A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator

Helium Ion-Assisted Wet Etching of Silicon Carbide with Extremely Low Roughness for High-Quality Nanofabrication

Silicon carbide (SiC) is a promising material for a wide range of applications, including mechanical nano-resonators, quantum photonics, and non-linear photonics. However, its chemical inertness poses challenges for etching in terms of resolution and smoothness. Herein, a novel approach known as helium ion-bombardment-enhanced etching (HIBEE) is presented to achieve high-quality SiC etching. The HIBEE technique utilizes a focused helium ion beam with a typical ion energy of 30 keV to disrupt the crystal lattices of SiC, thus enabling wet etching using hydrofluoric acids and hydrogen peroxide. The etching mechanism is verified via simulations and characterization. The use of a sub-nanometer beam spot of focused helium ions ensures fabrication resolution, and the resulting etched surface exhibits an extremely low roughness of ≈0.9 nm. One of the advantages of the HIBEE technique is that it does not require resist spin-coating and development processes, thus enabling the production of nanostructures on irregular SiC surfaces, such as suspended structures and sidewalls. Additionally, the unique interaction volume of helium ions with substrates enables the one-step fabrication of suspended nanobeam structures directly from bulk substrates. The HIBEE technique is expected to facilitate and accelerate the prototyping of high-quality SiC devices.

Five Low-Noise Stable Oscillators Referenced to the Same Multimode AlN/Si MEMS Resonator

We report on the first experimental demonstration of five self-sustaining feedback oscillators referenced to a single multimode resonator, using piezoelectric aluminum nitride on silicon (AlN/Si) microelectromechanical systems (MEMS) technology. Integrated piezoelectric transduction enables efficient readout of five resonance modes of the same AlN/Si MEMS resonator, at 10, 30, 65, 95, and 233 MHz with quality ( Q ) factors of 18 600, 4350, 4230, 2630, and 2138, respectively, at room temperature. Five stable self-sustaining oscillators are built, each referenced to one of these high- Q modes, and their mode-dependent phase noise and frequency stability (Allan deviation) are measured and analyzed. The 10, 30, 65, 95, and 233 MHz oscillators exhibit low phase noise of -116, -100, -105, -106, and -92 dBc/Hz at 1 kHz offset frequency, respectively. The 65 MHz oscillator yields the Allan deviation of 4×10-9 and 2×10-7 at 1 and 1000 s averaging time, respectively. The 10 MHz oscillator's low phase noise holds strong promise for clock and timing applications. The five oscillators' overall promising performance suggests suitability for multimode resonant sensing and real-time frequency tracking. This work also elucidates mode dependency in oscillator noise and stability, one of the key attributes of mode-engineerable resonators.

Transduction of Single Nanomechanical Pillar Resonators by Scattering of Surface Acoustic Waves

One of the challenges of nanoelectromechanical systems (NEMS) is the effective transduction of the tiny resonators. Vertical structures, such as nanomechanical pillar resonators, which are exploited in optomechanics, acoustic metamaterials, and nanomechanical sensing, are particularly challenging to transduce. Existing electromechanical transduction methods are ill-suited as they put constraints on the pillars' material and do not enable a transduction of freestanding pillars. Here, we present an electromechanical transduction method for single nanomechanical pillar resonators based on surface acoustic waves (SAWs). We demonstrate the transduction of freestanding nanomechanical platinum-carbon pillars in the first-order bending and compression mode. Since the principle of the transduction method is based on resonant scattering of a SAW by a nanomechanical resonator, our transduction method is independent of the pillar's material and not limited to pillar-shaped geometries. It represents a general method to transduce vertical mechanical resonators with nanoscale lateral dimensions.

Nonlinear Stiffness and Nonlinear Damping in Atomically Thin MoS2 Nanomechanical Resonators

We report on experimental measurements and quantitative analyses of nonlinear dynamic characteristics in ultimately thin nanomechanical resonators built upon single-layer, bilayer, and trilayer (1L, 2L, and 3L) molybdenum disulfide (MoS₂) vibrating drumhead membranes. This synergistic study with calibrated measurements and analytical modeling on observed nonlinear responses has led to the determination of nonlinear damping and stiffness coefficients at cubic and quintic orders for these two-dimensional (2D) resonators operating in the very high frequency (VHF) band (up to ∼90 MHz). We find that the quintic force can be ∼20% of the Duffing force at larger amplitudes, and thus, it generally cannot be ignored in a nonlinear dynamics analysis. This study provides the first quantification of nonlinear damping and frequency detuning characteristics in 2D semiconductor nanomechanical resonators and elucidates their origins and dependency on engineerable parameters, setting a foundation for future exploration and utilization of the rich nonlinear dynamics in 2D nanomechanical systems.

