Cross-plane heat conduction in thin films with ab-initio phonon dispersions and scattering rates

摘要

We present a first-principles study of the cross-plane thermal conductivity$\kappa_{\perp}$ in a wide variety of semiconductor thin films. We introduce asimple suppression model that matches variance-reduced Monte Carlo simulationswith ab-initio phonon dispersions and scattering rates within $\leq 5\%$ evenfor anisotropic compounds. This, in turn, enables accurate $\kappa_{\perp}$reconstruction from tabulated cumulative conductivity curves$\kappa_{\Sigma}(\Lambda_{\perp})$. We furthermore reveal, and explain, adistinct quasiballistic regime characterised by a fractional thicknessdependence $\kappa_{\perp} \sim L^{2-\alpha}$ in alloys (where $\alpha$ is theL\'evy exponent) and logarithmic dependence $\kappa_{\perp} \sim \ln(L)$ insingle crystals. These observations culminate in the formulation of two compactparametric forms for $\kappa_{\perp}(L)$ that can fit the first-principlescurves across the entire ballistic-diffusive range within a few percent for allinvestigated compounds.