Correction: Highly-sensitive wafer-scale transfer-free graphene MEMS condenser microphones.

[This corrects the article DOI: 10.1038/s41378-024-00656-x.].

Centimeter-scale nanomechanical resonators with low dissipation.

High-aspect-ratio mechanical resonators are pivotal in precision sensing, from macroscopic gravitational wave detectors to nanoscale acoustics. However, fabrication challenges and high computational costs have limited the length-to-thickness ratio of these devices, leaving a largely unexplored regime in nano-engineering. We present nanomechanical resonators that extend centimeters in length yet retain nanometer thickness. We explore this expanded design space using an optimization approach which judiciously employs fast millimeter-scale simulations to steer the more computationally intensive centimeter-scale design optimization. By employing delicate nanofabrication techniques, our approach ensures high-yield realization, experimentally confirming room-temperature quality factors close to theoretical predictions. The synergy between nanofabrication, design optimization guided by machine learning, and precision engineering opens a solid-state path to room-temperature quality factors approaching 10 billion at kilohertz mechanical frequencies - comparable to the performance of leading cryogenic resonators and levitated nanospheres, even under significantly less stringent temperature and vacuum conditions.

Highly-sensitive wafer-scale transfer-free graphene MEMS condenser microphones.

Since the performance of micro-electro-mechanical system (MEMS)-based microphones is approaching fundamental physical, design, and material limits, it has become challenging to improve them. Several works have demonstrated graphene's suitability as a microphone diaphragm. The potential for achieving smaller, more sensitive, and scalable on-chip MEMS microphones is yet to be determined. To address large graphene sizes, graphene-polymer heterostructures have been proposed, but they compromise performance due to added polymer mass and stiffness. This work demonstrates the first wafer-scale integrated MEMS condenser microphones with diameters of 2R = 220-320 µm, thickness of 7 nm multi-layer graphene, that is suspended over a back-plate with a residual gap of 5 µm. The microphones are manufactured with MEMS compatible wafer-scale technologies without any transfer steps or polymer layers that are more prone to contaminate and wrinkle the graphene. Different designs, all electrically integrated are fabricated and characterized allowing us to study the effects of the introduction of a back-plate for capacitive read-out. The devices show high mechanical compliances Cm = 0.081-1.07 µmPa-1 (10-100 × higher than the silicon reported in the state-of-the-art diaphragms) and pull-in voltages in the range of 2-9.5 V. In addition, to validate the proof of concept, we have electrically characterized the graphene microphone when subjected to sound actuation. An estimated sensitivity of S1kHz = 24.3-321 mV Pa-1 for a Vbias = 1.5 V was determined, which is 1.9-25.5 × higher than of state-of-the-art microphone devices while having a ~9 × smaller area.

Magnetic order in 2D antiferromagnets revealed by spontaneous anisotropic magnetostriction.

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. Here, we show that its temperature dependence in AF MPS3 (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization-induced anisotropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material's critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit.

Thermo-Magnetostrictive Effect for Driving Antiferromagnetic Two-Dimensional Material Resonators.

Magnetostrictive coupling has recently attracted interest as a sensitive method for studying magnetism in two-dimensional (2D) materials by mechanical means. However, its application in high-frequency magnetic actuators and transducers requires rapid modulation of the magnetic order, which is difficult to achieve with external magnets, especially when dealing with antiferromagnets. Here, we optothermally modulate the magnetization in antiferromagnetic 2D material membranes of metal phosphor trisulfides (MPS3), to induce a large high-frequency magnetostrictive driving force. From the analysis of the temperature-dependent resonance amplitude, we provide evidence that the force is due to a thermo-magnetostrictive effect, which significantly increases near the Neél temperature, due to the strong temperature dependence of the magnetization. By studying its angle dependence, we find the effect is observed to follow anisotropic magnetostriction of the crystal lattice. The results show that the thermo-magnetostrictive effect results in a strongly enhanced thermal expansion force near the critical temperature of magnetostrictive 2D materials, which can enable more efficient actuation of nano-magnetomechanical devices and can also provide a route for studying the high-frequency coupling among magnetic, mechanical, and thermodynamic degrees of freedom down to the 2D limit.

Ultra-sensitive graphene membranes for microphone applications.