A Piezoelectrically Excited ZnO Nanowire Mass Sensor with Closed-Loop Detection at Room Temperature

One-dimensional nanobeam mass sensors offer an unprecedented ability to measure tiny masses or even the mass of individual molecules or atoms, enabling many interesting applications in the fields of mass spectrometry and atomic physics. However, current nano-beam mass sensors suffer from poor real-time test performance and high environment requirements. This paper proposes a piezoelectrically excited ZnO nanowire (NW) mass sensor with closed-loop detection at room temperature to break this limitation. It is detected that the designed piezo-excited ZnO NW could operate at room temperature with a resonant frequency of 417.35 MHz, a quality factor of 3010, a mass sensitivity of -8.1 Hz/zg, and a resolution of 192 zg. The multi-field coupling dynamic model of ZnO NW mass sensor under piezoelectric excitation was established and solved. The nonlinear amplitude-frequency characteristic formula, frequency formula, modal function, sensitivity curve, and linear operating interval were obtained. The ZnO NW mass sensor was fabricated by a top-down method and its response to ethanol gas molecules was tested at room temperature. Experiments show that the sensor has high sensitivity, good closed-loop tracking performance, and high linearity, which provides great potential for the detection of biochemical reaction process of biological particles based on mechanics.

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.

A Precise Closed-Loop Controlled ZnO Nanowire Resonator Operating at Room Temperature

To realize the real-time measurement of masses of nanoparticles, virus molecules, organic macromolecules, and gas molecules, and to analyze their physical and chemical properties, a ZnO nanowire (NW) resonator operating at room temperature with an ultrahigh resonant frequency, real-time detection, and high precision was designed and developed in this study. The machining method is simple and easy to integrate into an integrated circuit. A closed-loop detection system based on a phase-locked loop (PLL) and frequency modulation technology (FM) was used to perform closed-loop testing of electromagnetically excited ZnO NW. The first-order resonance frequency of the resonator was 10.358 MHz, the quality factor Q value was about 600, the frequency fluctuation value f_RMS was about 300 Hz, and the FM range could reach 200 kHz. The equivalent circuit model of the resonator was established, the parasitic parameters during the test were obtained, and the frequency accuracy and phase noise of the resonator were analyzed and tested. The experimental results show that the closed-loop system can automatically control the resonator in a wide range of frequency bands, with good tracking performance of the resonant frequency, small frequency fluctuation, and low phase noise level.

Reaching silicon-based NEMS performances with 3D printed nanomechanical resonators

The extreme miniaturization in NEMS resonators offers the possibility to reach an unprecedented resolution in high-performance mass sensing. These very low limits of detection are related to the combination of two factors: a small resonator mass and a high quality factor. The main drawback of NEMS is represented by the highly complex, multi-steps, and expensive fabrication processes. Several alternatives fabrication processes have been exploited, but they are still limited to MEMS range and very low-quality factor. Here we report the fabrication of rigid NEMS resonators with high-quality factors by a 3D printing approach. After a thermal step, we reach complex geometry printed devices composed of ceramic structures with high Young’s modulus and low damping showing performances in line with silicon-based NEMS resonators ones. We demonstrate the possibility of rapid fabrication of NEMS devices that present an effective alternative to semiconducting resonators as highly sensitive mass and force sensors.

NEMS devices, nano-electro-mechanical systems, by virtue of their minute size, offer ultra-high sensitivity, though at the expense of manufacturing complexity. Here, Stassi et al succeed in manufacturing high quality factor NEMS devices using high resolution 3D printing.

Nonreciprocal magnon laser

A nonreciprocal magnon laser is proposed in a compound cavity optomagnonical system consisting of an yttrium iron garnet sphere coupled to a spinning resonator. On the basis of the magnon-induced Brillouin scattering process making it possible to achieve a magnon lasing action, the Fizeau light-dragging effect caused by the spinning of the resonator further results in significant modifications in the magnon gain and the threshold power of magnon lasing for different driving directions, and then a nonreciprocal magnon laser is realized. Especially, this nonreciprocal magnon laser is highly tunable by the spinning speed and the driving direction. Our work provides an experimentally feasible pathway for manipulating spin-wave excitations and may find intriguing phenomena at the crossroad between spintronics of the magnet and nonreciprocal optics.

High Dynamic Range Nanowire Resonators

Dynamic range quantifies the linear operation regime available in nanomechanical resonators. Nonlinearities dominate the response of flexural beams in the limit of very high aspect ratio and very small diameter, which leads to expectation of low dynamic range for nanowire resonators in general. However, the highest achievable dynamic range for nanowire resonators with practical dimensions remains to be determined. We report dynamic range measurements on singly clamped silicon nanowire resonators reaching remarkably high values of up to 90 dB obtained with a simple harmonic actuation scheme. We explain these measurements by a comprehensive theoretical examination of dynamic range in singly clamped flexural beams including the effect of tapering, a usual feature of semiconductor nanowires. Our analysis reveals the nanowire characteristics required for broad linear operation, and given the relationship between dynamic range and mass sensing performance, it also enables analytical determination of mass detection limits, reaching atomic-scale resolution for feasible nanowires.

