Parametric nanomechanical amplification at very high frequency

Helium Ion-Assisted Wet Etching of Silicon Carbide with Extremely Low Roughness for High-Quality Nanofabrication

Silicon carbide (SiC) is a promising material for a wide range of applications, including mechanical nano-resonators, quantum photonics, and non-linear photonics. However, its chemical inertness poses challenges for etching in terms of resolution and smoothness. Herein, a novel approach known as helium ion-bombardment-enhanced etching (HIBEE) is presented to achieve high-quality SiC etching. The HIBEE technique utilizes a focused helium ion beam with a typical ion energy of 30 keV to disrupt the crystal lattices of SiC, thus enabling wet etching using hydrofluoric acids and hydrogen peroxide. The etching mechanism is verified via simulations and characterization. The use of a sub-nanometer beam spot of focused helium ions ensures fabrication resolution, and the resulting etched surface exhibits an extremely low roughness of ≈0.9 nm. One of the advantages of the HIBEE technique is that it does not require resist spin-coating and development processes, thus enabling the production of nanostructures on irregular SiC surfaces, such as suspended structures and sidewalls. Additionally, the unique interaction volume of helium ions with substrates enables the one-step fabrication of suspended nanobeam structures directly from bulk substrates. The HIBEE technique is expected to facilitate and accelerate the prototyping of high-quality SiC devices.

Dynamical response and noise limit of a parametrically pumped microcantilever sensor in a Phase-Locked Loop

We investigate the response of a digitally controlled and parametrically pumped microcantilever used for sensing in a Phase-Locked Loop (PLL). We develop an analytical model for its dynamical response and obtain an explicit dependence on the rheological parameters of the surrounding viscous medium. Linearization of this model allows to find improved responsivity to density variations in the case of parametric suppression. Experiments with a commercial microcantilever validate the model, but also reveal an increase of frequency noise in the PLL associated with the parametric gain and phase, which, in most cases, restricts the attainable limit of detection. The noise in open-loop is studied by measuring the random fluctuations of the noise-driven deflection of the microcantilever, and a model for the power spectral density of amplitude, phase and frequency noises is discussed and used to explain the frequency fluctuations in the closed-loop PLL. This work concludes that parametric pumping in a PLL does not improve the sensing performance in applications requiring detecting frequency shifts.

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.

Real-time nanomechanical property modulation as a framework for tunable NEMS

Phase-change materials (PCMs) can switch between amorphous and crystalline states permanently yet reversibly. However, the change in their mechanical properties has largely gone unexploited. The most practical configuration using suspended thin-films suffer from filamentation and melt-quenching. Here, we overcome these limitations using nanowires as active nanoelectromechanical systems (NEMS). We achieve active modulation of the Young’s modulus in GeTe nanowires by exploiting a unique dislocation-based route for amorphization. These nanowire NEMS enable power-free tuning of the resonance frequency over a range of 30%. Furthermore, their high quality factors (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q$$\end{document}Q > 10⁴) are retained after phase transformation. We utilize their intrinsic piezoresistivity with unprecedented gauge factors (up to 1100) to facilitate monolithic integration. Our NEMS demonstrate real-time frequency tuning in a frequency-hopping spread spectrum radio prototype. This work not only opens up an entirely new area of phase-change NEMS but also provides a novel framework for utilizing functional nanowires in active mechanical systems.

Direct modulation of Young‟s Modulus to affect mechanical resonances in real-time has not been achieved before. Here, the authors leverage the dislocation migration phenomenon in GeTe nanowires to develop nanoelectromechanical systems with powerfree tuning of mechanical resonances within a range of 30%, high and stable quality and gauge factors.

Quality factor control of mechanical resonators using variable phononic bandgap on periodic microstructures

The quality factor (Q-factor) is an important parameter for mechanical resonant sensors, and the optimal values depend on its application. Therefore, Q-factor control is essential for microelectromechanical systems (MEMS). Conventional methods have some restrictions, such as additional and complicated equipment or nanoscale dimensions; thus, structural methods are one of the reasonable solutions for simplifying the system. In this study, we demonstrate Q-factor control using a variable phononic bandgap by changing the length of the periodic microstructure. For this, silicon microstructure is used because it has both periodicity and a spring structure. The bandgap change is experimentally confirmed by measuring the Q-factors of mechanical resonators with different resonant frequencies. The bandgap range varies depending on the extended structure length, followed by a change in the Q-factor value. In addition, the effects of the periodic structure on the Q-factor enhancement and the influence of stress on the structural length were evaluated. Although microstructures can improve the Q-factors irrespective of periodicity; the result of the periodic microstructure is found to be efficient. The proposed method is feasible as the novel Q-factor control technique has good compatibility with conventional MEMS.

