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Layered crystals are known to be good candidates for bulk thermoelectric applications as they open new ways to realise highly efficient devices. Two dimensional materials, isolated from layered materials, and their stacking into heterostructures have attracted intense research attention for nanoscale applications due to their high Seebeck coefficient and possibilities to engineer their thermoelectric properties. However, integration to thermoelectric devices is problematic due to their usually high thermal conductivities. Reporting on thermal transport studies between 150 and 300 K, we show that franckeite, a naturally occurring 2D heterostructure, exhibits a very low thermal conductivity which combined with its previously reported high Seebeck coefficient and electrical conductance make it a promising candidate for low dimensional thermoelectric applications. We find cross- and in-plane thermal conductivity values at room temperature of 0.70 and 0.88 W m−1 K−1, respectively, which is one of the lowest values reported today for 2D-materials. Interestingly, a 1.77 nm thick layer of franckeite shows very low thermal conductivity similar to one of the most widely used thermoelectric material Bi2Te3 with the thickness of 10–20 nm. We show that this is due to the low Debye frequency of franckeite and scattering of phonon transport through van der Waals interface between different layers. This observation open new routes for high efficient ultra-thin thermoelectric applications.\ud \ud

Graphene's (GR) remarkable mechanical and electrical properties-such as its Young's modulus, low mass per unit area, natural atomic flatness and electrical conductance-would make it an ideal material for micro and nanoelectromechanical systems (MEMS and NEMS). However, the difficulty of attaching GR to supports, coupled with naturally occurring internal defects in a few layer GR can significantly adversely affect the performance of such devices. Here, we have used a combined contact resonance atomic force microscopy (CR-AFM) and ultrasonic force microscopy (UFM) approach to characterise and map with nanoscale spatial resolution GR membrane properties inaccessible to most conventional scanning probe characterisation techniques. Using a multi-layer GR plate (membrane) suspended over a round hole, we show that this combined approach allows access to the mechanical properties, internal structure and attachment geometry of the membrane providing information about both the supported and suspended regions of the system. We show that UFM allows the precise geometrical position of the supported membrane-substrate contact to be located and provides an indication of the local variation of its quality in the contact areas. At the same time, we show that by mapping the position sensitive frequency and phase response of CR-AFM response, one can reliably quantify the membrane stiffness, and image the defects in the suspended area of the membrane. The phase and amplitude of experimental CR-AFM measurements show excellent agreement with an analytical model accounting for the resonance of the combined CR-AFM probe-membrane system. The combination of UFM and CR-AFM provide a beneficial combination for the investigation of few-layer NEMS systems based on two dimensional materials.

Advances in material design and device miniaturization lead to physical properties that may significantly differ from the bulk ones. In particular, thermal transport is strongly affected when the device dimensions approach the mean free path of heat carriers. Scanning Thermal Microscopy (SThM) is arguably the best approach for probing nanoscale thermal properties with few tens of nm lateral resolution. Typical SThM probes based on microfabricated Pd resistive probes (PdRP) using a spatially distributed heater and a nanoscale tip in contact with the sample provide high sensitivity and operation in ambient, vacuum, and liquid environments. Although some aspects of the response of this sensor have been studied, both for static and dynamic measurements, here we build an analytical model of the PdRP sensor taking into account finite dimensions of the heater that improves the precision and stability of the quantitative measurements. In particular, we analyse the probe response for heat flowing through a tip to the sample and due to probe selfheating and theoretically and experimentally demonstrate that they can differ by more than 50%, hence introducing significant correction in the SThM measurements. Furthermore, we analyzed the effect of environmental parameters such as sample and microscope stage temperatures and laser illumination, which allowed reducing the experimental scatter by a factor of 10. Finally, varying these parameters, we measured absolute values of heat resistances and compared these to the model for both ambient and vacuum SThM operations, providing a comprehensive pathway improving the precision of the nanothermal measurements in SThM.

