Surface adsorbate fluctuations and noise in nanoelectromechanical systems

A Hybrid Orbitrap-Nanoelectromechanical Systems Approach for the Analysis of Individual, Intact Proteins in Real Time

Nanoelectromechanical systems (NEMS)-based mass spectrometry (MS) is an emerging technique that enables determination of the mass of individual adsorbed particles by driving nanomechanical devices at resonance and monitoring the real-time changes in their resonance frequencies induced by each single molecule adsorption event. We incorporate NEMS into an Orbitrap mass spectrometer and report our progress towards leveraging the single-molecule capabilities of the NEMS to enhance the dynamic range of conventional MS instrumentation and to offer new capabilities for performing deep proteomic analysis of clinically relevant samples. We use the hybrid instrument to deliver E. coli GroEL molecules (801 kDa) to the NEMS devices in their native, intact state. Custom ion optics are used to focus the beam down to 40 μm diameter with a maximum flux of 25 molecules/second. The mass spectrum obtained with NEMS-MS shows good agreement with the known mass of GroEL.

Graphene nano-electromechanical mass sensor with high resolution at room temperature

The inherent properties of 2D materials-light mass, high out-of-plane flexibility, and large surface area-promise great potential for precise and accurate nanomechanical mass sensing, but their application is often hampered by surface contamination. Here we demonstrate a tri-layer graphene nanomechanical resonant mass sensor with sub-attogram resolution at room temperature, fabricated by a bottom-up process. We found that Joule-heating is effective in cleaning the graphene membrane surface, which results in a large improvement in the stability of the resonance frequency. We characterized the sensor by depositing Cr metal using a stencil mask and found a mass-resolution that is sufficient to weigh very small particles, like large proteins and protein complexes, with potential applications in the fields of nanobiology and medicine.

Nanomechanical Resonators: Toward Atomic Scale

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

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.

Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators

We investigate the sideband spectra of a driven nonlinear mode with its eigenfrequency being modulated at a low frequency (<1  kHz). This additional parametric modulation leads to prominent antiresonance line shapes in the sideband spectra, which can be controlled through the vibration state of the driven mode. We also establish a direct connection between the antiresonance frequency and the squeezing of thermal fluctuation in the system. Our Letter not only provides a simple and robust method for squeezing characterization, but also opens a new possibility toward sideband applications.

Electrical Low-Frequency 1/fγ Noise Due to Surface Diffusion of Scatterers on an Ultra-low-Noise Graphene Platform

Low-frequency 1/f γ noise is ubiquitous, even in high-end electronic devices. Recently, it was found that adsorbed O2 molecules provide the dominant contribution to flux noise in superconducting quantum interference devices. To clarify the basic principles of such adsorbate noise, we have investigated low-frequency noise, while the mobility of surface adsorbates is varied by temperature. We measured low-frequency current noise in suspended monolayer graphene Corbino samples under the influence of adsorbed Ne atoms. Owing to the extremely small intrinsic noise of suspended graphene, we could resolve a combination of 1/f γ and Lorentzian noise induced by the presence of Ne. We find that the 1/f γ noise is caused by surface diffusion of Ne atoms and by temporary formation of few-Ne-atom clusters. Our results support the idea that clustering dynamics of defects is relevant for understanding of 1/f noise in metallic systems.

Interrelation of Elasticity and Thermal Bath in Nanotube Cantilevers

We report the first study on the thermal behavior of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope -(173±65)  ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative description based on the coupling between the measured mechanical modes and the phonon thermal bath in the Akhiezer limit is discussed.

Microcantilever: Dynamical Response for Mass Sensing and Fluid Characterization

A microcantilever is a suspended micro-scale beam structure supported at one end which can bend and/or vibrate when subjected to a load. Microcantilevers are one of the most fundamental miniaturized devices used in microelectromechanical systems and are ubiquitous in sensing, imaging, time reference, and biological/biomedical applications. They are typically built using micro and nanofabrication techniques derived from the microelectronics industry and can involve microelectronics-related materials, polymeric materials, and biological materials. This work presents a comprehensive review of the rich dynamical response of a microcantilever and how it has been used for measuring the mass and rheological properties of Newtonian/non-Newtonian fluids in real time, in ever-decreasing space and time scales, and with unprecedented resolution.

