Coupling of polar optical phonons to electrons in superlattices and isolated quantum wells

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Abstract
Theoretical models that treat optical lattice vibrations in heterostructures by viewing the lattice-matched crystalline media as isotropic homogeneous continua separated by smooth planar interfaces, offer conceptual simplicity and are, without doubt, computationally advantageous when calculations involving electron-phonon interactions are carried out. The two (apparently conflicting) continuum models, namely the hydrodynamic (HD) and the electromagnetic (EM) models, are discussed, their calculational frameworks in the context of semiconductor heterostructures examined and some of their predictions displayed. A statement of the HD model in terms of a polariton subset plus an LO subset is given, and this permits a transparent comparison with the EM model to be made. It is then shown that the EM model is a non-dispersive, non-retarded and subsequently mishandled version of the polariton subset of the HD model and it completely disallows proper considerations of longitudinal optical modes. The sources of the current controversies concerning HD versus EM boundary conditions-confined mode identification, existence of localized alloy interface LO modes and interface FK modes, Frohlich-type coupling e Phi together with the e Phi versus-(e/m*c)AT.p couplings to electrons-are all pointed out and discussed. A close agreement between some very recent predictions of the two models concerning interface mode contributions to energy relaxation is explained and this helps to clarify the nature of the conflict regarding other contributions. Further evidence in support of the HD model from recent theoretical and experimental results is pointed out.