Determination of group velocity based on nanoindentation using Si and SiO₂/Si wafers

The analyses of thermal transport properties can help improve the performance of high-tech semiconducting devices, such as thermoelectric generators and electronic devices. However, methods to measure thermal transport properties are limited, especially the group velocity and phonon mean free path (MFP) of thin films. Herein, we propose a simple technique to measure the group velocity and phonon MFP based on nanoindentation using Si and SiO₂/Si wafers. The group velocities, including the longitudinal, transverse, and average group velocities, were estimated using Young’s modulus, shear modulus, and Poisson’s ratio. The phonon MFP was estimated from the average group velocity, lattice thermal conductivity, and specific heat. The determined group velocities (∼6050 m/s) and phonon MFP (∼80 nm) when the Si wafer was used as a bulk material were in good agreement with the corresponding reference data. The influence of the underlying Si substrate increased when the indentation depth was increased when the SiO₂/Si wafer was used as a thin film (SiO₂ layer thickness, 200 nm). The influence of the underlying Si substrate existed even when the smallest indentation depth of 50 nm and the determined group velocities (∼4750 m/s) and phonon MFP (∼0.5 nm) were slightly different from those of the reference data. Therefore, although the accuracy of the measurement technique can be improved, this study verified that nanoindentation can be used to measure the group velocity and phonon MFP of materials. Furthermore, this technique opens a pathway for investigating the thermal transport properties of nanostructured materials.