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

Abstract

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.