Ab initio electronic structure of Ge(111)-(2$\times$1) surface in the presence of surface vacancy. Apllication to STM data analysis

We present the results of first principles modeling of Ge(111)-(2${\times}$1) surface in the presence of atomic vacancy in surface bi-layer. We showed that simple crystal structure defect affects surface electronic structure to the extent comparable with the influence of doping atom. We demonstrated the strong difference of surface LDOS structure above surface defects of different kind. We have proved that spatial oscillations of LDOS exist around individual surface vacancy in the same tunneling bias range as in case of donor doping atom on Ge(111)-(2${\times}$1) surface.