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We have performed the numerical modeling of Ge(111)-(2x1) surface electronicproperties in vicinity of P donor impurity atom located near the surface. Wehave found a notable increase of surface $LDOS$ around surface dopant near thebottom of empty surface states band $\pi^*$, which we called split state due toits limited spatial extent and energetic position inside the band gap. We show,that despite of well established bulk donor impurity energy level position atthe very bottom of conduction band, surface donor impurity on Ge(111)-(2x1)surface might produce energy level below Fermi energy, depending on impurityatom local environment. It was demonstrated, that impurity, located insubsurface atomic layers, is visible in STM experiment on Ge(111)-(2x1)surface. The quasi-1D character of impurity image, observed in STM experiments,is confirmed by our computer simulations with a note that a few $\pi$-bondeddimer rows may be affected by the presence of impurity atom.

Tunneling spectroscopy of phosphorus impurity atom on Ge(111)-(2x1) surface. {Ab initio} study