First-principles study ofSi34−xGexclathrates: Direct wide-gap semiconductors in Si-Ge alloys

Energetics and electronic states of ${\mathrm{Si}}_{34-x}{\mathrm{Ge}}_x$ clathrate alloys have been investigated. The atomistic structures, the equations of state, and the lineup of band structures for these clathrates are calculated using the Vanderbilt ultra-soft pseudopotential method within the local-density-functional formalism. Some of these ${\mathrm{Si}}_{34-x}{\mathrm{Ge}}_x$ clathrate alloys with an ideal $\mathrm{Fd}3\mathrm{}¯m$ symmetry are found to have direct band gap at the $\pi /a\left(111\right)\mathrm{}$ (L) point in the Brillouin zone. The entire band gap of the ${\mathrm{Si}}_{34-x}{\mathrm{Ge}}_x$ alloys is predicted to range between 1.2 and 2.0 eV. The total-energy difference between these clathrate alloys and the well-known ${\mathrm{sp}}^3$ Si-Ge alloys is less than 0.08 eV/atom. A method to synthesize these clathrate systems is also discussed. These Si-Ge clathrate alloys may find applications in optoelectronics semiconductor devices based on the Group-IV elements.