Methods of achieving high breakdown voltages in semiconductor devices by suppressing the surface flashover using high dielectric strength insulating encapsulation material are generally described. In one embodiment of the present invention, surface flashover in AlGaN/GaN heterostructure field-effect transistors (HFETs) is suppressed by using high dielectric strength insulating encapsulation material. Surface flashover in as-fabricated III-Nitride based HFETs limits the operating voltages at levels well below the breakdown voltages of GaN.