Umklapp Scattering and Heat Conductivity of Superlattices
  The mean free path of phonons in superlattices is estimated. It is shown to be strongly dependent on the superlattice period due to the Umklapp scattering in subbands. It first falls with increasing the superlattice period until it becomes comparable with the latter after what it rises back to the bulk value. Similar behavior is expected of heat conductivity, which is proportional to the mean free path. 
M.V. Simkin and G.D. Mahan