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. However, as material systems decrease to length scales less than the phonon mean-free paths, thermal transport can become much more impacted by scattering and transmission across interfaces between two materials than the intrinsic relaxation in the homogeneous solid. 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. Measurements were performed at room temperature using time-domain thermoreflectance and represent the first-reported values for interface conductance across several metal/native oxide/silicon and metal/sapphire interfaces. The various metal films provide a variable bandwidth of phonons incident on the metal/substrate interface. 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. We show that the accumulation function can be written as the product of a weighted average of the interfacial phonon transmission function and the accumulation of the temperature derivative of the phonon flux incident on the interface; this provides the framework to extract an average, spectrally dependent phonon transmissivity from a series of thermal boundary conductance measurements. 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. Based on the assumptions made in this work and the measurement results on different metals on native oxide/silicon and sapphire substrates, we demonstrate that high-frequency phonons dictate the transport across metal/Si interfaces, especially in low Debye temperature metals with low-cutoff frequencies.