Ultrawide Frequency Tuning of Atomic Layer van der Waals Heterostructure Electromechanical Resonators

We report on the experimental demonstration of atomically thin molybdenum disulfide (MoS₂)-graphene van der Waals (vdW) heterostructure nanoelectromechanical resonators with ultrawide frequency tuning. With direct electrostatic gate tuning, these vdW resonators exhibit exceptional tunability, in general, Δf/f₀ > 200%, for continuously tuning the same device and the same mode (e.g., from ∼23 to ∼107 MHz), up to Δf/f₀ ≈ 370%, the largest fractional tuning range in such resonators to date. This remarkable electromechanical resonance tuning is investigated by two different analytical models and finite element simulations. Furthermore, we carefully perform clear control experiments and simulations to elucidate the difference in frequency tuning between the heterostructure and single-material resonators. At a given initial strain level, the tuning range depends on the two-dimensional (2D) Young's moduli of the constitutive crystals; devices built on materials with lower 2D moduli show wider tuning ranges. This study exemplifies that vdW heterostructure resonators can retain unconventionally broad, continuous tuning, which is promising for voltage-controlled, tunable nanosystems.

Avoiding transduction-induced heating in suspended microchannel resonators using piezoelectricity

Calorimetry of single biological entities remains elusive. Suspended microchannel resonators (SMRs) offer excellent performance for real-time detection of various analytes and could hold the key to unlocking pico-calorimetry experiments. However, the typical readout techniques for SMRs are optical-based, and significant heat is dissipated in the sensor, altering the measurement and worsening the frequency noise. In this manuscript, we demonstrate for the first time full on-chip piezoelectric transduction of SMRs on which we focus a laser Doppler vibrometer to analyze its effect. We demonstrate that suddenly applying the laser to a water-filled SMR causes a resonance frequency shift, which we attribute to a local increase in temperature. When the procedure is repeated at increasing flow rates, the resonance frequency shift diminishes, indicating that convection plays an important role in cooling down the device and dissipating the heat induced by the laser. We also show that the frequency stability of the device is degraded by the laser source. In comparison to an optical readout scheme, a low-dissipative transduction method such as piezoelectricity shows greater potential to capture the thermal properties of single entities.

Microcantilever: Dynamical Response for Mass Sensing and Fluid Characterization

A microcantilever is a suspended micro-scale beam structure supported at one end which can bend and/or vibrate when subjected to a load. Microcantilevers are one of the most fundamental miniaturized devices used in microelectromechanical systems and are ubiquitous in sensing, imaging, time reference, and biological/biomedical applications. They are typically built using micro and nanofabrication techniques derived from the microelectronics industry and can involve microelectronics-related materials, polymeric materials, and biological materials. This work presents a comprehensive review of the rich dynamical response of a microcantilever and how it has been used for measuring the mass and rheological properties of Newtonian/non-Newtonian fluids in real time, in ever-decreasing space and time scales, and with unprecedented resolution.

A Chip-Scale Oscillation-Mode Optomechanical Inertial Sensor Near the Thermodynamical Limits

Modern navigation systems integrate the global positioning system (GPS) with an inertial navigation system (INS), which complement each other for correct attitude and velocity determination. The core of the INS integrates accelerometers and gyroscopes used to measure forces and angular rate in the vehicular inertial reference frame. With the help of gyroscopes and by integrating the acceleration to compute velocity and distance, precision and compact accelerometers with sufficient accuracy can provide small-error location determination. Solid-state implementations, through coherent readout, can provide a platform for high performance acceleration detection. In contrast to prior accelerometers using piezoelectric or capacitive readout techniques, optical readout provides narrow-linewidth high-sensitivity laser detection along with low-noise resonant optomechanical transduction near the thermodynamical limits. Here an optomechanical inertial sensor with an 8.2 μg Hz-1/2 velocity random walk (VRW) at an acquisition rate of 100 Hz and 50.9 μg bias instability is demonstrated, suitable for applications, such as, inertial navigation, inclination sensing, platform stabilization, and/or wearable device motion detection. Driven into optomechanical sustained-oscillation, the slot photonic crystal cavity provides radio-frequency readout of the optically-driven transduction with an enhanced 625 μg Hz-1 sensitivity. Measuring the optomechanically-stiffened oscillation shift, instead of the optical transmission shift, provides a 220× VRW enhancement over pre-oscillation mode detection.

Frequency stabilization and noise-induced spectral narrowing in resonators with zero dispersion

Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors including thermal noise, frequency noise of the resonator and noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the eigenfrequency on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large amplitudes. The spectral peak undergoes narrowing when the noise intensity is increased. With the resonator serving as the frequency-selecting element in a feedback loop, the phase noise at the extremum amplitude is ~3 times smaller than the minimal noise in the conventional nonlinear regime.

Designing miniaturized oscillators with stable frequencies is challenging due to nonlinearities. Here, the authors demonstrate reduced phase noise using zero dispersion phenomena in a micromechanical resonator designed with non-monotonic dependence of the frequency of eigenoscillations on energy.

Resonance tracking in a micromechanical device using phononic frequency combs

Micro and nanomechanical resonators have been extensively researched in recent decades for applications to time and frequency references, as well as highly sensitive sensors. Conventionally, the operation of these resonant sensors is implemented using a feedback oscillator to dynamically track variations in the resonant frequency. However, this approach places limitations on the frequency stability of the output response, particularly owing to near-carrier noise shaping, limiting measurement stabilities at short-to-moderate integration times. Here, in this paper, utilizing the recent experimental demonstration of phononic frequency combs, we demonstrate an alternative resonance tracking approach with the potential to provide significant improvements in near-carrier phase noise and long-term stability. In addition, we also showcase comb dynamics mediated resonant frequency modulation which indirectly points to the possible control of inevitable noise processes including thermomechanical fluctuations. This resonant tracking approach may also have general applicability to a number of other physical oscillators.

