First-principles quantitative prediction of the lattice thermal conductivity in random semiconductor alloys: the role of force-constant disorder

The standard theoretical understanding of the lattice thermal conductivity, $\kappa_{\ell}$, of semiconductor alloys assumes that mass disorder is the most important source of phonon scattering. In contrast, we show that the hitherto neglected contribution of force-constant (IFC) disorder is essential to accurately predict the $\kappa_{\ell}$ of those polar compounds characterized by a complex atomic-scale structure. We have developed an \emph{ab initio} method based on special quasirandom structures and Green's functions, and including the role of IFC disorder, and applied it in order to calculate the $\kappa_{\ell}$ of $\mathrm{In_{1-x}Ga_xAs}$ and $\mathrm{Si_{1-x}Ge_x}$ alloys. We show that, while for $\mathrm{Si_{1-x}Ge_x}$, phonon-alloy scattering is dominated by mass disorder, for $\mathrm{In_{1-x}Ga_xAs}$, the inclusion of IFC disorder is fundamental to accurately reproduce the experimentally observed $\kappa_{\ell}$. As the presence of a complex atomic-scale structure is common to most III-V and II-VI random semiconductor alloys, we expect our method to be suitable for a wide class of materials.