Dielectric continuum theory of the electronic structure of interfaces

General expressions for the density-density and potential-potential response functions, ground-state (i.e., surface) energy, and one-electron optical potential are derived for a model of planar interfaces between two media, each of which is described by a local frequency-dependent dielectric function. These expressions are utilized to evaluate the surface energies characteristic of interfaces between semiconductors (insulators) described by the uniform dielectic function ${{ε}}S({ω})=1+{{ω}}ₚ²{({{Δ}}²{-}{{ω}}²{-}{i{ω}}{{τ}})}^{{-}1}$ metals described by ${{ε}}M({ω})=1{-}{{{ω}}ₚ²}{{ω}({ω}+{i}{{τ}})}$, and the vacuum ${{ε}}V({ω}){≡}1$. Plasmon damping (i.e., nonzero ${{τ}}^{{-}1}$) is shown to limit the range of nonlocality of the one-electron optical potential to ${λ}{~}{({2{}{τ}}{m})}1/2$ and to decrease the surface energy. The surface energy of semiconductor interfaces is found to diminish monotonically with increases in the band-gap parameter ${E}g={}{Δ}$. The conventional expressions for the surface energy of metals as a function of their density, $n={m{{ω}}ₚ²}{4{π}{e}²}$, are recovered in the ${τ}{→}{∞}$ limit, although errors in some previous derivations of these expressions are displayed. Finally, the structure and limitations of local models of surface properties are examined critically, and the well-known hydrodynamic and step-density random-phase-approximation models of metal-vacuum interfaces are shown to be elementary consequences of classical electrostatics in the limit that εM(ω)=1-ωₚ²ω².