Large Piezoelectric Strain in Sub-10 Nanometer Two-Dimensional Polyvinylidene Fluoride Nanoflakes

Functional polymers such as polyvinylidene fluoride (PVDF) and its copolymers, which exhibit room-temperature piezoelectricity and ferroelectricity in two-dimensional (2D) limit, are promising candidates to substitute hazardous lead-based piezoceramics for flexible nanoelectronic and electromechanical energy-harvesting applications. However, realization of many polymers including PVDF in ultrathin 2D nanostructures with desired crystal phases and tunable properties remains challenging due to ineffective conventional synthesis methods. Consequently, it has remained elusive to obtain optimized piezoelectric performance of PVDF particularly in sub-10 nm regimes. Taking advantage of its high flexibility and easy processing, we fabricate ultrathin PVDF nanoflakes with thicknesses down to 7 nm by using a hot-pressing method. This thermo-mechanical strategy simultaneously induces robust thermodynamic α to electroactive β-phase transformation, with β fraction as high as 92.8% in sub-10 nm flakes. Subsequently, piezoelectric studies performed by using piezoresponse force microscopy reveal an excellent piezoelectric strain of 0.7% in 7 nm film and the highest piezoelectric coefficient ( d₃₃) achieved is -68 pm/V for 50 nm-thick nanoflakes, which is 13% higher than the piezoresponse from 50 nm-thick PZT nanofilms. Our results further suggest thickness modulation as an effective strategy to tune the piezoelectric performance of PVDF and affirm its supremacy over conventional piezoceramics especially at nanoscale. This work aims not only to help understand fundamental piezoelectricity of pure PVDF in sub-10 nm regimes but also provides an opportunity to realize other polymer-based 2D nanocrystals.

Exotic states in a simple network of nanoelectromechanical oscillators

Synchronization of oscillators, a phenomenon found in a wide variety of natural and engineered systems, is typically understood through a reduction to a first-order phase model with simplified dynamics. Here, by exploiting the precision and flexibility of nanoelectromechanical systems, we examined the dynamics of a ring of quasi-sinusoidal oscillators at and beyond first order. Beyond first order, we found exotic states of synchronization with highly complex dynamics, including weak chimeras, decoupled states, traveling waves, and inhomogeneous synchronized states. Through theory and experiment, we show that these exotic states rely on complex interactions emerging out of networks with simple linear nearest-neighbor coupling. This work provides insight into the dynamical richness of complex systems with weak nonlinearities and local interactions.

Observation of Nonreciprocal Wave Propagation in a Dynamic Phononic Lattice

Acoustic waves in a linear time-invariant medium are generally reciprocal; however, reciprocity can break down in a time-variant system. In this Letter, we report on an experimental demonstration of nonreciprocity in a dynamic one-dimensional phononic crystal, where the local elastic properties are dependent on time. The system consists of an array of repelling magnets, and the on-site elastic potentials of the constitutive elements are modulated by an array of electromagnets. The modulation in time breaks time-reversal symmetry and opens a directional band gap in the dispersion relation. As shown by experimental and numerical results, nonreciprocal mechanical systems like the one presented here offer opportunities to create phononic diodes that can serve for rectification applications.

A Temperature-Compensated Single-Crystal Silicon-on-Insulator (SOI) MEMS Oscillator with a CMOS Amplifier Chip

Self-sustained feedback oscillators referenced to MEMS/NEMS resonators have the potential for a wide range of applications in timing and sensing systems. In this paper, we describe a real-time temperature compensation approach to improving the long-term stability of such MEMS-referenced oscillators. This approach is implemented on a ~26.8 kHz self-sustained MEMS oscillator that integrates the fundamental in-plane mode resonance of a single-crystal silicon-on-insulator (SOI) resonator with a programmable and reconfigurable single-chip CMOS sustaining amplifier. Temperature compensation using a linear equation fit and look-up table (LUT) is used to obtain the near-zero closed-loop temperature coefficient of frequency (TCf) at around room temperature (~25 °C). When subject to small temperature fluctuations in an indoor environment, the temperature-compensated oscillator shows a >2-fold improvement in Allan deviation over the uncompensated counterpart on relatively long time scales (averaging time τ > 10,000 s), as well as overall enhanced stability throughout the averaging time range from τ = 1 to 20,000 s. The proposed temperature compensation algorithm has low computational complexity and memory requirement, making it suitable for implementation on energy-constrained platforms such as Internet of Things (IoT) sensor nodes.

