High-frequency acoustic devices based on two-dimensional (2D) materials are emerging platforms to design and manipulate the spatiotemporal response of acoustic waves for next-generation sensing and contactless actuation applications. Conventional actuation methods, however, cannot be applied to all 2D materials, are frequency-limited or influenced by substrate interactions. Therefore, a universal, high-frequency, on-chip actuation technique is needed. Here, we demonstrate that surface acoustic waves (SAWs) can efficiently actuate suspended 2D materials by exciting suspended graphene membranes with high-frequency (375 MHz) Rayleigh waves and mapping the resulting vibration field with atomic force acoustic microscopy (AFAM), enabling direct visualization of wave propagation without substrate interference. Acoustic waves traveling from supported to suspended graphene experience a reduction in acoustic wavelength from 10 μm to ∼2 μm due to the decrease in effective bending rigidity, leading to a decrease in wave velocity on suspended graphene. By varying the excitation frequency through laser photothermal actuation (0-100 MHz) and SAW excitation (375 MHz), we observed a phase velocity change from ∼160 m/s to ∼700 m/s. This behavior is consistent with the nonlinear dispersion of acoustic waves, as predicted by plate theory, in suspended graphene membranes. The geometry and bending rigidity of the membrane thus play key roles in modulating the acoustic wave pattern and wavelength. This combined SAW actuation and AFAM visualization scheme advances the understanding of acoustic transport at the nanoscale limit and provides a route toward the manipulation of localized wavefields for on-chip patterning and transport over 2D materials surfaces.

Current temperature sensors require regular recalibration to maintain reliable temperature measurement. Photonic/quantum-based approaches have the potential to radically change the practice of thermometry through provision of in situ traceability, potentially through practical primary thermometry, without the need for sensor recalibration. This article gives an overview of the European Partnership in Metrology (EPM) project: Photonic and quantum sensors for practical integrated primary thermometry (PhoQuS-T), which aims to develop sensors based on photonic ring resonators and optomechanical resonators for robust, small-scale, integrated, and wide-range temperature measurement. The different phases of the project will be presented. The development of the integrated optical practical primary thermometer operating from 4 K to 500 K will be reached by a combination of different sensing techniques: with the optomechanical sensor, quantum thermometry below 10 K will provide a quantum reference for the optical noise thermometry (operating in the range 4 K to 300 K), whilst using the high-resolution photonic (ring resonator) sensor the temperature range to be extended from 80 K to 500 K. The important issues of robust fibre-to-chip coupling will be addressed, and application case studies of the developed sensors in ion-trap monitoring and quantum-based pressure standards will be discussed.

Ultrasound is widely used in medical imaging, and emerging photo-acoustic imaging is crucial for disease diagnosis. Currently, high-end photo-acoustic imaging systems rely on piezo-electric materials for detecting ultrasound waves, which come with sensitivity, noise, and bandwidth limitations. Advanced applications demand a large matrix of broadband, high-resolution, and scalable ultrasound sensors. Silicon photonic circuits have been introduced to meet these requirements by detecting ultrasound-induced deformation and stress in silicon waveguides. Although higher sensitivities could facilitate the exploration of new applications, the high stiffness of the waveguide materials constrains the intrinsic sensitivity of the silicon photonic circuits to ultrasound signals. Here, we explore the impact of the mechanical properties of a polymer cladding on the sensitivity of silicon photonic ultrasound sensors. Our model and experiments reveal that optimizing the polymer cladding's stiffness enhances the resonance wavelength sensitivity. Experimentally, we show a fourfold increase in the sensitivity compared to the sensors without a cladding polymer and, a twofold sensitivity increase compared to the sensors with a cladding polymer of saturated cross-linking density. Interestingly, comparing experiments with the optomechanical model suggests that the change in Young's Modulus alone cannot explain the sensitivity increase. In conclusion, polymer-coated silicon photonic ultrasound sensors exhibit potential for advanced photo-acoustic imaging applications. It offers the prospect of increasing the ultrasound detection sensitivity of silicon photonic ultrasound sensors while using CMOS-compatible processes. This paves the way to integrate the polymer-coated silicon photonic ultrasound sensors with electronics to utilize the sensors in advanced medical imaging applications.

