Nanoelectromechanical Systems Resonators Research Articles

Strain-enhanced dynamic ranges in two-dimensional MoS2 and MoTe2 nanomechanical resonators

Two-dimensional (2D) materials are promising for atomic-scale, ultralow-power, and highly tunable resonant nanoelectromechanical systems (NEMS) in sensing, communications, and computing. Toward these applications, a broad and controllable linear dynamic range (DR) is desirable for increasing the signal-to-noise ratio (SNR) and reliability. Here, we develop a comprehensive strain-enhanced DR model for 2D NEMS resonators, which is experimentally verified through the tuning of DRs in 2D molybdenum disulfide (MoS2) and molybdenum ditelluride (MoTe2) NEMS resonators using gate-induced strain. We find that the resonance frequency, quality factor, and nonlinear coefficient are all tuned by the gate voltage, which enhance the DR together. Through the guidance of the DR tuning model, we demonstrate DR enhancement by up to 26.9 dB (from 69.5 to 96.4 dB) in a 2D MoS2 NEMS resonator by properly tuning the gate voltage, leading to a theoretical mass resolution of 26 yg (1 yg = 10−24 g). To accurately extract the DR, we further differentiate the quality factors for thermomechanical resonances and for resonances at the largest linear amplitude. This gate-enhanced DR model is also verified using a MoTe2 resonator, with DR enhancement of 7 dB (91.2 to 98.2 dB). The results provide a promising pathway for accurately predicting and optimizing the DRs in NEMS resonators, toward enhanced sensitivity and SNR in mass sensing, radio frequency signal processing, memory, and computing applications.

Toward practical mass spectrometry with nanomechanical pillar resonators by surface acoustic wave transduction

Nanoelectromechanical systems (NEMS) have shown outstanding performance in the detection of small masses down to single proton sensitivity. To obtain a high enough throughput for application in practical mass spectrometry, NEMS resonators are arranged in two-dimensional (2D) arrays. However, all state-of-the-art electromechanical transduction methods rely on electrical lines placed close to the mechanical resonators, which drastically restricts the density of 2D resonator arrays. An exception is the transduction by surface acoustic waves (SAWs), which has so far only been shown for the transduction of single nanomechanical pillar resonators. Here, we demonstrate the transduction of pillar pairs by SAWs. The pillars have a diameter of 700 nm and show a mass responsivity of −588 ± 98 ng−1. The distances between the pillar pairs are 70 nm and 14.3 µm. SAW transduction enabled us to measure both pillars of each pair with electrical lines no closer than 300 µm, illustrating the potential of SAWs to transduce dense arrays of pillar resonators, a crucial step toward practical mass spectrometry with NEMS.

Resonant Transducers Consisting of Graphene Ribbons with Attached Proof Masses for NEMS Sensors.

The unique mechanical and electrical properties of graphene make it an exciting material for nanoelectromechanical systems (NEMS). NEMS resonators with graphene springs facilitate studies of graphene's fundamental material characteristics and thus enable innovative device concepts for applications such as sensors. Here, we demonstrate resonant transducers with ribbon-springs made of double-layer graphene and proof masses made of silicon and study their nonlinear mechanics at resonance both in air and in vacuum by laser Doppler vibrometry. Surprisingly, we observe spring-stiffening and spring-softening at resonance, depending on the graphene spring designs. The measured quality factors of the resonators in a vacuum are between 150 and 350. These results pave the way for a class of ultraminiaturized nanomechanical sensors such as accelerometers by contributing to the understanding of the dynamics of transducers based on graphene ribbons with an attached proof mass.

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.

Dynamics of NEMS resonators across dissipation limits

The oscillatory dynamics of nanoelectromechanical systems (NEMS) is at the heart of many emerging applications in nanotechnology. For common NEMS, such as beams and strings, the oscillatory dynamics is formulated using a dissipationless wave equation derived from elasticity. Under a harmonic ansatz, the wave equation gives an undamped free vibration equation; solving this equation with the proper boundary conditions provides the undamped eigenfunctions with the familiar standing wave patterns. Any harmonically driven solution is expressible in terms of these undamped eigenfunctions. Here, we show that this formalism becomes inconvenient as dissipation increases. To this end, we experimentally map out the position- and frequency-dependent oscillatory motion of a NEMS string resonator driven linearly by a non-symmetric force at one end at different dissipation limits. At low dissipation (high Q factor), we observe sharp resonances with standing wave patterns that closely match the eigenfunctions of an undamped string. With a slight increase in dissipation, the standing wave patterns become lost, and waves begin to propagate along the nanostructure. At large dissipation (low Q factor), these propagating waves become strongly attenuated and display little, if any, resemblance to the undamped string eigenfunctions. A more efficient and intuitive description of the oscillatory dynamics of a NEMS resonator can be obtained by superposition of waves propagating along the nanostructure.

