Confined polar optical phonons in semiconductor double heterostructures: an improved continuum approach

Confined polar optical phonons are studied in a semiconductor double heterostructure (SDH) by using a generalization of the well-known continuous medium model theory. The treatment considers the coupling between the electro-mechanical oscillations and involves dispersive phonon modes. This approach has provided confined phonon frequency dispersions rather different from the dielectric continuum model, where just the electric aspect of these oscillations is analysed. In previous works, the theory had been used to analyse the phonon dispersions within a quadratic (parabolic) approximation, while presently we added the linear contributions by using a straightforward extension of the fundamental equations. This generalized version of the mentioned theoretical treatment leads to a long wavelength polar optical phonon description that shows 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 and their solutions for bulk and SDH cases. The results provide us with a complete description of the dispersive phonon modes and the associated electron–phonon Hamiltonian. The theory is applied to the case of a EuS/PbS/EuS quantum well.