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We investigated theoretically the phonon thermal conductivity of single layer graphene. The phonon dispersion for all polarizations and crystallographic directions in graphene lattice was obtained using the valence-force field method. The three-phonon Umklapp processes were treated exactly using an accurate phonon dispersion and Brillouin zone, and accouting for all phonon relaxation channels allowed by the momentum and energy conservation laws. The uniqueness of graphene was reflected in the two-dimensional phonon density of states and restrictions on the phonon Umklapp scattering phase-space. The phonon scattering on defects and graphene edges has been also included in the model. The calculations were performed for the Gruneisen parameter, which was determined from the ab initio theory as a function of the phonon wave vector and polarization branch, and for a range of values from experiments. It was found that the near room-temperature thermal conductivity of single layer graphene, calculated with a realistic Gruneisen parameter, is in the range ~ 2000 - 5000 W/mK depending on the defect concentration and roughness of the edges. Owing to the long phonon mean free path the graphene edges produce strong effect on thermal conductivity even at room temperature. The obtained results are in good agreement with the recent measurements of the thermal conductivity of suspended graphene.
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The minimization of electronics makes heat dissipation of related devices an increasing challenge. When the size of materials is smaller than the phonon mean free paths, phonons transport without internal scatterings and laws of diffusive thermal conduction fail, resulting in significant reduction in the effective thermal conductivity. This work reports, for the first time, the temperature dependent thermal conductivity of doped epitaxial 6H-SiC and monocrystalline porous 6H-SiC below room temperature probed by time-domain thermoreflectance. Strong quasi-ballistic thermal transport was observed in these samples, especially at low temperatures. Doping and structural boundaries were applied to tune the quasi-ballistic thermal transport since dopants selectively scatter high-frequency phonons while boundaries scatter phonons with long mean free paths. Exceptionally strong phonon scattering by boron dopants are observed, compared to nitrogen dopants. Furthermore, orders of magnitude reduction in the measured thermal conductivity was observed at low temperatures for the porous 6H-SiC compared to the epitaxial 6H-SiC. Finally, first principles calculations and a simple Callaway model are built to understand the measured thermal conductivities. Our work sheds light on the fundamental understanding of thermal conduction in technologically-important wide bandgap semiconductors such as 6H-SiC and will impact applications such as thermal management of 6H-SiC-related electronics and devices.
In the hydrodynamic regime, phonons drift with a nonzero collective velocity under a temperature gradient, reminiscent of viscous gas and fluid flow. The study of hydrodynamic phonon transport has spanned over half a century but has been mostly limited to cryogenic temperatures (~1 K) and more recently to low-dimensional materials. Here, we identify graphite as a three-dimensional material that supports phonon hydrodynamics at significantly higher temperatures (~100 K) based on first-principles calculations. In particular, by solving the Boltzmann equation for phonon transport in graphite ribbons, we predict that phonon Poiseuille flow and Knudsen minimum can be experimentally observed above liquid nitrogen temperature. Further, we reveal the microscopic origin of these intriguing phenomena in terms of the dependence of the effective boundary scattering rate on momentum-conserving phonon-phonon scattering processes and the collective motion of phonons. The significant hydrodynamic nature of phonon transport in graphite is attributed to its strong intralayer sp2 hybrid bonding and weak van der Waals interlayer interactions. As a boundary-sensitive transport regime, phonon hydrodynamics opens up new possibilities for thermal management and energy conversion.
In stark contrast with three-dimensional (3D) nanostructures, we show that boundary scattering in two-dimensional (2D) nanoribbons alone does not lead to a finite phonon mean free path. If combined with an intrinsic scattering mechanism, 2D boundary scattering does reduce the overall mean free path, however the latter does not scale proportionally to the ribbon width, unlike the well known Casimir regime occurring in 3D nanowires. We show that boundary scattering can be accounted for by a simple Mathiessen type approach for many different 3D nanowire cross sectional shapes, however this is not possible in the 2D nanoribbon case, where a complete solution of the Boltzmann transport equation is required. These facts have strong implications for the thermal conductivity of suspended nanostructures.
The heat flux autocorrelation functions of carbon nanotubes (CNTs) with different radius and lengths is calculated using equilibrium molecular dynamics. The thermal conductance of CNTs is also calculated using the Green-Kubo relation from the linear response theory. By pointing out the ambiguity in the cross section definition of single wall CNTs, we use the thermal conductance instead of conductivity in calculations and discussions. We find that the thermal conductance of CNTs diverges with the CNT length. After the analysis of vibrational density of states, it can be concluded that more low frequency vibration modes exist in longer CNTs, and they effectively contribute to the divergence of thermal conductance.
The Raman peak position and linewidth provide insight into phonon anharmonicity and electron-phonon interactions (EPI) in materials. For monolayer graphene, prior first-principles calculations have yielded decreasing linewidth with increasing temperature, which is opposite to measurement results. Here, we explicitly consider four-phonon anharmonicity, phonon renormalization, and electron-phonon coupling, and find all to be important to successfully explain both the $G$ peak frequency shift and linewidths in our suspended graphene sample at a wide temperature range. Four-phonon scattering contributes a prominent linewidth that increases with temperature, while temperature dependence from EPI is found to be reversed above a doping threshold ($hbaromega_G/2$, with $omega_G$ being the frequency of the $G$ phonon).
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