Raman Spectroscopic Probe for Nonlinear MoS2 Nanoelectromechanical Resonators.

Resonant nanoelectromechanical systems (NEMS) enabled by two-dimensional (2D) semiconductors have been actively explored and engineered for making ultrascaled transducers toward applications in ultralow-power signal processing, communication, and sensing. Although the transduction of miniscule resonant motions has been achieved by low-noise optical or electronic techniques, direct probing of strain in vibrating 2D semiconductor membranes and the interplay between the spectroscopic and mechanical properties are still largely unexplored. Here, we experimentally demonstrate dynamical phonon softening in atomically thin molybdenum disulfide (MoS2) NEMS resonators by directly coupling Raman spectroscopy with optical interferometry resonance motion detection. In single-layer, bilayer, and trilayer (1L to 3L) MoS2 circular membrane NEMS resonators, we show that high-amplitude nonlinear resonances can enhance the Raman signal amplitude, as well as introduce Raman modes softening up to 0.8 cm-1. These results shall pave the way for engineering the coupling and control between collective mechanical vibrations and Raman modes of the constituent crystals in 2D transducers.

Physical Foundations of Subatomic Attosecond Quantum Technologies for Storing Energy in Materials

The article discusses the current development of physical principles of subatomic quantum technologies using ultrashort attosecond energy pulses within the ranges of deep-UV and soft X-ray radiation. It is necessary as a foundation of the process of nondestructive high-capacity reverse energy harvesting using accumulating nanoelectromechanical systems (NEMS) of supra-atomic scale with linear dimensions of 0.1 nm up to 10 nm and subatomic thickness of boundary interfaces up to 0.1 nm. The article compares the physical principles of up-to-date femtosecond quantum technologies and the prospective attosecond quantum technologies. The latter aims to improve the capacity, controllability, and performance efficiency of quantum energy storages by utilizing quantum electronic excitations of hybrid nature. Harder and shorter by one or two orders of magnitude UV and X-ray impulses are required for attosecond energy storages, unlike the femtosecond ones. Quantum femtochemistry describes the reactions caused by optical spectrum radiation pulses. In the case of attosecond pulses, highly excited quantum entangled subatomic electron pairs demonstrate nonlinear energy pulse accumulation effects. Goldstone condensates of bosonic electron pairs produce boundary shells of compact cavities of a quantum-size NEMS resonator. Hybrid electronic excitations of NEMS are a specific feature of the nonlinear quantum subatomic response of materials to attosecond deep-UV and soft X-ray pulses. The attosecond physics of the processes is the basis for the development of new subatomic attosecond quantum technologies for storing energy in materials.

Strain-Modulated Dissipation in Two-Dimensional Molybdenum Disulfide Nanoelectromechanical Resonators.

Resonant nanoelectromechanical systems (NEMS) based on two-dimensional (2D) materials such as molybdenum disulfide (MoS2) are interesting for highly sensitive mass, force, photon, or inertial transducers, as well as for fundamental research approaching the quantum limit, by leveraging the mechanical degree of freedom in these atomically thin materials. For these mechanical resonators, the quality factor (Q) is essential, yet the mechanism and tuning methods for energy dissipation in 2D NEMS resonators have not been fully explored. Here, we demonstrate that by tuning static strain and vibration-induced strain in suspended MoS2 using gate voltages, we can effectively tune the Q in 2D MoS2 NEMS resonators. We further show that for doubly clamped resonators, the Q increases with larger DC gate voltage, while fully clamped drumhead resonators show the opposite trend. Using DC gate voltages, we can tune the Q by ΔQ/Q = 448% for fully clamped resonators, and by ΔQ/Q = 369% for doubly clamped resonators. We develop the strain-modulated dissipation model for these 2D NEMS resonators, which is verified against our measurement data for 8 fully clamped resonators and 7 doubly clamped resonators. We find that static tensile strain decreases dissipation while vibration-induced strain increases dissipation, and the actual dependence of Q on DC gate voltage depends on the competition between these two effects, which is related to the device boundary condition. Such strain dependence of Q is useful for optimizing the resonance linewidth in 2D NEMS resonators toward low-power, ultrasensitive, and frequency-selective devices for sensing and signal processing.

