Phonon group velocity and thermal conduction in superlattices

With the use of a face-centered cubic model of lattice dynamics we calculat e the group velocity of acoustic phonons in the growth direction of periodi c superlattices. Comparing with the case of bulk solids, this component of the phonon group velocity is reduced due to the flattening of the dispersio n curves associated with Brillouin-zone folding. The results are used to es timate semiquantitatively the effects on the lattice thermal conductivity i n Si/Ge and GaAs/AlAs superlattices. For a Si/Ge superlattice an order of m agnitude reduction is predicted in the ratio of superlattice thermal conduc tivity to phonon relaxation time [consistent with the results of P. Hyldgaa rd and G. D. Mahan, Phys. Rev. B 56, 10 754 (1997)]. For a GaAs/AlAs superl attice the corresponding reduction is rather small, i.e., a factor of 2-3. These effects are larger for the superlattices with larger unit period, con trary to the recent measurements of thermal conductivity in superlattices. [S0163-1829(99)05028-6].