Nanoelectromechanical Resonators Research Articles

Two-dimensional FePS3 nanoelectromechanical resonators with local-gate electrostatic tuning at room temperature

Nanoelectromechanical systems (NEMS) enabled by two-dimensional (2D) magnetic materials are promising candidates for exploring ultrasensitive detection and magnetostrictive phenomena, thanks to their high mechanical stiffness, high strength, and ultralow mass. The resonance modes of such vibrating membrane NEMS can be probed optically and also manipulated mechanically via electrostatically induced strain. Electrostatic frequency tuning of 2D magnetic NEMS resonators is, thus, an important means of investigating magneto-mechanical coupling mechanisms. Toward realizing magneto-mechanical coupled devices, we build circular drumhead iron phosphorus trisulfide (FePS3) NEMS resonators with different diameters (3–7 μm). Here, we report on experimental demonstration of tunable antiferromagnet FePS3 drumhead resonators with the highest fractional frequency tuning range up to Δf/f0 = 32%. Combining experimental results and analytical modeling of the resonance frequency scaling, we attain quantitative understanding of the elastic behavior of FePS3, including the transition from “membrane” to “plate” regime, with built-in tension (γ) ranging from 0.1 to 2 N/m. This study not only offers methods for investigating mechanical properties of ultrathin membranes of magnetic 2D materials but also provides important guidelines for designing future high-performance magnetic NEMS resonators.

Advances in Single Particle Mass Analysis.

Single particle mass analysis methods allow the measurement and characterization of individual nanoparticles, viral particles, as well as biomolecules like protein aggregates and complexes. Several key benefits are associated with the ability to analyze individual particles rather than bulk samples, such as high sensitivity and low detection limits, and virtually unlimited dynamic range, as this figure of merit strictly depends on analysis time. However, data processing and interpretation of single particle data can be complex, often requiring advanced algorithms and machine learning approaches. In addition, particle ionization, transfer, and detection efficiency can be limiting factors for certain types of analytes. Ongoing developments in the field aim to address these challenges and expand the capabilities of single particle mass analysis techniques. Charge detection mass spectrometry is a single particle version of mass spectrometry in which the charge (z) is determine independently from m/z. Nano-electromechanical resonator mass analysis relies on changes in a nanoscale device's resonance frequency upon deposition of a particle to directly derive its inertial mass. Mass photometry uses interferometric video-microscopy to derive particle mass from the intensity of the scattered light. A common feature of these approaches is the acquisition of single particle data, which can be filtered and concatenated in the form of a particle mass distribution. In the present article, dedicated to our honored colleague Richard Cole, we cover the latest technological advances and applications of these single particle mass analysis approaches.

Fine structure of current noise spectra in nanoelectromechanical resonators

We study the frequency-dependent noise of a suspended carbon nanotube quantum dot nanoelectromechanical resonator induced by electron-vibration coupling. Using a rigorous Keldysh diagrammatic technique, we establish a formal framework connecting the vibrational properties to electrical measurements. We find that the noise power spectrum exhibits a narrow resonant peak at the frequency of the vibrational modes. However, this fine structure tends to disappear due to a coherent cancellation effect when the tunneling barriers are tuned to a symmetric point. Notably, measuring the electrical current noise spectra provides a sensitive alternative method for detecting the damping and dephasing of quantum vibrational modes.

Coherent interferometric control of strongly-coupled nano-electromechanical resonators

The interferometric control of dissipation in a two-port system is a fruitful concept enabling the enhancement or cancellation of the input amplitudes as a function of their relative phases. Here, beyond the canonical configuration of Coherent Perfect Absorption (CPA), we apply this concept to two simultaneously excited strongly-coupled nanoscale electromechanical resonators submitted to independently controlled phase-shifted excitations. Both subsystems are read simultaneously by optical means allowing us to completely reconstruct the signature of coherent annihilation or amplification on both quadrature. We evidence that the mechanical modes amplitude can be enhanced or inhibited with respect to the case of single port excitation while phase experiences strong variations with the excitation imbalance and phase difference. Meanwhile, phase singularities with opposite topological charges are observed for mechanical normal modes. Close to the phase singularity, we demonstrate that the input of a weak phase modulation induces a large, pure phase modulation of the normal mode. These experimental demonstrations are fully modelled via the mechanical dynamical equations of our system. The interferometric control may open avenues for low-power amplitude controlled phase modulation schemes and vice-versa for potential switches and logical gates.

