Two types of samples were investigated by X-ray crystal truncation rod (CTR) and X-ray reflectivity measurements. One type was grown on sapphire substrate with nitridation process before deposition of low-temperature (LT)-AlN buffer layer. The other type was grown on sapphire substrate without the nitridation process. With the nitridation process, crystalline AlN was formed on the sapphire substrate and the LT-AlN buffer layer became crystalline. However, the crystalline quality of GaN and GaInN layer on the crystalline LT-AlN buffer layer was poor. It suggests that the lattice-mismatching between the crystallized AlN and GaN degrades the crystalline quality of GaN and GaInN layers. On the other hand, without the nitridation process, the LT-AlN buffer layer was amorphous or poor crystalline layer and the crystalline quality of GaN and GaInN on the LT-AlN buffer layer was good. It indicates that the amorphous or poor crystalline LT-AlN buffer layer works well as a buffer layer.