In this presentation, we introduce an innovative experimental methodology designed to systematically examine the contributions of phonons with varying mean free paths (MFPs) to the thermal conductivity in metal oxide thin films, including: -Ga₂O₃, -Ga₂O₃, Cr₂O₃, and ZnO. Our approach specifically targets the quasi-ballistic regime (Knudsen number Kn >> 1), characterized by phonon MFPs that exceed the film thickness (d), and is distinguished by its ability to deliver high-resolution data on the thickness dependence of thermal conductivity in terms of phonon MFPs. To accomplish this, we fabricated gradient samples with continuously decreasing thicknesses reaching sub-10 nm scales (as low as 3 nm), thereby enabling unprecedented spatial resolution and direct access to quasi-ballistic transport phenomena.

Our findings indicate that the suppression of phonons with reduced thickness is not uniform but is significantly influenced by the thermal boundary conductance at the film-substrate interface, as demonstrated in the case of a Ge/GaAs thermal interface. Notably, minimal interface conductance substantially diminishes the suppression of phonons with longer mean free paths (MFPs), highlighting the critical role of interfaces in governing quasi-ballistic thermal transport. Complementary in-plane transient thermal grating (TTG) experiments conducted at the FERMI synchrotron facility corroborate our observations, showing consistency with established harmonic suppression functions typical of TTG experiments. In contrast, frequency-domain thermoreflectance measurements reveal that suppression functions significantly deviate from steady-state assumptions and closely align with forms observed in TTG studies. We discuss the selection of a specific suppression function tailored to our experimental geometry and boundary conditions, emphasizing its complexity and sensitivity to experimental parameters. This comprehensive analysis elucidates the interplay among phonon mean free paths, interface thermal conductance, and various transport regimes, providing valuable insights critical for nanoscale thermal management strategies.

We further illustrate the versatility and robustness of our methodology by applying it to a range of technologically significant and diverse oxide materials. In each instance, we directly derive the phonon accumulation function as a function of maximum phonon mean free paths (MFPs), thereby yielding an intrinsic material property that is independent of specific excitation conditions and boundary constraints. Our approach offers a straightforward yet powerful technique for conducting detailed analyses of phonon MFP spectra at length scales below 10 nm, thereby significantly enhancing our understanding of nanoscale heat transport mechanisms.