The ability of a material to conduct heat is usually based on the atomic structure of the material and the thermal properties’ knowledge. The material’s thermal properties may change when their system is put on the nanometer scale[3]. The divergence of the thermal conductivity in two-dimensional crystals means that the crystal’s anharmonicity is not considered sufficient for the restoration of the thermal equilibrium. Hence, there is a need for one to consider either limiting the size of the system or introducing disorder to have the finite value of the thermal conductivity[4].

Availability of the few layers of graphene of high quality has led to the experimentation on the evolution of the thermal properties of the system’s dimensionality from 3D to 2D[5]. The initial measurements of the thermal properties of graphene showed a thermal conductivity that is above the bulk limit of graphite

Keywords: graphene, phonon, thermal conductivity, scattering, the dispersion relation

Graphene, a recently 2-D developed allotrope of the nanocarbon, is known as a single atomic layer of graphite[2]. The strongest bonds result from the in-plane covalent hexagonallysp2 between the carbon atoms, which are significantly more potent than the sp3diamond bonding. The planes of graphene on the graphite crystal are due to weak van der Waal forces between them.&nbsp. The anisotropic nature of the crystals can be used to determine the thermal attributes of graphene.

The elimination of heat loss in electronic devices has been a problem encountered by various electronic industry researchers. Therefore, the industry has put more effort and resources in searching for better materials that dissipate less heat to improve the innovations of the next generations of integrated circuits (ICs) designs and 3-D electronic devices. Thermal properties issues have been encountered both in the photonic and optoelectronic devices[6].

Metals usually contain electrons that are delocalized which enable them to carry a charge from one point to another. Contrary, graphene electrons are arranged in a pi-bond model which allows interconnectivity with the neighboring atoms as they travel from one atom to another[5].