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.
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