Two-dimensional structural modulation in epitaxialCaF2overlayers on Si(111)

Using high-resolution x-ray diffraction a ${\mathrm{CaF}}_2$ thin film epitaxially grown on a Si(111) substrate is found to exhibit an incommensurately modulated structure parallel to the heterointerface. The overlayer consists of a triangular network of discommensurations, separating regions with two different site occupations of the interfacial Ca, H3 and T4. The two-dimensional spatial modulation of the overlayer is induced by the competition between the strong atomic bonding to the substrate and the bonding in the film. Remarkably, the in-plane periodic lattice distortion generated at the interface propagates many atomic layers through the ${\mathrm{CaF}}_2$ film.