Microphones exploit the motion of suspended membranes to detect sound waves. Since the microphone performance can be improved by reducing the thickness and mass of its sensing membrane, graphene-based microphones are expected to outperform state-of-the-art microelectromechanical (MEMS) microphones and allow further miniaturization of the device. Here, we present a laser vibrometry study of the acoustic response of suspended multilayer graphene membranes for microphone applications. We address performance parameters relevant for acoustic sensing, including mechanical sensitivity, limit of detection and nonlinear distortion, and discuss the trade-offs and limitations in the design of graphene microphones. We demonstrate superior mechanical sensitivities of the graphene membranes, reaching more than 2 orders of magnitude higher compliances than commercial MEMS devices, and report a limit of detection as low as 15 dBSPL, which is 10-15 dB lower than that featured by current MEMS microphones.

Graphene nano-electromechanical mass sensor with high resolution at room temperature.

The inherent properties of 2D materials-light mass, high out-of-plane flexibility, and large surface area-promise great potential for precise and accurate nanomechanical mass sensing, but their application is often hampered by surface contamination. Here we demonstrate a tri-layer graphene nanomechanical resonant mass sensor with sub-attogram resolution at room temperature, fabricated by a bottom-up process. We found that Joule-heating is effective in cleaning the graphene membrane surface, which results in a large improvement in the stability of the resonance frequency. We characterized the sensor by depositing Cr metal using a stencil mask and found a mass-resolution that is sufficient to weigh very small particles, like large proteins and protein complexes, with potential applications in the fields of nanobiology and medicine.

Ultrasound Pulse Emission Spectroscopy Method to Characterize Xylem Conduits in Plant Stems.

Although it is well known that plants emit acoustic pulses under drought stress, the exact origin of the waveform of these ultrasound pulses has remained elusive. Here, we present evidence for a correlation between the characteristics of the waveform of these pulses and the dimensions of xylem conduits in plants. Using a model that relates the resonant vibrations of a vessel to its dimension and viscoelasticity, we extract the xylem radii from the waveforms of ultrasound pulses and show that these are correlated and in good agreement with optical microscopy. We demonstrate the versatility of the method by applying it to shoots of ten different vascular plant species. In particular, for Hydrangea quercifolia, we further extract vessel element lengths with our model and compare them with scanning electron cryomicroscopy. The ultrasonic, noninvasive characterization of internal conduit dimensions enables a breakthrough in speed and accuracy in plant phenotyping and stress detection.

Diamagnetic Composites for High-Q Levitating Resonators.

Levitation offers extreme isolation of mechanical systems from their environment, while enabling unconstrained high-precision translation and rotation of objects. Diamagnetic levitation is one of the most attractive levitation schemes because it allows stable levitation at room temperature without the need for a continuous power supply. However, dissipation by eddy currents in conventional diamagnetic materials significantly limits the application potential of diamagnetically levitating systems. Here, a route toward high-Q macroscopic levitating resonators by substantially reducing eddy current damping using graphite particle based diamagnetic composites is presented. Resonators that feature quality factors Q above 450 000 and vibration lifetimes beyond one hour are demonstrated, while levitating above permanent magnets in high vacuum at room temperature. The composite resonators have a Q that is >400 times higher than that of diamagnetic graphite plates. By tuning the composite particle size and density, the dissipation reduction mechanism is investigated, and the Q of the levitating resonators is enhanced. Since their estimated acceleration noise is as low as some of the best superconducting levitating accelerometers at cryogenic temperatures, the high Q and large mass of the presented composite resonators positions them as one of the most promising technologies for next generation ultra-sensitive room temperature accelerometers.

Ultrathin Piezoelectric Resonators Based on Graphene and Free-Standing Single-Crystal BaTiO3.

Suspended piezoelectric thin films are key elements enabling high-frequency filtering in telecommunication devices. To meet the requirements of next-generation electronics, it is essential to reduce device thickness for reaching higher resonance frequencies. Here, the high-quality mechanical and electrical properties of graphene electrodes are combined with the strong piezoelectric performance of the free-standing complex oxide, BaTiO3 (BTO), to create ultrathin piezoelectric resonators. It is demonstrated that the device can be brought into mechanical resonance by piezoelectric actuation. By sweeping the DC bias voltage on the top graphene electrode, the BTO membrane is switched between the two poled ferroelectric states. Remarkably, ferroelectric hysteresis is also observed in the resonance frequency, magnitude and Q-factor of the first membrane mode. In the bulk acoustic mode, the device vibrates at 233 GHz. This work demonstrates the potential of combining van der Waals materials with complex oxides for next-generation electronics, which not only opens up opportunities for increasing filter frequencies, but also enables reconfiguration by poling, via ferroelectric memory effect.

Symmetry-Breaking-Induced Frequency Combs in Graphene Resonators.

Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena-like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we demonstrate a route for generating mechanical frequency combs in graphene resonators undergoing symmetry-breaking forces. We use electrostatic force to break the membrane's out-of-plane symmetry and tune its resonance frequency toward a one-to-two internal resonance, thus achieving strong coupling between two of its mechanical modes. When increasing the drive level, we observe splitting of the fundamental resonance peak, followed by the emergence of a frequency comb regime. We attribute the observed physics to a nonsymmetric restoring potential and show that the frequency comb regime is mediated by Neimark bifurcation of the periodic solution. These results demonstrate that mechanical frequency combs and chaotic dynamics in 2D material resonators can emerge near internal resonances due to symmetry-breaking.

Direct Wafer-Scale CVD Graphene Growth under Platinum Thin-Films.

Since the transfer process of graphene from a dedicated growth substrate to another substrate is prone to induce defects and contamination and can increase costs, there is a large interest in methods for growing graphene directly on silicon wafers. Here, we demonstrate the direct CVD growth of graphene on a SiO2 layer on a silicon wafer by employing a Pt thin film as catalyst. We pattern the platinum film, after which a CVD graphene layer is grown at the interface between the SiO2 and the Pt. After removing the Pt, Raman spectroscopy demonstrates the local growth of monolayer graphene on SiO2. By tuning the CVD process, we were able to fully cover 4-inch oxidized silicon wafers with transfer-free monolayer graphene, a result that is not easily obtained using other methods. By adding Ta structures, local graphene growth on SiO2 is selectively blocked, allowing the controlled graphene growth on areas selected by mask design.

Sensitive Transfer-Free Wafer-Scale Graphene Microphones.

During the past decades micro-electromechanical microphones have largely taken over the market for portable devices, being produced in volumes of billions yearly. Because performance of current devices is near the physical limits, further miniaturization and improvement of microphones for mobile devices poses a major challenge that requires breakthrough device concepts, geometries, and materials. Graphene is an attractive material for enabling these breakthroughs due to its flexibility, strength, nanometer thinness, and high electrical conductivity. Here, we demonstrate that transfer-free 7 nm thick multilayer graphene (MLGr) membranes with diameters ranging from 85-155 to 300 µm can be used to detect sound and show a mechanical compliance up to 92 nm Pa-1, thus outperforming commercially available MEMS microphones of 950 µm with compliances around 3 nm Pa-1. The feasibility of realizing larger membranes with diameters of 300 µm and even higher compliances is shown, although these have lower yields. We present a process for locally growing graphene on a silicon wafer and realizing suspended membranes of patterned graphene across through-silicon holes by bulk micromachining and sacrificial layer etching, such that no transfer is required. This transfer-free method results in a 100% yield for membranes with diameters up to 155 µm on 132 fabricated drums. The device-to-device variations in the mechanical compliance in the audible range (20-20000 Hz) are significantly smaller than those in transferred membranes. With this work, we demonstrate a transfer-free method for realizing wafer-scale multilayer graphene membranes that is compatible with high-volume manufacturing. Thus, limitations of transfer-based methods for graphene microphone fabrication such as polymer contamination, crack formation, wrinkling, folding, delamination, and low-tension reproducibility are largely circumvented, setting a significant step on the route toward high-volume production of graphene microphones.

Probing nanomotion of single bacteria with graphene drums.

Motion is a key characteristic of every form of life1. Even at the microscale, it has been reported that colonies of bacteria can generate nanomotion on mechanical cantilevers2, but the origin of these nanoscale vibrations has remained unresolved3,4. Here, we present a new technique using drums made of ultrathin bilayer graphene, where the nanomotion of single bacteria can be measured in its aqueous growth environment. A single Escherichia coli cell is found to generate random oscillations with amplitudes of up to 60 nm, exerting forces of up to 6 nN to its environment. Using mutant strains that differ by single gene deletions that affect motility, we are able to pinpoint the bacterial flagella as the main source of nanomotion. By real-time tracing of changes in nanomotion on administering antibiotics, we demonstrate that graphene drums can perform antibiotic susceptibility testing with single-cell sensitivity. These findings deepen our understanding of processes underlying cellular dynamics, and pave the way towards high-throughput and parallelized rapid screening of the effectiveness of antibiotics in bacterial infections with graphene devices.

Self-Sealing Complex Oxide Resonators.

