advantage of the superior electrical properties and biocompatibility of SiC, the developed SiC-on-glass platform offers unprecedented potentials for high-temperature electronics as well as bioapplications.

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.

Measuring and imaging nanomechanical motion with laser light

We discuss several techniques based on laser-driven interferometers and cavities to measure nanomechanical motion. With increasing complexity, they achieve sensitivities reaching from thermal displacement amplitudes, typically at the picometer scale, all the way to the quantum regime, in which radiation pressure induces motion correlated with the quantum fluctuations of the probing light. We show that an imaging modality is readily provided by scanning laser interferometry, reaching a sensitivity on the order of 10 fm / Hz 1 / 2 , and a transverse resolution down to 2 μ m . We compare this approach with a less versatile, but faster (single-shot) dark-field imaging technique.

Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy

Black phosphorus (P) has emerged as a layered semiconductor with a unique crystal structure featuring corrugated atomic layers and strong in-plane anisotropy in its physical properties. Here, we demonstrate that the crystal orientation and mechanical anisotropy in free-standing black P thin layers can be precisely determined by spatially resolved multimode nanomechanical resonances. This offers a new means for resolving important crystal orientation and anisotropy in black P device platforms in situ beyond conventional optical and electrical calibration techniques. Furthermore, we show that electrostatic-gating-induced straining can continuously tune the mechanical anisotropic effects on multimode resonances in black P electromechanical devices. Combined with finite element modeling (FEM), we also determine the Young's moduli of multilayer black P to be 116.1 and 46.5 GPa in the zigzag and armchair directions, respectively.

Interferometric Motion Detection in Atomic Layer 2D Nanostructures: Visualizing Signal Transduction Efficiency and Optimization Pathways

Atomic layer crystals are emerging building blocks for enabling new two-dimensional (2D) nanomechanical systems, whose motions can be coupled to other attractive physical properties in such 2D systems. Optical interferometry has been very effective in reading out the infinitesimal motions of these 2D structures and spatially resolving different modes. To quantitatively understand the detection efficiency and its dependence on the device parameters and interferometric conditions, here we present a systematic study of the intrinsic motion responsivity in 2D nanomechanical systems using a Fresnel-law-based model. We find that in monolayer to 14-layer structures, MoS₂ offers the highest responsivity among graphene, h-BN, and MoS₂ devices and for the three commonly used visible laser wavelengths (633, 532, and 405 nm). We also find that the vacuum gap resulting from the widely used 300 nm-oxide substrate in making 2D devices, fortunately, leads to close-to-optimal responsivity for a wide range of 2D flakes. Our results elucidate and graphically visualize the dependence of motion transduction responsivity upon 2D material type and number of layers, vacuum gap, oxide thickness, and detecting wavelength, thus providing design guidelines for constructing 2D nanomechanical systems with optimal optical motion readout.

Piezoresistive effect in p-type 3C-SiC at high temperatures characterized using Joule heating

Cubic silicon carbide is a promising material for Micro Electro Mechanical Systems (MEMS) applications in harsh environ-ments and bioapplications thanks to its large band gap, chemical inertness, excellent corrosion tolerance and capability of growth on a Si substrate. This paper reports the piezoresistive effect of p-type single crystalline 3C-SiC characterized at high temperatures, using an in situ measurement method. The experimental results show that the highly doped p-type 3C-SiC possesses a relatively stable gauge factor of approximately 25 to 28 at temperatures varying from 300 K to 573 K. The in situ method proposed in this study also demonstrated that, the combination of the piezoresistive and thermoresistive effects can increase the gauge factor of p-type 3C-SiC to approximately 20% at 573 K. The increase in gauge factor based on the combination of these phenomena could enhance the sensitivity of SiC based MEMS mechanical sensors.

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.

High-speed multiple-mode mass-sensing resolves dynamic nanoscale mass distributions

Simultaneously measuring multiple eigenmode frequencies of nanomechanical resonators can determine the position and mass of surface-adsorbed proteins, and could ultimately reveal the mass tomography of nanoscale analytes. However, existing measurement techniques are slow (<1 Hz bandwidth), limiting throughput and preventing use with resonators generating fast transient signals. Here we develop a general platform for independently and simultaneously oscillating multiple modes of mechanical resonators, enabling frequency measurements that can precisely track fast transient signals within a user-defined bandwidth that exceeds 500 Hz. We use this enhanced bandwidth to resolve signals from multiple nanoparticles flowing simultaneously through a suspended nanochannel resonator and show that four resonant modes are sufficient for determining their individual position and mass with an accuracy near 150 nm and 40 attograms throughout their 150-ms transit. We envision that our method can be readily extended to other systems to increase bandwidth, number of modes, or number of 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.