Spilling of electronic states in Pb quantum wells.

Energy-dependent apparent step heights of two-dimensional ultrathin Pb islands grown on the Si(111)6 x 6-Au surface have been investigated by a combination of scanning tunneling microscopy, first-principles densityfunctional theory, and the particle-in-a-box model calculations. The apparent step height shows the thickness-and energy-dependent oscillatory behaviors, which are 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. [ABSTRACT FROM AUTHOR]