  The near-field photoluminescence of a gated two-dimensional electron gas is
measured. We use the negatively charged exciton, formed by binding of an
electron to a photo-excited electron-hole pair, as an indicator for the local
presence of charge. Large spatial fluctuations in the luminescence intensity of
the negatively charged exciton are observed. These fluctuations are shown to be
due to electrons localized in the random potential of the remote ionized
donors. We use these fluctuations to image the electrons and donors
distribution in the plane.
