Evidence of Surface Loss as Ubiquitous Limiting Damping Mechanism in SiN Micro- and Nanomechanical Resonators.

Silicon nitride (SiN) micro- and nanomechanical resonators have attracted a lot of attention in various research fields due to their exceptionally high quality factors (Qs). Despite their popularity, the origin of the limiting loss mechanisms in these structures has remained controversial. In this Letter we propose an analytical model combining acoustic radiation loss with intrinsic loss. The model accurately predicts the resulting mode-dependent Qs of low-stress silicon-rich and high-stress stoichiometric SiN membranes. The large acoustic mismatch of the low-stress membrane to the substrate seems to minimize radiation loss and Qs of higher modes (n∧m≥3) are limited by intrinsic losses. The study of these intrinsic losses in low-stress membranes reveals a linear dependence with the membrane thickness. This finding was confirmed by comparing the intrinsic dissipation of arbitrary (membranes, strings, and cantilevers) SiN resonators extracted from literature, suggesting surface loss as ubiquitous damping mechanism in thin SiN resonators with Q_{surf}=ßh and ß=6×10^{10}±4×10^{10} m^{-1}. Based on the intrinsic loss the maximal achievable Qs and Qf products for SiN membranes and strings are outlined.

Optical detection of radio waves through a nanomechanical transducer.

Low-loss transmission and sensitive recovery of weak radio-frequency and microwave signals is a ubiquitous challenge, crucial in radio astronomy, medical imaging, navigation, and classical and quantum communication. Efficient up-conversion of radio-frequency signals to an optical carrier would enable their transmission through optical fibres instead of through copper wires, drastically reducing losses, and would give access to the set of established quantum optical techniques that are routinely used in quantum-limited signal detection. Research in cavity optomechanics has shown that nanomechanical oscillators can couple strongly to either microwave or optical fields. Here we demonstrate a room-temperature optoelectromechanical transducer with both these functionalities, following a recent proposal using a high-quality nanomembrane. A voltage bias of less than 10 V is sufficient to induce strong coupling between the voltage fluctuations in a radio-frequency resonance circuit and the membrane's displacement, which is simultaneously coupled to light reflected off its surface. The radio-frequency signals are detected as an optical phase shift with quantum-limited sensitivity. The corresponding half-wave voltage is in the microvolt range, orders of magnitude less than that of standard optical modulators. The noise of the transducer--beyond the measured 800 pV Hz-1/2 Johnson noise of the resonant circuit--consists of the quantum noise of light and thermal fluctuations of the membrane, dominating the noise floor in potential applications in radio astronomy and nuclear magnetic imaging. Each of these contributions is inferred to be 60 pV Hz-1/2 when balanced by choosing an electromechanical cooperativity of ~150 with an optical power of 1 mW. The noise temperature of the membrane is divided by the cooperativity. For the highest observed cooperativity of 6,800, this leads to a projected noise temperature of 40 mK and a sensitivity limit of 5 pV Hz-1/2. Our approach to all-optical, ultralow-noise detection of classical electronic signals sets the stage for coherent up-conversion of low-frequency quantum signals to the optical domain.

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.

Nonlinear mode-coupling in nanomechanical systems.

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.

Optimal operating points of oscillators using nonlinear resonators.

We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.

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 long-standing 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.

Passive phase noise cancellation scheme.

We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction is realized by a passive device consisting 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 instability, the coupled resonators exhibit self-oscillations which arise as a response to the parametric driving, rather than by application of active feedback. 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.

Fast on-wafer electrical, mechanical, and electromechanical characterization of piezoresistive cantilever force sensors.

