Dr Paul Kinsler. [Acknowledgements & Feedback]

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Dielectric Continuum Model

The DCM demands that D_z = epsilon E_z and E_{par} are continuous across interfaces.

From Babiker-Z-1998:
• S-polarised TO-phonon modes are unconstrained at the boundaries, as these conditions are automatically satisfied. Thus there are independent modes of this type in each layer.
• P-polarised confined TO-phonon and LO-phonon modes are unconstrained at the boundaries, as these demanding vanishing polarization at \pm infinity and continuity confines them to a single layer. Thus there are independent modes of this type in each layer.
• P-polarised interface TO-phonon and LO-phonon modes need to match the boundary-conditions, and so we get interface modes that are localised near the interfaces, but actually extend across the entire structure.

There are no hybrid-phonons, as in Ridley-1993. Babiker-Z-1998 do a revised accurate version of the DC-model applied to both bulk and heterostructures.

The DC-model allows FK-phonons (IP-phonons), in contrast to the HD-model. These are interface polaritons, and in the unretarded limit their energy is almost totally mechanical, although their dispersion is the usual EM one (k^2/(epsilon.mu)). Although their interaction with electrons is A.p; their primarily mechanical nature means that it can be approximated by an e.phi term (see Ridley-1997, chapter 8).

At the end, though, the hybrid-phonon model is the most exact, and the EM boundary-conditions of the DC-model are incorporated into it. However, in practise the DC-model with confined LO-phonons and IP-phonons will give accurate total scattering rates. Further, the best way to model the IP-phonons in the DC-model is by solving for its potential.

The motivation for the DC-model seems to have been convenience, but it gave the wrong results for resonant Raman scattering measurements, as these have selection rules based on the parity of the electron and phonon wavefuntions, and the DC-model and HD-model predict opposite confined LO-phonon parities. The HD-model agreed with experiment, although for (other) systems the DC-model seemed to work fine. If you belive Babiker-1992's convincing (or forceful) arguments, this model tends to mislead about the labeling of the phonon modes, and consequently mislead about the electron - phonon interaction as well.

cf HD-model (hydrodynamic)

XINDEX: log-file, hybrid-phonon, boundary-condition, Ridley-B-1991, Ridley-ACB-1994, LO-phonon, HD-model, Babiker-Z-1998, index-file, log-file.

19971127 1210 11 12 19980112 14 16 23

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