Although 2D materials hold great potential for next-generation pressure sensors, recent studies revealed that gases permeate along the membrane-surface interface, necessitating additional sealing procedures. In this work, we demonstrate the use of free-standing complex oxides as self-sealing membranes that allow the reference cavity beneath to be sealed by a simple anneal. To test the hermeticity, we study the gas permeation time constants in nanomechanical resonators made from SrRuO3 and SrTiO3 membranes suspended over SiO2/Si cavities which show an improvement up to 4 orders of magnitude in the permeation time constant after annealing the devices. Similar devices fabricated on Si3N4/Si do not show such improvements, suggesting that the adhesion increase over SiO2 is mediated by oxygen bonds that are formed at the SiO2/complex oxide interface during the self-sealing anneal. Picosecond ultrasonics measurements confirm the improvement in the adhesion by 70% after annealing.

Spiderweb Nanomechanical Resonators via Bayesian Optimization: Inspired by Nature and Guided by Machine Learning.

From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel "torsional soft-clamping" mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.

Tunable Strong Coupling of Mechanical Resonance between Spatially Separated FePS3 Nanodrums.

Coupled nanomechanical resonators made of two-dimensional materials are promising for processing information with mechanical modes. However, the challenge for these systems is to control the coupling. Here, we demonstrate strong coupling of motion between two suspended membranes of the magnetic 2D material FePS3. We describe a tunable electromechanical mechanism for control over both the resonance frequency and the coupling strength using a gate voltage electrode under each membrane. We show that the coupling can be utilized for transferring data between drums by amplitude modulation. Finally, we also study the temperature dependence of the coupling and how it is affected by the antiferromagnetic phase transition characteristic of this material. The presented electrical coupling of resonant magnetic 2D membranes holds the promise of transferring mechanical energy over a distance at low electrical power, thus enabling novel data readout and information processing technologies.

Chemical Design and Magnetic Ordering in Thin Layers of 2D Metal-Organic Frameworks (MOFs).

Through rational chemical design, and thanks to the hybrid nature of metal-organic frameworks (MOFs), it is possible to prepare molecule-based 2D magnetic materials stable at ambient conditions. Here, we illustrate the versatility of this approach by changing both the metallic nodes and the ligands in a family of layered MOFs that allows the tuning of their magnetic properties. Specifically, the reaction of benzimidazole-type ligands with different metal centers (MII = Fe, Co, Mn, Zn) in a solvent-free synthesis produces a family of crystalline materials, denoted as MUV-1(M), which order antiferromagnetically with critical temperatures that depend on M. Furthermore, the incorporation of additional substituents in the ligand results in a novel system, denoted as MUV-8, formed by covalently bound magnetic double layers interconnected by van der Waals interactions, a topology that is very rare in the field of 2D materials and unprecedented for 2D magnets. These layered materials are robust enough to be mechanically exfoliated down to a few layers with large lateral dimensions. Finally, the robustness and crystallinity of these layered MOFs allow the fabrication of nanomechanical resonators that can be used to detect─through laser interferometry─the magnetic order in thin layers of these 2D molecule-based antiferromagnets.

Squeeze-Film Effect on Atomically Thin Resonators in the High-Pressure Limit.

The resonance frequency of membranes depends on the gas pressure due to the squeeze-film effect, induced by the compression of a thin gas film that is trapped underneath the resonator by the high-frequency motion. This effect is particularly large in low-mass graphene membranes, which makes them promising candidates for pressure-sensing applications. Here, we study the squeeze-film effect in single-layer graphene resonators and find that their resonance frequency is lower than expected from models assuming ideal compression. To understand this deviation, we perform Boltzmann and continuum finite-element simulations and propose an improved model that includes the effects of gas leakage and can account for the observed pressure dependence of the resonance frequency. Thus, this work provides further understanding of the squeeze-film effect and provides further directions into optimizing the design of squeeze-film pressure sensors from 2D materials.

Controlling the anisotropy of a van der Waals antiferromagnet with light.

Van der Waals magnets provide an ideal playground to explore the fundamentals of low-dimensional magnetism and open opportunities for ultrathin spin-processing devices. The Mermin-Wagner theorem dictates that as in reduced dimensions isotropic spin interactions cannot retain long-range correlations, the long-range spin order is stabilized by magnetic anisotropy. Here, using ultrashort pulses of light, we control magnetic anisotropy in the two-dimensional van der Waals antiferromagnet NiPS3 Tuning the photon energy in resonance with an orbital transition between crystal field split levels of the nickel ions, we demonstrate the selective activation of a subterahertz magnon mode with markedly two-dimensional behavior. The pump polarization control of the magnon amplitude confirms that the activation is governed by the photoinduced magnetic anisotropy axis emerging in response to photoexcitation of ground state electrons to states with a lower orbital symmetry. Our results establish pumping of orbital resonances as a promising route for manipulating magnetic order in low-dimensional (anti)ferromagnets.