Parametric Nanomechanical Amplification at Very High Frequency

Parametric resonance and amplification are important in both fundamental physics and technological applications. Here we report very high frequency (VHF) parametric resonators and mechanical-domain amplifiers based on nanoelectromechanical systems (NEMS). Compound mechanical nanostructures patterned by multilayer, top-down nanofabrication are read out by a novel scheme that parametrically modulates longitudinal stress in doubly clamped beam NEMS resonators. Parametric pumping and signal amplification are demonstrated for VHF resonators up to ~ 130 MHz and provide useful enhancement of both resonance signal amplitude and quality factor. We find that Joule heating and reduced thermal conductance in these nanostructures ultimately impose an upper limit to device performance. We develop a theoretical model to account for both the parametric response and nonequilibrium thermal transport in these composite nanostructures. The results closely conform to our experimental observations, elucidate the frequency and threshold-voltage scaling in parametric VHF NEMS resonators and sensors, and establish the ultimate sensitivity limits of this approach

Efficient parametric amplification in high and very high frequency piezoelectric nanoelectromechanical systems

Parametric amplification in nanomechanical structures is demonstrated by modulating a purely intrinsic mechanical parameter of the system—the stress—via piezoelectric electromechanical coupling. Large resonance amplitude and quality factor enhancement due to parametric pumping are observed under both vacuum and ambient pressure conditions. Exploration of the region of parametric instability yields results that agree with parametric amplification theory

Stress-Induced Variations in the Stiffness of Micro- and Nanocantilever Beams

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

Signal Amplification by Sensitive Control of Bifurcation Topology

We describe a novel amplification scheme based on inducing dynamical changes to the topology of a bifurcation diagram of a simple nonlinear dynamical system. We have implemented a first bifurcation-topology amplifier using a coupled pair of parametrically driven high-frequency nanoelectromechanical systems resonators, demonstrating robust small-signal amplification. The principles that underlie bifurcation-topology amplification are simple and generic, suggesting its applicability to a wide variety of physical, chemical, and biological systems

A Passive Phase Noise Cancellation Element

We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the output of a conventional oscillator at a frequency close to the sum of the linear mode frequencies. Above the threshold for parametric response, the coupled resonators exhibit self-oscillation at an inherent frequency. We find operating points of the device for which this periodic signal is immune to frequency noise in the driving oscillator, providing a way to clean its phase noise. We present results for the effect of thermal noise to advance a broader understanding of the overall noise sensitivity and the fundamental operating limits

Piezoelectric nanoelectromechanical resonators based on aluminum nitride thin films

We demonstrate piezoelectrically actuated, electrically tunable nanomechanical resonators based on multilayers containing a 100-nm-thin aluminum nitride (AlN) layer. Efficient piezoelectric actuation of very high frequency fundamental flexural modes up to ~80 MHz is demonstrated at room temperature. Thermomechanical fluctuations of AlN cantilevers measured by optical interferometry enable calibration of the transduction responsivity and displacement sensitivities of the resonators. Measurements and analyses show that the 100 nm AlN layer employed has an excellent piezoelectric coefficient, d_(31)=2.4 pm/V. Doubly clamped AlN beams exhibit significant frequency tuning behavior with applied dc voltage

Multifunctional Nanomechanical Systems via Tunably Coupled Piezoelectric Actuation

Efficient actuation is crucial to obtaining optimal performance from nanoelectromechanical systems (NEMS). We employed epitaxial piezoelectric semiconductors to obtain efficient and fully integrated NEMS actuation, which is based on exploitation of the interaction between piezoelectric strain and built-in charge depletion. The underlying actuation mechanism in these depletion-mediated NEMS becomes important only for devices with dimensions approaching semiconductor depletion lengths. The induced actuation forces are controlled electrically, and resonant excitation approaching single-electron efficiency is demonstrated. The fundamental electromechanical coupling itself can be programmed by heterostructure band engineering, externally controllable charge depletion, and crystallographic orientation. These attributes are combined to realize a prototype, mechanically based, exclusive-or logic element

Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators

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

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 dual-gate configuration with both bottom-gate and side-gate capable of tuning the resonance frequency through capacitive coupling. Interestingly, downward resonance frequency shifting is observed with increasing side-gate voltage, which can be attributed to the capacitive softening of spring constant. Furthermore, in-plane vibrational modes exhibit 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 new possibility for nonlinear operation of nanotube resonators.Comment: 12 pages/ 3 figure