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International audience; Due to their unique size-dependent properties, nanoparticles (NPs) have many industrial and biomedical applications. Although NPs are generally characterized based on the size or morphological analysis, the mass of whole particles can be of interest as it represents the total amount of material in the particle regardless of shape, density, or elemental composition. In addition, the shape of nonspherical NPs presents a conceptual challenge, making them difficult to characterize in terms of size or morphological characteristics. Here, we used a novel nano-electro-mechanical sensor mass spectrometry (NEMS-MS) technology to characterize the mass distributions of various NPs. For standard spherical gold NPs, mass distributions covered the range from ∼5 to 250 MDa (8 to ∼415 attograms). Applying the density of gold (19.3 g/cm3) and assuming perfect sphericity, these mass measurements were used to compute the equivalent diameters of the NPs. The sizes determined agreed well with the transmission electron microscopy (TEM) imaging data, with deviations of ∼1.4%. Subsequently, we analyzed the mass distribution of ∼50 nm synthetic silicon dioxide particles, having determined their size by electron microscopy (SEM and TEM). Their estimated density was in line with the literature values derived from differential mobility analyzer and aerosol particle mass analyzer data. Finally, we examined the intact gold nanotetrapods and obtained a mass distribution revealing their controlled polydispersity. The presence of polyethylene glycol coating was also quantified and corroborated nuclear magnetic resonance observations. Our results demonstrate the potential of NEMS-MS-based measurements as an effective means to characterize NPs, whatever their composition, shape or density.

Chaotic systems, presenting complex and nonreproducible dynamics, may be found in nature, from the interaction between planets to the evolution of weather, but can also be tailored using current technologies for advanced signal processing. However, the realization of chaotic signal generators remains challenging due to the involved dynamics of the underlying physics. In this paper, we experimentally and numerically present a disruptive approach to generate a chaotic signal from a micromechanical resonator. This technique overcomes the long-established complexity of controlling the buckling in micro/nanomechanical structures by modulating either the amplitude or the frequency of the driving force applied to the resonator in the nonlinear regime. The experimental characteristic parameters of the chaotic regime, namely, the Poincaré sections and Lyapunov exponents, are directly comparable to simulations for different configurations. These results confirm that this dynamical approach is transposable to any kind of micro/nanomechanical resonator, from accelerometers to microphones. We demonstrate a direct application exploiting the mixing properties of the chaotic regime by transforming an off-the-shelf microdiaphragm into a true random number generator conforming to the National Institute of Standards and Technology specifications. The versatility of this original method opens new paths to combine the unique properties of chaos with the exceptional sensitivity of microstructures, leading to emergent microsystems.

Nanomechanical mass spectrometry has proven to be well suited for the analysis of high mass species such as viruses. Still, the use of one-dimensional devices such as vibrating beams forces a trade-off between analysis time and mass resolution. Complex readout schemes are also required to simultaneously monitor multiple resonance modes, which degrades resolution. These issues restrict nanomechanical MS to specific species. We demonstrate here single-particle mass spectrometry with nano-optomechanical resonators fabricated with a Very Large Scale Integration process. The unique motion sensitivity of optomechanics allows designs that are impervious to particle position, stiffness or shape, opening the way to the analysis of large aspect ratio biological objects of great significance such as viruses with a tail or fibrils. Compared to top-down beam resonators with electrical read-out and state-of-the-art mass resolution, we show a three-fold improvement in capture area with no resolution degradation, despite the use of a single resonance mode., The use of one dimensional devices in nanomechanical mass spectrometry leads to a trade-off between analysis time and resolution. Here, the authors report single-particle mass spectrometry using integrated optomechanical resonators, impervious to particle position, stiffness or shape.

