Piezoelectric AlGaN/GaN FETs on SiC with high carrier mobility have been fabricated yielding IDS=450 mA/mm and gm=200 mS/mm. In the on-state, under UV-illumination, the devices sustain a drain voltage of VDS=49 V, corresponding to a power dissipation of 26.5 W/mm. On turn-on of the device from the pinch-off state, a significant delay in the drain current build-up is observed. This effect depends on the pinch-off time and the pinch-off voltage and can be removed by either a brief UV-illumination or a VDS>25 V applied in the on-state. The drain current transients are characterized by a relaxation time τ, which is in the order of several hundred seconds. From the temperature dependence of τ, an activation energy of about 280 meV and a capture cross section of 4.4·10−18cm2 were determined. The devices show pronounced persistent photoconductivity (PPC) and the drain current ID is sensitive to illumination.