PURPOSE: To improve the facility of munufacture and contrive the integration by obtaining an ohmic contact of a low resistance value and good reproducibility by utilizing the fact that the Schottky barrier B between a Schottky metal and an InxGa1-xAs semiconductor crystal reduces by depending on the value (x).

CONSTITUTION: In a compound semiconductor device which has an AlGaAs/ GaAs hetero junction structure and performs high speed actions by utilizing bi- dimensional electron gas, the value (x) of the N type InxGa1-xAs semiconductor layer 5 is varied gradually to a desired value (x) from the value (x)=0, so that a barrier potential Δ(=EC-EF) generated in the metallic material, the Schottky barrier B, and the N type InxGa1-xAs semiconductor layer becomes the relation B≤δ and Δ≤δ, as compared with the hetero junction barrier potential δ generated at the interface of the bi-demensional gas layer 7. Thereby, a good ohmic contact can be obtained, the contact resistances of a source electrode and a drain electrode have the uniform values thereof. Since the reproducibility is good, and the manufacture is facilitated while the integration can be increased.