In this paper, we present observations of the amplitude and frequency noise of two self-sustained oscillating modes of a single micromechanical resonator under fractional synchronization. The resonant modes which comprise the self-sustained oscillators have a 3:1 ratio of frequencies. Increasing the amplitude of the low-frequency oscillator increases the range of frequencies over which the oscillations synchronize; inversely, increasing the amplitude of the high-frequency oscillator decreases the synchronization range. We show that by increasing the amplitude of either mode, the white noise in amplitude and frequency of the higher mode will decrease in the synchronized regime. We also show that when synchronized the frequency fluctuations of the higher frequency mode can be reduced by four times in comparison with the fluctuations of the same oscillator operating at the same amplitude when not synchronized. The same amount of reduction is also observed in the amplitude fluctuations of the higher frequency mode. These observations create a path toward exploitation of fractional synchronization for the purposes of noise reduction in both amplitude and frequency of micromechanical oscillators. [2018-0301]

When studying viruses, the most prevalent aspects that come to mind are their structural and functional features, but this leaves in the shadows a quite universal characteristic: their mass. Even if approximations can be derived from size and density measurements, the multi MDa to GDa mass range, featuring a majority of viruses, has so far remained largely unexplored. Recently, nano-electromechanical resonator-based mass spectrometry (NEMS-MS) has demonstrated the ability to measure the mass of intact DNA filled viral capsids in excess of 100 MDa. However, multiple factors have to be taken in consideration when performing NEMS-MS measurements. In this article, phenomena influencing NEMS-MS mass estimates are listed and discussed, including some particle's extraneous physical properties (size, aspect ratio, stiffness), and the influence of frequency noise and device fabrication defects. These factors being accounted for, we could begin to notice subtler effects linked with (e.g.) particle desolvation as a function of operating parameters. Graphical abstract.

We report on a piezoelectric micromachined ultrasonic transducer (PMUT) driven in a nonlinear regime, generating chaotic amplitude modulated ultrasonic waves. At large enough drives, the PMUT enters in the Duffing regime which opens a hysteresis with two available states. By modulating the frequency of the driving signal, the system may switch between both states, and selecting the appropriate modulation frequency enables to enter in the chaotic regime. The chaos is then imprinted as a modulation of the PMUT’s amplitude. We characterize this regime in the three accessible domains: electrical, mechanical and acoustic, and demonstrate they are fully correlated. We then focus on the generated acoustic signals and demonstrate that the chaotic modulation propagates according to the PMUT’s linear regime. Remarkably, the detected acoustic waves are strongly correlated to the on-chip piezoelectric measurements, regardless of the acoustic beam profile. The frequency spectrum of the chaotic modulation spreads around the ultrasonic carrier, mimicking a noise modulated carrier signal. We exploit this property for jamming applications where the chaotic PMUT is used to mask surrounding acoustic waves. Unlike most jamming applications, our approach does not require driving signals with a broad frequency spectrum, the noisy pattern arising directly from the structure’s dynamics. Using two PMUTs, one in the linear and the other in the nonlinear regime, we realize a proof-of-concept where the ultrasound generated by the first PMUT is drowned out by the chaotic PMUT signal. We demonstrate that the carrier frequency of the jamming PMUT does not need to match perfectly the one of the linear PMUT. This chaos generation is generic and could be adapted to any PMUT, and thanks to the rich frequency spectrum of the chaotic modulation, the frequency of the signal to jam does not need to be precisely known.

International audience; Due to their physical properties, nanomechanical sensors (NEMS) can achieve mass measurements in the mega- to gigadalton range, which is hardly obtained with conventional mass-spectrometers. However, NEMS signals are subject to noise, causing a loss of mass resolution and thus emphasizing the need of noise control. We propose a denoising model that relies on a total variation formulation, which deals with different noise models (particularly colored noise) affecting NEMS. The model also takes into account the physics of NEMS, such as the non-linear coupling between signals of individual NEMS. The performance of the proposed model is tested on simulated data which parameters are chosen similar to true experimental conditions. The obtained results confirm the interest of our model with a mass-resolution increase over 20% compared to methods used in literature.

