Stability and electronic structure of Ge(1 0 5)1 × 2: a first-principles theoretical study

We studied stability and electronic structure of the Ge(1 0 5)1 × 2 surface by density functional theory (DFT) calculations. We show that the (0 0 1) surface is more stable than the (1 0 5) surface if the in-plane lattice constant is equal to the equilibrium lattice constant of Ge ( a_Ge), while (1 0 5) becomes much more stable than (0 0 1) when the in-plane lattice constant is compressed to a_Si. This stability change is in agreement with experimental observations that Ge(1 0 5) is stable on the Si substrate, and the reason can be explained from the differences in the surface bond lengths of the two surfaces. Because the Ge-Ge length is considerably elongated near the Ge(1 0 5) surface, the surface bond lengths approach their equilibrium values by compressing the in-plane lattice constant from a_Ge to a_Si, and (1 0 5) becomes fairly stable. Band calculations revealed that the gap between occupied and unoccupied surface states are quite large, suggesting the stability of the surface.