We perform molecular dynamics (MD) simulations with phonon spectral analysis aiming at understanding the two dimensional (2D) thermal transport in suspended and supported graphene. Within the framework of equilibrium MD simulations, we perform spectral energy density (SED) analysis to obtain the lifetime of individual phonon modes. The per-mode contribution to thermal conductivity is then calculated to obtain the lattice thermal conductivity in the temperature range 300-650 K. In contrast to prior studies, our results suggest that the contribution from out-of-plane acoustic (or ZA) branch to thermal conductivity is around 25-30% in suspended single-layer graphene (SLG) at room temperature. The thermal conductivity is found to reduce when SLG is put on amorphous SiO2 substrate. Such reduction is attributed to the strengthened scattering in all phonon modes in the presence of the substrate. Among them, ZA modes are mostly affected with their contribution to thermal conductivity reduced to around 15%. As a result, thermal transport is dominated by in-plane acoustic phonon modes in supported SLG.
We reported the basal-plane thermal conductivity in exfoliated bilayer hexagonal boron nitride h-BN that was measured using suspended prepatterned microstructures. The h-BN sample suitable for thermal measurements was fabricated by dry-transfer method, whose sample quality, due to less polymer residues on surfaces, is believed to be superior to that of PMMA-mediated samples. The measured room temperature thermal conductivity is around 484 Wm-1K-1(+141 Wm-1K-1/ -24 Wm-1K-1) which exceeds that in bulk h-BN, providing experimental observation of the thickness-dependent thermal conductivity in sus…
Graphene exhibits extraordinary electronic and mechanical properties, and extremely high thermal conductivity. Being a very stable atomically thick membrane that can be suspended between two leads, graphene provides a perfect test platform for studying thermal conductivity in two-dimensional systems, which is of primary importance for phonon transport in low-dimensional materials. Here we report experimental measurements and non-equilibrium molecular dynamics simulations of thermal conduction in suspended single layer graphene as a function of both temperature and sample length. Interestingly …
Establishment of a new technique or extension of an existing technique for thermal and thermoelectric measurements to a more challenging system is an important task to explore the thermal and thermoelectric properties of various materials and systems. The bottleneck lies in the challenges in measuring the thermal contact resistance. In this work, we applied electron beam self-heating technique to derive the intrinsic thermal conductivity of suspended Molybdenum Disulfide (MoS2) ribbons and the thermal contact resistance, with which the interfacial thermal resistance between few-layer MoS2 and …
Raman and photoluminescence (PL) measurements were performed on suspended and supported MoS2 up to 6 trilayers (TLs). The difference in the dielectric environment of suspended and supported MoS2 does not lead to large differences in the PL or Raman spectra. Most of the apparent difference in the PL intensity can be explained by the interference effect except for 1TL MoS2. The positions of the Raman peaks are not much different between suspended and supported MoS2. The relative intensities, on the other hand, show some differences between suspended and supported samples. In particular, the inte…
Modifying phonon thermal conductivity in nanomaterials is important not only for fundamental research but also for practical applications. However, the experiments on tailoring the thermal conductivity in nanoscale, especially in two-dimensional materials, are rare due to technical challenges. In this work, we demonstrate in-situ thermal conduction measurement of MoS2 and find that its thermal conductivity can be continuously tuned to a required value from crystalline to amorphous limits. The reduction of thermal conductivity is understood from phonon-defects scatterings that decrease the phon…
The sticking probability of cold atomic hydrogen on suspended graphene calculated by Lepetit and Jackson [Phys. Rev. Lett. {\bf 107}, 236102 (2011)] does not include the effect of fluctuations from low-frequency vibrations of graphene. These fluctuations suppress the sticking probability for low incident energies ($\lesssim 15$ meV).
