Decomposition of coherent and incoherent phonon conduction in superlattices and random multilayers

Abstract

Nonequilibrium molecular dynamics (NEMD) simulations on conceptual binary Lennard-Jones systems show that the thermal conductivity ($\ensuremath{\kappa}$) of a superlattice (SL) can be significantly reduced by randomizing the thicknesses of its layers, by which a SL becomes a random multilayer (RML). Such reduction in $\ensuremath{\kappa}$ is a clear signature of coherent phonon that can be localized in RMLs. We build a two-phonon model that divides the overall heat conduction into coherent and incoherent phonon contributions. In SL both coherent and incoherent phonons contribute to heat conduction, while in RML coherent phonons are localized so only incoherent phonons contribute. This model can fit the length dependence of the thermal conductances predicted in our NEMD simulations very well. The ballistic-limit thermal conductance and the intrinsic mean free path (MFP) of both coherent and incoherent phonons, and the localization length of coherent phonons, are obtained by fitting our model to the NEMD simulation results. The significant increase in $\ensuremath{\kappa}$ of SL with total length is due to the long MFP of coherent phonons, and the lower $\ensuremath{\kappa}$ of RML than SL is caused by the localization of coherent phonons.