Gallium nitride material structures, including devices, and methods associated with the same are provided. In some embodiments, the structures include one or more isolation regions which electrically isolate adjacent devices. One aspect of the invention is the discovery that the isolation regions also can significantly reduce the leakage current of devices (e.g., transistors) made from the structures, particularly devices that also include a passivating layer formed on a surface of the gallium nitride material. Lower leakage currents can result in increased power densities and operating voltages, amongst other advantages.