Phonon group velocity and thermal conduction in superlattices

With the use of a face-centered cubic model of lattice dynamics we calculate the group velocity of acoustic phonons in the growth direction of periodic superlattices. Comparing with the case of bulk solids, this component of the phonon group velocity is reduced due to the flattening of the dispersion curves associated with Brillouin-zone folding. The results are used to estimate semiquantitatively the effects on the lattice thermal conductivity in Si/Ge and GaAs/AlAs superlattices. For a Si/Ge superlattice an order of magnitude reduction is predicted in the ratio of superlattice thermal conductivity to phonon relaxation time consistent with the results of P. Hyldgaard and G. D. Mahan, Phys. Rev. B 56, 10 754 (1997). For a GaAs/AlAs superlattice the corresponding reduction is rather small, i.e., a factor of 2--3. These effects are larger for the superlattices with larger unit period, contrary to the recent measurements of thermal conductivity in superlattices.