The effect of bulk impurities on localized surface states

The effect of the occurrence of bulk impurities in a crystal on the existence and localization of surface states is examined by investigating a simple one-dimensional model. It is found that the bulk impurity has a small effect on the existence conditions for localized states associated with the surface, but the degree of localization of the corresponding charge density can be altered appreciably by the presence of such impurities. The penetration depth associated with localized surface levels can be much greater that than estimated for a pure crystal. The charge density associated with the electrons which occupy localized surface states may vary in a real crystal over a broader region near the surface than would be deduced from models of pure crystals. This will affect physical quantities, such as surface impedance, which are dependent on this charge distribution.