Imaging Nanomechanical Vibrations and Manipulating Parametric Mode Coupling via Scanning Microwave Microscopy.

In this study, we present a novel platform based on scanning microwave microscopy for manipulating and detecting tiny vibrations of nanoelectromechanical resonators using a single metallic tip. The tip is placed on the top of a grounded silicon nitride membrane, acting as a movable top gate of the coupled resonator. We demonstrate its ability to map mechanical modes and investigate mechanical damping effects in a capacitive coupling scheme, based on its spatial resolution. We also manipulate the energy transfer coherently between the mode of the scanning tip and the underlying silicon nitride membrane, via parametric coupling. Typical features of optomechanics, such as anti-damping and electromechanically induced transparency, have been observed. Since the microwave optomechanical technology is fully compatible with quantum electronics and very low temperature conditions, it should provide a powerful tool for studying phonon tunnelling between two spatially separated vibrating elements, which could potentially be applied to quantum sensing.

Ultrahigh-quality graphene resonators by liquid-based strain-engineering.

Two-dimensional (2D) material-based nanoelectromechanical (NEM) resonators are expected to be enabling components in hybrid qubits that couple mechanical and electromagnetic degrees of freedom. However, challenges in their sensitivity and coherence time have to be overcome to realize such mechanohybrid quantum systems. We here demonstrate the potential of strain engineering to realize 2D material-based resonators with unprecedented performance. A liquid-based tension process was shown to enhance the resonance frequency and quality factor of graphene resonators six-fold. Spectroscopic and microscopic characterization reveals a surface-energy enhanced wall interaction as the origin of this effect. The response of our tensioned resonators is not limited by external loss factors and exhibits near-ideal internal losses, yielding superior resonance frequencies and quality factors to all previously reported 2D material devices. Our approach represents a powerful method of enhancing 2D NEM resonators for future quantum systems.

Modeling Nanoelectromechanical Resonator Signals for Experimental Mass Measurements: A Total Variation Formulation

Modeling Nanoelectromechanical Resonator Signals for Experimental Mass Measurements: A Total Variation Formulation

Nonlinearity and temperature dependence of CVD graphene nanoelectromechanical resonator

As a two-dimensional material, graphene has outstanding properties, with high electron mobility and mechanical resistance. Therefore, it has good prospects to be used in nanoelectromechanical resonators for sensitive mass detection. Previously, a graphene resonator with graphene/metal contact able to zeptogram level sensing and a with quality factor of 42 at RT was presented. However, over-etching under the metal contacts degrades the quality factor, and resonators with metal/graphene/metal contacts were fabricated to overcome this issue. A quality factor of 350 at RT was obtained for a device with width = 0.8 μm and length = 1 μm. Tunning of the resonance frequency from 9.6 to 13.5 MHz with dc gate bias is demonstrated. Temperature reduction from 300 K to 30 K increased the resonance frequency by about 4–6 MHz. The temperature influence on nonlinearity is also discussed, with a resonator demonstrating softening and hardening nonlinearities at cryogenic temperatures.

Coupled Nanomechanical Graphene Resonators: A Promising Platform for Scalable NEMS Networks.

Arrays of coupled nanoelectromechanical resonators are a promising foundation for implementing large-scale network applications, such as mechanical-based information processing and computing, but their practical realization remains an outstanding challenge. In this work, we demonstrate a scalable platform of suspended graphene resonators, such that neighboring resonators are persistently coupled mechanically. We provide evidence of strong coupling between neighboring resonators using two different tuning methods. Additionally, we provide evidence of inter-resonator coupling of higher-order modes, demonstrating the rich dynamics that can be accessed with this platform. Our results establish this platform as a viable option for realizing large-scale programmable networks, enabling applications such as phononic circuits, tunable waveguides, and reconfigurable metamaterials.

Nanomechanical vibrational response from electrical mixing measurements

Driven nanomechanical resonators based on low-dimensional materials are routinely and efficiently detected with electrical mixing measurements. However, the measured signal is a non-trivial combination of the mechanical eigenmode displacement and an electrical contribution, which makes the extraction of the driven mechanical response challenging. Here, we report a simple yet reliable method to extract solely the driven mechanical vibrations by eliminating the contribution of pure electrical origin. This enables us to measure the spectral mechanical response as well as the driven quadratures of motion. This method is crucial for nanomechanical vibrations in the nonlinear regime, since the shape of the mechanical response depends on the physics at work. We further show how to calibrate the measured signal into units of displacement. Our method marks a key step forward in the study of nanoelectromechanical resonators based on low-dimensional materials in the nonlinear regime.

