Sound velocity of AlxGa1−xN thin films obtained by surface acoustic-wave measurements

To determine the sound velocity in wurtzite ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N},$ we have used surface acoustic-wave (SAW) delay lines on ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N}\mathrm{/c-}{\mathrm{Al}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{3}}.$ ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N}$ films with compositions from $\text{x=0}$ to $\text{x=1}$ were grown by plasma-induced molecular beam epitaxy. Starting from published data, we fine tuned the values of the elastic moduli used in numerical calculations such that the simulated and measured dispersion of the SAW were in good agreement. Based on these values, the surface and bulk acoustic-wave velocities of single-crystal ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N}$ were determined as functions of the composition. The resulting SAW velocities ranged from 3700 to 5760 m/s for GaN and AlN, respectively.