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 new 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 efforts 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

Ultra-High Frequency Nanoelectromechanical Systems with Low-Noise Technologies for Single-Molecule Mass Sensing

Advancing today's very rudimentary nanodevices toward functional nanosystems with considerable complexity and advanced performance imposes enormous challenges. This thesis presents the research on ultra-high frequency (UHF) nanoelectromechanical systems (NEMS) in combination with low-noise technologies that enable single-molecule mass sensing and offer promises for NEMS-based mass spectrometry (MS) with single-Dalton sensitivity. The generic protocol for NEMS resonant mass sensing is based on real-time locking and tracking of the resonance frequency as it is shifted by the mass-loading effect. This has been implemented in two modes: (i) creating an active self-sustaining oscillator based on the NEMS resonator, and (ii) a higher-precision external oscillator phase-locking to and tracking the NEMS resonance. The first UHF low-noise self-sustaining NEMS oscillator has been demonstrated by using a 428MHz vibrating NEMS resonator as the frequency reference. This stable UHF NEMS oscillator exhibits ~0.3ppm frequency stability and ~50zg (1zg = 10-21 g) mass resolution with its excellent wideband-operation (~0.2MHz) capability. Given its promising phase noise performance, the active NEMS oscillator technology also offers important potentials for realizing NEMS-based radio-frequency (RF) local oscillators, voltage-controlled oscillators (VCOs), and synchronized oscillators and arrays that could lead to nanomechanical signal processing and communication. The demonstrated NEMS oscillator operates at much higher frequency than conventional crystal oscillators and their overtones do, which opens new possibilities for the ultimate miniaturization of advanced crystal oscillators. Low-noise phase-locked loop (PLL) techniques have been developed and engineered to integrate with the resonance detection circuitry for the passive UHF NEMS resonators. Implementations of the NEMS-PLL mode with generations of low-loss UHF NEMS resonators demonstrate improving performance, namely, reduced noise and enhanced dynamic range. Very compelling frequency stability of ~0.02ppm and unprecedented mass sensitivity approaching 1zg has been achieved with a typical 500MHz device in the narrow-band NEMS-PLL operation. Retaining high quality factors (Q's) while scaling up frequency has become crucial for UHF NEMS resonators. Extensive measurements, together with theoretical modeling, have been performed to investigate various energy loss mechanisms and their effects on UHF devices. This leads to important insights and guidelines for device Q-engineering. The first VHF/UHF silicon nanowire (NW) resonators have been demonstrated based on single-crystal Si NWs made by bottom-up chemical synthesis nanofabrication. Pristine Si NWs have well-faceted surfaces and exhibit high Q's (Q ≈ 13100 at 80MHz and Q ≈ 5750 at 215MHz). Given their ultra-small active mass and very high mass responsivity, these Si NWs also offer excellent mass sensitivity in the ~10?50zg range. These UHF NEMS and electronic control technologies have demonstrated promising mass sensitivity for kilo-Dalton-range single-biomolecule mass sensing. The achieved performance roadmap, and that extended by next generations of devices, clearly indicates realistic and viable paths toward the single-Dalton mass sensitivity. With further elaborate engineering, prototype NEMS-MS is optimistically within reach.</p