New Alternating Current Noise Analytics Enables High Discrimination in Gas Sensing

Feature analysis has been increasingly considered as an important way to enhance the discrimination performance of gas sensors. In this work, a new analytical method based on alternating current noise spectrum is developed to discriminate chemically and structurally similar gases with remarkable performance. Compared with the conventional analytics based on the maximum, integral, and time of response, the noise spectrum of electrical response introduces a new informative feature to discriminate chemical gases. In experiment, three chemically and structurally similar gases, mesitylene, toluene, and o-xylene, are tested on ZnO thin film gas sensors. The result indicated that the noise analytics assisted by the support vector machine algorithm discriminated these similar gases with 94.2% in precision, about 20% higher than those obtained by conventional methods. Such a new alternating current noise analytics is very promising for application in sensors for high discrimination precision.

Mass Sensing for the Advanced Fabrication of Nanomechanical Resonators

We report on a nanomechanical engineering method to monitor matter growth in real time via e-beam electromechanical coupling. This method relies on the exceptional mass sensing capabilities of nanomechanical resonators. Focused electron beam-induced deposition (FEBID) is employed to selectively grow platinum particles at the free end of singly clamped nanotube cantilevers. The electron beam has two functions: it allows both to grow material on the nanotube and to track in real time the deposited mass by probing the noise-driven mechanical resonance of the nanotube. On the one hand, this detection method is highly effective as it can resolve mass deposition with a resolution in the zeptogram range; on the other hand, this method is simple to use and readily available to a wide range of potential users because it can be operated in existing commercial FEBID systems without making any modification. The presented method allows one to engineer hybrid nanomechanical resonators with precisely tailored functionalities. It also appears as a new tool for studying the growth dynamics of ultrathin nanostructures, opening new opportunities for investigating so far out-of-reach physics of FEBID and related methods.

Measuring Frequency Fluctuations in Nonlinear Nanomechanical Resonators

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS₂ and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive to date. In this article we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly clamped beams, in a cryogenic environment. We report on the same T/ f dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected damping fluctuations, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure δ f/ f₀ lies in the range 0.5-0.01 ppm (consistent with the literature for cryogenic MHz devices) and decreases with mode number in the range studied. The technique can be applied to any type of nanomechanical structure, enabling progress toward the understanding of intrinsic sources of noise in these devices.

Pillared graphene as an ultra-high sensitivity mass sensor

Hybrid structure of graphene sheets supported by carbon nanotubes (CNTs) sustains unique properties of both graphene and CNTs, which enables the utilization of advantages of the two novel materials. In this work, the capability of three-dimensional pillared graphene structure used as nanomechanical sensors is investigated by performing molecular dynamics simulations. The obtained results demonstrate that: (a) the mass sensitivity of the pillared graphene structure is ultrahigh and can reach at least 1 yg (10⁻²⁴ g) with a mass responsivity 0.34 GHz · yg⁻¹; (b) the sizes of pillared graphene structure, particularly the distance between carbon nanotube pillars, have a significant effect on the sensing performance; (c) an analytical expression can be derived to detect the deposited mass from the resonant frequency of the pillared graphene structure. The performed analyses might be significant to future design and application of pillared graphene based sensors with high sensitivity and large detecting area.

Nano-Optomechanical Systems for Gas Chromatography

Microgas chromatography (GC) is promising for portable chemical analysis. We demonstrate a nano-optomechanical system (NOMS) as an ultrasensitive mass detector in gas chromatography. Bare, native oxide, silicon surfaces are sensitive enough to monitor volatile organic compounds at ppm levels, while simultaneously demonstrating chemical selectivity. The NOMS is able to sense GC peaks from derivatized metabolites at physiological concentrations. This is an important milestone for small-molecule quantitation assays in next generation metabolite analyses for applications such as disease diagnosis and personalized medicine. The optical microring, which plays an important role in the nanomechanical signal transduction mechanism, can also be used as an analyte concentration sensor. Different adsorption kinetics regimes are realized at different temperatures allowing temporary condensation of the analyte onto the sensor surfaces. This effect amplifies the signal, resulting in a 1 ppb level limit of detection, without partition enhancement from absorbing media. This sensitivity bodes well for NOMS as universal, ultrasensitive detectors in micro-GC, breath analysis, and other chemical-sensing applications.

