Using first-principles density functional theory, we discuss doping of the Si(001) surface by a single substitutional phosphorus or arsenic atom. We show that there are two competing atomic structures for isolated Si-P and Si-As heterodimers, and that the donor electron is delocalized over the surface. We also show that the Si atom dangling bond of one of these heterodimer structures can be progressively charged by additional electrons. It is predicted that surface charge accumulation as a result of tip-induced band bending leads to structural and electronic changes of the Si-P and Si-As heterodimers which could be observed experimentally. Scanning tunneling microscopy (STM) measurements of the Si-P heterodimer on a n-type Si(001) surface reveal structural characteristics and a bias-voltage dependent appearance, consistent with these predictions. STM measurements for the As:Si(001) system are predicted to exhibit similar behavior to P:Si(001).