We investigate the thermal conductivity of suspended graphene as a function of the density of defects, ND, introduced in a controllable way. Graphene layers are synthesized using chemical vapor deposition, transferred onto a transmission electron microscopy grid, and suspended over ~7.5-micrometer size square holes. Defects are induced by irradiation of graphene with the low-energy electron beam (20 keV) and quantified by the Raman D-to-G peak intensity ratio. As the defect density changes from 2.0x10^10 cm-2 to 1.8x10^11 cm-2 the thermal conductivity decreases from ~(1.8+/-0.2)x10^3 W/mK to ~…
Building smaller transistors with enhanced functionality is critical in extending the limits of Moores law and meeting the demands of the electronics industry. Here we demonstrate transistor operation in a suspended single carbon nanotube (CNT) using feedback-enabled radiation pressure of a near-field focused laser that enabled significant changes in conductivity of the CNT. Further, using in-situ tip-enhanced Raman spectroscopy, we show that the change in conductivity of over five orders in magnitude is accompanied by self-induced defect states within the CNT. The entire structure is less tha…
Mapping the thermal transport properties of materials at the nanoscale is of critical importance for optimizing heat conduction in nanoscale devices. Several methods to determine the thermal conductivity of materials have been developed, most of them yielding an average value across the sample, thereby disregarding the role of local variations. Here, we present a method for the spatially-resolved assessment of the thermal conductivity of suspended graphene by using a combination of confocal Raman thermometry and a finite-element calculations-based fitting procedure. We demonstrate the working …
We extract experimentally the electronic thermal conductivity, $K_{e}$, in suspended graphene which we dope using a back-gate electrode. We make use of two-point dc electron transport at low bias voltages and intermediate temperatures (50 - 160 K), where the electron and lattice temperatures are decoupled. The thermal conductivity is proportional to the charge conductivity times the temperature, confirming that the Wiedemann-Franz relation is obeyed in suspended graphene. We extract an estimate of the Lorenz coefficient as 1.1 to 1.7 $\times 10^{-8}$ W $Ω$K$^{-2}$. $K_e$ shows a transistor eff…
Monolayer WS2 has been a competitive candidate in electrical and optoelectronic devices due to its superior optoelectronic properties. To tackle the challenge of thermal management caused by the decreased size and concentrated heat in modern ICs, it is of great significance to accurately characterize the thermal conductivity of the monolayer WS2, especially with substrate supported. In this work, the dual-wavelength flash Raman method is used to experimentally measure the thermal conductivity of the suspended and the Si/SiO2 substrate supported monolayer WS2 at a temperature range of 200 K - 4…
Recent experiments have reported evidence of dominant electron-hole scattering in the electric conductivity of suspended bilayer graphene near charge neutrality. According to these experiments, plots of the electric conductivity as a function of $μ/k_BT$ (chemical potential scaled with temperature) obtained for different temperatures in the range of $12\rm{K}\lesssim T \lesssim 40\rm{K}$ collapse on a single curve independent of $T$. In a recent theory, this observation has been taken as an indication that the main sub-dominant scattering process is not electron-impurity but electron-phonon. H…
The electrical response of two-dimensional electron gas to vibrations of a nanomechanical cantilever containing it is studied. Vibrations of perpendicularly oriented cantilevers are experimentally shown to change oppositely the conductivity near their bases. This indicates the piezoelectric nature of electromechanical coupling. A physical model is developed, which quantitatively explains the experiment. It shows that the main origin of the conductivity change is a rapid change in the mechanical stress on the boundary between suspended and non-suspended areas, rather than the stress itself.
