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We calculate the lattice thermal conductivity ($\kappa$) for cubic(zinc-blende) and hexagonal (wurtzite) phases for 8 semiconductors using$\textit{ab initio}$ calculations and solving the Phonon Boltzmann TransportEquation, explaining the different behavior of the ratio $\kappa_{\rmhex}/\kappa_{\rm cub}$ between the two phases. We show that this behaviordepends on the relative importance of two antagonistic factors: anharmonicity,which we find to be always higher in the cubic phase; and the accessible phasespace, which is higher for the less symmetric hexagonal phase. Based on that,we develop a method that predicts the most conducting phase---cubic orhexagonal---where other more heuristic approaches fail. We also present resultsfor nanowires made of the same materials, showing the possibility to tune$\kappa_{\rm hex}/\kappa_{\rm cub}$ over a wide range by modifying theirdiameter, thus making them attractive materials for complex phononic andthermoelectric applications/systems.

Thermal conductivity for III-V and II-VI semiconductor wurtzite and zinc-blende polytypes: the role of anharmonicity and phase space