Helium-atom-scattering study of the dispersion curves of step-localized phonons on Cu(211) and Cu(511)

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Abstract
The surface phonon dispersion curves of two different regularly stepped vicinal copper surfaces have been measured using high resolution inelastic helium-atom scattering. The Cu(211) and Cu(511) surfaces were chosen since they have comparable step distances but different terrace orientations (111) and (100), respectively. The Rayleigh mode was measured over the entire Brillouin zone along azimuths parallel and perpendicular to the step edge directions. For both surfaces backfolding of the Rayleigh mode was observed along the direction perpendicular to the step edges, while parallel to the step edges, a step localized mode with optical character and a weak dispersion were also found. For the Cu(511) surface, an additional longitudinal mode and an energy gap for the Rayleigh mode at the zone boundary could be identified, whereas on Cu(211), an additional horizontal mode could be identified. The low zone boundary energy observed for the latter mode can be related to the relaxation of the step atoms. The experimental data can be well explained by theoretical slab calculations in the framework of a single force constant model.