with the emergence of quantum technologies mastering thermal management is required, especially at the nanoscale. It is now accepted that thermal metamaterials (phononic diodes, themo-crystals) based on phonon manipulation are made possible especially at sub-Kelvin temperatures. In these extreme limits of low temperature and low dimension, phonon heat conduction enters into a quantum regime where the phonon exchange obeys the Landauer formalism. In this regime, phonon transport is governed by the value of the transmission coefficients between the ballistic conductor and the thermal reservoirs. Here, we report an ultra-sensitive thermal experiments made on a ballistic 1D phonon conductor using a new micro-platform suspended sensor. We achieved the measurement of thermal conductance with a resolution of $\Delta \mathrm{K}=\mathrm{K}$ of 1.5% and an unprecedented power sensitivity of few attoWatts around 100 mK. We show that the ballistic thermal transport is dominated by non-ideal transmission coefficients and not by the quantized thermal conductance of the nanowire itself. The measurements reveal scattering mechanisms dominated by phonon diffusion in the reservoirs. Since amorphous silicon nitride are used in that experiment we suspect that scattering of phonons on tunneling two Level systems (TLS) may be at the origin of the reduction of thermal transport. Complementary specific heat experiments are confirming that hypothesis of significant phonon-TLS scattering. The demonstration of the breakdown of the thermal conductance quantization is a major result for the phonon physics, showing that optimized thermal coupling to reservoirs from a 1D structure might be difficult to obtain. This limitation of heat transport in the quantum regime may have significant impacts on the design of modern thermal circuits and nanoelectronics (Josephson junction, quantum solid state devices). This high resolution experimental achievement gives new insight of heat transport in the quantum regime, a scientific goal that has remained uncertain till now.

International audience; Thermal transport properties of amorphous materials at low temperatures are governed by the interaction between phonons and localized excitations referred to as tunneling two level systems (TLS). The temperature variation of the thermal conductivity of these amorphous materials is considered as universal and is characterized by a quadratic power law. This is well described by the phenomenological TLS model even though its microscopic explanation is still elusive. Here, by scaling down to the nanometer scale amorphous systems much below the bulk phonon-TLS mean free path, we probed the robustness of that model in restricted geometry systems. Using very sensitive thermal conductance measurements, we demonstrate that the temperature dependence of the thermal conductance of silicon nitride nanostructures remains mostly quadratic independently of the nanowire section. It is not following the cubic power law in temperature as expected in a Casimir-Ziman regime of boundary limited thermal transport. This shows a thermal transport counter intuitively dominated by phonon-TLS interactions and not by phonon-boundary scattering in the nanowires. This could be ascribed to an unexpected high density of TLS on the surfaces which still dominates the phonon diffusion processes at low temperatures and explains why the universal quadratic temperature dependence of thermal conductance still holds for amorphous nanowires.

We have studied the first three symmetric out-of-plane flexural resonance modes of a goalpost silicon micro-mechanical device. Measurements have been performed at 4.2K in vacuum, demonstrating high Qs and good linear properties. Numerical simulations have been realized to fit the resonance frequencies and produce the mode shapes. These mode shapes are complex, since they involve distortions of two coupled orthogonal bars. Nonetheless, analytic expressions have been developed to reproduce these numerical results, with no free parameters. Owing to their generality they are extremely helpful, in particular to identify the parameters which may limit the performances of the device. The overall agreement is very good, and has been verified on our nano-mechanical version of the device., Journal of Low Temperature Physics (2013)

We present results from a study of the dissipation in nanomechanical gold resonators. We fabricated a nanomechanical resonator consisting of a gold wire of width 300 nm, thickness 80 nm and length 7.5 μm by etching away the underlying GaAs substrate. At low temperatures the resonator had a fundamental frequency of about 7.95 MHz, in part due to tension arising from differential thermal contraction between the gold beam and the underlying semiconductor substrate. The dissipation in the resonator was measured using the magnetomotive method over the temperature range 1 K to 10 mK. We find that the Q-factor of the resonator increases by more than a factor of four between 600 mK and 10 mK. The dissipation follows a weak power law dependence on temperature, ∝T0.5, from approximately 30 mK to 600 mK.

