Phonons in parabolic-quantum-well structures fabricated with semiconductor alloys are studied. We calculate frequencies, displacement patterns, and densities of states for lattice vibrations in a (GaAs)N1(Ga_1-x{Al}ₓ$As${)}N2$(001) superlattice where the GaAs layers are replaced by a mixed crystal ${Ga}_{1{{-}}xs}AlₓₛAs with Al fraction xₛ varying quadratically with atomic layer s. The influence of disorder, composition, and the two-mode behavior of optical phonons are investigated within a random-element-isodisplacement model, generalized to layered structures with arbitrary composition profiles.
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Bechstedt et al. (1993) studied this question.
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