Materials for electronically controllable microactuators.

Abstract: Electronically controllable actuators have shrunk to remarkably small dimensions, thanks to recent advances in materials science. Currently, multiple classes of actuators can operate at the micron scale, be patterned using lithographic techniques, and be driven by complementary metal oxide semiconductor (CMOS)-compatible voltages, enabling new technologies, including digitally controlled micro-cilia, cell-sized origami structures, and autonomous microrobots controlled by onboard semiconductor electronics. This field is poised to grow, as many of these actuator technologies are the firsts of their kind and much of the underlying design space remains unexplored. To help map the current state of the art and set goals for the future, here, we overview existing work and examine how key figures of merit for actuation at the microscale, including force output, response time, power consumption, efficiency, and durability are fundamentally intertwined. In doing so, we find performance limits and tradeoffs for different classes of microactuators based on the coupling mechanism between electrical energy, chemical energy, and mechanical work. These limits both point to future goals for actuator development and signal promising applications for these actuators in sophisticated electronically integrated microrobotic systems.

Transduction of Single Nanomechanical Pillar Resonators by Scattering of Surface Acoustic Waves.

One of the challenges of nanoelectromechanical systems (NEMS) is the effective transduction of the tiny resonators. Vertical structures, such as nanomechanical pillar resonators, which are exploited in optomechanics, acoustic metamaterials, and nanomechanical sensing, are particularly challenging to transduce. Existing electromechanical transduction methods are ill-suited as they put constraints on the pillars' material and do not enable a transduction of freestanding pillars. Here, we present an electromechanical transduction method for single nanomechanical pillar resonators based on surface acoustic waves (SAWs). We demonstrate the transduction of freestanding nanomechanical platinum-carbon pillars in the first-order bending and compression mode. Since the principle of the transduction method is based on resonant scattering of a SAW by a nanomechanical resonator, our transduction method is independent of the pillar's material and not limited to pillar-shaped geometries. It represents a general method to transduce vertical mechanical resonators with nanoscale lateral dimensions.

Symmetry-Breaking-Induced Frequency Combs in Graphene Resonators.

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

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.

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

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

High Dynamic Range Nanowire Resonators.

Dynamic range quantifies the linear operation regime available in nanomechanical resonators. Nonlinearities dominate the response of flexural beams in the limit of very high aspect ratio and very small diameter, which leads to expectation of low dynamic range for nanowire resonators in general. However, the highest achievable dynamic range for nanowire resonators with practical dimensions remains to be determined. We report dynamic range measurements on singly clamped silicon nanowire resonators reaching remarkably high values of up to 90 dB obtained with a simple harmonic actuation scheme. We explain these measurements by a comprehensive theoretical examination of dynamic range in singly clamped flexural beams including the effect of tapering, a usual feature of semiconductor nanowires. Our analysis reveals the nanowire characteristics required for broad linear operation, and given the relationship between dynamic range and mass sensing performance, it also enables analytical determination of mass detection limits, reaching atomic-scale resolution for feasible nanowires.

Optical Transduction for Vertical Nanowire Resonators.

We describe an optical transduction mechanism to measure the flexural mode vibrations of vertically aligned nanowires on a flat substrate with high sensitivity, linearity, and ease of implementation. We demonstrate that the light reflected from the substrate when a laser beam strikes it parallel to the nanowires is modulated proportionally to their vibration, so that measuring such modulation provides a highly efficient resonance readout. This mechanism is applicable to single nanowires or arrays without specific requirements regarding their geometry or array pattern, and no fabrication process besides the nanowire generation is required. We show how to optimize the performance of this mechanism by characterizing the split flexural modes of vertical silicon nanowires in their full dynamic range and up to the fifth mode order. The presented transduction approach is relevant for any application of nanowire resonators, particularly for integrating nanomechanical sensing in functional substrates based on vertical nanowires for biological applications.

Electrothermally Tunable Graphene Resonators Operating at Very High Temperature up to 1200 K.

The unique negative thermal expansion coefficient and remarkable thermal stability of graphene make it an ideal candidate for nanoelectromechanical systems (NEMS) with electrothermal tuning. We report on the first experimental demonstration of electrothermally tuned single- and few-layer graphene NEMS resonators operating in the high frequency (HF) and very high frequency (VHF) bands. In single-, bi-, and trilayer (1L, 2L, and 3L) graphene resonators with carefully controlled Joule heating, we have demonstrated remarkably broad frequency tuning up to Δ f/ f0 ≈ 310%. Simultaneously, device temperature variations imposed by Joule heating are monitored using Raman spectroscopy; we find that the device temperature increases from 300 K up to 1200 K, which is the highest operating temperature known to date for electromechanical resonators. Using the measured frequency and temperature variations, we further extract both thermal expansion coefficients and thermal conductivities of these devices. Comparison with graphene electrostatic gate tuning indicates that electrothermal tuning is more efficient. The results clearly suggest that the unique negative thermal expansion coefficient of graphene and its excellent tolerance to very high temperature can be exploited for engineering highly tunable and robust graphene transducers for harsh and extreme environments.

