Martial Defoort

Slippage and Boundary Layer Probed in an Almost Ideal Gas by a Nanomechanical Oscillator

We measure the interaction between ⁴He gas at 4.2 K and a high-quality nanoelectromechanical string device for its first three symmetric modes (resonating at 2.2, 6.7, and 11 MHz with quality factor Q>0.1×10⁶) over almost 6 orders of magnitude in pressure. This fluid can be viewed as the best experimental implementation of an almost ideal monoatomic and inert gas of which properties are tabulated. The experiment ranges from high pressure where the flow is of laminar Stokes-type presenting slippage down to very low pressures where the flow is molecular. In the molecular regime, when the mean-free path is of the order of the distance between the suspended nanomechanical probe and the bottom of the trench, we resolve for the first time the signature of the boundary (Knudsen) layer onto the measured dissipation. Our results are discussed in the framework of the most recent theories investigating boundary effects in fluids (both analytic approaches and direct simulation Monte Carlo methods).

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

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 nonlinear 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 nonlinear 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 electromechanical devices.

Evidence for the role of normal-state electrons in nanoelectromechanical damping mechanisms at very low temperatures.

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.

Audio mixing in a tri-port nano-electro-mechanical device

We report on experiments performed on a cantilever-based tri-port nano-electro-mechanical (NEMS) device. Two ports are used for actuation and detection through the magnetomotive scheme, while the third port is a capacitively coupled gate electrode. By applying a low frequency voltage signal on the gate, we demonstrate mixing in the mechanical response of the device, even for low magnetomotive drives without resorting to conduction measurements through the NEMS. The technique can thus be used, in particular, in the linear regime as an alternative to nonlinear mixing for normal conducting devices. An analytic theory is presented reproducing the data without free parameters.

Thermal conductivity measurement of suspended Si-N membranes from 10 K to 275 K using the 3ω-Völklein method

The thermal properties of suspended thin films prepared by the micro-machining process have been measured using the 3ω dynamic method coupled to a Volklein geometry. A transducer (heater/thermometer) centered on the membrane is driven by an ac current causing periodic thermal oscillations. The measurement of the temperature oscillation on the membrane is made at the third harmonic using a Wheatstone bridge set up. Here by coupling the 3ω method to a Volklein geometry (suspended membrane) we obtained a highly sensitive technique to measure the thermal conductance with a resolution of (ΔK/K = 10−3) and a sensitivity of the order of nanoWatt/K, thanks to a very sensitive niobium nitride thermometry. This method is applied to measure the in-plane thermal conductivity of 100 nm silicon nitride membrane, in the temperature range of 10–275 K.

Nonlinear frequency transduction of nanomechanical Brownian motion

We report on experiments addressing the non-linear interaction between a nano-mechanical mode and position fluctuations. The Duffing non-linearity transduces the Brownian motion of the mode, and of other non-linearly coupled ones, into frequency noise. This mechanism, ubiquitous to all weakly-nonlinear resonators thermalized to a bath, results in a phase diffusion process altering the motion: two limit behaviors appear, analogous to motional narrowing and inhomogeneous broadening in NMR. Their crossover is found to depend non-trivially on the ratio of the frequency noise correlation time to its magnitude. Our measurements obtained over an unprecedented range covering the two limits match the theory of Y. Zhang and M. I. Dykman, Phys. Rev. B 92, 165419 (2015), with no free parameters. We finally discuss the fundamental bound on frequency resolution set by this mechanism, which is not marginal for bottom-up nanostructures.

Scaling laws for the bifurcation escape rate in a nanomechanical resonator.

We report on experimental and theoretical studies of the fluctuation-induced escape time from a metastable state of a nanomechanical Duffing resonator in a cryogenic environment. By tuning in situ the nonlinear coefficient γ we could explore a wide range of the parameter space around the bifurcation point, where the metastable state becomes unstable. We measured in a relaxation process the distribution of the escape times. We have been able to verify its exponential distribution and extract the escape rate Γ. We investigated the scaling of Γ with respect to the distance to the bifurcation point and γ, finding an unprecedented quantitative agreement with the theoretical description of the stochastic problem. Simple power scaling laws turn out to hold in a large region of the parameter space, as anticipated by recent theoretical predictions. These unique findings, implemented in a model dynamical system, are relevant to all systems experiencing underdamped saddle-node bifurcation.

Modal “self-coupling” as a sensitive probe for nanomechanical detection

We present a high-sensitivity measurement technique for mechanical nanoresonators. Due to intrinsic nonlinear effects, different flexural modes of a nanobeam can be coupled while driving each of them on resonance. This mode-coupling scheme is dispersive and one mode resonance shifts with respect to the motional amplitude of the other. The same idea can be implemented on a single mode, exciting it with two slightly detuned signals. This two-tone scheme is used here to measure the resonance lineshape of one mode through a frequency shift in the response of the device. The method acts as an amplitude-to-frequency transduction which ultimately suffers only from phase noise of the local oscillator used and of the nanomechanical device itself. We also present a theory which reproduces the data without free parameters.