It was recalled that Shockley surface states at metal surfaces decayed exponentially into the crystal, and typically penetrated to several interplanar spacings. Within this depth, defects such as impurity atoms scattered the surface state electrons and gave rise to characteristic standing-wave patterns in the local density of states outside of the surface (like those which had recently been detected, using scanning tunnelling microscopy, due to scattering by adatoms). A multiple scattering theory was developed here in order to model the situation, and was applied to impurities which were near to the Cu(111) surface.

S.Crampin: Journal of Physics - Condensed Matter, 1994, 6[40], L613-8