Addressing geometric nonlinearities with cantilever microelectromechanical systems: Beyond the Duffing model

Collin, Eddy; Bunkov, Yu. M.; Godfrin, H.

doi:10.1103/physrevb.82.235416

Cited by 27 publications

(50 citation statements)

References 40 publications

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“…3 the data are presented as a function of the drive current, for three magnetic fields (two in the S and the other one in the N states). When the lineshape becomes too nonlinear, we can still recompute the nonlinear FWHH from the height of the resonance peak, making sure the frequency sweep has been performed in the proper upwards/downwards direction with respect to β [32]. FWHH obtained from "brute force" fits of the nonlinear lines are also displayed (open symbols; see Supplemental Material [45]).…”

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confidence: 99%

Evidence for the Role of Normal-State Electrons in Nanoelectromechanical Damping Mechanisms at Very Low Temperatures

et al. 2013

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We report on experiments performed at low temperatures on aluminum covered silicon nanoelectromechanical resonators. The substantial difference observed between the mechanical dissipation in the normal and superconducting states measured within the same device unambiguously demonstrates the importance of normal-state electrons in the damping mechanism. The dissipative component becomes vanishingly small at very low temperatures in the superconducting state, leading to exceptional values for the quality factor of such small silicon structures. A critical discussion is given within the framework of the standard tunneling model. PACS numbers: 85.85.+j, 62.30.+d, 62.40.+i, Micro and nanomechanical devices are under intense investigation for both their promising instrumental applications and their implication in fundamental issues of physics. These devices are ultra-sensitive mass [1] and force detectors [2], they can be used in their linear [3] or nonlinear regimes [4] to implement various signal processing schemes [5,6]. In a more fundamental realm, they can be thought of as probes for non-newtonian deviations to gravity at small scales [7], for refined studies of the Casimir force [8], and for the study of quantum fluids [9]. Moreover, nanoresonators themselves cooled to their quantum ground state tackle problems that have been around quantum mechanics since the early beginning, with the possibility of controlling a mechanical collective macroscopic degree of freedom at the quantum level [10][11][12][13].Having high quality devices is desirable in many of these fields. However, it is well known that the quality factor Q of mechanical structures becomes worse as their size is reduced [14], while internal stresses have been found to drastically increase the Q in silicon-nitride nanobeams [15]. Although it is clear that the surfaceto-volume ratio is a key ingredient for the understanding of mechanical dissipation, a proper theoretical explanation covering all experiments remains elusive [16][17][18][19]. Nanomechanical friction mechanisms thus deserve to be understood from both an engineering and a fundamental condensed matter physics point of view.Almost all nanoresonators used in dissipation experiments possess a metallic coating used to actuate and detect the motion. This layer has an essential impact on the mechanical properties, since it adds mass and surface stresses which significantly modify the dissipation characteristics [16,20]. Most experiments are performed with normal conducting metals; only little is known about superconductor-covered nanodevices [13,21,22].Addressing dissipation mechanisms requires a broad temperature range to be explored, within the Kelvin and sub-Kelvin range. Common features are observed: the dissipation follows a power law T n below a certain temperature T * , with a crossover to a rather flat high temperature region that depends on the nature and size of the object. The resonance frequency shifts logarithmically at the lowest temperatures, and reveals a maximum around the same cr...

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confidence: 99%

Evidence for the Role of Normal-State Electrons in Nanoelectromechanical Damping Mechanisms at Very Low Temperatures

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“…The full lines are quadratic fits to the data from which we determine the nonlinear (Duffing) term, β, which appears for large displacements. Inset: example resonance line in the nonlinear regime (Color figure online) and can be positive or negative depending on whether the frequency shifts up or down [18]. As seen in Fig.…”

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confidence: 95%

Stressed Silicon Nitride Nanomechanical Resonators at Helium Temperatures

et al. 2012

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We have characterized the mechanical resonance properties (both linear and nonlinear) of various doubly-clamped silicon nitride nanomechanical resonators, each with a different intrinsic tensile stress. The measurements were carried out at 4 K and the magnetomotive technique was used to drive and detect the motion of the beams. The resonant frequencies of the beams are in the megahertz range, with quality factors of the order of 10 4 . We also measure the dynamic range of the beams and their nonlinear (Duffing) behaviour.

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“…Using the nonlinear coefficients of Ref. [23], we obtain in the high-Q limit: Error bars size of the order of the symbols (±150 Hz).…”

Section: Methodsmentioning

confidence: 99%

“…This geometry has been studied extensively in our group, from MEMS to NEMS scales with various metallic coatings [20][21][22][23][24]. In the following, the quoted displacement x corresponds to the motion of the paddle (top end of the cantilevers).…”

Section: Setupmentioning

confidence: 99%

In-situ comprehensive calibration of a tri-port nano-electro-mechanical device

Collin

Defoort

Lulla

et al. 2012

Review of Scientific Instruments

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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 (quasilinear) 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.

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Addressing geometric nonlinearities with cantilever microelectromechanical systems: Beyond the Duffing model

Cited by 27 publications

References 40 publications

Evidence for the Role of Normal-State Electrons in Nanoelectromechanical Damping Mechanisms at Very Low Temperatures

Evidence for the Role of Normal-State Electrons in Nanoelectromechanical Damping Mechanisms at Very Low Temperatures

Stressed Silicon Nitride Nanomechanical Resonators at Helium Temperatures

In-situ comprehensive calibration of a tri-port nano-electro-mechanical device

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