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

TL;DR

This paper develops a first-principles approach to accurately model cross-plane thermal conductivity in semiconductor thin films, revealing quasiballistic regimes and providing compact formulas for practical predictions.

Contribution

It introduces a suppression model matching Monte Carlo simulations with ab-initio data, enabling precise reconstruction of thermal conductivity across various materials and regimes.

Findings

Quasiballistic regime characterized by fractional thickness dependence in alloys.

Logarithmic thickness dependence observed in single crystals.

Two parametric formulas accurately fit first-principles curves across regimes.

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 $\leq 5\%$ 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.