Mechanical stiffening, bistability, and bit operations in a microcantilever
TL;DR: In this paper, the authors investigated the nonlinear dynamics of microcantilevers and showed that at strong driving, the cantilever amplitude is bistable and suggested several applications for the bistability of the canticle.
Abstract: We investigate the nonlinear dynamics of microcantilevers. We demonstrate mechanical stiffening of the frequency response at large amplitudes, originating from the geometric nonlinearity. At strong driving the cantilever amplitude is bistable. We map the bistable regime as a function of drive frequency and amplitude, and suggest several applications for the bistable microcantilever, of which a mechanical memory is demonstrated.
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TL;DR: This review provides insight into the mechanical phenomena that occur in suspended mechanical structures when either biological adsorption or interactions take place on their surface: mass, surface stress, effective Young's modulus and viscoelasticity.
Abstract: The advances in micro- and nanofabrication technologies enable the preparation of increasingly smaller mechanical transducers capable of detecting the forces, motion, mechanical properties and masses that emerge in biomolecular interactions and fundamental biological processes. Thus, biosensors based on nanomechanical systems have gained considerable relevance in the last decade. This review provides insight into the mechanical phenomena that occur in suspended mechanical structures when either biological adsorption or interactions take place on their surface. This review guides the reader through the parameters that change as a consequence of biomolecular adsorption: mass, surface stress, effective Young's modulus and viscoelasticity. The mathematical background needed to correctly interpret the output signals from nanomechanical biosensors is also outlined here. Other practical issues reviewed are the immobilization of biomolecular receptors on the surface of nanomechanical systems and methods to attain that in large arrays of sensors. We then describe some relevant realizations of biosensor devices based on nanomechanical systems that harness some of the mechanical effects cited above. We finally discuss the intrinsic detection limits of the devices and the limitation that arises from non-specific adsorption.
334 citations
TL;DR: The high-amplitude operation of a buckled resonator coupled to an optical cavity is demonstrated by using a highly efficient process to generate enough phonons in the resonator to overcome the energy barrier in the double-well potential.
Abstract: The ability to control mechanical motion with optical forces has made it possible to cool mechanical resonators to their quantum ground states. The same techniques can also be used to amplify rather than reduce the mechanical motion of such systems. Here, we study nanomechanical resonators that are slightly buckled and therefore have two stable configurations, denoted 'buckled up' and 'buckled down', when they are at rest. The motion of these resonators can be described by a double-well potential with a large central energy barrier between the two stable configurations. We demonstrate the high-amplitude operation of a buckled resonator coupled to an optical cavity by using a highly efficient process to generate enough phonons in the resonator to overcome the energy barrier in the double-well potential. This allows us to observe the first evidence for nanomechanical slow-down and a zero-frequency singularity predicted by theorists. We also demonstrate a non-volatile mechanical memory element in which bits are written and reset by using optomechanical backaction to direct the relaxation of a resonator in the high-amplitude regime to a specific stable configuration.
230 citations
TL;DR: A reprogrammable logic device based on the electrothermal frequency modulation scheme of a single microelectromechanical resonator, capable of performing all the fundamental 2- bit logic functions as well as n-bit logic operations, and promises an alternative electromechanical computing scheme.
Abstract: In modern computing, the Boolean logic operations are set by interconnect schemes between the transistors. As the miniaturization in the component level to enhance the computational power is rapidly approaching physical limits, alternative computing methods are vigorously pursued. One of the desired aspects in the future computing approaches is the provision for hardware reconfigurability at run time to allow enhanced functionality. Here we demonstrate a reprogrammable logic device based on the electrothermal frequency modulation scheme of a single microelectromechanical resonator, capable of performing all the fundamental 2-bit logic functions as well as n-bit logic operations. Logic functions are performed by actively tuning the linear resonance frequency of the resonator operated at room temperature and under modest vacuum conditions, reprogrammable by the a.c.-driving frequency. The device is fabricated using complementary metal oxide semiconductor compatible mass fabrication process, suitable for on-chip integration, and promises an alternative electromechanical computing scheme.
143 citations
TL;DR: An experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities and assessment of the validity of the approach is found.
