Quantum electronic stability and spectroscopy of ultrathin Pb films on $\mathrm{Si}\mathrm{}\left(111\right)7\times 7$

The growth of Pb on $\mathrm{Si}\mathrm{}\left(111\right)7\times 7$ has been studied with photoelectron spectroscopy. At low temperature (110 K), Pb grows in a quasi layer-by-layer mode that allows for the direct observation of discrete quantum well states. The quantum well states are analyzed in terms of the Bohr-Sommerfeld phase quantization model using a phenomenological phaseshift function and reduced quantum numbers. Fermi-level crossings occur when the film thickness $Nd=n({\lambda }_F/2),$ where d is the atomic layer spacing and ${\lambda }_F$ the bulk Fermi wavelength $(N,n$ are integers). The photoemission intensity from the quantum well states shows a strong modulation with photon energy which can be interpreted on the basis of the matrix elements for direct transitions in bulk Pb(111). The in-plane effective mass of the quantum well states is greatly enhanced in the vicinity of the substrate band edge. The present results provide important elements for understanding the growth morphology of Pb films in recent STM studies.