Photothermocapillary Oscillators

We present a new class of tunable light-driven oscillators based on mm-scale objects adsorbed at fluid interfaces. A fixed light source induces photothermal surface tension gradients (Marangoni stresses) that drive nanocomposite hydrogel discs away from a stable apex position atop a drop of water. The capillary forces on the disc increase with surface curvature; thus, they act to restore the disc to its original position. As the disc reenters the light source it again experiences Marangoni propulsion, leading to sustained oscillation for appropriate conditions. Propulsive forces can be modulated with incident light intensity, while the restoring force can be tuned via surface curvature-i.e., drop volume-providing highly tunable oscillatory behaviors. To our knowledge, this is the first example where Marangoni and capillary forces combine to incite sustained motion. As such, a model was developed that describes this behavior and provides key insights into the underlying control parameters. We expect that this simple approach will enable the study of more complex and coupled oscillatory systems.

Dynamic Control of the Coupling between Dark and Bright Excitons with Vibrational Strain

We numerically and experimentally investigate strain-induced coupling between dark and bright excitons and its dynamic control using a gallium arsenide (GaAs) micromechanical resonator. Uniaxial strain induced by the mechanical resonance efficiently detunes the exciton energies and modulates the coupling strength via the deformation potential in GaAs. This allows optical access to the long-lived dark states without using any external electromagnetic field. This field-free approach could be expanded to a wide range of solid-state materials, leading to on-chip excitonic memories and circuits based on micromechanical resonators.

Electrothermally Tunable Graphene Resonators Operating at Very High Temperature up to 1200 K

The unique negative thermal expansion coefficient and remarkable thermal stability of graphene make it an ideal candidate for nanoelectromechanical systems (NEMS) with electrothermal tuning. We report on the first experimental demonstration of electrothermally tuned single- and few-layer graphene NEMS resonators operating in the high frequency (HF) and very high frequency (VHF) bands. In single-, bi-, and trilayer (1L, 2L, and 3L) graphene resonators with carefully controlled Joule heating, we have demonstrated remarkably broad frequency tuning up to Δ f/ f₀ ≈ 310%. Simultaneously, device temperature variations imposed by Joule heating are monitored using Raman spectroscopy; we find that the device temperature increases from 300 K up to 1200 K, which is the highest operating temperature known to date for electromechanical resonators. Using the measured frequency and temperature variations, we further extract both thermal expansion coefficients and thermal conductivities of these devices. Comparison with graphene electrostatic gate tuning indicates that electrothermal tuning is more efficient. The results clearly suggest that the unique negative thermal expansion coefficient of graphene and its excellent tolerance to very high temperature can be exploited for engineering highly tunable and robust graphene transducers for harsh and extreme environments.

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.

Low-force spectroscopy on graphene membranes by scanning tunneling microscopy

Two-dimensional atomically flat sheets with a high mechanical flexibility are very attractive as ultrathin membranes but are also inherently challenging for microscopic investigations. We report on a method using Scanning Tunneling Microscopy (STM) under ultra-high vacuum conditions for non-indenting low-force spectroscopy on micrometer-sized freestanding graphene membranes. The method is based on applying quasi-static voltage ramps with active feedback at low tunneling currents and ultimately relies on the attractive electrostatic force between the tip and the membrane. As a result a bulge-test scenario can be established. The convenience and simplicity of the method relies on the fact that the loading force and the membrane deflection detection are both provided simultaneously by the STM. This permits the continuous measurement of the stress-strain relation. Electrostatic forces applied are typically below 1 nN and the membrane deflection is detected at sub-nanometer resolution. Experiments on single-layer graphene membranes with a strain of 0.1% reveal a two-dimensional elastic modulus E_2D = 220 N m^-1.

Temporal Dynamics of Localized Exciton-Polaritons in Composite Organic-Plasmonic Metasurfaces

We use femtosecond transient absorption spectroscopy to study the temporal dynamics of strongly coupled exciton-plasmon polaritons in metasurfaces of aluminum nanoantennas coated with J-aggregate molecules. Compared with the thermal nonlinearities of aluminum nanoantennas, the exciton-plasmon hybridization introduces strong ultrafast nonlinearities in the composite metasurfaces. Within femtoseconds after the pump excitation, the plasmonic resonance is broadened and shifted, showcasing its high sensitivity to excited-state modification of the molecular surroundings. In addition, we observe temporal oscillations due to the deep subangstrom acoustic breathing modes of the nanoantennas in both bare and hybrid metasurfaces. Finally, unlike the dynamics of hybrid states in optical microcavities, here, ground-state bleaching is observed with a significantly longer relaxation time at the upper polariton band.

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.

Optically driven ultra-stable nanomechanical rotor

Nanomechanical devices have attracted the interest of a growing interdisciplinary research community, since they can be used as highly sensitive transducers for various physical quantities. Exquisite control over these systems facilitates experiments on the foundations of physics. Here, we demonstrate that an optically trapped silicon nanorod, set into rotation at MHz frequencies, can be locked to an external clock, transducing the properties of the time standard to the rod’s motion with a remarkable frequency stability f_r/Δf_r of 7.7 × 10¹¹. While the dynamics of this periodically driven rotor generally can be chaotic, we derive and verify that stable limit cycles exist over a surprisingly wide parameter range. This robustness should enable, in principle, measurements of external torques with sensitivities better than 0.25 zNm, even at room temperature. We show that in a dilute gas, real-time phase measurements on the locked nanorod transduce pressure values with a sensitivity of 0.3%.