Giant parametric amplification and spectral narrowing in atomically thin MoS2 nanomechanical resonators

Pre-amplification of ultrasmall signals directly in the mechanical domain and boosting quality (Q) factors in nanoelectromechanical systems (NEMS) are intriguing scientific questions and technical challenges. These are particularly enticing in resonant NEMS enabled by emerging two-dimensional (2D) layered crystals, toward revealing fundamental limits and potential of 2D NEMS in both science explorations and engineering applications. Fortunately, their ultimately thin nature and unconventional elastic properties offer rich opportunities for manipulating oscillations via parametric and nonlinear effects. Here, we report on the experimental demonstration of giant parametric amplification and spectral linewidth narrowing in atomically thin molybdenum disulfide (MoS2) 2D NEMS resonators vibrating at ∼30–60 MHz. Parametric amplification is examined by photothermally modulating the stiffness of each atomic layer resonator at twice its resonance frequency (2f). Thanks to exceptionally efficient parametric effects in these atomically thin membranes, the parametric amplification of undriven thermomechanical resonance leads to giant parametric gains up to 3605 (71 dB) and spectral linewidth narrowing factors up to 1.8 × 105, before the onset of parametric oscillation. The remarkable parametric amplification and spectral narrowing (including effective Q boosting in the sub-threshold regime) in 2D NEMS validated in this study may open new possibilities for creating ultimately thin yet high-performance resonators and oscillators for signal transduction and sensing in classical and quantum engineering applications.

Atmospheric Pressure Mass Spectrometry of Single Viruses and Nanoparticles by Nanoelectromechanical Systems.

Mass spectrometry of intact nanoparticles and viruses can serve as a potent characterization tool for material science and biophysics. Inaccessible by widespread commercial techniques, the mass of single nanoparticles and viruses (>10MDa) can be readily measured by nanoelectromechanical systems (NEMS)-based mass spectrometry, where charged and isolated analyte particles are generated by electrospray ionization (ESI) in air and transported onto the NEMS resonator for capture and detection. However, the applicability of NEMS as a practical solution is hindered by their miniscule surface area, which results in poor limit-of-detection and low capture efficiency values. Another hindrance is the necessity to house the NEMS inside complex vacuum systems, which is required in part to focus analytes toward the miniscule detection surface of the NEMS. Here, we overcome both limitations by integrating an ion lens onto the NEMS chip. The ion lens is composed of a polymer layer, which charges up by receiving part of the ions incoming from the ESI tip and consequently starts to focus the analytes toward an open window aligned with the active area of the NEMS electrostatically. With this integrated system, we have detected the mass of gold and polystyrene nanoparticles under ambient conditions and with two orders-of-magnitude improvement in capture efficiency compared to the state-of-the-art. We then applied this technology to obtain the mass spectrum of SARS-CoV-2 and BoHV-1 virions. With the increase in analytical throughput, the simplicity of the overall setup, and the operation capability under ambient conditions, the technique demonstrates that NEMS mass spectrometry can be deployed for mass detection of engineered nanoparticles and biological samples efficiently.

Design of strongly nonlinear graphene nanoelectromechanical systems in quantum regime

We report on the analysis and design of atomically thin graphene resonant nanoelectromechanical systems (NEMS) that can be engineered to exhibit anharmonicity in the quantum regime. Analysis of graphene two-dimensional (2D) NEMS resonators suggests that with device lateral size scaled down to ∼10–30 nm, restoring force due to the third-order (Duffing) stiffness in graphene NEMS can rise to equal or even exceed the force of linear stiffness, enabling strongly nonlinear NEMS resonators with anharmonic potential energy that produces sufficient deviation from a quantum harmonic spectrum, which is necessary toward realizing NEMS qubits. Furthermore, the calculations provide device design guidelines and scaling of anharmonicity in graphene NEMS to facilitate future fabrication of graphene NEMS qubits with the desired nonlinear dynamical characteristics and performance. The results in this work shall help open possibilities for engineering a new type of qubits based on 2D resonant NEMS, which may offer a much more miniaturized, densely packed, and scalable qubit platform, supplementing today's mainstream technologies such as superconducting and trapped ion qubits.

