Beyond the isotropic-model approximation in the theory of thermal conductivity

Abstract

By the use of an iterative method the linearized phonon-Boltzmann equation for a dielectric solid subjected to a thermal gradient is solved in the frame of three-phonon interactions. In this way it is possible to calculate the thermal conductivity of rare-gas solids starting from the pair potential and accounting for the real Brillouin zone of the lattice. The numerical results are in full agreement with experiment and represent a considerable improvement with respect to those previously deduced for an isotropic solid.

Hydrodynamic phonon transport in suspended graphene

“…For the isotope scattering calculation, the 13 C isotope was treated as a point defect 61 . Using the calculated three-phonon and phonon-isotope scattering rates, the linearized Peierls-Boltzmann equation was solved with the iterative method 16 for the distribution function under a temperature gradient. For calculating scattering rates and solving the Peierls-Boltzmann equation, the first Brillouin zone was sampled with 70 Â 70 and 30 Â 30 Â 30 meshes for graphene and diamond, respectively.…”

“…work, we demonstrate from first-principles calculations that a displaced distribution of phonons can occur in graphene even in the presence of weak R-scattering, which validates the assumption of the displaced distribution used in the past studies 12,13 and correspondingly shows hydrodynamic phonon transport in graphene. The recent progress in calculating the phonon-phonon scattering matrix using first-principles 14,15 and numerical methods for solving the Peierls-Boltzmann equation 16,17 enable the calculation of phonon distributions in a specific material under a temperature gradient. This first principles-based method has been demonstrated to be highly accurate and have predictive power for phonon transport in many materials including graphene 15,[18][19][20][21][22][23] .…”

Intrinsic lattice thermal conductivity of semiconductors from first principles

“…In fact, to the contrary, they provide a dominant scattering channel for the heat-carrying acoustic phonons which, if removed would precipitate a dramatic increase in the thermal conductivity. 9,10 The calculated intrinsic lattice thermal conductivities for silicon and germanium between 100 and 300 K are compared with measured values 13,14 in Fig. 1.…”

“…A small temperature gradient ٌT is taken to perturb the phonon distribution function n = n 0 + n 1 , where is a short hand for ͑q , j͒, n 0 ϵ n 0 ͑ ͒ is the equilibrium ͑Bose͒ phonon distribution function, and the nonequilibrium part n 1 produces the thermal current. The PBE is 4,9,10 v · ٌT ‫ץ‬n 0…”

Cross-plane phonon transport in thin films

“…The overriding challenge in solving the BTE is modeling the collision operator. Although methods have been developed to evaluate it directly, 11,23,24 here we use the relaxationtime approximation to make solving the BTE more tractable. 25,26 Under this approximation, phonon transport is described by a set of mode-dependent relaxation times, ͑ , ͒, defined as the average time between scattering events.…”