We investigate the influence of near-surface doping atoms of in situ cleaved n- and p-doped InAs(110) on images acquired with constant frequency shift by dynamic mode scanning force microscopy (DM-SFM) in ultrahigh vacuum. The local arrangement of doping atoms near the surface determines the distribution of mobile charge carriers and thus the electrostatic surface potential, which affects the contrast observed in DM-SFM images. The experiments reveal a strong dependence of the type and density of these charge carriers on the sign and magnitude of the applied bias voltage. Additionally, we find that the achieved resolution is directly related to the overlap of the screened Coulomb potential of ionized neighboring doping atoms. On n-InAs(110), the overlap is very strong, and the contrast observed in large-scale DM-SFM images acquired on atomically flat terraces reflects the density distribution of the doping atoms. The bias dependence of the contrast can be interpreted by the presence of an accumulation, depletion, or inversion zone underneath the probe tip. On a p-InAs(110) sample with a nearly identical doping concentration, however, a screened Coulomb potential around individual doping atoms could be detected, since the screening length is smaller than their mean distance between dopings. In atomically resolved images, charged doping atoms as well as charged As vacancies could be identified.