We study the intrinsic transport properties of suspended graphene devices at high fields (>1 V/um) and high temperatures (>1000 K). Across 15 samples, we find peak (average) saturation velocity of 3.6x10^7 cm/s (1.7x10^7 cm/s), and peak (average) thermal conductivity of 530 W/m/K (310 W/m/K), at 1000 K. The saturation velocity is 2-4 times and the thermal conductivity 10-17 times greater than in silicon at such elevated temperatures. However, the thermal conductivity shows a steeper decrease at high temperature than in graphite, consistent with stronger effects of second-order three-phonon sca…
Thermal properties of suspended single-layer graphene membranes are investigated by characterization of their mechanical motion in response to a high-frequency modulated laser. A characteristic delay time $τ$ between the optical intensity and mechanical motion is observed, which is attributed to the time required to raise the temperature of the membrane. We find, however, that the measured time constants are significantly larger than the predicted ones based on values of the specific heat and thermal conductivity. In order to explain the discrepancy between measured and modeled tau, a model is…
Using nanoparticles to impart extrinsic rippling in graphene is a relatively new method to induce strain and to tailor the properties of graphene. Here we study the structure and elastic properties of graphene grown by chemical vapour deposition and transferred onto a continuous layer of SiO2 nanoparticles with diameters of around 25 nm, prepared by Langmuir-Blodgett technique on Si substrate. We show that the transferred graphene follows only roughly the morphology induced by nanoparticles. The graphene membrane parts bridging the nanoparticles are suspended and their adhesion to the AFM tip …
The tuning of electrical circuit resonance with a variable capacitor, or varactor, finds wide application with the most important being wireless telecommunication. We demonstrate an electromechanical graphene varactor, a variable capacitor wherein the capacitance is tuned by voltage controlled deflection of a dense array of suspended graphene membranes. The low flexural rigidity of graphene monolayers is exploited to achieve low actuation voltage in an ultra-thin structure. Large arrays comprising thousands of suspensions were fabricated to give a tunable capacitance of over 10 pF/mm$^2$, high…
We measure the thermal time constants of suspended single layer molybdenum disulfide drums by their thermomechanical response to a high-frequency modulated laser. From this measurement the thermal diffusivity of single layer MoS$_2$ is found to be 1.14 $\times$ 10$^{-5}$ m$^2$/s on average. Using a model for the thermal time constants and a model assuming continuum heat transport, we extract thermal conductivities at room temperature between 10 to 40 W/(m$\cdot$K). Significant device-to-device variation in the thermal diffusivity is observed. Based on statistical analysis we conclude that thes…
We report a record low thermal conductivity in polycrystalline MoS2 obtained by varying grain sizes and orientations in ultrathin films. By optimizing the sulphurisation parameters of nanometre-thick Mo layer, we could grow MoS2 films with tuneable morphologies. The thermal conductivity is extracted from a Raman laser power-dependent study on suspended samples. The lowest value of thermal conductivity of 0.27 Wm-1K-1, which reaches a similar value as teflon, is obtained in a polycrystalline sample formed by a combination of horizontally and vertically oriented grains, with respect to the bulk …
Suspended graphene is difficult to image by scanning probe microscopy due to the inherent van-der-Waals and dielectric forces exerted by the tip which are not counteracted by a substrate. Here, we report scanning tunneling microscopy data of suspended monolayer graphene in constant-current mode revealing a surprising honeycomb structure with amplitude of 50$-$200 pm and lattice constant of 10-40 nm. The apparent lattice constant is reduced by increasing the tunneling current $I$, but does not depend systematically on tunneling voltage $V$ or scan speed $v_{\rm scan}$. The honeycomb lattice of …
We investigate the effects of charged impurity distributions and carrier-carrier interactions on electronic transport in graphene on SiO$_2$ by employing a self-consistent coupled simulation of carrier transport and electrodynamics. We show that impurity clusters of characteristic width 40--50 nm generate electron--hole puddles of experimentally observed sizes. In the conductivity versus carrier density dependence, the residual conductivity and the linear-region slope are determined by the impurity distribution, and the measured slope can be used to estimate the impurity density in experiment.…
Nanostructured silicon is a promising material for thermoelectric conversion, because the thermal conductivity in silicon nanostructures can be strongly reduced with respect to that of bulk materials. We present thermal conductivity measurements, performed with the 3$ω$ technique, of suspended monocrystalline silicon thin films (nanomembranes or nanoribbons) with smooth and rough surfaces. We find evidence for a significant effect of surface roughness on phonon propagation: the measured thermal conductivity for the rough structures is well below that predicted by theoretical models which take …
