Energy dispersion of image states and surface states near the surface-Brillouin-zone boundary

The nearly-free-electron model of surface-state occurrence in the the projected s,p-band gaps of metals is extended to the study of the energy dispersion near the boundaries of the surface Brillouin zone. The model is applied to available photoemission and inverse-photoemission data in the Γ¯ Y¯ Γ¯ direction on Cu(110) and Ni(110). Good agreement is obtained for the energy dispersion away from Y¯ if $z_0$, the image-plane distance, has been chosen to force agreement at Y¯. In particular, the large effective masses (as high as 2.0m) which have been reported for the first image-induced surface state are explained.