Nanomechanical sensors that rely on intrinsic resonance frequencies usually present a tradeoff between sensitivity and bandwidth. In this work, the authors realise an optically driven nanorotor featuring high frequency stability and tunability over a large frequency range.

Piezo-generated charge mapping revealed through direct piezoelectric force microscopy

While piezoelectric and ferroelectric materials play a key role in many everyday applications, there are still a number of open questions related to their physics. To enhance our understanding of piezoelectrics and ferroelectrics, nanoscale characterization is essential. Here, we develop an atomic force microscopy based mode that obtains a direct quantitative analysis of the piezoelectric coefficient d₃₃. We report nanoscale images of piezogenerated charge in a thick single crystal of periodically poled lithium niobate (PPLN), a bismuth ferrite (BiFO₃) thin film, and lead zirconate titanate (PZT) by applying a force and recording the current produced by these materials. The quantification of d₃₃ coefficients for PPLN (14 ± 3 pC per N) and BFO (43 ± 6 pC per N) is in agreement with the values reported in the literature. Even stronger evidence of the reliability of the method is provided by an equally accurate measurement of the significantly larger d₃₃ of PZT.

Piezoelectrics and ferroelectrics are important for everyday applications, but methods to characterize these materials at the nanoscale are lacking. Here the authors present direct piezoelectric force microscopy, an AFM mode that can measure charges generated by the direct piezoelectric effect with nanoscale resolution.

Complex Dynamical Networks Constructed with Fully Controllable Nonlinear Nanomechanical Oscillators

Control of the global parameters of complex networks has been explored experimentally in a variety of contexts. Yet, the more difficult prospect of realizing arbitrary network architectures, especially analog physical networks that provide dynamical control of individual nodes and edges, has remained elusive. Given the vast hierarchy of time scales involved, it also proves challenging to measure a complex network's full internal dynamics. These span from the fastest nodal dynamics to very slow epochs over which emergent global phenomena, including network synchronization and the manifestation of exotic steady states, eventually emerge. Here, we demonstrate an experimental system that satisfies these requirements. It is based upon modular, fully controllable, nonlinear radio frequency nanomechanical oscillators, designed to form the nodes of complex dynamical networks with edges of arbitrary topology. The dynamics of these oscillators and their surrounding network are analog and continuous-valued and can be fully interrogated in real time. They comprise a piezoelectric nanomechanical membrane resonator, which serves as the frequency-determining element within an electrical feedback circuit. This embodiment permits network interconnections entirely within the electrical domain and provides unprecedented node and edge control over a vast region of parameter space. Continuous measurement of the instantaneous amplitudes and phases of every constituent oscillator node are enabled, yielding full and detailed network data without reliance upon statistical quantities. We demonstrate the operation of this platform through the real-time capture of the dynamics of a three-node ring network as it evolves from the uncoupled state to full synchronization.

Selective High-Frequency Mechanical Actuation Driven by the VO2 Electronic Instability

Relaxation oscillators consist of periodic variations of a physical quantity triggered by a static excitation. They are a typical consequence of nonlinear dynamics and can be observed in a variety of systems. VO₂ is a correlated oxide with a solid-state phase transition above room temperature, where both electrical resistance and lattice parameters undergo a drastic change in a narrow temperature range. This strong nonlinear response allows to realize spontaneous electrical oscillations in the megahertz range under a DC voltage bias. These electrical oscillations are employed to set into mechanical resonance a microstructure without the need of any active electronics, with small power consumption and with the possibility to selectively excite specific flexural modes by tuning the value of the DC electrical bias in a range of few hundreds of millivolts. This actuation method is robust and flexible and can be implemented in a variety of autonomous DC-powered devices.

Low-Power Photothermal Self-Oscillation of Bimetallic Nanowires

We investigate the nonlinear mechanics of a bimetallic, optically absorbing SiN-Nb nanowire in the presence of incident laser light and a reflecting Si mirror. Situated in a standing wave of optical intensity and subject to photothermal forces, the nanowire undergoes self-induced oscillations at low incident light thresholds of <1 μW due to engineered strong temperature-position (T-z) coupling. Along with inducing self-oscillation, laser light causes large changes to the mechanical resonant frequency ω₀ and equilibrium position z₀ that cannot be neglected. We present experimental results and a theoretical model for the motion under laser illumination. In the model, we solve the governing nonlinear differential equations by perturbative means to show that self-oscillation amplitude is set by the competing effects of direct T-z coupling and 2ω₀ parametric excitation due to T-ω₀ coupling. We then study the linearized equations of motion to show that the optimal thermal time constant τ for photothermal feedback is τ → ∞ rather than the previously reported ω₀ τ = 1. Lastly, we demonstrate photothermal quality factor (Q) enhancement of driven motion as a means to counteract air damping. Understanding photothermal effects on nano- and micromechanical devices, as well as nonlinear aspects of optics-based motion detection, can enable new device applications as oscillators or other electronic elements with smaller device footprints and less stringent ambient vacuum requirements.

