Session B6: Thermal Properties of Graphene and Graphene Derivatives

Nanoscale Thermal Transport in Graphene Interfaces

We have investigated nanoscale thermal transport in epitaxial graphene systems using first-principles calculations and the Landauer formalism for phonon transport. Two types of interfaces are investigated: graphene-dielectric and graphene-metal heterojunctions. Hexagonal boron nitride (h-BN), SiC and SiC with hydrogen passivation (SiC-H) are studied as potential dielectric substrate materials for graphene devices. As for graphene-metal contacts, we have considered Au and Ti as prototypical systems for physisorbed and chemisorbed metal contacts, respectively. The interfacial thermal resistances of h-BN/G system is 5.3 10$^{-9}$ Km$^{2}$/W at room temperature, which is approximately one order of magnitude smaller than that of SiC/G system (55-79 10$^{-9}$ Km$^{2}$/W). Further analysis shows that heat conduction at the graphene interfaces is dominated by low-lying acoustic phonons and the thermal resistances strongly depend on atomic details at the interface such as lattice mismatch, disorder and surface reconstruction. Our work demonstrates the importance of developing a microscopic description of phonon dynamics at heterogeneous interfaces to engineer and design devices with optimal thermal management.   

Isotope impurity doping in graphene

Isotope impurities provide a powerful technique to study phonon related properties of graphene. The advantage of this approach is that phonon frequencies or thermal properties can be modified so that we can identify the origin of the interaction in the unknown optical spectra without changing either the electrical or chemical properties. In the presence of a $^{13}$C isotope impurity in a normally $^{12}$C lattice, the phonon wavefunction of graphene becomes localized. When we discuss the electron-phonon interaction of graphene, we treat phonons in terms of a delocalized wavefunction. However, in real graphene, we know that 2\% of the atoms are $^{13}$C and thus phonons have a finite lifetime, which results in a natural width in the Raman spectra. Many experimental results were obtained recently related to isotopic doping of graphene and carbon nanotubes and its effect on Raman spectra. In this work, we calculate the localization length of the phonons as well as the power law dependence for this effect. At the same time, we calculate the phonon lifetime of the different phonon modes within first order perturbation theory to elucidate the physical mechanisms behind isotope doping and to provide further insight into the experimental results.   

Polarization and electric field dependent electron-phonon interaction in graphene and graphene oxide

Raman spectroscopy has been emerged as one of the important tool to understand various physical properties of graphene and graphene oxide. In this study, polarized Raman scattering has been performed to understand the electron-phonon interaction in connection with the second order Raman scattering process (2D band) in monolayer, bilayer and suspended bilayer graphene. The 2D Raman band shows strong polarization dependent irrespective of number of graphene layers. This effect has been explained on the basis of anisotropic photon scattering through the nodes at the~K-point of the Brillouin zone in graphene during optical absorption. We also explored the electron-phonon interaction in graphene oxide in presence of electric field. The in-situ Raman studies show significant changes in the D and G Raman bands. In particular, the splitting of G band was observed with increase in voltage which indicates the electric field can alter the deformation-potential mediated electron-phonon interaction in graphene oxide. The electrical conductivity of graphene oxide was also found to increase dramatically with increase in voltage.   

High-fidelity phonon transport simulation in graphene devices using efficient, variance-reduced Monte Carlo methods

In this talk we consider thermal transport in graphene at sufficiently small scales that diffusive transport (Fourier's law) is no longer valid. In this regime, the Boltzmann transport equation may be used to describe thermal transport, and Monte Carlo is the typical solution method, especially in the context of device simulation. Unfortunately, due to the slow rate of convergence of Monte Carlo solutions with the number of samples, such simulations can be prohibitively costly. By employing a recently developed variance-reduced Monte Carlo method, we are able to efficiently simulate the Boltzmann equation for phonon transport without resorting to approximations for reducing the problem complexity or dimensionality, such as neglecting phonon-phonon scattering events, or modeling boundary scattering as a homogeneous relaxation (scattering) process. We use our simulations to characterize the error associated with these approximations in the context of thermal transport in graphene devices, but also to study thermal transport in novel two-dimensional geometries.   

Thermal transport in graphene-based nanostructures

Thermal conductivity of graphene and graphene-based nanostructures, such as graphene nanoribbons (GNRs), CVD-grown polycrystalline graphene (PCG), and nano-patterned single-layer graphene (SLG), is of great interest due to their potential applications as logic devices, high-frequency amplifiers, and heat spreaders in future nanoelectronic circuits. Both line edge roughness (LER) and substrate scattering have been shown to impact thermal transport and reduce graphene's record thermal conductivity; however, the combination of these two mechanisms, which will both be present simultaneously in supported nanostructures, has not been explored previously, and their combined impact on thermal transport has not be assessed. We solve the phonon Boltzmann transport equation and calculate the thermal conductivity tensor in a variety of suspended and supported graphene nanostructures. We show that there is a competition between LER and substrate scattering processes, leading to a high degree of directional anisotropy of thermal conductivity. We demonstrate that transport in narrow ribbons (W$<$100 nm) and PCG or nano-SLG with small feature sizes is dominated by roughness scattering and highly anisotropic. We discuss different avenues of controlling thermal transport in graphene-based devices.   

