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We report a scanning nanoelectrometer based on a two-dimensional electron gas (2DEG) transistor in GaAs/AlGaAs, whose gate electrode is combined with a metal-coated cantilever probe. In this system, local electric potential is detected through gate effects for the 2DEG detector caused by electrical polarization of the probe. Using this technique, we have demonstrated mapping of the electric potential distribution for 2DEG samples in a GaAs/AlGaAs interface and in a graphene surface. Time-resolved measurements of local potential are also presented.