Phonon-Phonon Interactions in Strongly Bonded Solids: Selection Rules and Higher-Order Processes

We show that the commonly used lowest-order theory of phonon-phonon interactions frequently fails to accurately describe the anharmonic phonon decay rates and thermal conductivity (kappa), even among strongly bonded crystals. Applying a first-principles theory that includes both the lowest-order three-phonon and the higher-order four-phonon processes to 17 zinc blende semiconductors, we find that the lowest-order theory drastically overestimates the measured kappa for many of these materials, while inclusion of four-phonon scattering gives significantly improved agreement with measurements. We identify new selection rules on three-phonon processes that help explain many of these failures in terms of anomalously weak anharmonic phonon decay rates predicted by the lowest-order theory competing with four-phonon processes. We also show that zinc blende compounds containing boron (B), carbon (C), or nitrogen (N) atoms have exceptionally weak four-phonon scattering, much weaker than in compounds that do not contain B, C, or N atoms. This new understanding helps explain the ultrahigh kappa in several technologically important materials like cubic boron arsenide, boron phosphide, and silicon carbide. At the same time, it not only makes the possibility of achieving high kappa in materials without B, C, or N atoms unlikely, but it also suggests that it may be necessary to include four-phonon processes in many future studies. Our work gives new insights into the nature of anharmonic processes in solids and demonstrates the broad importance of higher-order phonon-phonon interactions in assessing the thermal properties of materials.