Quantum size effects in the low temperature layer-by-layer growth of Pb on Ge(001)

The electronic properties of thin metallic films deviate from the corresponding bulk ones when the film thickness is comparable with the wavelength of the electrons at the Fermi level. This phenomenon, referred to as quantum size effect (QSE), is also expected to affect the film morphology and structure leading to the "electronic growth" of metals on semiconductors. Such effect may be observed when metals are grown on substrates held at low temperature and are manifested through the occurrence of "magical" thickness islands or critical thickness for layer-by-layer growth. In particular, layer-by-layer growth of Pb(111) films has been reported for deposition on Ge(001) below similar to130 K. An extremely flat morphology is preserved throughout deposition from four up to a dozen of monolayers. These flat films are shown to be metastable and to reorganize into large clusters uncovering the first Pb layer pseudomorphic to the underlying Ge(001) substrate already at room temperature. Indications of QSE induced structural variations of the growing films have been reported for Pb growth on both Si(111) and Ge(001). In the latter case, the apparent height of the Pb(111) monatomic step was shown to change in an oscillatory fashion by He atom scattering (HAS) during layer-by-layer growth at low temperature. The extent of the structural QSE has been obtained by a comparison of the HAS data with X-ray diffraction (XRD) and reflectivity experiments. Whereas step height variations as large as 20% have been measured by HAS reflectivity, the displacement of the atomic planes from their bulk position, as measured by XRD, has been found to mainly affect the topmost Pb layer, but with a lower extent, i.e. the QSE observed by HAS are mainly due to a perpendicular displacement of the topmost layer charge density. The effect of the variable surface relaxation on the surface vibration has been studied from the acoustic dispersion of the low energy phonons, as measured by inelastic HAS.