A method for fabricating a semiconductor device is disclosed. The method includes sequentially forming a first semiconductor layer, a second semiconductor layer and a semiconductor cap layer containing a p-type impurity element on a substrate, forming a dielectric layer having an opening after the forming of the semiconductor cap layer, forming a third semiconductor layer containing a p-type impurity element on the semiconductor cap layer exposed from the opening of the dielectric layer, and forming a gate electrode on the third semiconductor layer.