Spilling of electronic states in Pb Quantum Wells

Energy-dependent apparent step heights of two-dimensional ultra-thin Pb islands grown on the Si(111)6$\times$6Au surface have been investigated by a combination of scanning tunneling microscopy, first-principles density functional theory and the particle in a box model calculations. The apparent step height shows the thickness and energy dependent oscillatory behavior, which is directly related to the spilling of electron states into the vacuum exhibiting a quantum size effect. This has been unambiguously proven by extensive first-principles scanning tunneling microscopy and spectroscopy simulations. An electronic contribution to the apparent step height is directly determined. At certain energies it reaches values as high as a half of the atomic contribution. The applicability of the particle in a box model to the spilling of electron states is also discussed.