Boundary Conditions Dictate Frequency Dependence of Thermal Conductivity in Silicon

Nonlocal thermal transport has attracted enormous attention in recent decades. In particular, frequency-dependent thermal conductivity has been extensively studied via time-domain thermoreflectance (TDTR). However, certain questions regarding frequency-dependent thermal transport remain unanswered within reported theories and experiments. For example, previous TDTR measurements on Si did not reveal apparent frequency dependence, in stark contrast to semiconductor alloys and two-dimensional materials, despite its broad spectrum of phonon mean free paths. In this work, we unveil a distinct frequency dependence of thermal transport in an Al/Si sample with an atomically sharp interface, while the dependence diminishes in the Al/SiO₂/Si sample with a naturally formed SiO₂ interlayer. The observed frequency dependence in Al/Si stems from thermal nonequilibrium between low- and high-energy phonons in Si as Al has a close Debye temperature to that of Si, while the diffuse interface of Al/SiO₂/Si enables efficient energy exchange and destroys thermal nonequilibrium. Additionally, frequency dependence reemerges in the Al/SiO₂/Si sample at 80 K, since the reduced phonon reflection at the interface preserved thermal nonequilibrium in Si. This work highlights the role of boundary conditions in frequency-dependent thermal transport.