A method for growing a single crystal GaN film at least 2 microns thick on a Si substrate is disclosed. The method includes growing a prelayer, a buffer layer including AlN on the Si substrate and a plurality of GaN layers and AlN layers deposited alternatively on the top of the AlN buffer layer. By controlling the deposition conditions and timings of the plurality of GaN layers and AlN layers, the single crystal GaN film can be grown thicker than 2 microns without cracks or pits.