high - quality al 1 - x in x n layers and alinn / gan bragg mirrors near lattice - matched to gan layers are grown by metalorganic vapor - phase epitaxy on a gan buffer layer with no cracks over full 2 - inch sapphire wafers . the index contrast relative to gan is 6 . 5 % to 11 % for wavelengths ranging from 950 nm to 380 nm . a crack - free , 20 pairs al 0 . 84 in 0 . 16 n / gan distributed bragg reflector is grown , centered at 515 nm with over 90 % reflectivity and a 35 nm stopband . high - quality alinn lattice matched to gan can be used in gan - based optoelectronics , for waveguides and for mirror structures in resonant - cavity light - emitting diodes and monolithic fabry - pérot cavities , for example .