Radiation and Internal Loss Engineering of High-Stress Silicon Nitride Nanobeams

High-stress Si₃N₄ nanoresonators have become an attractive choice for electro- and optomechanical devices. Membrane resonators can achieve quality factor (Q)-frequency (f) products exceeding 10¹³ Hz, enabling (in principle) quantum coherent operation at room temperature. String-like beam resonators possess smaller Q × f products; however, on account of their significantly lower mass and mode density, they remain a canonical choice for precision force, mass, and charge sensing, and have recently enabled Heisenberg-limited position measurements at cryogenic temperatures. Here we explore two techniques to enhance the Q of a nanomechanical beam. The techniques relate to two main loss mechanisms: internal loss, which dominates for high aspect ratios and f ≲ 100 MHz, and radiation loss, which dominates for low aspect ratios and f ≳ 100 MHz. First, we show that by embedding a nanobeam in a 1D phononic crystal (PnC), it is possible to localize its flexural motion and shield it against radiation loss. Using this method, we realize f > 100 MHz modes with Q ≈ 10⁴, consistent with internal loss and contrasting sharply with unshielded beams of similar dimensions. We then study the Q × f product of high-order modes of millimeter-long nanobeams. Taking advantage of the mode-shape dependence of stress-induced "loss dilution", we realize a f ≈ 4 MHz mode with Q × f ≈ 9 × 10¹² Hz. Our results complement recent work on PnC-based "soft-clamping" of nanomembranes, in which mode localization is used to enhance loss dilution. Combining these strategies should enable ultra-low-mass nanobeam oscillators that operate deep in the quantum coherent regime at room temperature.

A convenient method for large-scale STM mapping of freestanding atomically thin conductive membranes

Two-dimensional atomically flat sheets with a high flexibility are very attractive as ultrathin membranes but are also inherently challenging for microscopic investigations. We report on a method using Scanning Tunneling Microscopy (STM) under ultra-high vacuum conditions for large-scale mapping of several-micrometer-sized freestanding single and multilayer graphene membranes. This is achieved by operating the STM at unusual parameters. We found that large-scale scanning on atomically thin membranes delivers valuable results using very high tip-scan speeds combined with high feedback-loop gain and low tunneling currents. The method ultimately relies on the particular behavior of the freestanding membrane in the STM which is much different from that of a solid substrate.

Direct observation of coherent energy transfer in nonlinear micromechanical oscillators

Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. The fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.

Optomechanics of Single Aluminum Nanodisks

Aluminum nanostructures support tunable surface plasmon resonances and have become an alternative to gold nanoparticles. Whereas gold is the most-studied plasmonic material, aluminum has the advantage of high earth abundance and hence low cost. In addition to understanding the size and shape tunability of the plasmon resonance, the fundamental relaxation processes in aluminum nanostructures after photoexcitation must be understood to take full advantage of applications such as photocatalysis and photodetection. In this work, we investigate the relaxation following ultrafast pulsed excitation and the launching of acoustic vibrations in individual aluminum nanodisks, using single-particle transient extinction spectroscopy. We find that the transient extinction signal can be assigned to a thermal relaxation of the photoexcited electrons and phonons. The ultrafast heating-induced launching of in-plane acoustic vibrations reveals moderate binding to the glass substrate and is affected by the native aluminum oxide layer. Finally, we compare the behavior of aluminum nanodisks to that of similarly prepared and sized gold nanodisks.

Sensing of single electrons using micro and nano technologies: a review

During the last three decades, the remarkable dynamic features of microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS), and advances in solid-state electronics hold much potential for the fabrication of extremely sensitive charge sensors. These sensors have a broad range of applications, such as those involving the measurement of ionization radiation, detection of bio-analyte and aerosol particles, mass spectrometry, scanning tunneling microscopy, and quantum computation. Designing charge sensors (also known as charge electrometers) for electrometry is deemed significant because of the sensitivity and resolution issues in the range of micro- and nano-scales. This article reviews the development of state-of-the-art micro- and nano-charge sensors, and discusses their technological challenges for practical implementation.

Nanomechanical Infrared Spectroscopy with Vibrating Filters for Pharmaceutical Analysis

Standard infrared spectroscopy techniques are well-developed and widely used. However, they typically require milligrams of sample and can involve time-consuming sample preparation. A promising alternative is represented by nanomechanical infrared spectroscopy (NAM-IR) based on the photothermal response of a nanomechanical resonator, which enables the chemical analysis of picograms of analyte directly from a liquid solution in only a few minutes. Herein, we present NAM-IR using perforated membranes (filters). The method was tested with the pharmaceutical compound indomethacin to successfully perform a chemical and morphological analysis on roughly 100 pg of sample. With an absolute estimated sensitivity of 109±15 fg, the presented method is suitable for ultrasensitive vibrational spectroscopy.

Optimal waveform for the entrainment of oscillators perturbed by an amplitude-modulated high-frequency force

We analyze limit cycle oscillators under perturbation constructed as a product of two signals, namely, an envelope with a period close to natural period of an oscillator and a high-frequency carrier signal. A theory for obtaining an envelope waveform that achieves the maximal frequency interval of entrained oscillators is presented. The optimization problem for fixed power and maximal allowed amplitude is solved by employing the phase reduction method and the Pontryagin's maximum principle. We have shown that the optimal envelope waveform is a bang-bang-type solution. Also, we have found "inversion" symmetry that relates two signals with different powers but the same interval of entrained frequencies. The theoretical results are confirmed numerically on FitzHugh-Nagumo oscillators.

