The presence of a 2D electron gas (2DEG) in GaN/Al_xGa_1–xN heterostructures with low aluminum mole fraction is found to depend on the residual background impurity concentration in the GaN/AlGaN layer stack. At a residual donor level of 2 × 10¹⁶ cm⁻³, a 2DEG is absent at 300 K in dark environment. Such a 2DEG can be generated at the GaN/AlGaN interface either by illumination with ultraviolet light or by applying an electrostatic potential. The latter results in inherently normally-off switching characteristics of lateral field-effect transistors.