When studying viruses, the most prevalent aspects that come to mind are their structural and functional features, but this leaves in the shadows a quite universal characteristic: their mass. Even if approximations can be derived from size and density measurements, the multi MDa to GDa mass range, featuring a majority of viruses, has so far remained largely unexplored. Recently, nano-electromechanical resonator–based mass spectrometry (NEMS-MS) has demonstrated the ability to measure the mass of intact DNA filled viral capsids in excess of 100 MDa. However, multiple factors have to be taken in consideration when performing NEMS-MS measurements. In this article, phenomena influencing NEMS-MS mass estimates are listed and discussed, including some particle’s extraneous physical properties (size, aspect ratio, stiffness), and the influence of frequency noise and device fabrication defects. These factors being accounted for, we could begin to notice subtler effects linked with (e.g.) particle desolvation as a function of operating parameters.

This paper addresses the impact of cubic nonlinearity on the operation of a rate-integrating gyroscope (RIG). It is demonstrated that below the bifurcation threshold, cubic nonlinearity results in angle-dependent frequency split between the two resonant modes of the gyroscope, which impacts angle-dependent bias, quadrature error, and controller efficacy in addition to distorting the scale factor due to off-resonant excitation. These errors are experimentally demonstrated using a high- $Q$ disk resonator gyroscope, which are shown to be in close agreement with theory. A method of compensating for angle-dependent frequency error is proposed and experimentally validated. It is demonstrated that mode mismatch can be experimentally reduced to the level of thermal noise, effectively cancelling the effects of nonlinearity and eliminating the distortion of readout angle.

International audience; The first Very Large Scale Integration process with variable shape beam lithography for optomechanical devices is presented. State of the art performance was obtained with silicon microdisk resonators showing 1 million optical quality factors and 10 -17 m.Hz (-1/2) displacement resolution. Single-particle mass spectrometry could be performed with these optomechanical resonators in vacuum. The devices retained high performance when directly immersed in liquid media, allowing for biosensing experiments. These results open the door to large, dense arrays of optomechanical sensors.

One of the main challenges to overcome to perform nanomechanical mass spectrometry analysis in a practical time frame stems from the size mismatch between the analyte beam and the small nanomechanical detector area. We report here the demonstration of mass spectrometry with arrays of 20 multiplexed nanomechanical resonators; each resonator is designed with a distinct resonance frequency which becomes its individual address. Mass spectra of metallic aggregates in the MDa range are acquired with more than one order of magnitude improvement in analysis time compared to individual resonators. A 20 NEMS array is probed in 150 ms with the same mass limit of detection as a single resonator. Spectra acquired with a conventional time-of-flight mass spectrometer in the same system show excellent agreement. We also demonstrate how mass spectrometry imaging at the single-particle level becomes possible by mapping a 4-cm-particle beam in the MDa range and above., Nano-electro-mechanical system-based mass spectrometry holds promise for detecting supramolecular assemblies at large molecular weights, but its efficiency is too poor to be practical. Sage et al. overcome this problem using a nanomechanical resonator array, which significantly decreases detection time.

Bridging the mass gap Viruses and many large biomolecule complexes are in a mass range that is challenging to measure with conventional mass spectrometry methods. Nanomechanical resonators can determine masses of impacting molecules, but separation methods often lose too much of the sample to be efficient. Dominguez-Medina et al. used an aerodynamic lens that improved separation and focusing of nebulized molecules with increasing mass. The mass of both filled and empty viral capsids was determined with an array of 20 nanoresonators. Science , this issue p. 918

In this paper we present our observations of the effect of mutual fractional synchronization of two oscillators created from two distinct resonance modes of a single micromechanical resonator on the noise of the oscillators. The modes have a 3:1 fractional frequency ratio and by increasing the amplitude of the lower frequency mode the synchronization range will increase. We show by increasing the amplitude of the lower frequency mode, the white noise in frequency and amplitude of the higher mode will decrease. We show that when synchronized the frequency fluctuations of the higher frequency mode will reduce 4 times in comparison with the fluctuations of the same oscillator operating at the same amplitude when not synchronized. The same amount of reduction is also observed in the amplitude fluctuations of the higher frequency mode.

In this paper, we study the occurrence of synchronization between the two degenerate resonance modes of a microdisk resonator gyroscope. Recently, schemes involving the simultaneous actuation of the two vibration modes of the gyroscope have been implemented as a promising new method to increase their performance. However, this strategy might result in synchronization between the two modes, which would maintain frequency mode-matching but also may produce problems, such as degrading stability and sensitivity. Here, we demonstrate for the first time synchronization between the degenerate modes of a microgyroscope and show that synchronization arising from mutual coupling dramatically reduces frequency instability at the cost of increased amplitude instability. We present an alternative synchronization scheme that suppresses this drawback while still taking advantage of a passive frequency mode-match operation.

