Apparent Barrier Height in Scanning Tunneling Microscopy Revisited

The apparent barrier height ${\phi }_{\mathrm{ap}}$, that is, the rate of change of the logarithm of the conductance with tip-sample separation in a scanning tunneling microscope (STM), has been measured for Ni, Pt, and Au single crystal surfaces. The results show that ${\phi }_{\mathrm{ap}}$ is constant until point contact is reached rather than decreasing at small tunneling gap distances, as previously reported. The findings for ${\phi }_{\mathrm{ap}}$ can be accounted for theoretically by including the relaxations of the tip-surface junction in an STM due to the strong adhesive forces at close proximity. These relaxation effects are shown also to be generally relevant under imaging conditions at metal surfaces.