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

Modeling and analysis of a resonant nanosystem

The majority of investigations into nanoelectromechanical resonators focus on a single area of the resonator\u27s function. This focus varies from the development of a model for a beam\u27s vibration, to the modeling of electrostatic forces, to a qualitative explanation of experimentally-obtained currents. Despite these efforts, there remains a gap between these works, and the level of sophistication needed to truly design nanoresonant systems for efficient commercial use. Towards this end, a comprehensive system model for both a nanobeam resonator and its related experimental setup is proposed. Furthermore, a simulation arrangement is suggested as a method for facilitating the study of the system-level behavior of these devices in a variety of cases that could not be easily obtained experimentally or analytically. ^ The dynamics driving the nanoresonator\u27s motion, as well as the electrical interactions influencing the forcing and output of the system, are modeled, experimentally validated, and studied. The model seeks to develop both a simple circuit representation of the nanoresonator, and to create a mathematical system that can be used to predict and interpret the observed behavior. Due to the assumptions used to simplify the model to a point of reasonable comprehension, the model is most accurate for small beam deflections near the first eigenmode of the beam. ^ The process and results of an experimental investigation are documented, and compared with a circuit simulation modeling the full test system. The comparison qualitatively proves the functionality of the model, while a numerical analysis serves to validate the functionality and setup of the circuit simulation. The use of the simulation enables a much broader investigation of both the electrical behavior and the physical device\u27s dynamics. It is used to complement an assessment of the tuning behavior of the system\u27s linear natural frequency by demonstrating the tuning behavior of the full nonlinear response. The simulation is used to demonstrate the difficulties with the contemporary mixing approach to experimental data collection and to complete a variety of case studies investigating the use of the nanoresonator systems in practical applications, such as signal filtering. Many of these case studies would be difficult to complete analytically, but results are quickly achieved through the use of the simulation

Graphene NanoElectroMechanical Resonators and Oscillators

Made of only one sheet of carbon atoms, graphene is the thinnest yet strongest material ever exist. Since its discovery in 2004, graphene has attracted tremendous research effort worldwide. Guaranteed by the superior electrical and excellent mechanical properties, graphene is the ideal building block for NanoElectroMechanical Systems (NEMS). In the first parts of the thesis, I will discuss the fabrications and measurements of typical graphene NEMS resonators, including doubly clamped and fully clamped graphene mechanical resonators. I have developed a electrical readout technique by using graphene as frequency mixer, demonstrated resonant frequencies in range from 30 to 200 MHz. Furthermore, I developed the advanced fabrications to achieve local gate structure, which led to the real-time resonant frequency detection under resonant channel transistor (RCT) scheme. Such real-time detection improve the measurement speed by 2 orders of magnitude compared to frequency mixing technique, and is critical for practical applications. Finally, I employed active balanced bridge technique in order to reduce overall electrical parasitics, and demonstrated pure capacitive transduction of graphene NEMS resonators. Characterizations of graphene NEMS resonators properties are followed, including resonant frequency and quality factor ($Q$) tuning with tension, mass and temperatures. A simple continuum mechanics model was constructed to understand the frequency tuning behavior, and it agrees with experimental data extremely well. In the following parts of the thesis, I will discuss the behavior of graphene mechanical resonators in applied magnetic field, {i.e.} in Quantum Hall (QH) regime. The couplings between mechanical motion and electronic band structure turned out to be a direct probe for thermodynamic quantities, {i.e.}, chemical potential and compressibility. For a clean graphene resonators, with quality factors of $1 \times 10^4$, it underwent resonant frequency oscillations as applied magnetic field increases. The chemical potential of graphene shifts smoothly within each LL, causing the resonant frequency to change in an explicit pattern. Between LLs, the finite compressibility caused the resonant frequency changing dramatically. The overall oscillations of resonant frequency with the applied magnetic field could be fitted with only disorder potential as free parameter. Compared with conventional electronic transport technique, such mechanical measurements proven to be a more direct and powerful tool, which we used o study the properties of graphene's ground states in broken symmetry states. In the last part this thesis, I will present the study of graphene NEMS oscillators with positive feedback loop. The demonstrated oscillators are self-sustained (without external radio frequency, RF, stimulus), and the oscillation frequencies can be controlled by tension{i.e.}, (applied gate voltage). I also carefully studied the influence of feedback gain and phase, as well as linewidth compression as function of temperature

