The spherical-wave method for evaluating the electronic wave functions of a semi-infinite muffin-tin lattice is applied to the (001) and (110) surfaces of copper. It is demonstrated to be a feasible calculational procedure capable of yielding detailed information about the electronic wave functions in the vicinity of a metal surface. Since he focus of this paper is on the interpretation of the external current in field emission and photo-induced field emission, consideration is restricted to states which have no transverse momentum. The electronic states are evaluated over an energy range of about 0.5 Ry near the Fermi level using two different models of the surface potential. The one-dimensional density of states is calculated for several layers close to the surface of the crystal, and its approach to bulk behavior is described. A surface resonance and a surface state of ${\Delta }_1$ symmetry are found on the (001) surface, and surface resonances of ${\Sigma }_1$ and ${\Sigma }_3$ symmetry are found on the (110) surface. The application of these results to the energy dependence of the external current in field emission and photo-induced field emission is discussed.

• Received 9 June 1977

DOI:https://doi.org/10.1103/PhysRevB.18.5365