Quasi-harmonic theory for phonon thermal boundary conductance at high temperatures

Abstract

We derive a theoretical model for phonon thermal boundary conductance across solid interfaces in the high temperature classical limit using quasi-harmonic thermodynamics, an approach that accounts for phonon anharmonicity effects on energy density changes via thermal expansion. Commonly used predictive models based on harmonic theory predict a thermal boundary conductance in the classical limit that is that constant and independent of temperature. Thus, these theories do not capture the increase in thermal boundary conductance with increasing temperature that has been reported in numerous molecular dynamics and anharmonic non-equilibrium Green’s function simulations. Our model accounts for anharmonic effects on the thermal boundary conductance via an increased internal energy of the material through an additional quasi-harmonic term that includes the material’s Grüneisen parameter. We show good agreement between our model calculations and the predicted thermal boundary conductance across a heavy argon/argon interface determined via molecular dynamics simulations. Further, our results also capture the contribution of inelastic scattering to thermal boundary conductance across a silicon/germanium interface predicted from anharmonic nonequilibrium Green’s functions simulations. Our quasi-harmonic thermodynamic-based theory suggests that an increase in thermal boundary conductance with an increase in temperature above the Debye temperature is due to anharmonicity in the materials adjacent to the interface, which is captured by the thermal expansion-driven phonon energy density changes in the materials. This theory is also consistent with prior molecular dynamics and anharmonic non-equilibrium Green’s function simulations that suggest that inelastic scattering effects on thermal boundary conductance are driven by phononic processes in materials near the interface and not at the interface. This model can help in screening materials for high interface density composites to increase thermal conductance and mitigate temperature in a range of applications.