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Surface and Interface Optical-Phonon Modes in a Finite Four-Layer Heterostructure of Polar Crystals

The dispersion relation and eigenvector for the surface and interface optical-phonon modes in a finite four-layer heterostructure of polar crystals have been derived by using the dielectric continuum model. Moreover, as practical examples, the dispersion relations for some interesting structures such as finite and semi-infinite step quantum wells and a semi-infinite single quantum well are given for the first time.