Influence of the Lattice Potential on the Electronic Structure of Metallic Interfaces: Dipole Effects

We investigate the influence of the electronic energy-band structure on the self-consistent charge density and potential at solid-vacuum interfaces. A Kronig-Penny model in which the potential due to the positive ions is simulated by planar attractive $\delta$-function potentials is used to describe the electron-ion interactions. The magnitude of the exchange-correlation potential is held fixed throughout the self-consistent calculation. Outside the surface, the charge density responsible for the Hartree potential is given by the actual electron density. Inside the surface it is given by the difference between the actual electron density and the electron density which would exist if no surface were present. In general, lattice-potential-induced alterations of the free-electron (i.e., uniform) bulk charge density may result in a substantial (e.g., 50%) decrease in the size of the surface dipole potential. This decrease is caused by the occurrence of smaller charge deviations at the surface. The magnitude of these deviations is influenced strongly by relatively small changes in the parameters of the model. One-dimensional models predict substantially larger charge deviations than those obtained using three-dimensional models.