Mass sensing with graphene and carbon nanotube mechanical resonators

In recent years, carbon nanotube and graphene mechanical resonators have attracted considerable attention because of their unique properties. Their high resonance frequencies, high quality factors and their ultra-low mass turn them into exceptional sensors of minuscule external forces and masses. Their sensing capabilities hold promise for scanning probe microscopy, magnetic resonance imaging and mass spectrometry. Moreover, they are excellent probes for studying mechanical motion in the quantum regime, investigating nonlinear dynamics and carrying out surface science experiments on crystalline low-dimensional systems. A goal for fully exploiting the potential of mechanical resonators remains: Reaching the fundamental limit of the resolution of mass sensing imposed by the thermomechanical noise of the resonator. Currently, limitations are typically due to noise in the motion transduction. Nanotube and graphene resonators are particularly sensitive to noise in the detection since their intrinsically small dimensions result in minuscule transduced electrical or optical signals. This thesis researches ways for improving the mass resolution of the intrinsically smallest mechanical resonator systems, which are based on suspended graphene and carbon nanotubes. For this, we follow two complementary pathways. We first see how far we can go in terms of mass resolution with graphene resonators by reducing their size. We fabricate double clamped graphene resonators with submicron lengths and measure their mechanical properties at 4.2 K. The frequency stability of the resonators allows us to evaluate their mass resolution. We show that the frequency stability of graphene resonators is limited by the imprecision of the detection of the mechanical motion. We then develop a new electrical downmixing scheme to read-out the mechanical motion with a lower noise compared to previous techniques. It utilizes a RLC resonator together with an amplifier based on a high electron mobility transistor operated at 4.2 K. The signal to noise ratio is improved thanks to signal read-out at higher frequency (1.6 MHz compared to 1-10 kHz) and low temperature amplification. We observe an improved frequency stability measuring a carbon nanotube mechanical resonator with this read-out. The stability is no longer limited by the measurement instrumentation noise but by the device itself. Observing the intrinsic fluctuations of the resonator allows in future experiments to study surface science phenomena. We present some preliminary results that hint to the observation of the diffusion of xenon atoms on the surface of the resonator and to the adsorption of single fullerene molecules.En los últimos años, los resonadores mecánicos de nanotubos de carbono y grafeno han atraído una atención considerable debido a sus propiedades únicas. Sus altas frecuencias de resonancia, sus factores de calidad altos y su masa extremadamente baja los convierten en sensores excepcionales de fuerzas externas y masas minúsculas. Sus capacidades de detección son prometedoras para la microscopía con sonda de barrido, la tomografía por resonancia magnética y la espectrometría de masas. Además, son sondas excelentes para estudiar el movimiento mecánico en el régimen cuántico, investigar la dinámica no lineal y llevar a cabo experimentos de ciencia de superficie en sistemas cristalinos de baja dimensión. La explotación de todo el potencial de los resonadores mecánicos sigue siendo un objetivo: alcanzar el límite fundamental de la resolución de la detección de masas impuesta por el ruido termomecánico del resonador. Actualmente, las limitaciones se deben normalmente al ruido en la transducción de movimiento. Los resonadores de nanotubos y grafeno son particularmente sensibles al ruido en la detección, ya que sus dimensiones intrínsecamente pequeñas producen señales eléctricas u ópticas transducidas minúsculas. Esta tesis investiga formas de mejorar la resolución de masa de los sistemas de resonadores mecánicos intrínsecamente más pequeños, que se basan en grafeno suspendido y nanotubos de carbono. Para esto, seguimos dos caminos complementarios. Primero vemos hasta dónde podemos llegar en términos de resolución de masa con resonadores de grafeno al reducir su tamaño. Fabricamos resonadores de grafeno de doble sujeción con longitudes submicrométricas y medimos sus propiedades mecánicas a 4,2 K. La estabilidad de la frecuencia de los resonadores nos permite evaluar su resolución de masa. Mostramos que la estabilidad de la frecuencia de los resonadores de grafeno está limitada por la imprecisión de la detección del movimiento mecánico. Luego desarrollamos un nuevo esquema de downmixing eléctrico para leer el movimiento mecánico con un ruido más bajo en comparación con las técnicas anteriores. Utiliza un resonador RLC junto con un amplificador basado en un transistor de alta movilidad de electrones operado a 4,2 K. La relación señal / ruido se mejora gracias a la lectura de la señal a mayor frecuencia (1,6 MHz en comparación con 1-10 kHz) y a la amplificación a temperatura baja. Observamos una mejor estabilidad de la frecuencia midiendo un resonador mecánico de nanotubos de carbono con esta lectura. La estabilidad ya no está limitada por el ruido de la instrumentación de medición, sino por el propio dispositivo. Observar las fluctuaciones intrínsecas del resonador permite en futuros experimentos estudiar fenómenos de ciencia de superficie. Presentamos algunos resultados preliminares que apuntan a la observación de difusión de átomos de xenón en la superficie del resonador y a la adsorción de moléculas individuales de fulereno

