Model potential of dimer system and coherence length of electron injected by scanning tunneling microscope on Ge(0Â 0Â 1) surface

An improved model potential of the dimer system on the Ge(0 0 1) surface is obtained on the basis of the results of first-principles calculations. The electron-vibration coupling constant on the Ge(0 0 1) surface is obtained using the improved model potential. We propose a new theoretical formula for the coherence length of the tunneling electron injected by scanning tunneling microscope onto the semiconductor surface band. In the formula, the decoherence of the propagating electron is attributed to the strong electron-vibration coupling. The formula semi-quantitatively reproduces the decay length of the standing wave observed on the Ge(0 0 1) surface, and explains why the decay length of the standing wave on the Ge(0 0 1) surface is short even though the surface-localized bands on the Ge(0 0 1) surface are semiconductive.