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, ${\kappa }_{\mathrm{\ell }}$, 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 ${\kappa }_{\mathrm{\ell }}$ 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 ${\kappa }_{\mathrm{\ell }}$ of $\mathrm{I}{\mathrm{n}}_{1-\mathrm{x}}\mathrm{G}{\mathrm{a}}_{\mathrm{x}}\mathrm{A}\mathrm{s}$ and $\mathrm{S}{\mathrm{i}}_{1-\mathrm{x}}\mathrm{G}{\mathrm{e}}_{\mathrm{x}}$ alloys. We show that, while for $\mathrm{S}{\mathrm{i}}_{1-\mathrm{x}}\mathrm{G}{\mathrm{e}}_{\mathrm{x}}$, phonon-alloy scattering is dominated by mass disorder, for $\mathrm{I}{\mathrm{n}}_{1-\mathrm{x}}\mathrm{G}{\mathrm{a}}_{\mathrm{x}}\mathrm{A}\mathrm{s}$, the inclusion of IFC disorder is fundamental to accurately reproduce the experimentally observed ${\kappa }_{\mathrm{\ell }}$. 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.