Influence of the topmost two layers on the collective excitations of a finite superlattice

We have analyzed the influence of the topmost two layers on the properties of the collective excitations of a finite superlattice structure. For semi-infinite superlattices the effect of the topmost layers on the collective excitations was discussed by Streight and Mills [Phys. Rev. B 29, 6337 (1987)]. We extend the discussion to the case of a superlattice with a finite number of periods, in which the thickness and the dielectric constant of the topmost two layers may differ from those of the layers below. A general dispersion relation for the finite superlattice is derived and applied to finite GaAs-AlAs superlattices. The dispersion curves and the electrostatic potentials show that several modes change in character with varied thickness of the topmost two layers. This change of the mode character is reflected in the electron-energy-loss spectra calculated in the framework of the dielectric theory.