Devices and systems comprising high current/high voltage GaN semiconductor devices are disclosed. A GaN die, comprising a lateral GaN transistor, is sandwiched between an overlying header and an underlying composite thermal dielectric layer. Fabrication comprises providing a conventional GaN device structure fabricated on a low cost silicon substrate (GaN-on-Si die), mechanically and electrically attaching source, drain and gate contact pads of the GaN-on-Si die to corresponding contact areas of conductive tracks of the header, then entirely removing the silicon substrate. The exposed substrate-surface of the epi-layer stack is coated with the composite dielectric thermal layer. Preferably, the header comprises a ceramic dielectric support layer having a CTE matched to the GaN epi-layer stack. The thermal dielectric layer comprises a high dielectric strength thermoplastic polymer and a dielectric filler having a high thermal conductivity. This structure offers improved electrical breakdown resistance and effective thermal dissipation compared to conventional GaN-on-Si device structures.