Based on ab initio calculations, boron-doped Si(113) surfaces have been simulated and atomic structures of the surfaces have been proposed. It has been determined that surface features of empty and filled states that are separately localized at pentamers and adatoms indicates a low surface density of B atoms, while it is attributed to heavy doping of B atoms at the second layer that pentamers and adatoms are both present in an image of scanning tunnelling microscopy. B doping at the second layer should be balanced by adsorbed B or Si atoms beside the adatoms and inserted B interstitials below the adatoms.