Significant reduction of lattice thermal conductivity due to phonon confinement in graphene nanoribbons

Lattice thermal conductivity, kappa(p), of suspended and supported graphene nanoribbons (GNRs) is studied over a wide temperature range, taking into account the dispersive nature of confined acoustic phonon modes. Employing a modified Callaway model, an expression for kappa(p) is developed, considering the explicit contributions from in-plane longitudinal, transverse, and torsional acoustic, and out-of-plane flexural acoustic phonon modes. Numerical calculations of kappa(p) (T) are presented assuming the confined acoustic phonons to be scattered by sample boundaries, impurities, and other phonons via both normal and umklapp processes. The effect of phonon confinement is to modify the phonon group velocities and the temperature dependence of kappa(p). In a suspended 5-nm-wide GNR at room temperature, a decrease in kappa(p) by similar to 70% is predicted. Our study brings out the relative importance of the contributing phonon modes and reveals the influence of flexural phonons on kappa(p) as a marked shoulder at low temperatures. The role of the various sample-dependent scattering mechanisms is examined. The substrate, in supported GNRs, is shown to curtail the phonon mean free path and suppress the low-temperature kappa(p). Our results are in good agreement with recent experimental data of Bae et al. [M. H. Bae, Z. Li, Z. Aksamija, P. N. Martin, F. Xiong, Z. Y. Ong, I. Knezevic, and E. Pop, Nat. Commun. 4, 1734 (2013)] for supported GNRs.