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.

@en

Resonators based on two-dimensional (2D) materials have exceptional properties for application as nanomechanical sensors, which allows them to operate at high frequencies with high sensitivity. However, their performance as nanomechanical sensors is currently limited by their low quality ( Q )-factor. Here, we make use of micro-electromechanical systems (MEMS) to apply pure in-plane mechanical strain, enhancing both their resonance frequency and Q-factor. In contrast to earlier work, the 2D material resonators are fabricated on the MEMS actuators without any wet processing steps using a dry-transfer method. A platinum clamp, which is deposited by electron beam-induced deposition, is shown to be effective in fixing the 2D membrane to the MEMS and preventing slippage. By in-plane straining the membranes in a purely mechanical fashion, we increase the tensile energy, thereby diluting dissipation. This way, we show how dissipation dilution can increase the Q -factor of 2D material resonators by 91%. The presented MEMS actuated dissipation dilution method does not only pave the way toward higher Q -factors in resonators based on 2D materials, but also provides a route toward studies of the intrinsic loss mechanisms of 2D materials in the monolayer limit.

@en

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.

@en

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.).

@en

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.

@en

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.

@en

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”.

@en

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.

@en

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.

@en

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.@en

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.@en

The ultimate isolation offered by levitation provides new opportunities for studying fundamental science and realizing ultra-sensitive floating sensors. Among different levitation schemes, diamagnetic levitation is attractive because it allows stable levitation at room temperature without a continuous power supply. While the dynamics of diamagnetically levitating objects in the linear regime are well studied, their nonlinear dynamics have received little attention. Here, we experimentally and theoretically study the nonlinear dynamic response of graphite resonators that levitate in permanent magnetic traps. By large amplitude actuation, we drive the resonators into nonlinear regime and measure their motion using laser Doppler interferometry. Unlike other magnetic levitation systems, here we observe a resonance frequency reduction with amplitude in a diamagnetic levitation system that we attribute to the softening effect of the magnetic force. We then analyze the asymmetric magnetic potential and construct a model that captures the experimental nonlinear dynamic behavior over a wide range of excitation forces. We also investigate the linearity of the damping forces on the levitating resonator, and show that although eddy current damping remains linear over a large range, gas damping opens a route for tuning nonlinear damping forces via the squeeze-film effect.@en

Graphene-drum-enabled nanomotion detection can play an important role in probing life at the nanoscale. By combining micro- and nanomechanical systems with optics, nanomotion sensors bridge the gap between mechanics and cellular biophysics. They have allowed investigation of processes involved in metabolism, growth, and structural organization of a large variety of microorganisms, ranging from yeasts to bacterial cells. Using graphene drums, these processes can now be resolved at the single-cell level. In this Perspective, we discuss the key achievements of nanomotion spectroscopy and peek forward into the prospects for application of this single-cell technology in clinical settings. Furthermore, we discuss the steps required for implementation and look into applications beyond microbial sensing.

@en

Acoustic levitation is an attractive and versatile technique that offers several advantages in terms of particle size, range, reconfigurability, and ease of use with respect to alternative levitating techniques. In this paper, we study the use of active damping to improve the response time and positioning precision of an acoustic levitator operating in air. We use a laser Doppler vibrometer to measure the velocity of a levitated particle. Using this information, a control algorithm is designed and implemented to provide active damping. By system identification and modeling, we demonstrate that the active damper mechanism is well-predictable by models and can be electronically reconfigured and controlled.

@en

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. 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 inducing anistropic 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.

@en

The resonance frequency of ultra-thin layered nanomaterials changes nonlinearly with the tension induced by the pressure from the surrounding gas. Although the dynamics of pressurized nanomaterial membranes have been extensively explored, recent experimental observations show significant deviations from analytical predictions. Here, we present a multi-mode continuum model that captures the nonlinear pressure-frequency response of pre-tensioned membranes undergoing large deflections. We validate the model using experiments conducted on polysilicon nanodrums excited opto-thermally and subjected to pressure changes in the surrounding medium. We demonstrate that considering the effect of pressure on the nanodrum tension is not sufficient for determining the resonance frequencies. In fact, it is essential to also account for the change in the membrane’s shape in the pressurized configuration, the mid-plane stretching, and the contributions of higher modes to the mode shapes. Finally, we show how the presented high-frequency mechanical characterization method can serve as a fast and contactless method for determining Young’s modulus of ultra-thin membranes.

@en

Ultrasound is widely used in medical imaging, and photo-acoustics is an upcoming imaging modality for the diagnosis of diseases. Future applications require a large matrix of small, sensitive, and broadband ultrasound sensors. However, current high-end systems still use piezo-electric material to detect ultrasound, with limited sensitivity and bandwidth. Silicon photonic circuits can meet the requirements of size, bandwidth, and scalability when designed as ultrasound sensors. Namely, a silicon photonic waveguide deforms when the ultrasound pressure waves impinge on it, leading to a change in effective refractive index, n_e, due to geometrical and photo-elastic effects [1]. However, these effects are weak, which limits the intrinsic sensitivity of silicon photonic ultrasound sensors [2]. To significantly enhance sensitivity, silicon waveguides have been combined with acousto-mechanical structures, which achieved acoustomechanical-noise-limited sensing [3], but this is not compatible with standard photonic platforms. Besides that, recent demonstrations of waveguides coated with polymers also improved sensitivity of the silicon photonic ultrasound sensors significantly, but not sufficient to reach acoustomechnical-noise-limited sensing [4]. Here, we study the effect of mechanical and opto-mechanical properties of polymer claddings on the sensitivity of silicon photonic ultrasound sensors. Our aim is to enhance the sensitivity of these devices by implementing tailored polymer coatings. First, we model the refractive index sensitivity of these type of waveguides, i.e. the change in effective refractive index n_e due to the incident ultrasound plane-wave with a pressure P, and we (Equation presented) where n_c, p₁₂, E, and v are refractive index, elasto-optic coefficient, Young's modulus (stiffness), and Poisson's ratio of the cladding material, respectively. We assume the change in cladding index dominates sensitivity.

@en

Bacteria that are resistant to antibiotics present an increasing burden on healthcare. To address this emerging crisis, novel rapid antibiotic susceptibility testing (AST) methods are eagerly needed. Here, we present an optical AST technique that can determine the bacterial viability within 1 h down to a resolution of single bacteria. The method is based on measuring intensity fluctuations of a reflected laser focused on a bacterium in reflective microwells. Using numerical simulations, we show that both refraction and absorption of light by the bacterium contribute to the observed signal. By administering antibiotics that kill the bacteria, we show that the variance of the detected fluctuations vanishes within 1 h, indicating the potential of this technique for rapid sensing of bacterial antibiotic susceptibility. We envisage the use of this method for massively parallelizable AST tests and fast detection of drug-resistant pathogens.

@en

Heat transport by acoustic phonons in two-dimensional (2D) materials is fundamentally different from that in 3D crystals because the out-of-plane phonons propagate in a unique way that strongly depends on tension and bending rigidity. Here, using optomechanical techniques, we experimentally demonstrate that the heat transport time in freestanding graphene membranes is significantly higher than the theoretical prediction, and decreases by as much as 33% due to an electrostatically induced tension of 0.07 N/m. Using phonon scattering and Debye models, we explain these observations by the tension-enhanced acoustic impedance match of flexural phonons at the boundary of the graphene membrane. Thus, we experimentally elucidate the tunability of phononic heat transport in 2D materials by tension, and open a route towards electronic devices and circuits for high-speed control of temperature at the nanoscale.

@en

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.

@en