Theory of the quantum size effect in simple metals

Using the self-consistent pseudopotential technique and planarly averaged one-dimensional potential (quantum well) we provide a rigorous basis for understanding the quantum size effect and dimensionality of thin metal films. The density of states, work function, surface energy, and vertical surface relaxations, subband energies, and surface charge density are found to vary as a function of film thickness. The density of states has a ladder-type structure (characteristic of a two-dimensional electron system); its value at the Fermi level changes in quantized steps with film thickness, L. The relative position of the Fermi level between subbands, which changes with L, provides an interesting explanation for the variation in physical properties. © 1986 The American Physical Society.