Torsional Resonators Based on Inorganic Nanotubes.

We study for the first time the resonant torsional behaviors of inorganic nanotubes, specifically tungsten disulfide (WS2) and boron nitride (BN) nanotubes, and compare them to that of carbon nanotubes. We have found WS2 nanotubes to have the highest quality factor (Q) and torsional resonance frequency, followed by BN nanotubes and carbon nanotubes. Dynamic and static torsional spring constants of the various nanotubes were found to be different, especially in the case of WS2, possibly due to a velocity-dependent intershell friction. These results indicate that inorganic nanotubes are promising building blocks for high-Q nanoelectromechanical systems (NEMS).

Temperature-Dependent Adhesion of Graphene Suspended on a Trench.

Graphene deposited over a trench has been studied in the context of nanomechanical resonators, where experiments indicate adhesion of the graphene sheet to the trench boundary and sidewalls leads to self-tensioning; however, this adhesion is not well understood. We use molecular dynamics to simulate graphene deposited on a trench and study how adhesion to the sidewalls depends on substrate interaction, temperature, and curvature of the edge of the trench. Over the range of parameters we study, the depth at the center of the sheet is approximately linear in substrate interaction strength and temperature but not trench width, and we explain this using a one-dimensional model for the sheet configuration.

Graphene Squeeze-Film Pressure Sensors.

The operating principle of squeeze-film pressure sensors is based on the pressure dependence of a membrane's resonance frequency, caused by the compression of the surrounding gas which changes the resonator stiffness. To realize such sensors, not only strong and flexible membranes are required, but also minimization of the membrane's mass is essential to maximize responsivity. Here, we demonstrate the use of a few-layer graphene membrane as a squeeze-film pressure sensor. A clear pressure dependence of the membrane's resonant frequency is observed, with a frequency shift of 4 MHz between 8 and 1000 mbar. The sensor shows a reproducible response and no hysteresis. The measured responsivity of the device is 9000 Hz/mbar, which is a factor 45 higher than state-of-the-art MEMS-based squeeze-film pressure sensors while using a 25 times smaller membrane area.

Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy.

Black phosphorus (P) has emerged as a layered semiconductor with a unique crystal structure featuring corrugated atomic layers and strong in-plane anisotropy in its physical properties. Here, we demonstrate that the crystal orientation and mechanical anisotropy in free-standing black P thin layers can be precisely determined by spatially resolved multimode nanomechanical resonances. This offers a new means for resolving important crystal orientation and anisotropy in black P device platforms in situ beyond conventional optical and electrical calibration techniques. Furthermore, we show that electrostatic-gating-induced straining can continuously tune the mechanical anisotropic effects on multimode resonances in black P electromechanical devices. Combined with finite element modeling (FEM), we also determine the Young's moduli of multilayer black P to be 116.1 and 46.5 GPa in the zigzag and armchair directions, respectively.

Electromechanically Tunable Suspended Optical Nanoantenna.

Coupling mechanical degrees of freedom with plasmonic resonances has potential applications in optomechanics, sensing, and active plasmonics. Here we demonstrate a suspended two-wire plasmonic nanoantenna acting like a nanoelectrometer. The antenna wires are supported and electrically connected via thin leads without disturbing the antenna resonance. As a voltage is applied, equal charges are induced on both antenna wires. The resulting equilibrium between the repulsive Coulomb force and the restoring elastic bending force enables us to precisely control the gap size. As a result the resonance wavelength and the field enhancement of the suspended optical nanoantenna can be reversibly tuned. Our experiments highlight the potential to realize large bandwidth optical nanoelectromechanical systems.

Pathway to the piezoelectronic transduction logic device.

The piezoelectronic transistor (PET) has been proposed as a transduction device not subject to the voltage limits of field-effect transistors. The PET transduces voltage to stress, activating a facile insulator-metal transition, thereby achieving multigigahertz switching speeds, as predicted by modeling, at lower power than the comparable generation field effect transistor (FET). Here, the fabrication and measurement of the first physical PET devices are reported, showing both on/off switching and cycling. The results demonstrate the realization of a stress-based transduction principle, representing the early steps on a developmental pathway to PET technology with potential to contribute to the IT industry.

Switchable Coupling of Vibrations to Two-Electron Carbon-Nanotube Quantum Dot States.

