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.

We develop an analytical model for the thermal boundary conductance between a solid and a liquid. By infusing recent developments in the phonon theory of liquid thermodynamics with diffuse mismatch theory, we derive a closed form model that can predict the effects of wetting on the thermal boundary conductance across an interface between a solid and a classical liquid. We account for the complete wetting (hydrophilicity), or lack thereof (hydrophobicity), of the liquid to the solid by considering varying contributions of transverse mode interactions between the solid and liquid interfacial layers; this transverse coupling relationship is determined with local density of states calculations from molecular dynamics simulations between Lennard-Jones solids and a liquids with different interfacial interaction energies. We present example calculations for the thermal boundary conductance between both hydrophobic and hydrophilic interfaces of Al/water and Au/water, which show excellent agreement with measured values reported by Ge et al. [Z. Ge, D. G. Cahill, and P. V. Braun, Phys. Rev. Lett. 96, 186101 (2006)]. Our model does not require any fitting parameters and is appropriate to model heat flow across any planar interface between a solid and a classical liquid.

13 The advances in phonon spectroscopy in homogeneous solids have unveiled extremely useful physics 14 regarding the contribution of phonon energies and mean free paths to the thermal transport in solids. How15 ever, as material systems decrease to length scales less than the phonon mean free paths, thermal transport 16 can become much more impacted by scattering and transmission across interfaces between two materials 17 than the intrinsic relaxation in the homogeneous solid. To elucidate the fundamental interactions driv18 ing this thermally-limiting interfacial phonon scattering process, we analytically derive and experimentally 19 measure a thermal boundary conductance accumulation function. We develop a semi-classical theory to 20 calculate the thermal boundary conductance accumulation function across interfaces using the diffuse mis21 match model (DMM), and validate this derivation by measuring the interface conductance between nine 22 different metals on native oxide/silicon substrates and five different metals on sapphire substrates. Mea23 surements were performed at room temperature using time-domain thermoreflectance and represent the 24 first-reported values for interface conductance across several metal/native oxide/silicon and metal/sapphire 25 interfaces. The various metal films provide a variable bandwidth of phonons incident on the metal/substrate 26 interface. This method of varying phonons cutoff frequency in the film while keeping the same substrate 27 allows us to mimic the accumulation of thermal boundary conductance and thus provides a direct method to 28 experimentally validate our theory. We show that the accumulation function can be written as the product 29 of an average interfacial phonon transmission function and the accumulation of the temperature derivative 30 of the phonon flux incident on the interface; this provides the framework to extract an average, spectrally 31 dependent phonon transmissivity from a series of thermal boundary conductance measurements. Based on 32 the assumptions made in this work and the measurement results on different metals on native oxide/silicon 33 and sapphire substrates, we demonstrate that thermal transport across solid interfaces may not necessarily 34 be dictated by phonon mismatch of materials and interfacial transmission, but is rather directly correlated 35 to the temperature derivative of phonon flux incident on the interface. 36