Ground-state energy of aD−ion in two-dimensional semiconductors

The ground-state energy of a $D^{-}$ ion (a donor impurity ion with two attached electrons) in a two-dimensional semiconductor is calculated using a variational approach and is found to be about -4.48 Ry. The ground-state energy of a hydrogenic system in two dimensions is known to be -4 Ry. Thus the binding energy of a $D^{-}$ ion, defined as the energy required to remove one of the two electrons from the $D^{-}$ ion to infinity, is about 0.48 Ry. This is about 12% of the ground-state energy of a hydrogenic system in two dimensions. This is to be compared with the binding energy of a $D^{-}$ ion in three dimensions which is 5.55% of the hydrogenic ground-state energy. The relevance of our results to the problem of a $D^{-}$ ion in thin-quantum-well structures is discussed.