  Confined polar optical phonons are studied in a semiconductor double
heterostructure (SDH) by means of a generalization of a theory developed some
years ago and based on a continuous medium model. The treatment considers the
coupling of electro-mechanical oscillations and involves dispersive phonons.
This approach has provided results beyond the usually applied dielectric
continuum models, where just the electric aspect of the oscillations is
analyzed. In the previous works on the subject the theory included phonon
dispersion within a quadratic (parabolic) approximation, while presently linear
contributions were added by a straightforward extension of the fundamental
equations. The generalized version of the mentioned theoretical treatment leads
to a description of long wavelength polar optical phonons showing a closer
agreement with experimental data and with calculations along atomistic models.
This is particularly important for systems where the linear contribution to
dispersion becomes predominant. We present a systematic derivation of the
underlying equations, their solutions for the bulk and SDH cases, providing us
a complete description of the dispersive modes and the associated
electron-phonon Hamiltonian. The results obtained are applied to the case of a
EuS/PbS/EuS quantum-well.
