Surface geometry and STM image of the Sn/Ge(1 1 1)-3×3 reconstruction

A theoretical analysis of the STM image of the Sn/Ge(1 1 1)-(3×3) surface is presented. In a first step, the atomic structure is reached using a combination of local-orbital and plane-wave density functional methods. We found a ground state geometry presenting two different types of Sn adatoms, with vertical positions differing by ∼0.3 Å. In a second step, this geometry was used to analyze the tunneling currents of this surface in a typical STM experiment. In our approach, a Keldysh formalism is used with a coupling between tip and the sample defined by Bardeen-matrix elements: the tunneling currents are found to depend on the semiconductor surface density of states and these Bardeen coupling elements. We study the STM surface corrugation for positive and negative biases and find that both STM images are complementary of each other, in good agreement with the experimental evidence.