A semiconductor device in provided having a substrate and a semiconductor layer formed on a main surface of the substrate. A plurality of first island electrodes and a plurality of second island electrodes are placed over the semiconductor layer. The plurality of first island electrodes and second island electrodes are spaced apart from each other so as to be alternatively arranged to produce two-dimensional active regions in all feasible areas of the semiconductor layer. Each side of the first island electrodes is opposite a side of the second island electrodes. The semiconductor device can also include a plurality of strip electrodes that are formed in the regions between the first island electrodes and the second island electrodes. The strip electrodes serve as the gate electrodes of a multi-island transistor. The first island electrodes serve as the source electrodes of the multi-island transistor. The second island electrodes serve as the drain electrodes of the multi-island transistor. A plurality of connections to the gate electrodes are provided at each interstice defined by corners of the first island electrodes and the second island electrodes.