Large binding due to dispersive screening and bloch function interference in many-valley semiconductors

We derive here a generalization of the effective mass equation which includes the intervalley mixing for many-valley semiconductors. This equation is numerically solved with a model impurity potential for donors in silicon. The results show an extreme sensitivity to the short-range impurity potential and a shallow-deep instability. The combined effect of dispersive screening and many-valley interference gives a deep ground state. This seem to be in agreement with the experimental situation for hydrogen and muonium impurities, to which the chosen model potential applies.