Metallic Interfaces. II. Influence of the Exchange-Correlation and Lattice Potentials

Abstract

An electron-gas model of a metallic interface is constructed by joining two semi-infinite half-planes of unequal positive charge and adding electrons until a charge-neutral system is achieved. Our earlier treatment of this model is extended in several directions. The exchange-and-correlation effective one-electron potential, formerly taken in the "dipole approximation" to equal its bulk value in each material, is calculated using the local-density approximation. In the case where the low-density material has the smaller separation energy, the size of its depletion region and the height of the barrier potential are increased. In the case where the low-density material has the larger separation energy, the use of the local-density exchange-and-correlation potential scarcely alters the results obtained using the dipole approximation. A modified self-consistent free-electron model of a metal-intrinsic semiconductor junction adequately accounts for several features of the experimental data concerning the dependence of the barrier height on the components and method of fabrication of the junction. A primary effect of energy gaps associated with the periodic potential is the introduction of a long-range contribution to the junction potential in the semiconductor. An examination of (solvable) one-dimensional models suggests that if the semiconductor energy gaps are small relative to the metal bandwidth, then the modified free-electron model correctly describes the modification of the short-range (\ensuremath{\sim}1-5 \AA{}) dipole layers at the metal-semiconductor interface. In this case the modified free-electron model adequately determines the barrier height at the interface, although it never describes the details of the space-charge potential in the semiconductor.