Optical Phonon Modes in a Double Heterostructure of Polar Crystals

The equation of motion for the polarization vector for a double heterostructure of polar crystals is solved exactly within the framework of the continuum model. There exist only two types of phonon modes, the interface modes and the confined bulk modes, whose eigenvectors are obtained explicity. Dispersion relations are derived analytically for the interface modes, while the confined bulk modes are dispersionless, a fact consistent with the model. It is also found that in Raman scattering experiments, the symmetric interface modes are predominantly longitudinal LO and the antisymmetric interface modes transversal TO. In the central region of the Brillouin zone, however, they both split into two branches oscillating at LO and TO frequencies, respectively. Possibly reinterpretation of various experiments are briefly discussed. JHD