A HEMT-type field-effect semiconductor device has a main semiconductor region comprising two layers of dissimilar materials such that a two-dimensional electron gas layer is generated along the heterojunction between the two layers. A source and a drain electrode are placed in spaced positions on a major surface of the main semiconductor region. Between these electrodes, a gate electrode is received in a recess in the major surface of the main semiconductor region via a p-type metal oxide semiconductor film whereby a depletion zone is normally created in the electron gas layer, with a minimum of turn-on resistance and gate leak current.