Quantum-well states and the bias-dependent apparent height of monatomic steps on Pb(111) thin films

The apparent height h of a monatomic step on the upper surface of thin Pb(111) films, as measured by scanning tunneling microscopy in constant-current mode, is found to oscillate with bias voltage U. The oscillation period matches that of the local differential conductance dI/dU and the tip displacement rate dz/dU as the bias voltage is swept. This correlation indicates that the observed height variations originate from coherent resonant tunnelling through quantum-well states in thin Pb(111) films. We argue that the extrema of the apparent step height occur at bias voltages where the local densities of states of Pb(111) terraces of different thicknesses are equal.