Graphene is the nature's 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 graphene's 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.

We have batch-fabricated a microdevice consisting of two adjacent symmetric silicon nitride membranes suspended by long silicon nitride beams for measuring thermophysical properties of one-dimensional nanostructures (nanotubes, nanowires, and nanobelts) bridging the two membranes. A platinum resistance heater/thermometer is fabricated on each membrane. One membrane can be Joule heated to cause heat conduction through the sample to the other membrane. Thermal conductance, electrical conductance, and Seebeck coefficient can be measured using this microdevice in the temperature range of 4-400 K of an evacuated Helium cryostat. Measurement sensitivity, errors, and uncertainty are discussed. Measurement results of a 148 nm and a 10 nm-diameter single wall carbon nanotube bundle are presented.

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.

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.

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.

Graphene is nature's 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 Young's 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 graphene's large negative thermal expansion coefficient.

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%).

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-layer graphene are higher than those of encased few-layer graphene of similar thickness measured previously [Jang et al., Nano Lett. 10, 3909 (2010)].