LAUSR

The out-of-plane thermal conductivity and elastic constant of epitaxial [100] $^{12}\mathrm{C}/^{13}\mathrm{C}$ superlattice diamonds with layer thicknesses of 1, 30, and 100 nm are evaluated by picosecond ultrasound spectroscopy. The measured elastic constants of the superlattices are equivalent to those of single-layer diamond thin films. This result confirms our success in synthesizing superlattice specimens with few defects at the interfaces. Therefore, the phonon transport behavior is governed by the mass difference, not the interfacial defects. The measured thermal conductivity of the superlattices is lower than that of a pure $^{12}\mathrm{C}$ isotope diamond thin film. We estimated the lattice thermal conductivity using the lattice dynamics calculation, attributing the lowered thermal conductivity to the decrease in the phonon group velocity in superlattices. We further consider the effect of mini-umklapp scattering in the superlattice, which explains the dependence of the thermal conductivity on the layer thickness. We reveal that the mini-umklapp scattering effect becomes significant only for an isotope diamond superlattice because of the high Debye temperature and large relative mass difference.