Theory of shallow donor impurity near-surface states in Si and Ge

Previously developed methods for determining the wave functions and energy levels of shallow donor impurities on the surface or in the bulk of a semiconductor have been extended to the case of impurities at a finite depth from the surface. Calculations were performed for impurities near either a (100) or (111) surface in Sci and for a (111) surface in Ge. The ground state and the excited state having the largest electric dipole coupling to the ground state wete determined. In addition, the optical absorption cross section for transitions from the ground state to this excited state were calculated for surface and near surface states. These results were used to calculate a theoretical absorption spectrum for Si doped uniformly to a depth of 10 atomic layers.