A method of fabricating a semiconductor device with a composite contact is provided. The fabrication includes forming the composite contact to a semiconductor layer in a semiconductor structure. The composite contact is formed by forming a DC conducting electrode attached to a semiconductor layer in a semiconductor structure and forming a capacitive electrode that is partially over the DC conducting electrode and extends beyond the DC conducting electrode. The composite contact provides a combined resistive-capacitive coupling to the semiconductor layer. As a result, a contact impedance is reduced when the corresponding semiconductor device is operated at high frequencies.