FOUNDATIONS OF THE ENVELOPE-FUNCTION THEORY FOR PHONONS IN HETEROSTRUCTURES

A one-dimensional envelope-function model is developed for the treatment of long-wavelength optical phonons in InAs/GaSb and related superlattices. The long-wavelength model is derived from an exact envelope-function formalism that is fully equivalent to the standard force-constant model of discrete lattice dynamics. Two new interface-related terms appear in the analysis, neither of which is included in current phenomenological models for GaAs/AlAs superlattices. The first describes the change in reduced mass at the interface, and is important for both longitudinal and transverse vibrations; the second describes the change in the optical force constant at the interface, and is important primarily for transverse vibrations. A comparison of the continuum model with discrete calculations shows good numerical agreement for all long-wavelength modes, including those modes which are tightly bound to the interfaces.