The present invention relates, for example, to a semiconductor structure containing multiple parallel channels in which several parallel conductive channels are formed within the semiconductor structure. Electric contact or electrostatic control over all these channels is done by three-dimensional electrode structures. The multiple channel structure with three-dimensional electrodes can be applied to semiconductors devices such as field effect transistors, diodes, and other similar electronic or quantum-effect devices. This structure is practical for materials where multiple parallel conduction channels can be formed, such as in III-V semiconductors. Ill-Nitride semiconductors with such structures are described which can lead to increased power density, reduced on-resistance and improved device performance, in addition to reducing dynamic on-resistance, and improving the stability of their threshold voltage and reliability.