Probing Linear to Nonlinear Damping in 2D Semiconductor Nanoelectromechanical Resonators toward a Unified Quality Factor Model.

In resonant nanoelectromechanical systems (NEMS), the quality (Q) factor is essential for sensing, communication, and computing applications. While a large vibrational amplitude is useful for increasing the signal-to-noise ratio, the damping in this regime is more complex because both linear and nonlinear damping are important, and an accurate model for Q has not been fully explored. Here, we demonstrate that by combining the time-domain ringdown and frequency-domain resonance measurements, we extract the accurate Q for two-dimensional (2D) MoS2 and MoTe2 NEMS resonators at different vibration amplitudes. In particular, in the transition region between linear and nonlinear damping, Q can be precisely extracted by fitting to the ringdown characteristics. By varying AC driving, we tune the Q by ΔQ/Q = 269% and extract the nonlinear damping coefficient. We develop the dissipation model that well captures the linear to nonlinear damping, providing important insights for accurately modeling and optimizing Q in 2D NEMS resonators.

Nanoelectromechanical resonators for gigahertz frequency control based on hafnia–zirconia–alumina superlattices

Nanoelectromechanical resonators for gigahertz frequency control based on hafnia–zirconia–alumina superlattices

Fabrication of silicon nitride membrane nanoelectromechanical resonator

In this work, we present details of the nanofabrication process for achieving a silicon nitride nanoelectromechanical resonator, consisting of a membrane covered with a thin aluminium layer capacitively coupled to a suspended top gate. Critical nanofabrication steps have been discussed, including the XeF2 selective etching process to release the silicon nitride membrane from the substrate and the reflow process to fabricate a top gate of a suspended membrane. This ultra-clean and CMOS-compatible process allows the silicon nitride membrane to have a high quality factor (∼1.1×104) at room temperature and offers access to electrical integration with external circuits with high efficiency. In addition, we also demonstrate parametric amplification and de-amplification of the input signals by exploiting this suspended top gate. The measurement results of phase-sensitive amplifications have also been well fit by analytical caculations. The present work provides essential building blocks for further exploration of silicon nitride membrane based nanoelectromechanical resonators that can be efficiently integrated into large-scale electrical circuits.

Research on Dissipation Dilution Mechanism and Boundary Dissipation Suppression Technique for High-Stress Graphene Nanoelectromechanical Resonator

The low-quality factor is a key bottleneck for the engineering and commercial application of graphene nanoelectromechanical resonators at room temperature. The hypothesis in dissipation dominated by the ohmic loss is difficult to cover this phenomenon. Mechanical loss may still be on the list of the main causes for the quality factor stress-modulation characteristics of graphene resonators. The dissipation dilution theory reveals the intrinsic energy and dissipation mechanism of the traditional high-stress silicon-based resonator, which may also be applied to two-dimensional (2D) materials if dominated by mechanical loss. Based on Zener’s model of anelasticity, combined with the edge-corrected mode shape, the stress dilution mechanism of the bending potential dissipation of the graphene resonator is revealed. On this basis, the resonator dissipation is decomposed into boundary dissipation and non-boundary dissipation parts, and the steep rise phenomenon of the bending dissipation density (curvature) in the boundary region is analyzed through theoretical calculation. The analysis reveals that boundary dissipation is dominant in bending dissipation. To effectively suppress the boundary dissipation, a novel design of a graphene resonator via soft-clamped phononic crystal (PnC) is proposed. The existence of localized mode (LM) and effective suppression of boundary dissipation are verified in the simulations of both triangular and honeycomb PnC lattices. The theoretical model developed in this paper provides a new window into the dissipation properties of graphene nanoelectromechanical resonators, and the design of graphene resonators via soft-clamped PnC is expected to provide a new route toward high-quality factors at room temperature.

