We provide a detailed description of a general procedure by which a nano/micro-mechanical resonator can be calibrated using its thermal motion. A brief introduction to the equations of motion for such a resonator is presented, followed by a detailed derivation of the corresponding power spectral density (PSD) function. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.
Contactless characterization of mechanical resonances using Fabry-Perot interferometry is a powerful tool to study the mechanical and dynamical properties of atomically thin membranes. However, amplitude calibration is often not performed, or only possible by making assumptions on the device parameters such as its mass or the temperature. In this work, we demonstrate a calibration technique that directly measures the oscillation amplitude by detecting higher harmonics that arise from nonlinearities in the optical transduction. Employing this technique, we calibrate the resonance amplitude of two-dimensional nanomechanical resonators, without requiring knowledge of their mechanical properties, actuation force, geometric distances or the laser intensity.
We report on experiments performed in vacuum and at cryogenic temperatures on a tri-port nano-electro-mechanical (NEMS) device. One port is a very non-linear capacitive actuation, while the two others implement the magnetomotive scheme with a linear input force port and a (quasi-linear) output velocity port. We present an experimental method enabling a full characterization of the nanomechanical device harmonic response: the non-linear capacitance function $C(x)$ is derived, and the normal parameters $k$ and $m$ (spring constant and mass) of the mode under study are measured through a careful definition of the motion (in meters) and of the applied forces (in Newtons). These results are obtained with a series of purely electric measurements performed without disconnecting/reconnecting the device, and rely only on known DC properties of the circuit, making use of a thermometric property of the oscillator itself: we use the Young modulus of the coating metal as a thermometer, and the resistivity for Joule heating. The setup requires only three connecting lines without any particular matching, enabling the preservation of a high impedance NEMS environment even at MHz frequencies. The experimental data are fit to a detailed electrical and thermal model of the NEMS device, demonstrating a complete understanding of its dynamics. These methods are quite general and can be adapted (as a whole, or in parts) to a large variety of elecromechanical devices.
We study a hybrid nano-mechanical system coupled to a spin ensemble as a quantum simulator to favor a quantum interference effect, the electromagnetically induced transparency (EIT). This system consists of two nano-mechanical resonators (NAMRs), each of which coupled to a nuclear spin ensemble. It could be regarded as a crucial element in the quantum network of NAMR arrays coupled to spin ensembles. Here, the nuclear spin ensembles behave as a long-lived transducer to store and transfer the NAMRs quantum information. This system shows the analog of EIT effect under the driving of a probe microwave field. The double-EIT phenomenon emerges in the large $N$ (the number of the nuclei) limit with low excitation approximation, because the interactions between the spin ensemble and the two NAMRs are reduced to the coupling of three harmonic oscillators. Furthermore, the group velocity is reduced in the two absorption windows.
Here, we demonstrate the fabrication of single-layer MoS2 mechanical resonators. The fabricated resonators have fundamental resonance frequencies in the order of 10 MHz to 30 MHz (depending on their geometry) and their quality factor is about ~55 at room temperature in vacuum. The dynamical properties clearly indicate that monolayer MoS2 membranes are in the membrane limit (i.e., tension dominated), in contrast to their thicker counterparts, which behave as plates. We also demonstrate clear signatures of nonlinear behaviour of our atomically thin membranes, thus providing a starting point for future investigations on the nonlinear dynamics of monolayer nanomechanical resonators.
Coupled nanomechanical resonators are interesting for both fundamental studies and practical applications as they offer rich and tunable oscillation dynamics. At present, the mechanical coupling in such systems is often mediated by a fixed geometry, such as a joint clamping point of the resonators or a displacement-dependent force. Here we show a graphene-integrated electromechanical system consisting of two physically separated mechanical resonators -- a comb-drive actuator and a suspended silicon beam -- that are tunably coupled by a graphene membrane. The graphene membrane, moreover, provides a sensitive electrical read-out for the two resonating systems silicon structures showing 16 different modes in the frequency range from 0.4~to 24~MHz. In addition, by pulling on the graphene membrane with an electrostatic potential applied to one of the silicon resonators, we control the mechanical coupling, quantified by the $g$-factor, from 20 kHz to 100 kHz. Our results pave the way for coupled nanoelectromechanical systems requiring controllable mechanically coupled resonators.
B. D. Hauer
,C. Doolin
,K. S. D. Beach
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(2013)
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"A general procedure for thermomechanical calibration of nano/micro-mechanical resonators"
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Kevin Beach
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