Frequency fluctuations in silicon nanoresonators

Frequency stability is key to the performance of nanoresonators. This stability is thought to reach a limit with the resonator's ability to resolve thermally induced vibrations. Although measurements and predictions of resonator stability usually disregard fluctuations in the mechanical frequency response, these fluctuations have recently attracted considerable theoretical interest. However, their existence is very difficult to demonstrate experimentally. Here, through a literature review, we show that all studies of frequency stability report values several orders of magnitude larger than the limit imposed by thermomechanical noise. We studied a monocrystalline silicon nanoresonator at room temperature and found a similar discrepancy. We propose a new method to show that this was due to the presence of frequency fluctuations, of unexpected level. The fluctuations were not due to the instrumentation system, or to any other of the known sources investigated. These results challenge our current understanding of frequency fluctuations and call for a change in practices.

Devil's staircase in an optomechanical cavity

We study self-excited oscillations (SEOs) in an on-fiber optomechanical cavity. While the phase of SEOs randomly diffuses in time when the laser power injected into the cavity is kept constant, phase locking may occur when the laser power is periodically modulated in time. We investigate the dependence of phase locking on the amplitude and frequency of the laser-power modulation. We find that phase locking can be induced with a relatively low modulation amplitude provided that the ratio between the modulation frequency and the frequency of SEOs is tuned close to a rational number of relatively low hierarchy in the Farey tree. To account for the experimental results, a one-dimensional map, which allows evaluating the time evolution of the phase of SEOs, is theoretically derived. By calculating the winding number of the one-dimensional map, the regions of phase locking can be mapped in the plane of modulation amplitude and modulation frequency. Comparison between the theoretical predictions and the experimental findings yields a partial agreement.

Resonating Behaviour of Nanomachined Holed Microcantilevers

The nanofabrication of a nanomachined holed structure localized on the free end of a microcantilever is here presented, as a new tool to design micro-resonators with enhanced mass sensitivity. The proposed method allows both for the reduction of the sensor oscillating mass and the increment of the resonance frequency, without decreasing the active surface of the device. A theoretical analysis based on the Rayleigh method was developed to predict resonance frequency, effective mass, and effective stiffness of nanomachined holed microresonators. Analytical results were checked by Finite Element simulations, confirming an increase of the theoretical mass sensitivity up to 250%, without altering other figures of merit. The nanomachined holed resonators were vibrationally characterized, and their Q-factor resulted comparable with solid microcantilevers with same planar dimensions.

Tunable micro- and nanomechanical resonators

Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.

Synchronization in an optomechanical cavity

We study self-excited oscillations (SEO) in an on-fiber optomechanical cavity. Synchronization is observed when the optical power that is injected into the cavity is periodically modulated. A theoretical analysis based on the Fokker-Planck equation evaluates the expected phase space distribution (PSD) of the self-oscillating mechanical resonator. A tomography technique is employed for extracting PSD from the measured reflected optical power. Time-resolved state tomography measurements are performed to study phase diffusion and phase locking of the SEO. The detuning region inside which synchronization occurs is experimentally determined and the results are compared with the theoretical prediction.

Observation of decoherence in a carbon nanotube mechanical resonator

In physical systems, decoherence can arise from both dissipative and dephasing processes. In mechanical resonators, the driven frequency response measures a combination of both, whereas time-domain techniques such as ringdown measurements can separate the two. Here we report the first observation of the mechanical ringdown of a carbon nanotube mechanical resonator. Comparing the mechanical quality factor obtained from frequency- and time-domain measurements, we find a spectral quality factor four times smaller than that measured in ringdown, demonstrating dephasing-induced decoherence of the nanomechanical motion. This decoherence is seen to arise at high driving amplitudes, pointing to a nonlinear dephasing mechanism. Our results highlight the importance of time-domain techniques for understanding dissipation in nanomechanical resonators, and the relevance of decoherence mechanisms in nanotube mechanics.

Interplay of driving and frequency noise in the spectra of vibrational systems

We study the spectral effect of the fluctuations of the vibration frequency. Such fluctuations play a major role in nanomechanical and other mesoscopic vibrational systems. We find that, for periodically driven systems, the interplay of the driving and frequency fluctuations results in specific spectral features. We present measurements on a carbon nanotube resonator and show that our theory allows not only the characterization of the frequency fluctuations but also the quantification of the decay rate without ring-down measurements. The results bear on identifying the decoherence of mesoscopic oscillators and on the general problem of resonance fluorescence and light scattering by oscillators.

