Wanyoung Jang

Controlled ripple texturing of suspended graphene and ultrathin graphite membranes

Graphene is the natures thinnest elastic membrane, with exceptional mechanical and electrical properties. We report the direct observation and creation of one-dimensional (1D) and 2D periodic ripples in suspended graphene sheets, using spontaneously and thermally induced longitudinal strains on patterned substrates, with control over their orientations and wavelengths. We also provide the first measurement of graphenes thermal expansion coefficient, which is anomalously large and negative, ~ -7x10^-6 K^-1 at 300K. Our work enables novel strain-based engineering of graphene devices.Graphene is natures thinnest elastic material and displays exceptional mechanical and electronic properties. Ripples are an intrinsic feature of graphene sheets and are expected to strongly influence electronic properties by inducing effective magnetic fields and changing local potentials. The ability to control ripple structure in graphene could allow device design based on local strain and selective bandgap engineering. Here, we report the first direct observation and controlled creation of one- and two-dimensional periodic ripples in suspended graphene sheets, using both spontaneously and thermally generated strains. We are able to control ripple orientation, wavelength and amplitude by controlling boundary conditions and making use of graphenes negative thermal expansion coefficient (TEC), which we measure to be much larger than that of graphite. These results elucidate the ripple formation process, which can be understood in terms of classical thin-film elasticity theory. This should lead to an improved understanding of suspended graphene devices, a controlled engineering of thermal stress in large-scale graphene electronics, and a systematic investigation of the effect of ripples on the electronic properties of graphene.

Thermal Conductivity of Nanocrystalline Silicon: Importance of Grain Size and Frequency-Dependent Mean Free Paths

The thermal conductivity reduction due to grain boundary scattering is widely interpreted using a scattering length assumed equal to the grain size and independent of the phonon frequency (gray). To assess these assumptions and decouple the contributions of porosity and grain size, five samples of undoped nanocrystalline silicon have been measured with average grain sizes ranging from 550 to 64 nm and porosities from 17% to less than 1%, at temperatures from 310 to 16 K. The samples were prepared using current activated, pressure assisted densification (CAPAD). At low temperature the thermal conductivities of all samples show a T(2) dependence which cannot be explained by any traditional gray model. The measurements are explained over the entire temperature range by a new frequency-dependent model in which the mean free path for grain boundary scattering is inversely proportional to the phonon frequency, which is shown to be consistent with asymptotic analysis of atomistic simulations from the literature. In all cases the recommended boundary scattering length is smaller than the average grain size. These results should prove useful for the integration of nanocrystalline materials in devices such as advanced thermoelectrics.

Thermal contact resistance between graphene and silicon dioxide

The thermal contact resistance between graphene and silicon dioxide was measured using a differential 3ω method. The sample thicknesses were 1.2 (single-layer graphene), 1.5, 2.8, and 3.0 nm, as determined by atomic force microscopy. All samples exhibited approximately the same temperature trend from 42 to 310 K, with no clear thickness dependence. The contact resistance at room temperature ranges from 5.6×10−9 to 1.2×10−8 m2 K/W, which is significantly lower than previous measurements involving related carbon materials. These results underscore graphene’s potential for applications in microelectronics and thermal management structures.

Thickness-Dependent Thermal Conductivity of Encased Graphene and Ultrathin Graphite

The thermal conductivity of graphene and ultrathin graphite (thickness from 1 to ∼20 layers) encased within silicon dioxide was measured using a heat spreader method. The thermal conductivity increases with the number of graphene layers, approaching the in-plane thermal conductivity of bulk graphite for the thickest samples, while showing suppression below 160 W/m-K at room temperature for single-layer graphene. These results show the strong effect of the encasing oxide in disrupting the thermal conductivity of adjacent graphene layers, an effect that penetrates a characteristic distance of approximately 2.5 nm (∼7 layers) into the core layers at room temperature.