Schlieren imaging is a widely applied optical technique for visualizing small refractive index changes in transparent media. An emerging application of schlieren is real-time monitoring and optimization of ultrasound pressure fields for acoustic levitation applications. However, the typically nonlinear relationship between the schlieren intensity and the pressure field complicates deducing the latter from the former. Here, we propose a method to remove this nonlinear relationship, thereby permitting a more quantitative analysis of the pressure variations in the levitation field. By exploiting the harmonic nature of the pressure field using phase-shifted stroboscopic schlieren images we extract the linear part of the schlieren intensity. This linear part is proportional to the instantaneous pressure gradient. The method is successfully employed experimentally and validated by comparing it to simulated acoustic levitation fields. Thereby, our work paves the way towards an improved quantitative analysis of periodic schlieren images that is easily implemented and is particularly suitable for the analysis of ultrasound pressure fields for acoustic levitation applications.

Crystal defects in hexagonal boron nitride (hBN) are emerging as versatile nanoscale optical probes with a wide application profile, spanning the fields of nanophotonics, biosensing, bioimaging, and quantum information processing. However, generating these crystal defects as reliable optical emitters remains challenging due to the need for deterministic defect placement and precise control of the emission area. Here, we demonstrate an approach that integrates microspheres with hBN crystal lattices to enhance both hBN defect generation and optical signal readout. This technique harnesses microspheres to amplify light–matter interactions at the nanoscale through two mechanisms: focused femtosecond (fs) laser irradiation into a photonic nanojet (PNJ) for highly localized defect generation and enhanced light collection via the whispering gallery mode (WGM) effect. Our microsphere-assisted defect generation method reduces the emission area by a factor of 5 and increases the fluorescence collection efficiency by approximately 10 times compared to microsphere-free samples. These advancements in defect generation precision and signal collection efficiency open new possibilities for optical emitter manipulation in hBN, with potential applications in quantum technologies and nanoscale sensing.

Nanomechanical resonances of two-dimensional (2D) materials are sensitive probes for condensedmatter physics, offering new insights into magnetic and electronic phase transitions. Despite extensive research, the influence of the spin dynamics near a phase transition on the nonlinear dynamics of 2D membranes has remained largely unexplored. Here, we investigate nonlinear magneto-mechanical coupling to antiferromagnetic order in suspended FePS3-based heterostructure membranes. By monitoring the motion of these membranes as a function of temperature, we observe characteristic features in both nonlinear stiffness and damping close to the Néel temperature TN. We account for these experimental observations with an analytical magnetostriction model in which these nonlinearities emerge from a coupling between mechanical and magnetic oscillations, demonstrating that magneto-elasticity can lead to nonlinear damping. Our findings thus provide insights into the thermodynamics and magneto-mechanical energy dissipation mechanisms in nanomechanical resonators due to the material’s phase change and magnetic order relaxation.

A quantitative understanding of the microscopic mechanisms responsible for damping in van der Waals nanomechanical resonators remains elusive. In this work, we investigate van der Waals magnets, where the thermal expansion coefficient exhibits an anomaly at the magnetic phase transition due to magnetoelastic coupling. Thermal expansion mediates the coupling between mechanical strain and heat flow and determines the strength of thermoelastic damping (TED). Consequently, variations in the thermal expansion coefficient are reflected directly in TED, motivating our focus on this mechanism. We extend existing TED models to incorporate anisotropic thermal conduction, a critical property of van der Waals materials. By combining the thermodynamic properties of the resonator material with the anisotropic TED model, we examine dissipation as a function of temperature. Our findings reveal a pronounced impact of the phase transition on dissipation, along with transitions between distinct dissipation regimes controlled by geometry and the relative contributions of in-plane and out-of-plane thermal conductivity. These regimes are characterized by the resonant interplay between strain and in-plane or through-plane heat propagation. To validate our theory, we compare it to experimental data of the temperature-dependent mechanical resonances of FePS3 resonators.

Nonlinear dynamic simulations of mechanical resonators have been facilitated by the advent of computational techniques that generate nonlinear reduced order models (ROMs) using the finite element (FE) method. However, designing devices with specific nonlinear characteristics remains inefficient since it requires manual adjustment of the design parameters and can result in suboptimal designs. Here, we integrate an FE-based nonlinear ROM technique with a derivative-free optimization algorithm to enable the design of nonlinear mechanical resonators. The resulting methodology is used to optimize the support design of high-stress nanomechanical Si ₃N ₄ string resonators, in the presence of conflicting objectives such as simultaneous enhancement of Q-factor and nonlinear Duffing constant. To that end, we generate Pareto frontiers that highlight the trade-offs between optimization objectives and validate the results both numerically and experimentally. To further demonstrate the capability of multi-objective optimization for practical design challenges, we simultaneously optimize the design of nanoresonators for three key figure-of-merits in resonant sensing: power consumption, sensitivity and response time. The presented methodology can facilitate and accelerate designing (nano) mechanical resonators with optimized performance for a wide variety of applications. (Figure presented.)