Abstract: Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced nanomechanical devices; it has important implications for applications ranging from quantitative sensing to fundamental research. However, achieving accurate experimental characterization of nonlinearities in nanomechanical systems (NEMS) is problematic. Currently employed detection and actuation schemes themselves tend to be highly nonlinear, and this unrelated nonlinear response has been inadvertently convolved into many previous measurements. In this Letter we describe an experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities. By comparing predictions from Euler–Bernoulli theory for the intra- and intermodal nonlinearities of a doubly clamped beam, we assess the validity of our approach and find excellent agreement.
119 citations
TL;DR: In this paper, the Euler-Bernoulli beam theory is used to characterize the nonlinear response of nanomechanical cantilevers using an ultralinear detection system.
Abstract: Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro- and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation.
117 citations
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TL;DR: In this article, an electrostatic mechanism for tuning the nonlinearity of nanomechanical resonators and increasing their dynamic range for sensor applications is explored, and a theoretical model is developed that qualitatively explains the experimental results and serves as a simple guide for design of tunable nano-chanical devices.
Abstract: We explore an electrostatic mechanism for tuning the nonlinearity of nanomechanical resonators and increasing their dynamic range for sensor applications. We also demonstrate tuning the resonant frequency of resonators both upward and downward. A theoretical model is developed that qualitatively explains the experimental results and serves as a simple guide for design of tunable nanomechanical devices.
323 citations
TL;DR: An approach to mechanical logic based on nanoelectromechanical systems that is a variation on the Parametron architecture is proposed and, as a first step towards a possible nanomechanical computer, both bit storage and bit flip operations are demonstrated.
Abstract: The Parametron was first proposed as a logic-processing system almost 50 years ago1. In this approach the two stable phases of an excited harmonic oscillator provide the basis for logic operations2,3,4,5,6. Computer architectures based on LC oscillators were developed for this approach, but high power consumption and difficulties with integration meant that the Parametron was rendered obsolete by the transistor. Here we propose an approach to mechanical logic based on nanoelectromechanical systems7,8,9 that is a variation on the Parametron architecture and, as a first step towards a possible nanomechanical computer10,11,12, we demonstrate both bit storage and bit flip operations.
302 citations
TL;DR: A technique for detecting persistent currents that allows us to measure the persistent current in metal rings over a wide range of temperatures, ring sizes, and magnetic fields is developed.
Abstract: Quantum mechanics predicts that the equilibrium state of a resistive metal ring will contain a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. We have developed a technique for detecting persistent currents that allows us to measure the persistent current in metal rings over a wide range of temperatures, ring sizes, and magnetic fields. Measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons.
263 citations
TL;DR: In this article, the authors investigated the near-resonant, nonlinear dynamic response of microcantilevers in atomic force microscopy through numerical continuation techniques and simulations of discretized models of the micro cantilever interacting with a surface through a Lennard-Jones potential.
Abstract: The near‐resonant, nonlinear dynamic response of microcantilevers in atomic force microscopy is investigated through numerical continuation techniques and simulations of discretized models of the microcantilever interacting with a surface through a Lennard‐Jones potential. The tapping‐mode responses of two representative systems, namely a soft silicon probe‐silicon sample system and a stiff silicon probe‐polystyrene sample system, are studied. Van der Waals interactions are shown to lead to a softening nonlinearity of the periodic solution response, while the short‐range repulsive interactions lead to an overall hardening nonlinear response. Depending on the tip‐sample properties, the dynamics of the microcantilevers occur either in asymmetric single‐well potential regions or in asymmetric double‐well potential regions. In both cases, forced periodic motions of the probe tip destabilize through a sequence of period‐doubling bifurcations, while, in the latter, the tip can also escape the potential well to execute complex and unpredictable cross‐well dynamics. The results predict a broad range of nonlinear dynamic phenomena, many of which have been observed in the literature on experimental atomic force microscopy.
150 citations
TL;DR: The technique, in principle, provides a quantum nondemolition method of tracking a resonator's phase and achieves a 10 dB reduction in phase diffusion by using the technique on an oscillator whose frequency-controlling element is a nonlinear mechanical resonator.
Abstract: Resonators driven to self-oscillation via active feedback play an important role in technology. Among the stochastic processes driving phase diffusion in such oscillators is noise from the feedback amplifier. Here a technique is described by which phase diffusion due to this noise can be suppressed. We have achieved a 10 dB reduction in phase diffusion by using the technique on an oscillator whose frequency-controlling element is a nonlinear mechanical resonator. The technique, in principle, provides a quantum nondemolition method of tracking a resonator's phase.
139 citations