Measurements of Thermal Conductivity and Thermopower in Suspended Single and Few Layer Graphene

Detailed study on thermal conductivity and thermopower in suspended single and few layer graphene has been hampered by experimental challenges mainly due to the difficulty of obtaining suspended samples larger than a few micrometers. Here, we report on a high-yield process for the fabrication of suspended graphene samples of one to few atomic layers on micro-thermometer devices, which allow us to investigate electrical and thermal conductivity, and thermopower from 4 K to 500 K. We find that the thermal conductivity values in suspended graphene are largely limited by scattering with surface residues in as-made devices, and they can reach values comparable to those of bulk graphite after thorough cleaning of the sample surfaces. In addition, temperature-dependent thermopower results in suspended graphene are reported.   

Thermal Transport in Graphene from Large-scale Molecular Dynamics Simulations

Carbon-based materials display exceptional thermal properties. The thermal conductivity of carbon allotropes can range five orders of magnitude. In the bulk, amorphous carbon is a very poor heat conductor, with $\kappa \approx 0.01$ W/m/K, whereas diamond has the highest thermal conductivity among elemental solids, $\kappa \approx 2000$ W/m/K at room temperature. Even broader ranges can be achieved by considering carbon nanostructures. Thermal conductivities as large as $5000$ W/m/K have been measured for suspended graphene and carbon nanotubes. In spite of intense investigations, there is much controversy over the actual value of the thermal conductivity of graphene, both experimentally and theoretically. Here, we present results from equilibrium and non-equilibrium molecular dynamics simulations aimed at understanding the mechanism of heat transport in graphene. In particular, we investigate the influence of finite-size and uniaxial strain on the thermal conductivity of graphene, performing large scale molecular dynamics simulations of micrometer-size models containing up to $10^6$ atoms.   

Tunable thermal transport and negative differential thermal conductance in graphene nanoribbons

We have studied thermal transport in graphene nanoribbons (GNRs) using classical nonequilibrium molecular dynamics simulations. We show that the calculated thermal conductivity of GNRs can be dramatically tuned by the shape, isotope composition, defects, and chirality and hydrogen passivation of the edges [1-2]. For GNRs under large temperature bias beyond the linear response, we have studied negative differential thermal conductance (NDTC) [3]. The NDTC is found to vanish for a sufficiently long GNR whose temperature is fixed at one end. Furthermore, for diffusive thermal transport obeying differential Fourier's law in a generic one-dimensional system, we analytically show that NDTC requires temperature dependent thermal conductivity and simultaneously varying temperatures at both ends. We have also studied asymmetrical GNRs and observed thermal rectification [1] and direction dependent NDTC [3]. Our studies may be useful for nanoscale thermal managements and thermal signal processing using GNRs and understanding low dimensional thermal transport in general. \newline [1] J. Hu et. al., \textbf{Nano Letters 9}, 2730 (2009) \newline [2] J. Hu et. al., \textbf{Applied Physics Letters 97}, 133107 (2010) \newline [3] J. Hu et. al., \textbf{Applied Physics Letters 99}, 113101 (2011)   

Heat Transport in Graphene

We fabricated suspended graphene devices and measured their thermal conductivity, $\kappa$, as a function of both temperature, T, and charge carrier density, n. Heat transport is a powerful tool to obtain information about both the phononic and electronic properties of graphene. Recent heat transport experiments in graphene have shown a high $\kappa$, but a detailed mapping of graphene's heat conductivity versus T and n is not yet available. The measurement technique we developed is a two-point method which uses graphene as its own heat source (Joule heating) and thermometer (resistivity). We report $\kappa$ at temperatures ranging from 6 to 350 Kelvin, and at charge carrier densities close to the Dirac point up to about 1.5 $\times 10^{11}/cm^{2}$, in graphene crystals whose length varies from 250 nm up to one micron. We observed that the thermal conductivity increases by over two orders of magnitude over the temperature range, and that it also increases with the crystal's length. $\kappa$ can be tuned by an order of magnitude with gate voltage, opening the possibility of creating room temperature heat transistors.   

