Abstract
We explore the electronic structures of the Pb ultra-thin films grown on the Cu(111) and Si(111) surfaces using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). For Pb/Cu(111) system, empty quantum well (QW) states in Pb islands of different thickness are observed, and analyzed with the phase accumulation model to obtain a dispersion of energy (E) versus wave vector (k). The E-k dispersion reveals a linear relationship corresponding to the Pb bulk band structure along -L direction above the Fermi level. We use this linear dispersion to calculate the energy spacing between adjacent empty QW states. The calculated values of energy spacing of island thickness below eight atomic layers are not in agreement with the experimental measurements. This implies that the electronic structure of Pb films would be similar to that of the bulk when their thicknesses reach eight atomic layers. Since the empty QW states are detected by STS, their energies are inevitable affected by the electric field in the STM gap. We measure the energy shift of empty QW states in Pb islands on Cu(111) at different electric field. It is found that, with an increase of the electric field, the behavior of the energy shift can be grouped into two different modes for most QW states. In the first mode, the state energy moves toward high energy monotonically. In the second mode, the state energy shifts to a lower energy initially and then turns around to a higher energy. Moreover, we have observed that the QW states of higher energy behave in preference to the first mode, but they gradually change to the second mode as the Pb island becomes thicker. This thickness-dependent behavior reflects the existence of local expansion in the Pb islands, due to the electric field, and that the expansion is larger for a thicker island. The QW states can thus be used for studying the localized lattice deformation in the nanometer scale. For Pb/Si(111) system, we focus on observing unoccupied states of dense Pb overlayer with various phases. Our observations show that there appears to be an oscillatory feature with two distinct resonance peaks in tunneling spectra of all phases. It is known that the coverage of dense Pb overlayer, depending on the phase, is within the range of 1.2-1.3 monolayer. Our measurements reveal that the spacing decreases with the increment of coverage. The reduction of the energy spacing is attributed to the movement of high-energy peak toward lower energy with increasing the coverage. Moreover, the energy spacing of √7×√3 phase is nearly the same as that of 1×1 phase, implying that the coverage is identical for both phases.