The lattice thermal conductivity of superlattices is shown to depend on a new kind of umklapp scattering process, called a mini-umklapp, associated with the mini-Brillouin zone of the superlattice. Expressions for three-phonon mini-umklapp-scattering matrix elements are obtained for superlattices consisting of lattice-matched simple-cubic layers. The temperature dependence of the thermal conductivity is evaluated using an extension of Callaway's phenomenological model.
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Ren et al. (1982) studied this question.
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