Chapter 4 Surface States on Metals

Abstract

Publisher Summary This chapter discusses the surface states and resonances that exist on nominally clean and well-ordered metal surfaces. Two simple empirical models, which provide some intuition when and where surface states might occur, what their properties might be, and what they tell us about the surface, are presented. Bulk states exist with periodically varying amplitude throughout the crystal. It is found that if these bulk states are high enough in energy, then they match to free electron states in the vacuum and the electron in this state can leave the solid. Surface states are localized strictly to the surface region of the crystal but obviously are periodic in the two dimensions parallel to the surface. Surface resonance is equivalent to bulk wave functions with enlarged amplitude in the surface region of the crystal. The existence criteria for a Shockley state depend upon the choice of the terminating potential at the surface. The step potential used in the models required matching to a single exponentially decaying wave function outside the surface. State-of-the-art self-consistent calculations yield not only the energy-momentum parameters but also the charge distribution associated with surface state the wave functions.