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

\textbf{\textit{M}}-plane GaN thin films have been grown on $\beta $-LiGaO$_{2}$ (100) substrates by plasma-assisted molecular-beam epitaxy. In order to improve the quality, we tried to grow \textbf{\textit{M}}-plane GaN thin films on pre-annealed in vacuum and in air ambient LiGaO$_{2}$ (100) substrates. X-ray diffraction data indicated that the \textbf{\textit{M}}-plane GaN thin film grown on the LiGaO$_{2}$ (100) substrate pre-annealed in air ambient has better crystal quality than that grown on the LiGaO$_{2}$ (100) substrate pre-annealed in vacuum. In addition, we found that the strain between GaN and LiGaO$_{2}$ substrate can be relaxed by growing GaN thin film on pre-annealed LiGaO$_{2}$ substrate in air. It reveals that LiGaO$_{2}$ substrate annealing in air ambient can suppress the formation of lithium-rich surface effectively to grow a high quality \textbf{\textit{M}}-plane GaN thin film on the LiGaO$_{2}$ substrate.