Methods of characterizing electrical properties of a semiconductor layer structure on a wafer with topside semiconductor layers on an insulating or semi-insulating substrate, the semiconductor layer structure including a high electron mobility transistor (HEMT) heterostructure with a two-dimensional electron gas (2DEG) at a heterointerface between the semiconductor layers of the heterostructure. The methods include: (a) physically contacting the topside of the wafer within a narrow border zone at an edge of the wafer with a flexible metal cantilever electrode of a contacting device, wherein the flexible metal cantilever electrode contacts one or more of the semiconductor layers exposed at the narrow border zone so that the flexible metal cantilever electrode is in electrical contact with the 2DEG; and (b) applying corona charge bias and measuring a surface voltage of the semiconductor layers using a non-contact probe while maintaining the electrical contact with the 2DEG. The physical contacting to the topside of the wafer is noncontaminating and noninvasive to the semiconductor layers.