Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well

Lattice thermal conductivity of a quantum well limited by umklapp, impurity, and boundary scattering was investigated theoretically by taking into account dispersion of confined acoustic-phonon modes. We show that strong modification of phonon group velocities due to spatial confinement leads to a significant increase in the phonon relaxation rates. From the numerical calculations, we predict a decrease by an order of magnitude of the lattice thermal conductivity in a 100-\AA{}-wide free-standing quantum well. Our theoretical results are consistent with recent experimental investigations of the lateral thermal conductivity of nitride/silicon/oxide membranes conducted in our group.