Tunneling transport through the depletion layer under a GaAs {110} surface is studied with a low temperature scanning tunneling microscope (STM). The observed negative differential conductivity is due to a resonant enhancement of the tunneling probability through the depletion layer mediated by individual shallow acceptors. The STM experiment probes, for appropriate bias voltages, evanescent states in the GaAs band gap. Energetically and spatially resolved spectra show that the pronounced anisotropic contrast pattern of shallow acceptors occurs exclusively for this specific transport channel. Our findings suggest that the complex band structure causes the observed anisotropies connected with the zinc blende symmetry.