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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 $κ_{\perp}$ 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 $κ_{\perp}$ reconstruction from tabulated cumulative conductivity curves $κ_Σ(Λ_{\perp})$. We furthermore reveal, and explain, a distinct quasiballistic regime characterised by a fractional thickness dependence $κ_{\perp} \sim L^{2-α}$ in alloys (where $α$ is the Lévy exponent) and logarithmic dependence $κ_{\perp} \sim \ln(L)$ in single crystals. These observations culminate in the formulation of two compact parametric forms for $κ_{\perp}(L)$ that can fit the first-principles curves across the entire ballistic-diffusive range within a few percent for all investigated compounds.