Band Anticrossing in Dilute Germanium Carbides Using Hybrid Functionals
  Dilute germanium carbides (Ge1-xCx) offer a direct bandgap for compact silicon photonics, but widely varying results have been reported. This work uses ab initio simulations with HSE06 hybrid functionals and spin-orbit coupling to study the Ge1-xCx band structure behavior in the absence of defects. Contrary to Vegard's law, the conduction band minimum at k=0 is consistently found to decrease with increasing C content, while L and X valleys change much more slowly. A vanishing bandgap was observed for all alloys with x>0.017. Conduction bands deviate from a constant-potential band anticrossing model except near the center of the Brillouin zone. 
Chad A. Stephenson, William A. O'Brien, Meng Qi, Michael Penninger,   William Schneider, Mark A. Wistey
physics.comp-ph cond-mat.mtrl-sci