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 $\mathrm{Si}∕\mathrm{Ge}$ based structures.

Figure 1

Room temperature thermal conductivity of $N\times N$ superlattices along the superlattice axis, scaled by the calculated values for the bulk template (see the text), as a function of mass ratio of the constituents. The thin vertical line is for SiGe superlattices.

Figure 2

Phonon dispersions along the growth direction of $1\times 1$ (solid lines) and $2\times 2$ (dashed lines) SiGe superlattices for two in-plane wave vectors.

Figure 3

Umklapp and optic phonon scattering parameters, $\xi$ (solid lines) and $\zeta$ (dashed lines), as described in text, for $1\times 1$ and $2\times 2$ superlattices for increasing mass ratio of the constituents. The thin vertical line gives results for SiGe superlattices. $\xi$ and $\zeta$ are scaled by values for the bulk template material.