We consider a semi-infinite superlattice structure, with constituent $A$ characterized by dielectric constant ${\epsilon }_A\left(\omega \right)$ and constituent $B$ by ${\epsilon }_B\left(\omega \right)$, and examine collective excitations of the system in the absence of retardation effects. Also, we explore the energy-loss spectrum of electrons backscattered from such a structure. Detailed application is to the case where one constituent, a semiconductor or metal, contains free carriers, while the second is described by a frequency-independent dielectric function. Surface excitations (surface plasmons) on adjacent interfaces couple through macroscopic electric fields to form a propagating band of collective excitations of the whole structure capable of transporting energy normal to the interfaces. We then find surface excitations of the entire structure. These are linear superpositions of modes localized at successive interfaces, combined with an envelope function which decays exponentially as one moves down the stack. By explicit calculations of the energy-loss spectrum, we show how electron-energy-loss spectroscopy may be used to study these and other collective modes of the array.

• Received 8 August 1983

DOI:https://doi.org/10.1103/PhysRevB.29.1695