Fresnel transmission coefficients for thermal phonons at solid interfaces

Interfaces play an essential role in phonon-mediated heat conduction in solids, impacting applications ranging from thermoelectric waste heat recovery to heat dissipation in electronics. From a microscopic perspective, interfacial phonon transport is described by transmission and reflection coefficients, analogous to the well-known Fresnel coefficients for light. However, these coefficients have never been directly measured, and thermal transport processes at interfaces remain poorly understood despite considerable effort. Here, we report the first measurements of the Fresnel transmission coefficients for thermal phonons at a metal-semiconductor interface using ab-initio phonon transport modeling and a thermal characterization technique, time-domain thermoreflectance. Our measurements show that interfaces act as thermal phonon filters that transmit primarily low frequency phonons, leading to these phonons being the dominant energy carriers across the interface despite the larger density of states of high frequency phonons. Our work realizes the long-standing goal of directly measuring thermal phonon transmission coefficients and demonstrates a general route to study microscopic processes governing interfacial heat conduction. a These authors equally contributed to this work. 1 ar X iv :1 50 9. 07 80 6v 1 [ co nd -m at .m es -h al l] 2 5 Se p 20 15 Transport across interfaces in heterogeneous media is a fundamental physical process that forms the basis for numerous widely used technologies. For example, the reflection and transmission of light at interfaces, as described by the Fresnel equations, enables waveguiding with fiber-optics and anti-reflection coatings, among many other functionalities. Interfaces also play an essential role in phonon-mediated heat conduction in solids. Material discontinuities lead to thermal phonon reflections that are manifested on a macroscopic scale as a thermal boundary resistance (TBR), also called Kapitza resistance, Rk, that relates the temperature drop at the interface to the heat flux flowing across it. TBR exists at the interface between any dissimilar materials due to differences in phonon states on each side of the interface. Typical interfaces often possess defects or roughness which can lead to additional phonon reflections and hence higher TBR. TBR plays an increasingly important role in devices, particularly as device sizes decrease below the intrinsic mean free paths (MFPs) of thermal phonons. At sufficiently small length scales, TBR can dominate the total thermal resistance. For instance, the effective thermal conductivity of a superlattice can be orders of magnitude smaller than that of the constituent materials due to high TBR. This physical effect has been used to realize thermoelectrics with high efficiency and dense solids with exceptionally low thermal conductivity. On the other hand, TBR can lead to significant thermal management problems in applications such as LEDs and high power electronics. Thus both scientifically and for applications, a fundamental understanding of thermal transport across solid interfaces is essential. In principle, Fresnel transmission coefficients can also be used to provide a microscopic description of thermal phonon transport at interfaces owing to the similarities between photons and phonons. However, despite decades of work, the microscopic perspective of heat transport across interfaces remains poorly developed compared to that available for photons. Today, interfaces are most often studied using macroscopic measurements of TBR or thermal conductivity. For example, numerous works have studied interfacial thermal transport by observing the temperature dependence of the thermal conductivity or interface conductance, G = 1/Rk 17–21 or by correlating changes in bonding strength and interface conductance. However, these experimental approaches provide limited information about the transmission coefficients because the observable quantities are averaged over all phonons and thus obscure the microscopic processes of interest.