Ab initio study of surface electronic structure of phosphorus donor imputiry on Ge(111)-(2$\times$1) surface

We present the results of numerical modeling of Ge(111)-(2$\times$1) surface electronic properties in vicinity of P donor impurity atom near the surface. We show, that despite of well established bulk donor impurity energy level position at the very bottom of conduction band, surface donor impurity might produce energy level below Fermi energy, depending on impurity atom local environment. It was demonstrated, that impurity, located in subsurface atomic layers, is visible in STM experiment. The quasi-1D character of impurity image, observed in STM experiments, is confirmed by our computer simulations.