In-plane anisotropy characteristics of GaN epilayers grown on $A$-face sapphire substrates

We report on the structural in-plane anisotropy of GaN films grown on $A$-plane sapphire substrates by metal organic chemical vapor deposition. It is found that GaN:Si grown on $A$-face sapphire exhibits a strongly anisotropic wafer bending in the two orthogonal in-plane directions, with a $∼24%$ larger curvature along the $c$-axis of sapphire than along the $m$-axis. Using a model developed for an elastically anisotropic bilayer structure and using our curvature data, the anisotropic biaxial stresses in the two in-plane directions have been estimated as $σ1x≅−1.3GPa$ and $σ1y≅−1.1GPa$ along parallel and perpendicular to $c$-axis of sapphire, respectively. This anisotropic stress is also responsible for the distortion of the GaN hexagonal basal plane, as evidenced by x-ray diffraction measurements. The broadening of full width at half maximum of the GaN (0002) x-ray reflections varies with different azimuthal angles, correlated with the tilt of the $c$-axis of GaN. The in-plane epitaxial relationships between the GaN (0001) and $A$-face sapphire are found as $a$-axis of GaN aligned with $c$-axis of sapphire and $m$-axis of GaN aligned with $m$-axis of sapphire.