Polymorphism of group-IV carbides: Structures, (meta)stability, electronic, and transport properties

Herein we investigate the spectra of crystal structures and their metastability for elemental carbon and the entire set of group-IV monocarbides (SiC, GeC, and SnC) using the ab initio random structure sampling. All of the known structures of elemental C and SiC are correctly identified as high probability in the random sampling and the predicted metastabilities of polymorphs are consistent with the existing knowledge. Furthermore, we find the same four structure types, tetrahedrally bonded zincblende, wurtzite, and rhombohedral-$R\overline{3}m$, as well as octahedrally coordinated rocksalt at high pressure, as the only relevant polymorphs for all studied carbides. However, the rocksalt structure in GeC is shown to be dynamically unstable, contrary to SiC and SnC. Additionally, all GeC and SnC structures are found to have positive enthalpies of formation and are therefore unstable relative to decomposition. The tetrahedrally bonded polymorphs, especially the SnC ones, are predicted to have very high intrinsic (phonon-limited) electron mobilities comparable with the best known semiconductors. Additionally, wurtzite SnC is lattice matched to InN suggesting epitaxial growth as a possible avenue to realize wurtzite SnC.