Spatial distribution of local tunneling conductivity due to interference and Coulomb interaction effects for deep and shallow impurities on semiconductor surfaces

TL;DR

This paper theoretically investigates how interference and Coulomb interactions influence the local tunneling conductivity around impurities on semiconductor surfaces, revealing complex spatial effects measurable by STM/STS.

Contribution

It introduces a combined theoretical analysis of interference and Coulomb effects on tunneling conductivity for both deep and shallow impurities using Keldysh formalism.

Findings

Interference and Coulomb effects significantly alter tunneling conductivity near impurities.

Both effects are prominent at distances comparable to the lattice period.

Theoretical models match observed STM/STS features.

Abstract

Spatial distribution of local tunneling conductivity was investigated for deep and shallow impurities on semiconductor surfaces. Non-equilibrium Coulomb interaction and interference effects were taken into account and analyzed theoretically with the help of Keldysh formalism. Two models were investigated: mean field self-consistent approach for shallow impurity state and Hubbard-{I} model for deep impurity state. We have found that not only above the impurity but also at the distances comparable to the lattice period both effects interference between direct and resonant tunneling channels and on-site Coulomb repulsion of localized electrons strongly modifies form of tunneling conductivity measured by the scanning tunneling microscopy/spectroscopy (STM/STS).