Tunable Resonators for Nonlinear Modal Interactions

Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.

Effects of time-delayed feedback on the properties of self-sustained oscillators

Most self-sustained oscillations in biological systems and in technical applications are based on a feedback loop, and it is usually important to know how they will react when an external oscillatory force is applied. Here we investigate the effects that the introduction of a time delay in the feedback can have in the entrainment properties of self-sustained oscillators. To do this, we derive analytic expressions for the periodic trajectories and their asymptotic stability, for a generic external oscillatory force. This allows us to show that, for large quality factors, the resonance frequency does not depend on the feedback delay. When the external force is harmonic, it is shown that the largest entrainment range does not correspond to the time delay that gives the maximal response of the unforced oscillator. In fact, that delay gives the shortest entrainment range.

Micromachined Resonators: A Review

This paper is a review of the remarkable progress that has been made during the past few decades in design, modeling, and fabrication of micromachined resonators. Although micro-resonators have come a long way since their early days of development, they are yet to fulfill the rightful vision of their pervasive use across a wide variety of applications. This is partially due to the complexities associated with the physics that limit their performance, the intricacies involved in the processes that are used in their manufacturing, and the trade-offs in using different transduction mechanisms for their implementation. This work is intended to offer a brief introduction to all such details with references to the most influential contributions in the field for those interested in a deeper understanding of the material.

Self-Sustained Micromechanical Oscillator with Linear Feedback

Autonomous oscillators, such as clocks and lasers, produce periodic signals without any external frequency reference. In order to sustain stable periodic motion, there needs to be an external energy supply as well as nonlinearity built into the oscillator to regulate the amplitude. Usually, nonlinearity is provided by the sustaining feedback mechanism, which also supplies energy, whereas the constituent resonator that determines the output frequency stays linear. Here, we propose a new self-sustaining scheme that relies on the nonlinearity originating from the resonator itself to limit the oscillation amplitude, while the feedback remains linear. We introduce a model for describing the working principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical oscillator.

Frequency fluctuations in silicon nanoresonators

Frequency stability is key to the performance of nanoresonators. This stability is thought to reach a limit with the resonator's ability to resolve thermally induced vibrations. Although measurements and predictions of resonator stability usually disregard fluctuations in the mechanical frequency response, these fluctuations have recently attracted considerable theoretical interest. However, their existence is very difficult to demonstrate experimentally. Here, through a literature review, we show that all studies of frequency stability report values several orders of magnitude larger than the limit imposed by thermomechanical noise. We studied a monocrystalline silicon nanoresonator at room temperature and found a similar discrepancy. We propose a new method to show that this was due to the presence of frequency fluctuations, of unexpected level. The fluctuations were not due to the instrumentation system, or to any other of the known sources investigated. These results challenge our current understanding of frequency fluctuations and call for a change in practices.

Metrology of electromagnetic static actuation of MEMS microbridge using atomic force microscopy

The objective of this paper is to describe application of atomic force microscopy (AFM) for characterization and calibration of static deflection of electromagnetically and/or thermally actuated micro-electromechanical (MEMS) bridge. The investigated MEMS structure is formed by a silicon nitride bridge and a thin film metal path enabling electromagnetic and/or thermal deflection actuation. We present how static microbridge deflection can be measured using contact mode AFM technology with resolution of 0.05nm in the range of up to tens of nm. We also analyze, for very small structure deflections and under defined and controlled load force varied in the range up to ca. 32nN, properties of thermal and electromagnetical microbridge deflection actuation schemes.

Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures

Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke's law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale.

Internal Electron Tunneling Enabled Ultrasensitive Position/Force Peapod Sensors

The electron quantum tunneling effect guarantees the ultrahigh spatial resolution of the scanning tunneling microscope (STM), but there have been no other significant applications of this effect after the invention of STM. Here we report the implementation of electron-tunneling-based high sensitivity transducers using a peapod B4C nanowire, where discrete Ni6Si2B nanorods are embedded in the nanowire in a peapod form. The deformation of the nanowire provides a higher order scaling effect between conductivity and deformation strain, thus allowing the potentials of position and force sensing at the picoscale.

A self-stabilized coherent phonon source driven by optical forces

We report a novel injection scheme that allows for “phonon lasing” in a one-dimensional opto-mechanical photonic crystal, in a sideband unresolved regime and with cooperativity values as low as 10⁻². It extracts energy from a cw infrared laser source and is based on the triggering of a thermo-optical/free-carrier-dispersion self-pulsing limit-cycle, which anharmonically modulates the radiation pressure force. The large amplitude of the coherent mechanical motion acts as a feedback that stabilizes and entrains the self-pulsing oscillations to simple fractions of the mechanical frequency. A manifold of frequency-entrained regions with two different mechanical modes (at 54 and 122 MHz) are observed as a result of the wide tuneability of the natural frequency of the self-pulsing. The system operates at ambient conditions of pressure and temperature in a silicon platform, which enables its exploitation in sensing, intra-chip metrology or time-keeping applications.