The Breakdown of Effective Mass Equations Due to Rapidly Varying Potentials

One of the major causes for the breakdown of the effective mass theory of shallow impurity states in semiconductors is the rapid variation of the potential in the impurity core region. A formalism is developed for treating this breakdown and then applied to the ground state of donor impurities in silicon in the following cases: 1) a simple coulomb potential; 2) potentials that account both for the spatial dependence of the dielectric constant and for the difference between the charge distributions of the core of the impurity atom and the silicon atom it replaces for P , As, and Sb impurities. It is shown that the breakdown is negligible for a coulomb potential and for P impurities, but significant for As and Sb impurities.