AlGaN/GaN HEMTs are disclosed having a thin AlGaN layer to reduce trapping and also having additional layers to reduce gate leakage and increase the maximum drive current. One HEMT according to the present invention comprises a high resistivity semiconductor layer with a barrier semiconductor layer on it. The barrier layer has a wider bandgap than the high resistivity layer and a 2DEG forms between the layers. Source and drain contacts contact the barrier layer, with part of the surface of the barrier layer uncovered by the contacts. An insulating layer is included on the uncovered surface of the barrier layer and a gate contact is included on the insulating layer. The insulating layer forms a barrier to gate leakage current and also helps to increase the HEMT's maximum current drive. The invention also includes methods for fabricating HEMTs according to the present invention. In one method, the HEMT and its insulating layer are fabricated using metal-organic chemical vapor deposition (MOCVD). In another method the insulating layer is sputtered onto the top surface of the HEMT in a sputtering chamber.