Electron States near Boundaries

Abstract

There are three surface effects which may penetrate many shielding lengths into a metal. These are a charge-density oscillation, the addition of evanescent parts to the wave function, and a distortion of the momentum distribution of electrons. The amplitude of the charge oscillations is quite small and in most cases probably negligible. The additional evanescent parts may have a significant effect on the properties of a solid near its surface. They can cause optical transitions which do not conserve crystal momentum, a buildup of negative charge in the vicinity of the boundary, and a change in the electron wave functions at the surface. The characteristics of the evanescent parts are discussed in detail in the nearly free-electron approximation. They are dependent on the orientation of the boundary relative to the crystal axes and on the energy of the state. The same physical situation that adds evanescent parts to the wave function also distorts the momentum distribution of the electrons at a surface so that more electrons are moving parallel to the boundary than is the case in the interior. The momentum distortion penetrates into the interior a distance of the order of a mean free path of the electrons.