Characterisation and modelling of nonlinear resonance behaviour on very-high-frequency silicon nanoelectromechanical resonators

Characterisation and modelling of nonlinear resonance behaviour on very-high-frequency silicon nanoelectromechanical resonators

Effects of stochastic forces on the nonlinear behaviour of a silicon nitride membrane nanoelectromechanical resonator

In this work, we present the effects of stochastic force generated by white noise on the nonlinear dynamics of a circular silicon nitride membrane. By tuning the membrane to the Duffing nonlinear region, detected signals switching between low- and high-amplitudes have been observed. They are generated by noise-assisted random jumps between bistable states at room temperature and exhibit high sensitivity to the driving frequency. Through artificially heating different mechanical vibration modes by external input of white noise, the switching rate exhibits exponential dependence on the effective temperature and follows with Kramer‘s law. Furthermore, both the measured switching rate and activation energy exhibit sensitivity to the width of the hysteresis window in nonlinear response and the driving force, which is in qualitative agreement with the theoretical descriptions. Besides, white noise-induced hysteresis window squeezing and bifurcation point shifting have also been observed, which are attributed to the stochastic force modulation of the spring constant of the membrane. These studies are carried out in an all-electric operating scheme at room temperature, paving the way for the exploration of probability distribution-based functional elements that can be massively integrated on-chip.

Theoretical modelling of graphene system for nano-electromechanical resonator and force sensor

Theoretical modelling of graphene system for nano-electromechanical resonator and force sensor

Thermal IR Detection With Nanoelectromechanical Silicon Nitride Trampoline Resonators

Nanoelectromechanical (NEMS) resonators are promising uncooled thermal infrared (IR) detectors to overcome existing sensitivity limits. Here, we investigated NEMS trampoline resonators made of silicon nitride (SiN) as thermal IR detectors. Trampolines have an enhanced responsivity of more than two orders of magnitude compared to state-of-the-art SiN drums. The characterized NEMS trampoline IR detectors yield a sensitivity in terms of noise equivalent power (NEP) of 7 pW/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sqrt {\text {Hz}}$ </tex-math></inline-formula> and a thermal response time as low as 4 ms. The detector area features an impedance-matched metal thin-film absorber with a spectrally flat absorption of 50% over the entire mid-IR spectral range from 1 to 25 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> .

Superfluid He4 as a rigorous test bench for different damping models in nanoelectromechanical resonators

We have used nanoelectromechanical resonators to probe superfluid $^{4}\mathrm{He}$ at different temperature regimes, spanning over four orders of magnitude in damping. These regimes are characterized by the mechanisms which provide the dominant contributions to damping and the shift of the resonance frequency: tunneling two-level systems at the lowest temperatures, ballistic phonons and rotons at few hundred $\phantom{\rule{0.16em}{0ex}}\mathrm{m}\mathrm{K}$, and laminar drag in the two-fluid regime below the superfluid transition temperature as well as in the normal fluid. Immersing the nanoelectromechanical resonators in fluid increases their effective mass substantially, decreasing their resonance frequency. Dissipationless superflow gives rise to a unique possibility to dramatically change the mechanical resonance frequency in situ, allowing rigorous tests on different damping models in mechanical resonators. We apply this method to characterize tunneling two-level system losses and magnetomotive damping in the devices.

Electrically Tunable MXene Nanomechanical Resonators Vibrating at Very High Frequencies

As an emerging class of two-dimensional (2D) layered nanomaterial, MXene exhibits a number of intriguing properties, such as good electrical conductivity and high elastic modulus, and has witnessed continued growth in related device research. However, nanoscale MXene devices which leverage both the intrinsic electrical and mechanical properties of these 2D crystals have not been experimentally studied. Here we demonstrate nanoelectromechanical resonators based on 2D MXene crystals, where Ti3C2Tx drumheads with a wide range of thickness, from more than 50 layers all the way down to a monolayer, exhibit robust nanomechanical vibrations with fundamental-mode frequency f0 up to >70 MHz in the very high frequency (VHF) band, a displacement noise density down to 52 fm/Hz1/2, and a fundamental-mode frequency-quality factor product up to f0 × Q ≈ 6.85 × 109 Hz. By combining experimental results with theoretical calculations, we independently derive the Young's modulus of 2D Ti3C2Tx crystals to be 270-360 GPa, in excellent agreement with nanoindentation measurements, based on which we elucidate frequency scaling pathways toward microwave frequencies. We further demonstrate electrical tuning of resonance frequency in MXene resonators and frequency-shift-based MXene vacuum gauges with responsivity of 736%/Torr and detection range down to 10-4 Torr. Our study can lead to the design and creation of nanoscale vibratory devices that exploit the intrinsic electrical and mechanical properties in 2D MXene crystals.