Ultrawide Frequency Tuning of Atomic Layer van der Waals Heterostructure Electromechanical Resonators

We report on the experimental demonstration of atomically thin molybdenum disulfide (MoS₂)-graphene van der Waals (vdW) heterostructure nanoelectromechanical resonators with ultrawide frequency tuning. With direct electrostatic gate tuning, these vdW resonators exhibit exceptional tunability, in general, Δf/f₀ > 200%, for continuously tuning the same device and the same mode (e.g., from ∼23 to ∼107 MHz), up to Δf/f₀ ≈ 370%, the largest fractional tuning range in such resonators to date. This remarkable electromechanical resonance tuning is investigated by two different analytical models and finite element simulations. Furthermore, we carefully perform clear control experiments and simulations to elucidate the difference in frequency tuning between the heterostructure and single-material resonators. At a given initial strain level, the tuning range depends on the two-dimensional (2D) Young's moduli of the constitutive crystals; devices built on materials with lower 2D moduli show wider tuning ranges. This study exemplifies that vdW heterostructure resonators can retain unconventionally broad, continuous tuning, which is promising for voltage-controlled, tunable nanosystems.

Cylindrical Line-Feeding Growth of Free-Standing Silicon Nanohelices as Elastic Springs and Resonators

Three-dimensional (3D) construction of free-standing silicon (Si) nanohelices has been a formidable challenge for planar lithography and etching technology. We here demonstrate a convenient 3D growth and integration of Si nanohelices (SiNHs) upon bamboolike cylinders with corrugated sidewall grooves, where the indium catalyst droplets grow around the cylinders in a helical fashion, while consuming precoated amorphous Si (a-Si) thin film to produce crystalline Si nanowires on the sidewalls. At the end of each groove cycle, the droplets are enforced to linefeed/switch into the neighbor groove to continue a spiral growth of SiNHs with readily tunable diameter, pitch, aspect-ratio, and chiral/achiral symmetries. In addition, the SiNHs can be reliably released as free-standing units to serve as elastic links, supports and vibrational resonators. These results highlight the unexplored potential of high precision 3D self-assembly growth in constructing a wide range of sophisticated electromechanical, sensor, and optoelectronic functionalities.

Efficient Excitation of Micro/Nano Resonators and Their Higher Order Modes

We demonstrate a simple and flexible technique to efficiently activate micro/nano-electromechanical systems (MEMS/NEMS) resonators at their fundamental and higher order vibration modes. The method is based on the utilization of the amplified voltage across an inductor, L, of an LC tank resonant circuit to actuate the MEMS/NEMS resonator. By matching the electrical and mechanical resonances, significant amplitude amplification is reported across the resonators terminals. We show experimentally amplitude amplification up to twelve times, which is demonstrated to efficiently excite several vibration modes of a microplate MEMS resonator and the fundamental mode of a NEMS resonator.

Opto-thermally excited multimode parametric resonance in graphene membranes

In the field of nanomechanics, parametric excitations are of interest since they can greatly enhance sensing capabilities and eliminate cross-talk. Above a certain threshold of the parametric pump, the mechanical resonator can be brought into parametric resonance. Here we demonstrate parametric resonance of suspended single-layer graphene membranes by an efficient opto-thermal drive that modulates the intrinsic spring constant. With a large amplitude of the optical drive, a record number of 14 mechanical modes can be brought into parametric resonance by modulating a single parameter: the pre-tension. A detailed analysis of the parametric resonance allows us to study nonlinear dynamics and the loss tangent of graphene resonators. It is found that nonlinear damping, of the van der Pol type, is essential to describe the high amplitude parametric resonance response in atomically thin membranes.

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.

Parametric amplification in MoS2 drum resonator

Parametric amplification is widely used in diverse areas from optics to electronic circuits to enhance low level signals by varying relevant system parameters. Parametric amplification has also been performed in several micro-nano resonators including nano-electromechanical system (NEMS) resonators based on a two-dimensional (2D) material. Here, we report the enhancement of mechanical response in a MoS₂ drum resonator using degenerate parametric amplification. We use parametric pumping to modulate the spring constant of the MoS₂ resonator and achieve a 10 dB amplitude gain. We also demonstrate quality factor enhancement in the resonator with parametric amplification. We investigate the effect of cubic nonlinearity on parametric amplification and show that it limits the gain of the mechanical resonator. Amplifying ultra-small displacements at room temperature and understanding the limitations of the amplification in these devices is key for using these devices for practical applications.

Dynamic control for nanostructures through slowly ramping parameters

We propose a nanostructure control method which uses slowly ramping parameters. We demonstrate the dynamics of this method in both a nonlinear classical system and a quantum system. When a quantum mechanical two-level atom (quantum dot) is irradiated by an electric field with a slowly increasing frequency, there exists a sudden transition from ground (excited) to excited (ground) state. This occurs when the ramping rate is smaller than the square of the Rabi frequency. The transition arises when its "instant frequency"-the time derivative of the driving field phase-matches the resonance frequency, satisfying the Fermi golden rule. We also find that the parameter ramping is an efficient control manner for classical nanomechanical shuttles. For ramping of driving amplitudes, the shuttle's mechanical oscillation is amplified and even survives when the ramping is stopped outside the original oscillation region. This strange oscillation is due to the entrance into a multistable dynamic region in phase space. For ramping of driving frequencies, an onset of oscillation arises when the instant frequency enters the oscillation region. Thus, regardless of being classical or quantum, the instant frequency is physically relevant. We discuss in which conditions the dynamic control is efficient.

Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures

Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke's law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale.

Nanoscale Electromechanics To Measure Thermal Conductivity, Expansion, and Interfacial Losses

We study the effect of localized Joule heating on the mechanical properties of doubly clamped nanowires under tensile stress. Local heating results in systematic variation of the resonant frequency; these frequency changes result from thermal stresses that depend on temperature dependent thermal conductivity and expansion coefficient. The change in sign of the linear expansion coefficient of InAs is reflected in the resonant response of the system near a bath temperature of 20 K. Using finite element simulations to model the experimentally observed frequency shifts, we show that the thermal conductivity of a nanowire can be approximated in the 10-60 K temperature range by the empirical form κ = bT W/mK, where the value of b for a nanowire was found to be b = 0.035 W/mK(2), significantly lower than bulk values. Also, local heating allows us to independently vary the temperature of the nanowire relative to the clamping points pinned to the bath temperature. We suggest a loss mechanism (dissipation ~10(-4)-10(-5)) originating from the interfacial clamping losses between the metal and the semiconductor nanostructure.

Strong thermomechanical squeezing via weak measurement

We experimentally surpass the 3 dB limit to steady-state parametric squeezing of a mechanical oscillator. The localization of an atomic force microscope cantilever, achieved by optimal estimation, is enhanced by up to 6.2 dB in one position quadrature when a detuned parametric drive is used. This squeezing is, in principle, limited only by the oscillator Q factor. Used on low temperature, high frequency oscillators, this technique provides a pathway to achieve robust quantum squeezing below the zero-point motion. Broadly, our results demonstrate that control systems engineering can overcome well established limits in applications of nonlinear processes. Conversely, by localizing the mechanical position to better than the measurement precision of our apparatus, they demonstrate the usefulness of mechanical nonlinearities in control applications.

Wide bandwidth nanowire electromechanics on insulating substrates at room temperature

We study InAs nanowire resonators fabricated on sapphire substrate with a local gate configuration. The key advantage of using an insulating sapphire substrate is that it results in a reduced parasitic capacitance, thus allowing both wide bandwidth actuation and detection using a network analyzer as well as signal detection at room temperature. Both in-plane and out-of-plane vibrational modes of the nanowire can be driven and the nonlinear response of the resonators studied. In addition, this technique enables the study of variation of thermal strains due to heating in nanostructures.

Parametric amplification and self-oscillation in a nanotube mechanical resonator

A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the line shape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultralow force sensing experiments.

Homoclinic orbits and chaos in a pair of parametrically driven coupled nonlinear resonators

We study the dynamics of a pair of parametrically driven coupled nonlinear mechanical resonators of the kind that is typically encountered in applications involving microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS). We take advantage of the weak damping that characterizes these systems to perform a multiple-scales analysis and obtain amplitude equations, describing the slow dynamics of the system. This picture allows us to expose the existence of homoclinic orbits in the dynamics of the integrable part of the slow equations of motion. Using a version of the high-dimensional Melnikov approach, developed by G. Kovačič and S. Wiggins [Physica D 57, 185 (1992)], we are able to obtain explicit parameter values for which these orbits persist in the full system, consisting of both Hamiltonian and non-Hamiltonian perturbations, to form so-called Šilnikov orbits, indicating a loss of integrability and the existence of chaos. Our analytical calculations of Šilnikov orbits are confirmed numerically.

Capacitive spring softening in single-walled carbon nanotube nanoelectromechanical resonators

We report the capacitive spring softening effect observed in single-walled carbon nanotube (SWNT) nanoelectromechanical (NEM) resonators. The nanotube resonators adopt a dual-gate configuration with both bottom-gate and end-gate capable of tuning the resonance frequency through capacitive coupling. Interestingly, downward resonance frequency shifting is observed with increasing end-gate voltage, which can be attributed to the capacitive softening of the spring constant. Furthermore, in-plane vibrational modes exhibit a much stronger spring softening effect than out-of-plan modes. Our dual-gate design should enable the differentiation between these two types of vibrational modes and open up the new possibility for nonlinear operation of nanotube resonators.

Parametric amplification and back-action noise squeezing by a qubit-coupled nanoresonator

We demonstrate the parametric amplification and noise squeezing of nanomechanical motion utilizing dispersive coupling to a Cooper-pair box qubit. By modulating the qubit bias and resulting mechanical resonance shift, we achieve gain of 30 dB and noise squeezing of 4 dB. This qubit-mediated effect is 3000 times more effective than that resulting from the weak nonlinearity of capacitance to a nearby electrode. This technique may be used to prepare nanomechanical squeezed states.