We report transport measurements on a quantum dot in a partly suspended carbon nanotube. Electrostatic tuning allows us to modify and even switch "on" and "off" the coupling to the quantized stretching vibration across several charge states. The magnetic-field dependence indicates that only the two-electron spin-triplet excited state couples to the mechanical motion, indicating mechanical coupling to both the valley degree of freedom and the exchange interaction, in contrast to standard models.

BCN nanotubes as highly sensitive torsional electromechanical transducers.

Owing to their mechanically tunable electronic properties, carbon nanotubes (CNTs) have been widely studied as potential components for nanoelectromechanical systems (NEMS); however, the mechanical properties of multiwall CNTs are often limited by the weak shear interactions between the graphitic layers. Boron nitride nanotubes (BNNTs) exhibit a strong interlayer mechanical coupling, but their high electrical resistance limits their use as electromechanical transducers. Can the outstanding mechanical properties of BNNTs be combined with the electromechanical properties of CNTs in one hybrid structure? Here, we report the first experimental study of boron carbonitride nanotube (BCNNT) mechanics and electromechanics. We found that the hybrid BCNNTs are up to five times torsionally stiffer and stronger than CNTs, thereby retaining to a large extent the ultrahigh torsional stiffness of BNNTs. At the same time, we show that the electrical response of BCNNTs to torsion is 1 to 2 orders of magnitude higher than that of CNTs. These results demonstrate that BCNNTs could be especially attractive building blocks for NEMS.

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 Sensing for Mass Flow Control in Nanowire-Based Open Nanofluidic Systems.

Open nanofluidic systems, where liquids flow along the outer surface of nanoscale structures, provide otherwise unfeasible capabilities for extremely miniaturized liquid handling applications. A critical step toward fully functional applications is to obtain quantitative mass flow control. We demonstrate the application of nanomechanical sensing for this purpose by integrating voltage-driven liquid flow along nanowire open channels with mass detection based on flexural resonators. This approach is validated by assembling the nanowires with microcantilever resonators, enabling high-precision control of larger flows, and by using the nanowires as resonators themselves, allowing extremely small liquid volume handling. Both implementations are demonstrated by characterizing voltage-driven flow of ionic liquids along the surface of the nanowires. We find a voltage range where mass flow rate follows a nonlinear monotonic increase, establishing a steady flow regime for which we show mass flow control at rates from below 1 ag/s to above 100 fg/s and precise liquid handling down to the zeptoliter scale. The observed behavior of mass flow rate is consistent with a voltage-induced transition from static wetting to dynamic spreading as the mechanism underlying liquid transport along the nanowires.

Light-Induced Anisotropic Morphological Dynamics of Black Phosphorus Membranes Visualized by Dark-Field Ultrafast Electron Microscopy.

Black phosphorus (BP) is an elemental layered material with a strong in-plane anisotropic structure. This structure is accompanied by anisotropic optical, electrical, thermal, and mechanical properties. Despite interest in BP from both fundamental and technical aspects, investigation into the structural dynamics of BP caused by strain fields, which are prevalent for two-dimensional (2D) materials and tune the material physical properties, has been overlooked. Here, we report the morphological dynamics of photoexcited BP membranes observed using time-resolved diffractograms and dark-field images obtained via ultrafast electron microscopy. Aided by 4D reconstruction, we visualize the nonequilibrium bulging of thin BP membranes and reveal that the buckling transition is driven by impulsive thermal stress upon photoexcitation in real time. The bulging, buckling, and flattening (on strain release) showed anisotropic spatiotemporal behavior. Our observations offer insights into the fleeting morphology of anisotropic 2D matter and provide a glimpse into the mapping of transient, modulated physical properties upon impulsive excitation, as well as strain engineering at the nanoscale.

Highly Anisotropic Mechanical and Optical Properties of 2D Layered As2S3 Membranes.

Two-dimensional (2D) materials with strong in-plane anisotropy are of interest for enabling orientation-dependent, frequency-tunable, optomechanical devices. However, black phosphorus (bP), the 2D material with the largest anisotropy to date, is unstable as it degrades in air. In this work we show that As2S3 is an interesting alternative, with a similar anisotropy to bP, while at the same time having a much higher chemical stability. We probe the mechanical and optical anisotropy in As2S3 by three distinct angular-resolved experimental methods: Raman spectroscopy, atomic force microscopy (AFM), and resonance frequency analysis. Using a dedicated angle-resolved AFM force-deflection method, an in-plane anisotropy factor of [Formula: see text] is found in the Young's modulus of As2S3 with Ea-axis = 79.1 ± 10.1 GPa and Ec-axis = 47.2 ± 7.9 GPa. The high mechanical anisotropy is also shown to cause up to 65% difference in the resonance frequency, depending on crystal orientation and aspect ratio of membranes.