We used a low-temperature scanning tunneling microscope to study Zn-and Cd-doping atoms near the ͑110͒-cleavage surfaces of GaAs and InP at 4.2 K. The filled-state images showed centro-symmetric elevations while the empty-state images showed circular depressions. We attribute these features to the influence of the Coulomb potential of the ionized doping atoms on the number of states available for tunneling. In a few empty-state images of the GaAs͑110͒ surface, the depressions were surrounded by maxima, which are probably direct observations of Friedel oscillations. For the InP͑110͒ surface, all depressions were surrounded by noncentrosymmetric maxima. Upon moving the tip Fermi level to the bottom of the conduction band, we observed that the depressions turned into elevations with a triangular shape for both the GaAs͑110͒ and the InP͑110͒ surface. This shape was independent of the depth of the dopants, and the chemical nature of the dopants ͑Zn or Cd͒ did not influence the triangular shape either. The orientation of these triangular features was the same for all observed doping atoms and was geometrically determined with respect to the host lattice. Furthermore, we determined the location of a triangular feature with respect to a doping atom. The features were only visible when tunneling to the impurity band suggesting that the features are a direct image of the acceptor state although the origin of the triangular shape is not clear at present.