Accurate localization and delivery of biomolecules are pivotal for building tools to understand biology. The interactions of biomolecules with atomically flat 2D surfaces offer a means to realize both the localization and delivery, yet experimental utilization of such interactions has remained elusive. By combining single-molecule detection methods with computational approaches, we comprehensively characterize the interactions of individual DNA molecules with hexagonal boron nitride (hBN) surfaces. Our experiments directly show that, upon binding to a hBN surface, a DNA molecule retains its ability to diffuse along the surface. Further, we show that the magnitude and direction of such diffusion can be controlled by the DNA length, the surface topography, and atomic defects. We observe that the diffusion speed of the biomolecules is significantly lower than indicated by molecular dynamic simulations. Through computational analysis, we present the model based on temporary trapping by atomic defects that accounts for those observations. By fabricating a narrow hBN ribbon structure, we achieve pseudo-1D confinement, demonstrating its potential for nanofluidic guiding of biomolecules.

The unique properties of two-dimensional (2D) materials bring great promise to improve sensor performance and realise novel sensing principles. However, to enable their high-volume production, wafer-scale processes that allow integration with electronic readout circuits need to be developed. In this perspective, we review recent progress in on-chip 2D material sensors, and compare their performance to the state-of-the-art, with a focus on results achieved in the Graphene Flagship programme. We discuss transfer-based and transfer-free production flows and routes for complementary metal-oxide-semiconductor integration and prototype development. Finally, we give an outlook on the future of 2D material sensors, and sketch a roadmap towards realising their industrial and societal impact.

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 C_m = 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 S_1kHz = 24.3–321 mV Pa⁻¹ for a V_bias = 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. (Figure presented.).

As a consequence of their high strength, small thickness, and high flexibility, ultrathin graphene membranes show great potential for pressure and sound sensing applications. This study investigates the performance of multi-layer graphene membranes for microphone applications in the presence of air-loading. Since microphones need a flatband response over the full audible bandwidth, they require a sufficiently high mechanical resonance frequency. Reducing membrane thickness facilitates meeting this bandwidth requirement, and therefore, also allows increasing compliance and sensitivity of the membranes. However, at atmospheric pressure, air-loading effects can increase the effective mass, and thus, reduce the bandwidth of graphene and other 2D material-based microphones. To assess the severity of this performance-limiting effect, we characterize the acoustic response of multi-layer graphene membranes with a thickness of 8 nm in the pressure range from 30 to 1000 mbar, in air and helium environments. A bandwidth reduction by a factor ∼ 2.8 × for membranes with a diameter of 500 μm is observed. These measurements show that air-loading effects, which are usually negligible in conventional microphones, can lead to a substantial bandwidth reduction in ultrathin graphene microphones. With analytical and finite element models, we further analyze the performance limits of graphene microphones in the presence of air-loading effects.

Although strain engineering and soft-clamping techniques for attaining high Q-factors in nanoresonators have received much attention, their impact on nonlinear dynamics is not fully understood. In this study, we show that nonlinearity of high-Q Si₃N₄ nanomechanical string resonators can be substantially tuned by support design. Through careful engineering of support geometries, we control both stress and mechanical nonlinearities, effectively tuning nonlinear stiffness of two orders of magnitude. Our approach also allows control over the sign of the Duffing constant resulting in nonlinear softening of the mechanical mode that conventionally exhibits hardening behavior. We elucidate the influence of support design on the magnitude and trend of the nonlinearity using both analytical and finite element-based reduced-order models that validate our experimental findings. Our work provides evidence of the role of soft-clamping on the nonlinear dynamic response of nanoresonators, offering an alternative pathway for nullifying or enhancing nonlinearity in a reproducible and passive manner.

Motion is all around us, the universe is full of moving matter and this motion is surprisingly predictable. The field of science and engineering that studies time-dependent motion in the presence of forces is called Dynamics. In this book we will introduce the core concepts in dynamics and provide a comprehensive toolset to predict and analyse planar 2D motion of point masses and rigid bodies. The material includes kinematic analysis, Newton’s laws, Euler’s laws, the equations of motion, work, energy, impulse and momentum. Vector-based methods are discussed for systematically solving essentially any problem in 2D dynamics. The book provides a bachelor level introduction for any science and engineering student that can serve as a basis for more advanced courses in dynamics.

