Ab initio theory of the lattice thermal conductivity in diamond

We present a first-principles theoretical approach to calculate the lattice thermal conductivity of diamond based on an exact solution of the Boltzmann transport equation. Density-functional perturbation theory is employed to generate the harmonic and third-order anharmonic interatomic force constants that are required as input. A central feature of this approach is that it provides accurate representations of the interatomic forces and at the same time introduced no adjustable parameters. The calculated lattice thermal conductivities for isotopically enriched and naturally occurring diamond are both in very good agreement with experimental data. The role of the scattering of heat-carrying acoustic phonons by optic branch phonons is also investigated. We show that inclusion of this scattering channel is indispensable in properly describing the thermal conductivity of semiconductors and insulators. The accurate adjustable-parameter-free results obtained herein highlight the promise of this approach in providing predictive descriptions of the lattice thermal conductivity of materials.

Figure 1

Phonon dispersions of diamond. Ab initio calculations (solid line) and experiment (open diamonds).

Figure 2

The calculated intrinsic lattice thermal conductivity of diamond for the RTA (dashed line) and the full converged solution (solid line). Dotted line shows percent error of the RTA result compared to the full solution.

Figure 3

Lattice thermal conductivity of isotopically enriched and naturally occurring diamond as a function of temperature. Measured values (open triangles, squares, open diamonds, open circles, and crosses) are compared with the results of ab initio calculations (solid lines).

Figure 4

Lattice thermal conductivity of naturally occurring (dashed lines) and isotopically enriched (solid lines) Si and Ge as a function of temperature compared with the corresponding experimental values.

Figure 5

Isotopically enriched lattice thermal conductivity of diamond and Si from the full calculations (solid lines) and for the case where the acoustic-optic phonon-phonon scattering channels have been omitted (dashed lines). Measured values for isotopically enriched diamond and Si are also included.