We have studied the first three symmetric out-of-plane flexural resonance modes of a goalpost silicon micro-mechanical device. Measurements have been performed at 4.2K in vacuum, demonstrating high Qs and good linear properties. Numerical simulations have been realized to fit the resonance frequencies and produce the mode shapes. These mode shapes are complex, since they involve distortions of two coupled orthogonal bars. Nonetheless, analytic expressions have been developed to reproduce these numerical results, with no free parameters. Owing to their generality they are extremely helpful, in particular to identify the parameters which may limit the performances of the device. The overall agreement is very good, and has been verified on our nano-mechanical version of the device., Journal of Low Temperature Physics (2013)

We present an epitaxially-encapsulated 2×2mm2 quad-mass resonator (QMR) with shaped comb fingers for frequency tuning. While shaped electrodes have been used for frequency tuning of linear resonators, the device studied here has very high quality factor (g=100,000) resulting in a very narrowband resonance which, without the shaped electrodes, results in undesirable nonlinear behavior such as amplitude-frequency dependence and instability of the oscillator loop at large amplitudes. We demonstrate that through the shaped comb finger design, both frequency tuning (over 90Hz) and large amplitude oscillation (1.25 μm amplitude, a factor of 100 compared to performance without the shaped electrodes) are possible. Furthermore, we demonstrate how critical dimension loss in the fabrication process can change the shape of the designed shaped finger and introduce electrostatic stiffness hardening.

We report on experiments addressing the non-linear interaction between a nano-mechanical mode and position fluctuations. The Duffing non-linearity transduces the Brownian motion of the mode, and of other non-linearly coupled ones, into frequency noise. This mechanism, ubiquitous to all weakly-nonlinear resonators thermalized to a bath, results in a phase diffusion process altering the motion: two limit behaviors appear, analogous to motional narrowing and inhomogeneous broadening in NMR. Their crossover is found to depend non-trivially on the ratio of the frequency noise correlation time to its magnitude. Our measurements obtained over an unprecedented range covering the two limits match the theory of Y. Zhang and M. I. Dykman, Phys. Rev. B 92, 165419 (2015), with no free parameters. We finally discuss the fundamental bound on frequency resolution set by this mechanism, which is not marginal for bottom-up nanostructures., Article plus Supplementary Material

We demonstrate synchronization between two intrinsically coupled oscillators that are created from two distinct vibration modes of a single micromachined disk resonator. The modes have a 3:1 subharmonic frequency relationship and cubic, non-dissipative electromechanical coupling between the modes enables their two frequencies to synchronize. Our experimental implementation allows the frequency of the lower frequency oscillator to be independently controlled from that of the higher frequency oscillator, enabling study of the synchronization dynamics. We find close quantitative agreement between the experimental behavior and an analytical coupled-oscillator model as a function of the energy in the two oscillators. We demonstrate that the synchronization range increases when the lower frequency oscillator is strongly driven and when the higher frequency oscillator is weakly driven. This result suggests that synchronization can be applied to the frequency-selective detection of weak signals and other mechanical signal processing functions.

We have measured the thermal properties of suspended membranes from 10 K to 300 K for two amplitudes of internal stress (about 0.1 GPa and 1 GPa) and for two different thicknesses (50 nm and 100 nm). The use of the original 3 \omega -Volklein method has allowed the extraction of both the specific heat and the thermal conductivity of each SiN membrane over a wide temperature range. The mechanical properties of the same substrates have been measured at helium temperatures using nanomechanical techniques. Our measurements show that the thermal transport in freestanding SiN membranes is not affected by the presence of internal stress. Consistently, mechanical dissipation is also unaffected even though Qs increase with increasing tensile stress. We thus demonstrate that the theory developed by Wu and Yu [Phys. Rev. B 84, 174109 (2011)] does not apply to this amorphous material in this stress range. On the other hand, our results can be viewed as a natural consequence of the "dissipation dilution" argument [Y. L. Huang and P. R. Saulson, Rev. Sci. Instrum. 69, 544 (1998)] which has been introduced in the context of mechanical damping., Comment: 15 pages, 6 figures. Submitted to PRB

