A semiconductor device comprising: a semiconductor base made of a first semiconductor material of a first conductivity type; a hetero-semiconductor region forming a heterojunction with the semiconductor base and made of a second semiconductor material having a different band gap from the first semiconductor material; a first gate insulating film on which a first gate electrode is formed, is arranged adjacent to the heterojunction for insulating the first gate electrode from the semiconductor base; a source electrode formed in contact with the hetero-semiconductor region; a drain electrode formed in contact with the semiconductor base; and characterized by an electric field extending region arranged in contact with the hetero-semiconductor region and made of metal whose work function is greater than that of the first semiconductor material having the first conductivity type and that of the second semiconductor material, the metal being in contact with the source electrode, wherein the electric field extending region faces at least partly the first gate electrode, the first gate insulating film and hetero-semiconductor region interposed between the electric field extending region and the first gate electrode, the electric field extending region extending a built-in electric field into the hetero-semiconductor region, wherein the thickness of the hetero-semiconductor region between the first gate electrode and the electric field extending region is smaller than a sum of a distance for which an electric field of the first gate electrode extends from a junction interface between the gate insulating film and the hetero-semiconductor region into the hetero-semiconductor region, and a distance for which an electric field of the part of the electric field extending region facing the first gate electrode extends from a junction interface between the part of the electric field extending region facing the first gate electrode and the hetero-semiconductor region into the hetero-semiconductor region, when the source and the first gate electrode are grounded. a semiconductor base made of a first semiconductor material of a first conductivity type; a hetero-semiconductor region forming a heterojunction with the semiconductor base and made of a second semiconductor material having a different band gap from the first semiconductor material; a first gate insulating film on which a first gate electrode is formed, is arranged adjacent to the heterojunction for insulating the first gate electrode from the semiconductor base; a source electrode formed in contact with the hetero-semiconductor region; a drain electrode formed in contact with the semiconductor base; and characterized by an electric field extending region arranged in contact with the hetero-semiconductor region and made of metal whose work function is greater than that of the first semiconductor material having the first conductivity type and that of the second semiconductor material, the metal being in contact with the source electrode, wherein the electric field extending region faces at least partly the first gate electrode, the first gate insulating film and hetero-semiconductor region interposed between the electric field extending region and the first gate electrode, the electric field extending region extending a built-in electric field into the hetero-semiconductor region, wherein the thickness of the hetero-semiconductor region between the first gate electrode and the electric field extending region is smaller than a sum of a distance for which an electric field of the first gate electrode extends from a junction interface between the gate insulating film and the hetero-semiconductor region into the hetero-semiconductor region, and a distance for which an electric field of the part of the electric field extending region facing the first gate electrode extends from a junction interface between the part of the electric field extending region facing the first gate electrode and the hetero-semiconductor region into the hetero-semiconductor region, when the source and the first gate electrode are grounded.