Distance of the image plane from metal surfaces

The data base of surface-state energies on the metals Cu, Ag, Au, Ni, Pd, and Pt is assembled and, with the aid of a simple model, is used to estimate the distance of the image plane and its trends from surface to surface and metal to metal. The model combines a nearly-free-electron representation of the crystal with a Jones-Jennings-Jepsen ansatz for the saturated image barrier. The projected bulk-band gaps are taken from published determinations. Constraints are placed on the surface barrier parameters by appeal to the results of self-consistent first-principles slab calculations. The general experimental trend observed is for the image-plane distance $z_0$ to decrease in the sequence (111) to (001) to (110), in the same sense but not as rapidly as $z_J$, the distance of the effective jellium edge. This trend is rationalized using a simple model of the tail of the surface charge density. Typical values for $z_0$-$z_J$ fall in the range -0.2 to +0.5 a.u., with the larger values occurring for the 3d metals Cu and Ni.