AlGaN/GaN single heterostructures (SII) were frown on sapphire (0 0 0 1) substrates by plasma-assisted molecular beam epitaxy. It was found that multi-AlN buffer layers are effective to improve the two-dimensional electron gas (2DEG) mobility. High 2DEG mobility of about 1200 cm(2)/V s at room temperature was obtained by inserting 4 periods of AlN buffer layers. It is considered that the improvement resulted from the reduction of dislocations in the films by the multi-AlN buffer layers. It was also found that when the periods of the AIN buffer layer were 6, cracks were generated on the surface resulting in a reduction of the mobility.