Validation of a technological process requires an intensive characterization of the performance of the resulting devices, circuits, or systems. The technology for the fabrication of micro and nanoelectromechanical systems (MEMS and NEMS) is evolving rapidly, with new kind of device concepts for applications like sensing or harvesting are being proposed and demonstrated. However, the characterization tools and methods for these new devices are still not fully developed. Here, we present an on-wafer, highly precise, and rapid characterization method to measure the mechanical, electrical, and electromechanical properties of piezoresistive cantilevers. The setup is based on a combination of probe-card and atomic force microscopy technology, it allows accessing many devices across a wafer and it can be applied to a broad range of MEMS and NEMS. Using this setup we have characterized the performance of multiple submicron thick piezoresistive cantilever force sensors. For the best design we have obtained a force sensitivity Re(F) = 158µV/nN, a noise of 5.8 µV (1 Hz-1 kHz) and a minimum detectable force of 37 pN with a relative standard deviation of σ(r) ≈ 8%. This small value of σ(r), together with a high fabrication yield >95%, validates our fabrication technology. These devices are intended to be used as bio-molecular detectors for the measurement of intermolecular forces between ligand and receptor molecule pairs.

Fast and robust hydrogen sensors based on discontinuous palladium films on polyimide, fabricated on a wafer scale.

Fast hydrogen sensors based on discontinuous palladium (Pd) films on supporting polyimide layers, fabricated by a cost-efficient and full-wafer compatible process, are presented. The films, deposited by electron-beam evaporation with a nominal thickness of 1.5 nm, consist of isolated Pd islands that are separated by nanoscopic gaps. On hydrogenation, the volume expansion of Pd brings initially separated islands into contact which leads to the creation of new electrical pathways through the film. The supporting polyimide layer provides both sufficient elasticity for the Pd nanoclusters to expand on hydrogenation and a sufficiently high surface energy for good adhesion of both film and contacting electrodes. The novel order of the fabrication processes involves a dicing step prior to the Pd deposition and stencil lithography for the patterning of microelectrodes. This allows us to preserve the as-deposited film properties. The devices work at room temperature, show response times of a few seconds and have a low power consumption of some tens of nW.

Analysis of the blurring in stencil lithography.

A quantitative analysis of blurring and its dependence on the stencil-substrate gap and the deposition parameters in stencil lithography, a high resolution shadow mask technique, is presented. The blurring is manifested in two ways: first, the structure directly deposited on the substrate is larger than the stencil aperture due to geometrical factors, and second, a halo of material is formed surrounding the deposited structure, presumably due to surface diffusion. The blurring is studied as a function of the gap using dedicated stencils that allow a controlled variation of the gap. Our results show a linear relationship between the gap and the blurring of the directly deposited structure. In our configuration, with a material source of approximately 5 mm and a source-substrate distance of 1 m, we find that a gap size of approximately 10 microm enlarges the directly deposited structures by approximately 50 nm. The measured halo varies from 0.2 to 3 microm in width depending on the gap, the stencil aperture size and other deposition parameters. We also show that the blurring can be reduced by decreasing the nominal deposition thickness, the deposition rate and the substrate temperature.

Detection of bacteria based on the thermomechanical noise of a nanomechanical resonator: origin of the response and detection limits.

We have measured the effect of bacteria adsorption on the resonant frequency of microcantilevers as a function of the adsorption position and vibration mode. The resonant frequencies were measured from the Brownian fluctuations of the cantilever tip. We found that the sign and amount of the resonant frequency change is determined by the position and extent of the adsorption on the cantilever with regard to the shape of the vibration mode. To explain these results, a theoretical one-dimensional model is proposed. We obtain analytical expressions for the resonant frequency that accurately fit the data obtained by the finite element method. More importantly, the theory data shows a good agreement with the experiments. Our results indicate that there exist two opposite mechanisms that can produce a significant resonant frequency shift: the stiffness and the mass of the bacterial cells. Based on the thermomechanical noise, we analyse the regions of the cantilever of lowest and highest sensitivity to the attachment of bacteria. The combination of high vibration modes and the confinement of the adsorption to defined regions of the cantilever allows the detection of single bacterial cells by only measuring the Brownian fluctuations. This study can be extended to smaller cantilevers and other biological systems such as proteins and nucleic acids.