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The spatially resolved electronic structure of the epitaxial Au/MgO/GaAs(001) tunnel junction has been studied by ballistic electron emission microscopy. The Schottky barrier height of Au on the MgO/GaAs heterostructure is determined to be 3.90 eV, in good agreement with spatially averaged x-ray photoelectron spectroscopy measurements. Locally, two well-defined conduction channels are observed for electrons energies of 2.5 and 3.8 eV, i.e., below the conduction band minimum of the oxide layer. These conduction channels are attributed to band of defect states in the band-gap of the tunnel barrier related to oxygen vacancies in the MgO layer. These defect states are responsible for the low barrier height measured on magnetic tunnel junctions with epitaxial MgO(001) tunnel barriers.