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

Abstract

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 $\le 5\%$ 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 Lévy 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.

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