this preprint draft may differ slightly from the final published versionGraphene is a two-dimensional (2D) material with over 100-fold anisotropy of heat flow between the in-plane and out-of-plane directions. High inplane thermal conductivity is due to covalent sp 2 bonding between carbon atoms, whereas out-of-plane heat flow is limited by weak van der Waals coupling.Herein, we review the thermal properties of graphene, including its specific heat and thermal conductivity (from diffusive to ballistic limits) and the influence of substrates, defects, and other atomic modifications. We also highlight practical applications in which the thermal properties of graphene play a role. For instance, graphene transistors and interconnects benefit from the high in-plane thermal conductivity, up to a certain channel length. However, weak thermal coupling with substrates implies that interfaces and contacts remain significant dissipation bottlenecks. Heat flow in graphene or graphene composites could also be tunable through a variety of means, including phonon scattering by substrates, edges or interfaces. Ultimately, the unusual thermal properties of graphene stem from its 2D nature, forming a rich playground for new discoveries of heat flow physics and potentially leading to novel thermal management applications.MRS Bull. 37, 1273Bull. 37, (2012 Pop/Varshney/Roy 2
IntroductionGraphene is a two-dimensional (2D) material, formed of a lattice of hexagonally arranged carbon atoms. Graphene is typically referred to as a single layer of graphite, although common references also exist to bilayer or trilayer graphene. (See the introductory article in this issue.) Most thermal properties of graphene are derived from those of graphite and bear the imprint of the highly anisotropic nature of this crystal. 1 For instance, the in-plane covalent sp 2 bonds between adjacent carbon atoms are among the strongest in nature (slightly stronger than the sp 3 bonds in diamond), with a bonding energy of approximately 2 5.9 eV. By contrast, the adjacent graphene planes within a graphite crystal are linked by weak van der Waals interactions 2 (~50 meV) with a spacing 3 of h ≈ 3.35Å. Figure 1a displays the typical ABAB (also known as Bernal) stacking of graphene sheets within a graphite crystal.The strong and anisotropic bonding and the low mass of the carbon atomsgive graphene and related materials unique thermal properties. In this article we survey these unusual properties and their connection with the character of the underlying lattice vibrations. We examine both specific heat and thermal conductivity of graphene and related materials, and the conditions for achieving ballistic, scattering-free heat flow. We also investigate the role of atomistic lattice modifications and defects in tuning the thermal properties of graphene. Finally we explore the role of heat conduction in potential device applications and the possibility of architectures that allow control over the thermal anisotropy.
Phonon dispersion of grapheneTo understand the thermal ...