Relationship of Microscopic and Macroscopic Theories for Long‐Wavelength Optical Phonons in GaAs‐AlAs Superlattices

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Abstract
A critical comparison is made of the lattice‐vibrational properties resulting within the macroscopic continuum model and a closely parallel microscopic force‐constant model. The elastic and electric forces are treated in the same manner. However, the atomic structure of matter and the bulk phonon dispersion are neglected in the continuum approach. For that reason it cannot explain the optical frequency spectrum of a superlattice even not in the long‐wavelength limit. On the other hand, the principal line shape of the atomic displacement patterns for optical phonons can be satisfactorily described by envelopes, at least, if the arbitrariness inherent any theory neglecting dispersion is utilized in an appropriate way. This holds particularly for modes which are not accompanied by long‐range electric fields. For the other modes — the p‐polarized symmetrical phonons propagating not parallel to the superlattice axis — the problem of identification appears additionally since the interface character restricted to four modes in the dispersionless continuum approach is distributed among all symmetrical phonons within the microscopic theory.