A photon thermal diode

A thermal diode is a two-terminal nonlinear device that rectifies energy carriers (for example, photons, phonons and electrons) in the thermal domain, the heat transfer analogue to the familiar electrical diode. Effective thermal rectifiers could have an impact on diverse applications ranging from heat engines to refrigeration, thermal regulation of buildings and thermal logic. However, experimental demonstrations have lagged far behind theoretical proposals. Here we present the first experimental results for a photon thermal diode. The device is based on asymmetric scattering of ballistic energy carriers by pyramidal reflectors. Recent theoretical work has predicted that this ballistic mechanism also requires a nonlinearity in order to yield asymmetric thermal transport, a requirement of all thermal diodes arising from the second Law of Thermodynamics, and realized here using an ‘inelastic thermal collimator’ element. Experiments confirm both effects: with pyramids and collimator the thermal rectification is 10.9±0.8%, while without the collimator no rectification is detectable (<0.3%).

In Situ Observation of Electrostatic and Thermal Manipulation of Suspended Graphene Membranes

Graphene is natures thinnest elastic membrane, and its morphology has important impacts on its electrical, mechanical, and electromechanical properties. Here we report manipulation of the morphology of suspended graphene via electrostatic and thermal control. By measuring the out-of-plane deflection as a function of applied gate voltage and number of layers, we show that graphene adopts a parabolic profile at large gate voltages with inhomogeneous distribution of charge density and strain. Unclamped graphene sheets slide into the trench under tension; for doubly clamped devices, the results are well-accounted for by membrane deflection with effective Youngs modulus E = 1.1 TPa. Upon cooling to 100 K, we observe buckling-induced ripples in the central portion and large upward buckling of the free edges, which arises from graphenes large negative thermal expansion coefficient.

Thermal conductivity of suspended few-layer graphene by a modified T-bridge method

We measured the in-plane thermal conductivity of suspended few-layer graphene flakes by a modified T-bridge technique from 300 K to below 100 K. The thermal conductivities at room temperature are 389, 344, 302, and 596 W/m K for 2-, 3-, 4-, and 8-layer graphene, respectively. The thinner (2-, 3-, 4-layer) graphene samples did not show any clear thickness dependence, while the thicker (8-layer) sample clearly has higher thermal conductivity. In situ current annealing was used to remove polymer residues from the central portion of the 3- and 8-layer graphene samples, as confirmed by electrical transport measurements and post-experiment characterization by Raman and scanning electron microscopy, although some residues still remained near both ends (heater and heat sink). Comparing the 2, 3, and 4-layer samples suggests the annealing had little effect near room temperature but leads to increased thermal conductivity at low temperature. These results also show that the thermal conductivities of suspended few-l...

THERMAL RECTIFICATION BY BALLISTIC PHONONS IN ASYMMETRIC NANOSTRUCTURES

In analogy to an electrical diode, a thermal rectifier transports heat more easily in one direction than in the reverse direction. Among various possible nanoscale rectification mechanisms, a ballistic rectifier relies on asymmetric scattering of energy carriers, as has been suggested for phonon transport in a sawtooth nanowire [S. Saha, L. Shi, & R. Prasher, IMECE 2006] or nanowire with special surface specularity function [N.A. Roberts and D.G. Walker, ITherm 2008]. We have used a Landauer-Buttiker method as well as a Monte Carlo method to model the asymmetric heat transport in such nanostructures, with careful attention to boundary conditions that satisfy the 2nd Law of Thermodynamics. The calculations show that ballistic rectification is only significant at relatively large “thermal bias,” which causes significant anisotropy in the distribution function of energy carriers emitted at each of the two thermal contacts. We also propose experiments to observe this phenomenon using either phonons or photons.Copyright

Thermal Rectification by Ballistic Phonons

In analogy to the asymmetric transport of electricity in a familiar electrical diode, a thermal rectifier transports heat more favorably in one direction than in the reverse direction. One approach to thermal rectification is asymmetric scattering of phonons and/or electrons, similar to suggestions in the literature for a sawtooth nanowire [1] or 2-dimensional electron gas with triangular scatterers [2]. To model the asymmetric heat transport in such nanostructures, we have used phonon ray-tracing, focusing on characteristic lengths that are small compared to the mean free path of phonons in bulk. To calculate the heat transfer we use a transmission-based (Landauer-Buttiker) method. The system geometry is described by a four-dimensional transfer function that depends on the position and angle of phonon emission and absorption from each of two contacts. At small temperature gradients, the phonon distribution function is very close to the usual isotropic equilibrium (Bose-Einstein) distribution, and there is no thermal rectification. In contrast, at large temperature gradients, the anisotropy in the phonon distribution function becomes significant, and the resulting heat flux vs. temperature curve (analogous to I-V curve of a diode) reveals large thermal rectification.Copyright