We have measured the thermal properties of suspended membranes from 10 K to 300 K for two amplitudes of internal stress (about 0.1 GPa and 1 GPa) and for two different thicknesses (50 nm and 100 nm). The use of the original 3 \omega -Volklein method has allowed the extraction of both the specific heat and the thermal conductivity of each SiN membrane over a wide temperature range. The mechanical properties of the same substrates have been measured at helium temperatures using nanomechanical techniques. Our measurements show that the thermal transport in freestanding SiN membranes is not affected by the presence of internal stress. Consistently, mechanical dissipation is also unaffected even though Qs increase with increasing tensile stress. We thus demonstrate that the theory developed by Wu and Yu [Phys. Rev. B 84, 174109 (2011)] does not apply to this amorphous material in this stress range. On the other hand, our results can be viewed as a natural consequence of the "dissipation dilution" argument [Y. L. Huang and P. R. Saulson, Rev. Sci. Instrum. 69, 544 (1998)] which has been introduced in the context of mechanical damping., Comment: 15 pages, 6 figures. Submitted to PRB

We have measured the interaction between $^4$He gas at 4.2$~$K and a high-quality nano-electro-mechanical string device for its first 3 symmetric modes (resonating at 2.2$~$MHz, 6.7$~$MHz and 11$~$MHz with quality factor $Q > 0.1$ million) 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 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 nano-mechanical 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 Monte-Carlo DSMC simulations)., Editor's suggestion

We present a specific heat measurement technique adapted to thin or very thin suspended membranes from low temperature (8 K) to 300 K. The presented device allows the measurement of the heat capacity of a 70 ng silicon nitride membrane (50 or 100 nm thick), corresponding to a heat capacity of 1.4x10$^{-10}$ J/K at 8 K and 5.1x10$^{-8}$ J/K at 300 K. Measurements are performed using the 3$\omega$ method coupled to the V$\ddot{o}$lklein geometry. This configuration allows the measurement of both specific heat and thermal conductivity within the same experiment. A transducer (heater/thermometer) is used to create an oscillation of the heat flux on the membrane; the voltage oscillation appearing at the third harmonic which contains the thermal information is measured using a Wheatstone bridge set-up. The heat capacity measurement is performed by measuring the variation of the 3$\omega$ voltage over a wide frequency range and by fitting the experimental data using a thermal model adapted to the heat transfer across the membrane. The experimental data are compared to a regular Debye model; the specific heat exhibits features commonly seen for glasses at low temperature.

International audience; 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

International audience; 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 104.We also measure the dynamic range of the beams and their nonlinear (Duffing) behaviour

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., SI not provided

International audience; 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

International audience; 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 {\it 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

We present measurements of the dissipation and frequency shift in nanomechanical gold resonators at temperatures down to 10 mK. The resonators were fabricated as doubly-clamped beams above a GaAs substrate and actuated magnetomotively. Measurements on beams with frequencies 7.95 MHz and 3.87 MHz revealed that from 30 mK to 500 mK the dissipation increases with temperature as $T^{0.5}$, with saturation occurring at higher temperatures. The relative frequency shift of the resonators increases logarithmically with temperature up to at least 400 mK. Similarities with the behavior of bulk amorphous solids suggest that the dissipation in our resonators is dominated by two-level systems.

We present results from a study of the nonlinear intermodal coupling between different flexural vibrational modes of a single high-stress, doubly-clamped silicon nitride nanomechanical beam. The measurements were carried out at 100 mK and the beam was actuated using the magnetomotive technique. We observed the nonlinear behavior of the modes individually and also measured the coupling between them by driving the beam at multiple frequencies. We demonstrate that the different modes of the resonator are coupled to each other by the displacement induced tension in the beam, which also leads to the well known Duffing nonlinearity in doubly-clamped beams., Comment: 15 pages, 7 figures

International audience; The thermal properties of suspended thin films prepared by the micro-machining process have been measured using the 3! dynamic method coupled to a Volklein geometry. A transducer (heater/thermometer) centered on the membrane is driven by an ac current causingperiodic 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 3! method to a Voolklein geometry (suspended membrane) we obtained a highly sensitive techniqueto measure the thermal conductance with a resolution of (..K=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, inthe temperature range of 10-275 K