Described herein are semiconductor devices and structures with improved power handling and heat dissipation. Embodiments are suitable for implementation in gallium nitride. Devices may be provided as individual square or diamond-shaped dies having electrode terminals at the die corners, tapered electrode bases, and interdigitated electrode fingers. Device matrix structures include a plurality of device dies arranged on a substrate in a matrix configuration with interdigitated conductors. Device lattice structures are based on a unit cell comprising a plurality of individual devices, the unit cells disposed on a chip with geometric periodicity. Also described herein are methods for implementing the semiconductor devices and structures.