Characterization of textit{M}-plane GaN thin film grown on pre-annealing $\beta $-LiGaO$_{2}$ (100) substrate

We used the plasma-assisted molecular-beam epitaxy to grow the M-plane GaN thin films on $\beta $-lithium gallate, $\beta $-LiGaO$_2$, which had been annealed in vacuum and in air ambient. With the X-ray diffraction analysis, different azimuth angles (0$^{\circ}$ and 90$^{\circ}$) were applied in $\omega -$2$\theta $ scanning measurement. The signal of M-plane GaN was deviated from the normal value to be -0.147 in vacuum and -0.048 in air ambient, which showed that LGO substrate pre-annealed in air can reduce the compressive strains in the growing sample effectively. The same result was confirmed by the Raman scattering analysis. It showed that the sample pre-annealed in vacuum had E$_{2}$ phonon frequency which was shifted to 574.35 cm$^{-1}$ due to the stress and the sample pre-annealed in air had E$_{2}$ phonon frequency which was shifted only to 568.73 cm$^{-1}$. In conclusion, thermal annealing of $\beta $-LiGaO$_{2}$ substrate in air can improve the quality of growing M-plane GaN and effectively suppresses the formation of lithium-rich surface for the growth M-plane GaN thin films on $\beta $-LiGaO$_{2}$ substrate.