X-ray diffraction studies of trilayer oscillations in the preferred thickness of In films on Si(111)

Abstract

We report a surface x-ray diffraction study of the structure of In films grown on $\mathrm{Si}(111)\ensuremath{-}(7\ifmmode\times\else\texttimes\fi{}7)$ and $\mathrm{Si}(111)\ensuremath{-}(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})\ensuremath{-}\mathrm{In}$ substrates at a low temperature (135 K). The $(7\ifmmode\times\else\texttimes\fi{}7)$ reconstruction of the clean Si(111) surface is found to persist upon burial by the In. X-ray reflectivity measurements yield patterns that deviate strongly from the ideal case; the results suggest a complex In film structure, possibly distorted by the corrugated interfacial reconstruction. By contrast, In films grown on the $\mathrm{Si}(111)\ensuremath{-}(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})\ensuremath{-}\mathrm{In}$ surface exhibit reflectivity data that are much closer to the ideal case. The films are found to grow approximately layer by layer, resulting in a relatively small roughness. Upon annealing, the films develop preferred thicknesses at 10, 13, and 16 monolayers (MLs). Previous photoemission studies revealed preferred thicknesses at 4 and 7 MLs. Putting these results together, the preferred thickness sequence, 4, 7, 10, 13, and 16 ML, establishes a trilayer oscillation period. This period is expected from the known electronic structure of In, and arises from quantum confinement of the In valence electrons. This is the second example, after the well-known bilayer period in Pb, which shows quantum oscillations over a wide range of film thickness.