Structure Thermal Domain Size in μm-Thick Single Crystalline Sapphire Wafer Uncovered by Low-Momentum Phonon Scattering

The structure thermal domain (STD) size is a characteristic size that reflects the defect-energy carrier scattering. To date, it is still unclear how a material's grain structural characteristics are related to and determine the STD size. This work presents the first effort on such physics by measuring the STD size of μm-thick single crystalline sapphire wafers and interpreting it based on the crystallite size uncovered by X-ray diffraction (XRD). A novel measurement methodology is developed to measure the thermal reffusivity (<i>Θ</i>) at the zero temperature rise limit. This allows for high-precision determination of <i>Θ</i> at the 0 K limit (<i>Θ</i> ₀). <i>Θ</i> ₀ eliminates the effect of Umklapp phonon scattering and is solely determined by the grain boundary scattering of low-momentum phonons. Based on <i>Θ</i> ₀, the STD size is found to be 85.1 nm in the wafer's in-plane direction, while the XRD uncovers crystallite sizes of 283 nm in the cross-plane direction and 34.4 nm in the in-plane direction. The STD size is influenced by phonon scattering in all directions, more so by that in the heat conduction direction. It provides a new aspect in understanding the grain characteristic size from the viewpoint of phonon transport with a direction dependence.