Critical thickness of GaN thin films on sapphire (0001)

Synchrotron x-ray diffraction was employed to measure the lattice constants a and c of GaN films grown with an AlN buffer layer on sapphire (0001) over a thickness range of 50 Å to 1 μm. We used multiple reflections and a least-squares fit method for high reliability. As the thickness increased, the lattice constant a increased from 3.133 Å to 3.196 Å and c decreased from 5.226 Å to 5.183 Å. The expected trend was fitted to an equilibrium theory, allowing the critical thickness of GaN on AlN to be estimated at 29 Å ± 4 Å in good agreement with a theoretical prediction.