Quantum size effects in $\mathrm{Pb}∕\mathrm{Si}\left(111\right)$ investigated by laser-induced photoemission

We use laser-induced photoemission spectroscopy at $6\mathrm{eV}$ photon energy to investigate quantum well states of epitaxial Pb films on Si(111) as function of film thickness. The binding energies of the quantum well states were found in good agreement with density-functional calculations for a freestanding Pb slab. An oscillation of the work function with a period of 2 ML was observed as a function of film thickness, which correlates well with the oscillatory electron density at the Fermi level determined from the photoemission spectra.

Figure 1

(Color online) Photoemission spectra of $\mathrm{Pb}∕\mathrm{Si}\left(111\right)$ for various coverages observed on a Pb wedge of $4.0\mathrm{ML}∕\mathrm{mm}$ slope using $6.0\mathrm{eV}$ photon energy. The right panel shows a series of discrete QWS dispersing with Pb coverage. The silicon valence-band edge (VBE) is indicated. The upper panel displays the identical data in a false-color representation. The QWS binding energies (+) from a DFT calculation (Ref. 7) are included. In the left panel, the modulation of the low-energy cutoff is highlighted which is a direct measure of the global work function of the Pb film.

Figure 2

QWS binding energies as function of coverage as observed by PES and calculated by DFT (Ref. 7). The experimental QWS binding energies were determined from the peak maxima in the photoemission spectra and the error is given by the size of the symbols (엯). The gray shaded area indicates the fundamental Si band gap.

Figure 3

(Color online) Photoemission spectra of $\mathrm{Pb}∕\mathrm{Si}\left(111\right)$ measured at $5.3\mathrm{eV}$ photon energy on a wedge with $1.5\mathrm{ML}∕\mathrm{mm}$ slope. The Si valence-band edge (VBE), the QWS binding energies (+), and work function modulation (엯) calculated by DFT (Ref. 7) are indicated.

Figure 4

(Color online) Work function oscillations as a function of film thickness observed in the Pb wedges on Si(111) deduced from the photoemission spectra of Fig. 1 (∎) and Fig. 3 (엯). The measured data were offset by $+186\mathrm{meV}$ (∎) and $-183\mathrm{meV}$ (엯) in order to match the theoretical prediction from DFT (Ref. 7). The solid and dashed lines are fits of Eq. (2) to the data points convoluted with a Gaussian function taking into account the finite laser spot size. The upper panel shows the PES intensity $\rho \left(\mathrm{PES}\right)$ integrated over the region $(E-E_F>-0.35\mathrm{eV})$ of the Si band gap.