A semiconductor device has a sapphire substrate, a semiconductor layer made of GaN provided on the sapphire substrate, a multilayer film provided on the semiconductor layer, and an electrode in ohmic contact with the multilayer film. The multilayer film has been formed by alternately stacking two types of semiconductor layers having different amounts of piezopolarization or different amounts of spontaneous polarization and each containing an n-type impurity so that electrons are induced at the interface between the two types of semiconductor layers. This allows the contact resistance between the electrode and the multilayer film and a parasitic resistance in a current transmission path to be reduced to values lower than in a conventional semiconductor device.