Lattice thermal conductivity of superlattice structures

We give a quantitative inelastic phonon Boltzmann equation theory of thermal transport in quantum well superlattices due to anharmonic three phonon processes. The thermal conductivity is calculated as a function of the mass ratio of the constituent atoms and of the superlattice period. We show that there is a competition between the flattening of dispersions that inhibits heat flow and reduced umklapp scattering that enhances it. Both effects must be included consistently for a quantitative treatment. We apply this theory to realistic models of Si∕Ge based structures.