Cu:Si(111) incommensurate (5.55×5.55) surface reconstruction: Helium-beam measurements of diffraction and surface phonons

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Abstract
Elastic and inelastic atomic-helium scattering has been used to characterize the Cu:Si(111) ‘‘quasi-(5×5)’’ surface. The surface superlattice is incommensurate with the underlying Si(111) structure, 5.55 times larger, appears to be limited to the outermost layers, yet is not a simple incommensurate overlayer. The helium diffraction indicates a long-range coherence of the reconstruction which, while not incompatible with a two-dimensional quasicrystal, would severely restrict any quasicrystal correlation or tiling rules. The surface phonons have intriguing characteristics including a lack of band gaps at fractional-order ‘‘zone boundaries’’ and what seems to be a continuous transition from extended mode to local oscillator mode with increasing wave vector.