Thermal boundary conductance accumulation and interfacial phonon transmission: Measurements and theory

The advances in phonon spectroscopy in homogeneous solids have unveiled extremely useful physics regarding the contribution of phonon energies and mean-free paths to the thermal transport in solids. To elucidate the fundamental interactions driving this thermally limiting interfacial phonon scattering process, we analytically derive and experimentally measure a thermal boundary conductance accumulation function. We develop a semiclassical theory to calculate the thermal boundary conductance accumulation function across interfaces using the diffuse mismatch model, and validate this derivation by measuring the interface conductance between eight different metals on native oxide/silicon substrates and four different metals on sapphire substrates. This method of varying phonons' cutoff frequency in the film while keeping the same substrate allows us to mimic the accumulation of thermal boundary conductance and thus provides a direct method to experimentally validate our theory. Our approach provides a platform for analyzing the spectral phononic contribution to interfacial thermal transport in our experimentally measured data of metal/substrate thermal boundary conductance.