Knowledge of the mean free path distribution of heat-carrying phonons is key to understanding phonon-mediated thermal transport. We demonstrate that thermal conductivity measurements of thin membranes spanning a wide thickness range can be used to characterize how bulk thermal conductivity is distributed over phonon mean free paths. A non-contact transient thermal grating technique was used to measure the thermal conductivity of suspended Si membranes ranging from 15 to 1500 nm in thickness. A decrease in the thermal conductivity from 74% to 13% of the bulk value is observed over this thicknes…
The reduction of the thermal conductivity in nanostructures opens up the possibility of exploiting for thermoelectric purposes also materials such as silicon, which are cheap, available and sustainable but with a high thermal conductivity in their bulk form. The development of thermoelectric devices based on these innovative materials requires reliable techniques for the measurement of thermal conductivity on a nanometric scale. The approximations introduced by conventional techniques for thermal conductivity measurements can lead to unreliable results when applied to nanostructures, because h…
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$ω$ 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 us…
The measured frequencies and intensities of different first- and second- order Raman peaks of suspended graphene are used to show that optical phonons and different acoustic phonon polarizations are driven out of local equilibrium inside a sub-micron laser spot. The experimental results are correlated with a first principles-based multiple temperature model to suggest a considerably lower equivalent local temperature of the flexural phonons than those of other phonon polarizations. The finding reveals weak coupling between the flexural modes with hot electrons and optical phonons. Since the ul…
Studying thermal transport at the nanoscale poses formidable experimental challenges due both to the physics of the measurement process and to the issues of accuracy and reproducibility. The laser-induced transient thermal grating (TTG) technique permits non-contact measurements on nanostructured samples without a need for metal heaters or any other extraneous structures, offering the advantage of inherently high absolute accuracy. We present a review of recent studies of thermal transport in nanoscale silicon membranes using the TTG technique. An overview of the methodology, including an anal…
We describe Raman spectroscopy based method of measuring thermal conductivity of thin films, and review significant results achieved with this technique pertinent to graphene and other two-dimensional materials. The optothermal Raman method was instrumental for the discovery of unique heat conduction properties of graphene. In this method, Raman spectroscopy is used to determine the local temperature of the sample while the excitation laser is utilized as a heat source. The success of Raman spectroscopy in investigating thermal conductivity of suspended graphene and graphene-based thin films m…
Thermal conductivity measurements over variable lengths on nanostructures such as nanowires provide important information about the mean free paths (MFPs) of the phonons responsible for heat conduction. However, nearly all of these measurements have been interpreted using an average MFP even though phonons in many crystals possess a broad MFP spectrum. Here, we present a reconstruction method to obtain MFP spectra of nanostructures from variable-length thermal conductivity measurements. Using this method, we investigate recently reported length-dependent thermal conductivity measurements on Si…
In this article, we are proposing a thorough analysis of the cross, and the in-plane thermal conductivity of thin-film materials based on the 3$ω$ method. The analysis accommodates a 2D mathematical heat transfer model of a semi-infinite body and the details of the sample preparation followed by the measurement process. The presented mathematical model for the system considers a two-dimensional space for its solution. It enables the calculation of the cross-plane thermal conductivity with a single frequency measurement, the derived equation opens new opportunities for frequency-based and penet…
Imaging heat transport in suspended diamond nanostructures with integrated spin defect thermometers
Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院）；PROUD SA（PROUD公司）；Istituto Nazionale di Ricerca Metrologica (INRiM)（意大利国家计量研究所）；University of Stuttgart（斯图加特大学）
Strain can tune desirable electronic behavior in graphene, but there has been limited progress in controlling strain in graphene devices. In this paper, we study the mechanical response of graphene on substrates patterned with arrays of mesoscale pyramids. Using atomic force microscopy, we demonstrate that the morphology of graphene can be controlled from conformal to suspended depending on the arrangement of pyramids and the aspect ratio of the array. Non-uniform strains in graphene suspended across pyramids are revealed by Raman spectroscopy and supported by atomistic modeling, which also in…
