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.
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