In this letter, we investigate the dynamics of injection-locking a nonlinear micromechanical oscillator operating in different regimes of electromechanical nonlinearity to an external tone generated by a secondary oscillator. The micromechanical oscillator exhibits a combination of mechanical and electrostatic nonlinearities that were tuned using a bias voltage to adjust the relative importance of third-order and fifth-order stiffness nonlinearities. While it is well-known that third-order stiffness (Duffing) nonlinearity results in a synchronization range that increases with an oscillator's amplitude, little is known about the impact of other nonlinearities. We show that when using Duffing nonlinearity cancellation, higher order nonlinearities dominate, the synchronization range is smaller but has a greater rate-of-increase with oscillation amplitude. When both mechanical stiffness-hardening and electrostatic stiffness-softening nonlinearities are present, the frequency response follows an “s-curve” and, unlike the other conditions, the synchronization range does not increase monotonically with amplitude but instead reaches a minimum when both nonlinearities have similar magnitude. We develop a nonlinear resonator model and show that this model achieves good quantitative prediction of the measured synchronization range in all nonlinear operating regimes studied.

This paper describes the operation of a high quality factor gyroscope in various regimes where electromechanical nonlinearities introduce different forms of amplitude–frequency (A–f) dependence. Experiments are conducted using an epitaxially-encapsulated 2 × 2 mm2 quad-mass gyroscope (QMG) with a quality factor of 85 000. The device exhibits third-order Duffing nonlinearity at low bias voltages (15 V) due to the mechanical nonlinearity in the flexures and at high bias voltages (35 V) due to third-order electrostatic nonlinearity. At intermediate voltages (~26 V), these third-order nonlinearities cancel and the amplitude–frequency dependence is greatly reduced. A model is developed to demonstrate the connection between the electromechanical nonlinearities and the amplitude–frequency dependence, also known as the backbone curve. Gyroscope operation is demonstrated in each nonlinear operating regime and the key performance measures of the gyroscope's performance, angle random walk (ARW) and bias instability, are measured as a function of drive-mode vibration amplitude. We find that low ARW can be achieved even though the gyroscope's drive mode exhibits large amplitude–frequency dependence, and that bias instability is largely independent of the operating regime.

We have measured the interaction between $^4$He gas at 4.2$~$K and a high-quality nano-electro-mechanical string device for its first 3 symmetric modes (resonating at 2.2$~$MHz, 6.7$~$MHz and 11$~$MHz with quality factor $Q > 0.1$ million) over almost 6 orders of magnitude in pressure. This fluid can be viewed as the best experimental implementation of an almost-ideal monoatomic and inert gas which properties are tabulated. The experiment ranges from high pressure where the flow is of laminar Stokes-type presenting slippage, down to very low pressures where the flow is molecular. In the molecular regime, when the mean-free-path is of the order of the distance between the suspended nano-mechanical probe and the bottom of the trench we resolve for the first time the signature of the boundary (Knudsen) layer onto the measured dissipation. Our results are discussed in the framework of the most recent theories investigating boundary effects in fluids (both analytic approaches and Monte-Carlo DSMC simulations)., Editor's suggestion

International audience; We present a high-sensitivity measurement technique for mechanical nanoresonators. Due to intrinsic nonlinear effects, different flexural modes of a nanobeam can be coupled while driving each of them on resonance. This mode-coupling scheme is dispersive and one mode resonance shifts with respect to the motional amplitude of the other. The same idea can be implemented on a single mode, exciting it with two slightly detuned signals. This two-tone scheme is used here to measure the resonance lineshape of one mode through a frequency shift in the response of the device. The method acts as an amplitude-to-frequency transduction which ultimately suffers only from phase noise of the local oscillator used and of the nanomechanical device itself. We also present a theory which reproduces the data without free parameters