A cantilever-based resonator for reconfigurable nanomechanical computing

As silicon transistors face challenges in scaling, nanoelectromechanical systems (NEMS) have emerged as a promising candidate for computing due to the ultralow power consumption and high-temperature compatibility. Yet there is still limited research about highly reconfigurable NEMS-based computing devices that integrate multiple functionalities into a single device. In this work, we present the design, simulation, and verification of a cantilever-based NEMS resonator for highly reconfigurable logic functions. Using a single resonator with multiple inputs, the device can be reconfigured to perform AND, OR, XOR, and NOT logic operations, by changing the combination of inputs. We use both DC and AC voltages as inputs, where AC inputs can be used for better reconfigurability, and DC inputs offer higher On/Off ratio. The cantilever structure has low rigidity and large dynamic range, and thus only requires 5 mV of AC drive to achieve relatively large vibration amplitude. This work presents a unique platform where a single NEMS resonator can be used for reconfigurable computing.

Nanoelectromechanical Systems: Straining and Tuning Atomic Layer Nanoelectromechanical Resonators via Comb‐Drive MEMS Actuators (Adv. Mater. Technol. 2/2021)

In article number 2000794, Yong Xie, Philip X.-L. Feng, and co-workers demonstrate the additive and heterogeneous integration of 2D nanoelectromechanical systems (NEMS) onto micro actuators made of mainstream silicon-on-insulator (SOI) comb-drive microelectromechanical systems (MEMS), across several orders of magnitude in length scale, thus enabling a chip-scale platform for strain engineering of 2D crystals, and for broad frequency tuning and quality (Q) factor enhancement in atomically thin NEMS resonators.

Thermal hysteresis controlled reconfigurable MoS2 nanomechanical resonators.

Two-dimensional (2D) structures from layered materials have enabled a number of novel devices including resonant nanoelectromechanical systems (NEMS). 2D NEMS resonators are highly responsive to strain, allowing their resonance frequencies to be efficiently tuned over broad ranges, which is a feature difficult to attain in conventional micromachined resonators. In electrically configured and tuned devices, high external voltages are typically required to set and maintain different frequencies, limiting their applications. Here we experimentally demonstrate molybdenum disulfide (MoS2) nanomechanical resonators that can be reconfigured between different frequency bands with zero maintaining voltage in a non-volatile fashion. By leveraging the thermal hysteresis in these 2D resonators, we use heating and cooling pulses to reconfigure the device frequency, with no external voltage required to maintain each frequency. We further show that the frequency spacing between the bands can be tuned by the thermal pulse strength, offering full control over the programmable operation. Such reconfigurable MoS2 resonators may provide an alternative pathway toward small-form-factor and low-power tunable devices in future reconfigurable radio-frequency circuits with multi-band capability.

A system for probing Casimir energy corrections to the condensation energy

In this article, we present a nanoelectromechanical system (NEMS) designed to detect changes in the Casimir energy. The Casimir effect is a result of the appearance of quantum fluctuations in an electromagnetic vacuum. Previous experiments have used nano- or microscale parallel plate capacitors to detect the Casimir force by measuring the small attractive force these fluctuations exert between the two surfaces. In this new set of experiments, we aim to directly detect the shifts in the Casimir energy in a vacuum due to the presence of the metallic parallel plates, one of which is a superconductor. A change in the Casimir energy of this configuration is predicted to shift the superconducting transition temperature (Tc) because of the interaction between it and the superconducting condensation energy. In our experiment, we take a superconducting film, carefully measure its transition temperature, bring a conducting plate close to the film, create a Casimir cavity, and then measure the transition temperature again. The expected shifts are smaller than the normal shifts one sees in cycling superconducting films to cryogenic temperatures, so using a NEMS resonator in situ is the only practical way to obtain accurate, reproducible data. Using a thin Pb film and opposing Au surface, we observe no shift in Tc >12 µK down to a minimum spacing of ~70 nm at zero applied magnetic field.

