A method of growing gallium nitride on a spinel substrate by providing a supporting substrate having a surface, and disposing a plurality of buffer layers on the surface of the supporting substrate. The plurality of buffer layers including a first buffer layer of aluminum oxynitride having a low percentage of mismatch to the spinel substrate. The second buffer layer is disposed on the first buffer layer and includes a plurality of layers of a graded aluminum oxynitride having a low dislocation density. A third buffer layer of aluminum nitride is disposed on the second buffer layer. A fourth buffer layer of gallium nitride is disposed on the third buffer layer. Subsequently, a photonic device structure, such as a laser, LED or detector, an electronic device structure, such as a field effect transistor or modulation doped field effect transistor, or an optical waveguide is fabricated on the fourth buffer layer.