Electron States in a Semi-Infinite Metal

Abstract

A semi-infinite crystal extending from z = —∞ to z = 0 (we shall always assume that this is the case every time we refer to a semi-infinite crystal) can be viewed as a stack of atomic layers parallel to the given crystallographic plane (xy plane) but, in contrast to the infinite crystal considered in the previous chapter, we cannot assume, without further justification, that all layers are identical with each other. Obviously, the layers which lie away from the surface, deep into the solid, will be unaffected by the presence of the surface, but the top few layers are bound to be different from the bulk layers in more than one way. In the first instance the relative position of the atomic nuclei at the surface may be different from those in the bulk. For metals where a layer consists of a single plane of atoms (one atom per unit surface cell) this difference usually consists of a simple dilation away from or contraction towards the bulk of the metal of the top one or two layers. The analysis of relevant LEED experiments (see, e.g., Pendry, 1974; Van Hove and Tong, 1979) shows that the interlayer spacing changes by 10% or less for the first pair of layers, the change is much less for the second pair (second and third layers) and practically nonexistent further into the solid. There are cases, however [e.g., tungsten (100) below 350 K and possibly at higher temperatures], where lattice reconstruction does occur leading to a top (surface) layer with a different 2D unit cell (Debe and King, 1977; 1979; Felter, Barker, and Estrup, 1977). Reconstruction is much more common on semiconductor surfaces (see, e.g., Harrison, 1976).