Correspondence: Reply to ‘The experimental requirements for a photon thermal diode’

Budaev1 correctly identifies a fundamental symmetry error in several crucial experiments in our recent study2, specifically the results presented in Fig. 3c (the three filled and four striped bars, labeled ‘Col. 1’ and ‘Col. 2’, respectively) and Fig. 4. A suitable configuration for those measurements should have included identical (mirror-imaged) collimators at both hot and cold sides, as in Fig. 1a here. However, the actual experiments omitted the cold-side collimator, a choice made for experimental simplicity and which we believed was acceptable at the time based on a simple thermal model3 and the fact that TBBC 4 cTN , where TBBC and TN are the temperatures of the blackbody (BB) cavity and cold-side plate, respectively. However, upon careful reconsideration we now find that thermal model to be flawed, and we believe that omitting the cold-side collimator invalidated several key measurements. We provide a more detailed discussion of that thermal estimate, and the reasons for its failure, elsewhere3. Although we believe the heat flow (Q) measurements in ref. 2 were accurate for all of the configurations presented, due to the symmetry error none of those experimental configurations were actually relevant to the following two major claims, which therefore are invalidated for lack of experimental support: First, that these experiments demonstrated a thermal diode. Second, that the ‘inelastic thermal collimation’ mechanism is a suitable nonlinearity for realizing thermal rectification when combined with asymmetric scattering structures (for example, copper pyramids or etched triangular pores in silicon). The symmetry error1 does not apply to the experiments without thermal collimation, specifically the results presented in Fig. 3c for photons (the six leftmost, unfilled bars) and Supplementary Fig. 12 for phonons. Therefore, the last major conclusion of ref. 2 remains well-supported by the original experiments: Asymmetric scattering alone is insufficient to achieve thermal rectification. The rest of this Reply is devoted to another problem which we have only recently realized: a fundamental issue with the inelastic thermal collimation concept based on absorption, thermalization, and re-emission, as exemplified by the perforated graphite plate approach used in ref. 2. This leads us to now conclude that if it had used a correct two-plate symmetry as depicted here in Fig. 1a, the thermalizing graphite plate scheme as originally conceived2 could not rectify. The essence of the graphite plate approach is radiation absorption and re-emission by a solid plate of infinite thermal conductivity, as exemplified by Supplementary Fig. 4 of ref. 2. The motivating insight is that when analyzed as part of its adjacent BB reservoir, the combined effect of (BBþ collimator) is to convert a local boundary condition into a nonlocal one (or linear into nonlinear in the language originally used in ref. 2). This is depicted here in Fig. 1b, corresponding closely to Supplementary Fig. 5c of ref. 2. This shows how the graphite plate next to BB1 can convert the local equilibrium Bose-Einstein statistics fBE(T1) to a nonlocal, non-equilibrium reservoir boundary condition fNE,1(T1,T2), at the boundary between (BB1þ plate1) and the test section SA, as shown here in Fig. 1b. As noted below Supplementary Equation 5 of ref. 2, this functional form fNE,1(T1,T2) is a necessary condition for the heat transfer response function Q(T1,T2) through the test section SA to be non-symmetric upon the exchange T12T2. Analogous statements hold for the other boundary condition, at the interface between SA and (BB2þ plate2). However, the heat transfer analysis could just as well combine the graphite plates with the pyramids as a larger alternate test section, not considered in ref. 2 but indicated here in Fig. 1c as SB. Because the only distinction between Fig. 1b, c is in how the control volumes are drawn, with no changes to the physical system, clearly both approaches must give the same heat transfer response function Q(T1,T2). Yet because the boundary conditions in Fig. 1c are now ideal blackbodies, SB can be analyzed rigorously using radiation network analysis4, as indicated schematically here in Fig. 2. This network analysis accounts for the direct and indirect radiative exchanges between numerous differential areas which cover all surfaces, including pyramids and graphite plates. The approach can be generalized to handle surfaces with any combination of diffuse (for example, the BBs and graphite plates) and specular (for example, the copper pyramids and sidewalls) character4. The essential point is that the resulting matrix formulation of the heat transfer problem4 is fundamentally a linear relationship in terms of the BB emissive powers Eb,i1⁄4sTi, where s is the DOI: 10.1038/ncomms16136 OPEN