Carrier-stabilized hexagonal Ge

Germanium is crystalized in the cubic diamond structure, but its high energy hexagonal Ge (lonsdaleite) phase has many novel properties such as direct band gap. Using first-principles calculations, we show that the hexagonal lonsdaleite phase of Ge can be stabilized by introducing carriers, either electrons or holes, because Ge in the cubic and hexagonal phases form a type-I band alignment with both electrons and holes localized at the hexagonal site. This result is distinct from that in zinc-blende compounds such as ZnSe, because due to the lack of inversion symmetry, the crystal-field splitting, zone folding, and symmetry-controlled level repulsion between valence and conduction band states lead to a type-II band alignment between its cubic and hexagonal phases, so the hexagonal (wurtzite) phase of ZnSe can only be stabilized, in principle, by holes. This distinction reveals that, due to the symmetry differences, the well-investigated understanding of band structure differences between zinc-blende and wurtzite phases should not be simply extended to that of diamond and lonsdaleite phases despite the remarkable structure resemblance between the two cases.