Structural transitions and relaxation processes during the epitaxial growth of ultrathinCaF2films on Si(111)

Abstract

The structure and morphology of ultrathin lattice matched ${\text{CaF}}_{2}$ films of very few monolayers thickness, which were deposited on Si(111) substrates by molecular-beam epitaxy, have been studied in situ by synchrotron based grazing incidence x-ray diffraction. Even for the thinnest investigated film of three monolayers thickness, the in-plane structure of the ${\text{CaF}}_{2}$ film is determined by a lateral separation in two domains: a pseudomorphic phase assuming the lateral lattice constant of the Si(111) substrate and a completely relaxed phase. Analysis of the crystal truncation rods verifies that both phases adopt the entire homogeneous ${\text{CaF}}_{2}$ film thickness. Therefore, we propose that atomic steps of the substrate bypass the nucleation barrier for the formation of (Shockley partial) dislocations so that the film starts to relax below the classical critical film thickness. While the relaxed phase assumes also the ${\text{CaF}}_{2}$ bulk lattice constant for the vertical direction, the vertical lattice constant of the pseudomorphic phase increases due to the compressive lateral strain at the interface. This vertical expansion of the pseudomorphic phase, however, is larger than expected from the elastic constants of the ${\text{CaF}}_{2}$ bulk. The fraction of the pseudomorphic ${\text{CaF}}_{2}$ phase decreases with increasing film thickness. The interface between the pseudomorphic ${\text{CaF}}_{2}$ phase and the Si(111) substrate is characterized by Ca on ${T}_{4}$ sites, a smaller distance between the Si(111) substrate and the CaF interface layer and an expanded layer distance between CaF interface layer and the completely stoichiometric ${\text{CaF}}_{2}$ film.