a method for making a filed - effect semiconductor device includes the steps of forming a gate electrode on a semiconductor layer composed of a gallium nitride - based compound semiconductor represented by the formula al x in y ga 1 − x − y n , wherein x + y = 1 , 0 ≦ x ≦ 1 , and 0 ≦ y ≦ 1 ; and forming a source electrode and a drain electrode by self - alignment using the gate electrode as a mask . a field - effect semiconductor device fabricated by the method is also disclosed .