Effect of nitrogen and vacancy defects on the thermal conductivity of diamond: An ab initio Green's function approach

We show that impurities and vacancies affect the thermal conductivity much more strongly than what is predicted by widely accepted models. When local distortions around point defects are strong, standard perturbative approaches fail, and phonon scattering can only be accounted for by an exact Green's function calculation. We apply the theory to the study, from first-principles, of nitrogen and vacancy defects in diamond. The thermal conductivity is computed by solving the linearized Boltzmann transport equation. The Born approximation underestimates the phonon scattering cross sections of nitrogen and vacancies by factors of 3 and 10, respectively. Thermal conductivity calculations are in good agreement with experiment.

Figure 1

(a) Cross section for the 1D chain. (b) Cross section times group velocity for Si Keating potential, longitudinal phonon branch along the [100] direction. Solid line: $T$-matrix calculation. Dotted line: Born approximation. From bottom to top: $\Delta K/K=-0.10$ (black), $-0.50$ (red), $-0.95$ (green), $-1.00$ (blue).

Figure 2

(a) and (b) The [100] projection view of the N impurity and vacancy defects after the ab initio relaxation. Green: N atom. Blue: first coordination shell. Yellow: second and third coordination shells. (c) and (d) Bond distances and angles as a function of the distance to the defect. Dashed line: bulk values for diamond, 1.547 Å and ${109.47}^{\circ }$.

Figure 3

Cross sections times group velocity for substitutional N and vacancy defects in diamond, derived from the $T$ matrix and from the Born approximation. The arrow points at the resonance state (see text for details).

Figure 4

${\kappa }_L$ of diamond as a function of defect concentration. N and V stand for nitrogen and vacancy, respectively.