First-principles insight in structure-property relationships of hexagonal Si and Ge polytypes

Hexagonal SiGe is a promising material for combining electronic and photonic technologies. In this paper, the energetic, structural, elastic, and electronic properties of the hexagonal polytypes ($2H, 4H$, and $6H$) of silicon and germanium are thoroughly analyzed under equilibrium conditions. For this purpose, we apply state-of-the-art density functional theory. The phase diagram, obtained in the framework of a generalized Ising model, shows that the diamond structure is the most stable under ambient conditions, but hexagonal modifications are close to the phase boundary, especially for Si. Our band structure calculations using the modified-Becke-Johnson–local-density-approximation (MBJLDA) and Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functionals predict significant changes in electronic states with hexagonality. While Si crystals are always semiconductors with indirect band gaps, the hexagonal Ge polytypes have direct band gaps. The branch-point energies of the Si polytypes appear in the fundamental gaps, while for the Ge crystals they are below the valence band maxima. Band alignment based on the branch-point energy leads to type-I heterocrystalline interfaces between Ge polytypes, where electrons and holes can be trapped in the layer with the higher hexagonality.