Spatial mapping of multimode Brownian motions in high-frequency silicon carbide microdisk resonators

High-order and multiple modes in high-frequency micro/nanomechanical resonators are attractive for empowering signal processing and sensing with multi-modalities, yet many challenges remain in identifying and manipulating these modes, and in developing constitutive materials and structures that efficiently support high-order modes. Here we demonstrate high-frequency multimode silicon carbide microdisk resonators and spatial mapping of the intrinsic Brownian thermomechanical vibrations, up to the ninth flexural mode, with displacement sensitivities of ~7-14 fm Hz(-1/2). The microdisks are made in a 500-nm-carbide on 500-nm-oxide thin-film technology that facilitates ultrasensitive motion detection via scanning laser interferometry with high spectral and spatial resolutions. Mapping of these thermomechanical vibrations vividly visualizes the shapes and textures of high-order Brownian motions in the microdisks. Measurements on devices with varying dimensions provide deterministic information for precisely identifying the mode sequence and characteristics, and for examining mode degeneracy, spatial asymmetry and other effects, which can be exploited for encoding information with increasing complexity.

Graphene-based nanoresonator with applications in optical transistor and mass sensing

Graphene has received significant attention due to its excellent properties currently. In this work, a nano-optomechanical system based on a doubly-clamped Z-shaped graphene nanoribbon (GNR) with an optical pump-probe scheme is proposed. We theoretically demonstrate the phenomenon of phonon-induced transparency and show an optical transistor in the system. In addition, the significantly enhanced nonlinear effect of the probe laser is also investigated, and we further put forward a nonlinear optical mass sensing that may be immune to detection noises. Molecules, such as NH₃ and NO₂, can be identified via using the nonlinear optical spectroscopy, which may be applied to environmental pollutant monitoring and trace chemical detection.

Harnessing vacuum forces for quantum sensing of graphene motion

Position measurements at the quantum level are vital for many applications but also challenging. Typically, methods based on optical phase shifts are used, but these methods are often weak and difficult to apply to many materials. An important example is graphene, which is an excellent mechanical resonator due to its small mass and an outstanding platform for nanotechnologies, but it is largely transparent. Here, we present a novel detection scheme based upon the strong, dispersive vacuum interactions between a graphene sheet and a quantum emitter. In particular, the mechanical displacement causes strong changes in the vacuum-induced shifts of the transition frequency of the emitter, which can be read out via optical fields. We show that this enables strong quantum squeezing of the graphene position on time scales that are short compared to the mechanical period.

Atomic monolayer deposition on the surface of nanotube mechanical resonators

We study monolayers of noble gas atoms (Xe, Kr, Ar, and Ne) deposited on individual ultraclean suspended nanotubes. For this, we record the resonance frequency of the mechanical motion of the nanotube, since it provides a direct measure of the coverage. The latter is the number of adsorbed atoms divided by the number of the carbon atoms of the suspended nanotube. Monolayers form when the temperature is lowered in a constant pressure of noble gas atoms. The coverage of Xe monolayers remains constant at 1/6 over a large temperature range. This finding reveals that Xe monolayers are solid phases with a triangular atomic arrangement, and are commensurate with the underlying carbon nanotube. By comparing our measurements to theoretical calculations, we identify the phases of Ar and Ne monolayers as fluids, and we tentatively describe Kr monolayers as solid phases. These results underscore that mechanical resonators made from single nanotubes are excellent probes for surface science.

Embracing structural nonidealities and asymmetries in two-dimensional nanomechanical resonators

Mechanical exfoliation is a convenient and effective approach to deriving two-dimensional (2D) nanodevices from layered materials; but it is also generally perceived as unpreferred as it often yields devices with structural irregularities and nonidealities. Here we show that such nonidealities can lead to new and engineerable features that should be embraced and exploited. We measure and analyze high frequency nanomechanical resonators based on exfoliated 2D molybdenum disulfide (MoS2) structures, and focus on investigating the effects of structural nonidealities and asymmetries on device characteristics and performance. In high and very high frequency (HF/VHF) vibrating MoS2 devices based on diaphragms of ~2-5 μm in size, structural nonidealities in shape, boundary, and geometric symmetry all appear not to compromise device performance, but lead to robust devices exhibiting new multimode resonances with characteristics that are inaccessible in their 'ideal' counterparts. These results reveal that the seemingly irregular and nonideal 2D structures can be exploited and engineered for new designs and functions.

