Lifetime of phonons and spectral signature from scattering with doping centers

Since the seminal work of Elliott, Klemens, Talwar and Tamura, who laid out the theory in the seventies and eighties, the increase of computing power and development of ab-initio methods have allowed the simulation of phonon interaction with scattering centers, such as substitutions, vacancies and stacking defects with great accuracy (for example works by the groups of Stewart, Mingo or Chen). However, little improvement has been made to the theory beyond the initial real-space supercell formulation, which is based on a single-defect model, which can be non-convergent in perturbation theory.

We have developed a reciprocal space approach, which models the scattering center as a phonon-phonon interaction potential V(q,q') that can be computed at the density-functional perturbation theory level, i.e. via a standard phonon calculation, in a relatively small supercell and then Fourier interpolated to any q and q'. In this framework, the defect concentration is introduced in a natural way, the Tamura model for mass-defect scattering appears as the natural limit at V=0. The effect of the order is included explicitly, and the case of modulated disorder can be treated. The calculation of the full phonon self-energy allow the simulation of the vibrational spectra, including the activation of secondary spectral peaks with disorder.

In high doping materials, the inclusion of defect scattering, together with intrinsic anharmonic scattering, is required to accurately reproduce lattice-drive thermal transport properties.

The formulation can be extended to include unequivalent doping sites, and lattice defects that do not conserve the number of atoms: defects and inclusions.