Mechanical Properties of Low Dimensional Materials

Recent advances in low dimensional materials (LDMs) have paved the way for unprecedented technological advancements. The drive to reduce the dimensions of electronics has compelled researchers to devise newer techniques to not only synthesize novel materials, but also tailor their properties. Although micro and nanomaterials have shown phenomenal electronic properties, their mechanical robustness and a thorough understanding of their structure-property relationship are critical for their use in practical applications. However, the challenges in probing these mechanical properties dramatically increase as their dimensions shrink, rendering the commonly used techniques inadequate. This Dissertation focuses on developing techniques for accurate determination of elastic modulus of LDMs and their mechanical responses under tensile and shear stresses. Fibers with micron-sized diameters continuously undergo tensile and shear deformations through many phases of their processing and applications. Significant attention has been given to their tensile response and their structure-tensile properties relations are well understood, but the same cannot be said about their shear responses or the structure-shear properties. This is partly due to the lack of appropriate instruments that are capable of performing direct shear measurements. In an attempt to fill this void, this Dissertation describes the design of an inexpensive tabletop instrument, referred to as the twister, which can measure the shear modulus (G) and other longitudinal shear properties of micron-sized individual fibers. An automated system applies a pre-determined twist to the fiber sample and measures the resulting torque using a sensitive optical detector. The accuracy of the instrument was verified by measuring G for high purity copper and tungsten fibers. Two industrially important fibers, IM7 carbon fiber and Kevlar® 119, were found to have G = 17 and 2.4 GPa, respectively. In addition to measuring the shear properties directly on a single strand of fiber, the technique was automated to allow hysteresis, creep and fatigue studies. Zinc oxide (ZnO) semiconducting nanostructures are well known for their piezoelectric properties and are being integrated into several nanoelectro-mechanical (NEMS) devices. In spite of numerous studies on the mechanical response of ZnO nanostructures, there is not a consensus in its measured bending modulus (E). In this Dissertation, by employing an all-electrical Harmonic Detection of Resonance (HDR) technique on ZnO nanowhisker (NW) resonators, the underlying origin for electrically-induced mechanical oscillations in a ZnO NW was elucidated. Based on visual detection and electrical measurement of mechanical resonances under a scanning electron microscope (SEM), it was shown that the use of an electron beam as a resonance detection tool alters the intrinsic electrical character of the ZnO NW, and makes it difficult to identify the source of the charge necessary for the electrostatic actuation. A systematic study of the amplitude of electrically actuated as-grown and gold-coated ZnO NWs in the presence (absence) of an electron beam using an SEM (dark-field optical microscope) suggests that the oscillations seen in our ZnO NWs are due to intrinsic static charges. In experiments involving mechanical resonances of micro and nanostructured resonators, HDR is a tool for detecting transverse resonances and E of the cantilever material. To add to this HDR capability, a novel method of measuring the G using HDR is presented. We used a helically coiled carbon nanowire (HCNW) in singly-clamped cantilever configuration, and analyzed the complex (transverse and longitudinal) resonance behavior of the nonlinear geometry. Accordingly, a synergistic protocol was developed which (i) integrated analytical, numerical (i.e., finite element using COMSOL ®) and experimental (HDR) methods to obtain an empirically validated closed form expression for the G and resonance frequency of a singly-clamped HCNW, and (ii) provided an alternative for solving 12th order differential equations. A visual detection of resonances (using in situ SEM) combined with HDR revealed intriguing non-planar resonance modes at much lower driving forces relative to those needed for linear carbon nanotube cantilevers. Interestingly, despite the presence of mechanical and geometrical nonlinearities in the HCNW resonance behavior, the ratio of the first two transverse modes f2/f1 was found to be similar to the ratio predicted by the Euler-Bernoulli theorem for linear cantilevers

Nouveau concept de spectrométre de masse à base de réseaux de nanostructures résonantes