International audience; We have characterized the mechanical resonance properties (both linear and nonlinear) of various doubly-clamped silicon nitride nanomechanical resonators, each with a different intrinsic tensile stress. The measurements were carried out at 4 K and the magnetomotive technique was used to drive and detect the motion of the beams. The resonant frequencies of the beams are in the megahertz range, with quality factors of the order of 104.We also measure the dynamic range of the beams and their nonlinear (Duffing) behaviour

We report on experiments performed at low temperatures on aluminum covered silicon nanoelectromechanical resonators. The substantial difference observed between the mechanical dissipation in the normal and superconducting states measured within the same device unambiguously demonstrates the importance of normal-state electrons in the damping mechanism. The dissipative component becomes vanishingly small at very low temperatures in the superconducting state, leading to exceptional values for the quality factor of such small silicon structures. A critical discussion is given within the framework of the standard tunneling model., SI not provided

Resonators used in frequency-reference oscillators must maintain a stable frequency output even when subjected to temperature variations. The traditional solution is to construct the resonator from a material with a low temperature coefficient, such as AT-cut quartz, which can achieve absolute frequency stability on the order of ±25 ppm over commercial temperature ranges. In comparison, Si microresonators suffer from the disadvantage that silicon's temperature coefficient of frequency (TCF) is approximately two orders of magnitude greater than that of AT-cut quartz. In this paper, we present an in situ passive temperature compensation scheme for Si microresonators based on nonlinear amplitude-frequency coupling which reduces the TCF to a level comparable with that of an AT-quartz resonator. The implementation of this passive technique is generic to a variety of Si microresonators and can be applied to a number of frequency control and timing applications.

International audience; We report on experiments performed in vacuum and at cryogenic temperatures on a tri-port nano-electro-mechanical (NEMS) device. One port is a very non-linear capacitive actuation, while the two others implement the magnetomotive scheme with a linear input force port and a (quasilinear) output velocity port. We present an experimental method enabling a full characterization of the nanomechanical device harmonic response: the non-linear capacitance function C(x) is derived, and the normal parameters k and m (spring constant and mass) of the mode under study are measured through a careful definition of the motion (in meters) and of the applied forces (in Newtons). These results are obtained with a series of purely electric measurements performed without disconnecting/reconnecting the device, and rely only on known DC properties of the circuit, making use of a thermometric property of the oscillator itself: we use the Young modulus of the coating metal as a thermometer, and the resistivity for Joule heating. The setup requires only three connecting lines without any particular matching, enabling the preservation of a high impedance NEMS environment even at MHz frequencies. The experimental data are fit to a detailed electrical and thermal model of the NEMS device, demonstrating a complete understanding of its dynamics. These methods are quite general and can be adapted (as a whole, or in parts) to a large variety of elecromechanical devices

International audience; We report on experiments performed on a cantilever-based tri-port nano-electro-mechanical (NEMS) device. Two ports are used for actuation and detection through the magnetomotive scheme, while the third port is a capacitively coupled gate electrode. By applying a low frequency voltage signal on the gate, we demonstrate mixing in the mechanical response of the device, even for {\it low magnetomotive drives, without resorting to conduction measurements through the NEMS}. The technique can thus be used in particular in the linear regime, as an alternative to nonlinear mixing, for normal conducting devices. An analytic theory is presented reproducing the data without free parameters

International audience; The thermal properties of suspended thin films prepared by the micro-machining process have been measured using the 3! dynamic method coupled to a Volklein geometry. A transducer (heater/thermometer) centered on the membrane is driven by an ac current causingperiodic thermal oscillations. The measurement of the temperature oscillation on the membrane is made at the third harmonic using a Wheatstone bridge set up. Here by coupling the 3! method to a Voolklein geometry (suspended membrane) we obtained a highly sensitive techniqueto measure the thermal conductance with a resolution of (..K=K = 10-3) and a sensitivity of the order of nanoWatt/K, thanks to a very sensitive niobium nitride thermometry. This method is applied to measure the in-plane thermal conductivity of 100 nm silicon nitride membrane, inthe temperature range of 10-275 K