Resolution enhancement of suspended microchannel resonators for weighing of biomolecular complexes in solution

We introduce the use of correlation analysis to extend the dynamic range of suspended micro- and nanochannel resonator (SMR/SNR) mass sensors by over five orders of magnitude. This method can analyze populations of particles flowing through an embedded channel micromechanical resonator, even when the individual particle masses are far below the noise floor. To characterize the method, we measured the mass of polystyrene nanoparticles with 300 zg resolution. As an application, we monitored the time course of insulin amyloid formation from pre-fibrillar aggregates to mature fibrils of 15 MDa average mass. Results were compared with thioflavin-T (ThT) assays and electron microscopy (EM). Mass measurements offer additional information over ThT during the fluorescent inaccessible lag period, and the average fibril dimensions calculated from the mass signal are in good accordance with EM. In the future, we envision that more detailed modeling will allow the computational deconvolution of multicomponent samples, enabling the mass spectrometric characterization of a variety of biomolecular complexes, small organelles, and nanoparticles in solution.

Complex dynamics in nanosystems

Complex dynamics associated with multistability have been studied extensively in the past but mostly for low-dimensional nonlinear dynamical systems. A question of fundamental interest is whether multistability can arise in high-dimensional physical systems. Motivated by the ever increasing widespread use of nanoscale systems, we investigate a prototypical class of nanoelectromechanical systems: electrostatically driven Si nanowires, mathematically described by a set of driven, nonlinear partial differential equations. We develop a computationally efficient algorithm to solve the equations. Our finding is that multistability and complicated structures of basins of attraction are common types of dynamics, and the latter can be attributed to extensive transient chaos. Implications of these phenomena to device operations are discussed.

Surpassing fundamental limits of oscillators using nonlinear resonators

In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonator's anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nanoelectromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator's phase noise, as predicted by our model.

Electromechanical resonator based on electrostatically actuated graphene-doped PVP nanofibers

In this paper we present experimental results describing electrical readout of the mechanical vibratory response of graphene-doped fibers by employing electrical actuation. For a fiber resonator with an approximate radius of 850 nm and length of 100 μm, we observed a resonance frequency around 580 kHz with a quality factor (Q) of about 2511 in air at ambient conditions. Through the use of finite element simulations, we show that the reported frequency of resonance is relevant. We also show that the resonance frequency of the fiber resonators decreases as the bias potential is increased due to the electrostatic spring-softening effect.

Design, implementation, and application of a microresonator platform for measuring energy dissipation by internal friction in nanowires

Accurate measurements of internal friction in nanowires are required for the rational design of high-Q resonators used in nanoelectromechanical systems and for fundamental studies of nanomechanical behavior. However, measuring internal friction is challenging because of the difficulties associated with identifying the contributions of material dissipation to structural damping. Here, we present an approach for overcoming these difficulties by using a composite microresonator platform that is calibrated against the ultimate limits of thermoelastic damping. The platform consists of an array of nanowires patterned at the root of a low-loss single-crystal silicon microcantilever. The structure is processed using a lift-off technique, implemented using electron-beam lithography, to achieve excellent control over the size, alignment, dispersion and location of the nanowire array. As the first application of this platform, we measured internal friction at room temperature in aluminum nanowires that ranged from 50 to 100 nm in thickness and 100 to 400 nm in width. Internal friction is ~0.03 at frequencies of 6.5-21 kHz. Transmission electron microscopy of the nanocrystalline grain structure, and comparison with previously measured values of internal friction in continuous thin films of aluminum, suggest that grain-boundary sliding is a major source of internal friction in these nanowires.