The aim of the project is to bring a proof of concept of a simplified mass spectrometer architecture using an ultra dense network of NEMS in association with elements of CMOS circuit as sensors in order to amplify the signal in situ and adress them individually. Since several years, Roukes' team at Caltech has demonstrated a mass spectrometry with a NEMS. In parallel, the CEA/LETI-MINATEC has developped a fabrication approach called VLSI of NEMS and an electromecanical simulation method of these elements The first objective of this thesis is to study the noise phenomenon currently limiting our mass resolution in order to reach 10 Da instead of current 1000 Da on ranges going from 10 Da to 1MDa. In a second step, the concept of NEMS-based mass spectrometry is validated by comparison a nanometric cluster spectra with those from a conventional time-of-flight mass spectrometer. Then, a frequency addressing technique is applied on an NEMS array to allow for quasi simultaneous tracking of 20 different resonators. Finally, the NEMS array is inserted in the nanocluster bench to measure 20 spectra in parallel and validate a first proof of concept.L'enjeu du travail est d'apporter une preuve de concept d'une architecture simplifiée de spectromètre en utilisant comme détecteur un réseau ultra-dense de NEMS associés à des éléments de circuit CMOS afin d'amplifier le signal in situ et de les adresser individuellement. Depuis plusieurs années, l'équipe du professeur Roukes à CALTECH a présenté une démonstration de spectrométrie de masse avec un NEMS. En parallèle, le CEA/LETI-MINATEC a développé une approche de fabrication dite VLSI de NEMS et de simulation électromécanique de ces éléments. Le premier but de la thèse est l'étude des phénomènes de bruit limitant la résolution en masse afin d'atteindre 10 Da au lieu des 1000 Da actuels sur des rangs de masses large allant de 10Da à 1MDa. Dans un second temps, La concept de spectrométrie de masse à base de NEMS est validé en comparant des spectres obtenus sur des nano-agrégats de quelques nanomètres de diamètres avec ceux fournis par un spectromètre de masse temps-de-vol conventionnel. Puis, un système d'adressage fréquentiel de réseau de NEMS est mis en place pour permettre la mesure quasi simultanée de 20 résonateurs. Enfin, le réseau de NEMS est inséré dans le banc de nano-aggrégats pour mesurer 20 spectres de masses en parallèle et valider une première preuve de concept

Nonlinear dynamics and applications of MEMS and NEMS resonators.

Rich nonlinear behaviours have been observed in microelectromechanical and nanoelectromechanical systems (MEMS and NEMS) resonators. This dissertation has performed a systematic study of nonlinear dynamics in various MEMS and NEMS resonators that appear to be single, two coupled, arrayed, parametric driven and coupled with multiple-fields, with the aim of exploring novel applications. New study on dynamic performance of a single carbon nanotube resonator taking account of the surface induced initial stress has been performed. It is found that the initial stress causes the jumping points, the whirling and chaotic motions to appear at higher driving forces. Chaotic synchronization of two identical MEMS resonators has been theoretically achieved using Open-Plus-Closed-Loop (OPCL) method, and the coupled resonating system is designed as a mass detector that is believed to possess high resistance to noise. The idea of chaotic synchronization is then popularized into wireless sensor networks for the purpose of achieving secure communication. The arising of intrinsic localised mode has been studied in microelectromechanical resonators array that is designed intentionally for an energy harvester, which could potentially be used to achieve high/concentrated energy output. Duffing resonators with negative and positive spring constants can exhibit chaotic behaviour. Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos. Based on the principle of nanomechanical transistor and quantum shuttle mechanism, a high sensitive mass sensor that consists of two mechanically coupled NEMS resonators has been postulated, and the mass sensor which can be realized in large-scale has also been investigated and verified. Furthermore, an novel transistor that couples three physical fields at the same time, i.e. mechanical, optical and electrical, has been designed, and the coupled opto-electro-mechanical simulation has been performed. It is shown from the dynamic analysis that the stable working range of the transistor is much wider than that of the optical wave inside the cavity

Mechanical systems in the quantum regime

Mechanical systems are ideal candidates for studying quantumbehavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter include sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems are bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum {\it mechanics}.Comment: To appear in Phys. Re