Nonlinear forced vibration of bilayer van der Waals materials drum resonator

The interlayer shear effect could play a crucial role in the dynamic behaviors of the nanoelectromechanical system (NEMS) resonators based on multilayer van der Waals (vdW) materials. However, the interlayer shear effect is rarely considered in the nonlinear forced vibrations of this kind of resonators. In this study, the nonlinear static and dynamics behaviors of drum resonators based on double layer MoS2 (DLMoS2) are investigated using molecular dynamics simulations and a nonlinear circular sandwich plate model (NCSPM), respectively. The interlayer shear effect and the geometrical nonlinearity are systematically considered in the NCSPM. Our results show that comparing with drum resonators based on single layer MoS2 (SLMoS2), the DLMoS2 drum resonators exhibit higher fundamental frequency. The load–deflection curve of DLMoS2 shows clear hardening-type nonlinearity, and the deflections of DLMoS2 are smaller than that of SLMoS2 under the same uniform load per layer. In particular, both frequency sweep excitation simulations and the NCSPM show that the hardening-type nonlinearity of the DLMoS2 drum resonators is largely reduced due to the interlayer shear effect. Furthermore, DLMoS2 with different twist angle exhibits different interlayer shear strengths; thus, the nonlinear characteristic could be controlled by changing the twist angles in the DLMoS2 drum resonators. The present study should be of great help for designing NEMS resonators based on such vdW materials.

Resonant nano-electromechanical systems from 2D materials

Intriguing mechanical properties of two-dimensional (2D) atomically thin materials make them well suit for a new class of resonant NEMS. Resonant 2D NEMS show high fundamental frequencies, outstanding tenability and broad dynamic range due to the ultrahigh strength, ultralow mass density and ultrahigh strain stretchability. Recent work toward exploring fabrication and transduction techniques, device performances and the nonlinear dynamic characteristics of 2D NEMS are summed up. Nonlinear dynamic behaviors including nonlinear mode coupling, nonlinear damping and nonlinear pull-in instability are reported in 2D NEMS.

Performance of Nano-Electromechanical Systems as Nanoparticle Position Sensors

Nanoelectromechanical systems (NEMS) have been utilized as sensitive mass sensors in many applications such as single cell characterization, volatile organic biomarker detection and single molecule mass spectrometry. Using the frequency shift detection, mass of single analytes can be resolved. Mass detection sensitivity can be further improved by accurate measurement of the position, unlocking extra capabilities in nanoscale positioning and manipulation applications. Here, we studied the position sensing performance of two-mode NEMS resonators during detection of single 20 nm gold nanoparticles (GNPs). By recording the position of each particle with frequency shift sensing, the position detection accuracy was evaluated for different beam models and the results are validated by SEM imaging Our results indicate that the position sensing accuracy, and therefore the mass sensing accuracy, of nanomechanical resonators depends critically on the use of appropriate beam models.

Electromagnetic Metrology for Nano- Electromechanical Systems

This paper outlines how demands on electromagnetic metrology have developed over recent years with the continuing reduction in the typical length scale of electronic components and circuits. In addition, novel materials, especially 2-D self-supporting structures such as graphene, have properties quite unlike the conventional systems. At the nanoscale radical changes occur in techniques required and even in the physical quantities measured. This paper focusses on the example of a near-field scanning microwave microscope and its application to nano-electromechanical system resonators to illustrate these changes and challenge.

Multiplexed functionalization of nanoelectromechanical systems with photopatterned molecularly imprinted polymers

Implementing dedicated and reliable biochemical recognition functionalities onto nanoelectromechanical systems (NEMS) is of primary importance for their development as ultra-sensitive and highly-integrated biosensing devices. In this paper, we demonstrate the large-scale and multiplexed integration of molecularly imprinted polymers (MIPs) as highly stable biomimetic receptors onto arrays of nanocantilevers. Integration is carried out by spin-coating and photopatterning the polymer layers before releasing the nanostructures. We demonstrate that these biomimetic layers are robust enough to withstand the wet-etch of the sacrificial layer making this functionalization strategy compatible with further MEMS/NEMS processing. As a proof of concept, we fabricate NEMS resonators coated with a MIP using Boc-L-phenylalanine as the template molecule. We demonstrate the preserved molecular recognition ability of the patterned sensitive layer through the fluorescence detection of dansyl-L-phenylalanine, a fluorescent derivative of the template, and the mechanical integrity of the resonators by means of resonant frequency measurements.