Beat phenomena in metal nanowires, and their implications for resonance-based elastic property measurements

The elastic properties of 1D nanostructures such as nanowires are often measured experimentally through actuation of nanowires at their resonance frequency, and then relating the resonance frequency to the elastic stiffness using the elementary beam theory. In the present work, we utilize large scale molecular dynamics simulations to report a novel beat phenomenon in [110] oriented Ag nanowires. The beat phenomenon is found to arise from the asymmetry of the lattice spacing in the orthogonal elementary directions of [110] nanowires, i.e. the [110] and [001] directions, which results in two different principal moments of inertia. Because of this, actuations imposed along any other direction are found to decompose into two orthogonal vibrational components based on the actuation angle relative to these two elementary directions, with this phenomenon being generalizable to <110> FCC nanowires of different materials (Cu, Au, Ni, Pd and Pt). The beat phenomenon is explained using a discrete moment of inertia model based on the hard sphere assumption; the model is utilized to show that surface effects enhance the beat phenomenon, while effects are reduced with increasing nanowire cross-sectional size or aspect ratio. Most importantly, due to the existence of the beat phenomena, we demonstrate that in resonance experiments only a single frequency component is expected to be observed, particularly when the damping ratio is relatively large or very small. Furthermore, for a large range of actuation angles, the lower frequency is more likely to be detected than the higher one, which implies that experimental predictions of the Young's modulus obtained from resonance may in fact be under-predictions. The present study therefore has significant implications for experimental interpretations of the Young's modulus as obtained via resonance testing.

Frictional temperature rise in a sliding physisorbed monolayer of Kr/graphene

A quartz crystal microbalance (QCM) with a graphene/Ni(111) electrode has been used to probe frictional heating effects in Kr monolayers sliding on the microbalance electrode in response to its oscillatory motion. The temperatures of the sliding Kr monolayers are observed to rise approximately 13 K higher than their static counterparts, but show surprisingly little dependence on oscillation amplitude. Although counterintuitive, the observation can be explained by noting that the Kr surface residence times are limited, which effectively caps how much the temperature can rise.

Stress-induced variations in the stiffness of micro- and nanocantilever beams

The effect of surface stress on the stiffness of cantilever beams remains an outstanding problem in the physical sciences. While numerous experimental studies report significant stiffness change due to surface stress, theoretical predictions are unable to rigorously and quantitatively reconcile these observations. In this Letter, we present the first controlled measurements of stress-induced change in cantilever stiffness with commensurate theoretical quantification. Simultaneous measurements are also performed on equivalent clamped-clamped beams. All experimental results are quantitatively and accurately predicted using elasticity theory. We also present conclusive experimental evidence for invalidity of the long-standing and unphysical axial force model, which has been widely applied to interpret measurements using cantilever beams. Our findings will be of value in the development of micro- and nanoscale resonant mechanical sensors.

Cavity optoelectromechanical regenerative amplification

Cavity optoelectromechanical regenerative amplification is demonstrated. An optical cavity enhances mechanical transduction, allowing sensitive measurement even for heavy oscillators. A 27.3 MHz mechanical mode of a microtoroid was linewidth narrowed to 6.6 ± 1.4 mHz, 30 times smaller than previously achieved with radiation pressure driving in such a system. These results may have applications in areas such as ultrasensitive optomechanical mass spectroscopy.

A nanomechanical mass sensor with yoctogram resolution

Nanomechanical resonators have been used to weigh cells, biomolecules and gas molecules, and to study basic phenomena in surface science, such as phase transitions and diffusion. These experiments all rely on the ability of nanomechanical mass sensors to resolve small masses. Here, we report mass sensing experiments with a resolution of 1.7 yg (1 yg = 10(-24) g), which corresponds to the mass of one proton. The resonator is a carbon nanotube of length ∼150 nm that vibrates at a frequency of almost 2 GHz. This unprecedented level of sensitivity allows us to detect adsorption events of naphthalene molecules (C(10)H(8)), and to measure the binding energy of a xenon atom on the nanotube surface. These ultrasensitive nanotube resonators could have applications in mass spectrometry, magnetometry and surface science.

Diffusion-induced bistability of driven nanomechanical resonators

We study nanomechanical resonators with frequency fluctuations due to diffusion of absorbed particles. The diffusion depends on the vibration amplitude through inertial effect. We find that, if the diffusion coefficient D is sufficiently large, the resonator response to periodic driving displays bistability. The lifetime of the coexisting vibrational states exponentially increases with increasing D and displays a scaling dependence on the parameters close to bifurcation points.