Crystallographic and electronic contribution to the apparent step height in nanometer-thin Pb(111) films grown on Cu(111)

Thermal roughening of Pb(111) films grown on Cu(111) produces three-dimensional (3D) islands of different number of layers allowing the simultaneous and direct measurement by scanning tunneling microscopy (STM) of the step height for different thicknesses in real space. The apparent step heights separating adjacent layers show several oscillations with amplitudes of up to 0.8-1.4A around the bulk interlayer distance as a function of film thickness. The oscillations have bilayer periodicity with a superimposed longer beating period that produces a phase slip every eight layers. Based on first- principles calculations of Pb(111) free standing slabs, we can identify the relevant electronic states responsible for these quantum size effects. In addition, we can distinguish between geometric and electronic contributions to the apparent step heights measured on the STM images.