Correction to: Microsystems & Nanoengineering https://doi.org/10.1038/s41378-024-00656-x published online 21 February 2024 After publication of this article¹, it was brought to our attention that two pressure values were not correctly copied from the submitted original work to the published version. Correction 1 (from PDF, Page 4 of 9): “These membranes show resonance frequencies above the audible range (f₀₁ > 20 kHz) at 1 × 10³ mbar by piezo-shaker actuation”. The described phrase needs to be changed reporting the right pressure value of 1 × 10⁻³ mbar. The new phrase will be: “These membranes show resonance frequencies above the audible range (f₀₁ > 20 kHz) at 1 × 10⁻³ mbar by piezo-shaker actuation”. Correction 2 (from PDF, Page 4 of 9): “Energy losses and dampening are minimized due to the low pressure of 1 × 10³ mbar”. Again, the described phrase needs to be changed reporting the right pressure value of 1 × 10⁻³ mbar. The new phrase will be: “Energy losses and dampening are minimized due to the low pressure of 1 × 10⁻³ mbar”.

Multi-material direct ink writing (DIW) of smart materials opens new possibilities for manufacturing complex-shaped structures with embedded sensing and actuation capabilities. In this study, DIW of UV-curable piezoelectric actuators is developed, which do not require high-temperature sintering, allowing direct integration with structural materials. Through particle size and ink rheology optimization, the highest d₃₃^*g₃₃ piezoelectric constant compared to other DIW fabricated piezo composites is achieved, enabling tunable actuation performance. This is used to fabricate ultrasound transducers by printing piezoelectric vibrating membranes along with their support structures made from a structural ink. The impact of transducer design and scaling up transducer dimensions on the resonance behavior to design millimeter-scale ultrasound transducers with desired out-of-plane displacement is explored. A significant increase in output pressure with increasing membrane dimensions is observed. Finally, a practical application is demonstrated by using the printed transducer for accurate proximity sensing using time of flight measurements. The scalability and flexibility of the reported DIW of piezo composites can open up new advancements in biomedical, human-computer interaction, and aerospace fields.

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here, we introduce a methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a manufacturing process to create ultra-large graphene drums with diameters of up to 1000 μm. We solve the inverse problem of a Föppl–von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced methodology allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.

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.

Heat transport in two dimensions is fundamentally different from that in three dimensions. As a consequence, the thermal properties of 2D materials are of great interest, from both scientific and application points of view. However, few techniques are available for the accurate determination of these properties in ultrathin suspended membranes. Here, we present an optomechanical methodology for extracting the thermal expansion coefficient, specific heat, and thermal conductivity of ultrathin membranes made of 2H-TaS₂, FePS₃, polycrystalline silicon, MoS₂, and WSe₂. The obtained thermal properties are in good agreement with the values reported in the literature for the same materials. Our work provides an optomechanical method for determining the thermal properties of ultrathin suspended membranes, which are difficult to measure otherwise. It provides a route toward improving our understanding of heat transport in the 2D limit and facilitates engineering of 2D structures with a dedicated thermal performance.

The high susceptibility of ultrathin two-dimensional (2D) material resonators to force and temperature makes them ideal systems for sensing applications and exploring thermomechanical coupling. Although the dynamics of these systems at high stress has been thoroughly investigated, their behavior near the buckling transition has received less attention. Here, we demonstrate that the force sensitivity and frequency tunability of 2D material resonators are significantly enhanced near the buckling bifurcation. This bifurcation is triggered by compressive displacement that we induce via thermal expansion of the devices, while measuring their dynamics via an optomechanical technique. We understand the frequency tuning of the devices through a mechanical buckling model, which allows to extract the central deflection and boundary compressive displacement of the membrane. Surprisingly, we obtain a remarkable enhancement of up to 14× the vibration amplitude attributed to a very low stiffness of the membrane at the buckling transition, as well as a high frequency tunability by temperature of more than 4.02$\%$ K−1. The presented results provide insights into the effects of buckling on the dynamics of free-standing 2D materials and thereby open up opportunities for the realization of 2D resonant sensors with buckling-enhanced sensitivity.