Raman Measurements of Thermal Transport in Suspended Monolayer Graphene of Variable Sizes in Vacuum and Gaseous Environments

Using micro-Raman spectroscopy, the thermal conductivity of a graphene monolayer grown by chemical vapor deposition and suspended over holes with different diameters ranging from 2.9 to 9.7 $\mu $m was measured in vacuum, thereby eliminating errors caused by heat loss to the surrounding gas. The obtained thermal conductivity values of the suspended graphene range from (2.6$\pm $0.9) to (3.1$\pm $1.0)$\times $10$^{3}$Wm$^{-1}$K$^{-1}$ near 350 K without showing the sample size dependence predicted for suspended, clean, and flat graphene crystal. The lack of sample size dependence is attributed to the relatively large measurement uncertainty as well as grain boundaries, wrinkles, defects, or polymeric residue that are possibly present in the measured samples. Moreover, from Raman measurements performed in air and CO$_{2}$ gas environments near atmospheric pressure, the heat transfer coefficient for air and CO$_{2}$ was determined and found to be (2.9+5.1/-2.9) and (1.5+4.2/-1.5)$\times $10$^{4}$Wm$^{-2}$K$^{-1}$, respectively, when the graphene temperature was heated by the Raman laser to about 510 K.   

Effect of electron-electron interactions in thermoelectric power in graphene

Thermoelectric power (TEP) of graphene is previously measured in the disorder limited transport regime where the semiclassical Mott relation agrees with experimental data. In this presentation, we report the TEP measurement on graphene samples deposited on hexa boron nitride substrates where drastic suppression of disorder is achieved. Our results show that at high temperatures where the inelastic scattering rate due to electron-electron (e-e) interactions is higher than the elastic scattering rate by disorders, the measured TEP exhibit a large enhancement compared to the expected TEP from the Mott relation. We also investigated TEP in the quantum Hall regime at a high magnetic fields, where we observed symmetry broken integer quantum Hall and fractional quantum Hall states due to the strong e-e interactions.   

Derivative relations between electrical and thermoelectric quantum transport coefficients in graphene

We find that the empirical relation between the longitudinal and Hall resistivities (i.e. $R_{xx}$ and $R_{xy})$ and its counterpart between the Seebeck and Nernst coefficients (i.e. $S_{xx}$ and $S_{xy})$, both originally discovered in conventional two-dimensional electron gases [1,2], hold surprisingly well for graphene in the quantum transport regime except near the Dirac point. These empirical relations can be described by the following equations: \[ R_{xx} =\alpha _r \cdot \frac{B}{n}\frac{dR_{xy} }{dB}, \quad S_{yx} =\alpha _s \cdot \frac{B}{n}\frac{dS_{xx} }{dB} \] Here R and S are electrical resistivity and thermoelectric conductivity tensor respectively. The validity of the relations is cross-examined by independently varying the magnetic field and the carrier density in graphene. We demonstrate that the pre-factor, \textit{$\alpha $}$_{s}$, does not depend on carrier density in graphene. By tuning the carrier mobility therefore the degree of disorders, we find that the pre-factor stays unchanged. Our experimental results validate both derivative relations for massless Dirac fermions except near the Dirac point. \\[4pt] [1] A. M. Chang and D. C. Tsui, Solid State Commun. \textbf{56}, 153 (1985).\\[0pt] [2] B. Tieke et al, Phys. Rev. Lett. \textbf{78}, 4621 (1997).   

Ultra-sensitive thermal measurements of graphene: pathway to single microwave photon detector

As a result of the linear energy spectrum and low dimensionality, electrons in graphene have astoundingly small thermal conductance and heat capacitance. By developing a large bandwidth, high sensitivity Johnson noise measurement technique at microwave frequency, we can measure the temperature of graphene electrons down to a precision of 0.1 mK within 1 second. This enables us to study the thermal properties of this wonder material: for instance, we have measured the energy transfer from electrons to phonons at 1 pW/K $\mu$m$^2$ level and a record-low heat capacity, only about 100 kB/$\mu$m$^2$, at low temperature. We have applied these exotic thermal quantities to make a graphene bolometer and mixer. Our measurement data agree well with the theory that the proposed graphene caloriometer should have single photon sensitivity from IR down to microwave regime at ultra-low temperature.   

Nano Peltier cooling device from geometric effects using a single graphene nanoribbon

Based on the phenomenon of curvature-induced doping in graphene we propose a class of Peltier cooling devices, produced by geometrical effects, without gating. We show how a graphene nanoribbon laid on an array of curved nano cylinders can be used to create a targeted cooling device. Using theoretical calculations and experimental inputs, we predict that the cooling power of such a device can approach $1kW/cm^2$, on par with the best known techniques using standard lithography methods. The structure proposed here helps pave the way toward designing graphene electronics which use geometry rather than gating to control devices.   

Electrical breakdown of graphene and few-layer graphene structures

The electrical breakdown of graphene and few-layer graphene (FLG) structures are investigated. To better understand the dynamics of these nano-scale thermal effects, we investigate graphene and FLG structures of various dimensions and find that significant joule heating occurs inducing the structures to evolve. A distinct change in the behavior during electrical stressing indicates that different mechanisms and geometrical effects occur at the various stages of evolution. The results could have implications on the development of high current carrying nanoscale graphene devices. Supported in part by NSF Award No. DMR-0805136, the Kentucky NSF EPSCoR program through award EPS-0814194, and the University of Kentucky Center for Advanced Materials.