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

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