Variational solutions of simple quantum systems subject to variable boundary conditions. II. Shallow donor impurities near semiconductor interfaces: Si, Ge

Variational solutions to the effective-mass equations describing hydrogenic donor impurities located near semiconductor-vacuum and semiconductor-insulator interfaces are presented and discussed. Results for the ground and excited eigenstate, binding energy, and spectra as a function of the location of the impurity from the semiconductor-vacuum interface are presented for Si(001) and Ge(111) surfaces. The electronic binding energy of a hydrogenic donor impurity as a function of its distance from the interface both into the insulator or into the semiconductor is studied in detail for the Si-SiO₂ case. The effect of an external electric field on the impurity binding energy is investigated and the results are compared with other recent theoretical calculations and experimental data.