SOME NEW APPROACHES TO SHALLOW IMPURITY STATES

A variational calculation of shallow surface impurity states including image-charge and anisotropic mass effects was performed using two different sets of orthogonal functions. The first set was obtained by varying the Bohr radius in the hydrogenic functions, separately for each state. In the second set the Bohr radius was allowed to become anisotropic and the elements were separately treated as variational parameters. In each case it was shown that with certain restrictions on the variational parameters the set remained complete and orthogonal. General expressions for the energy eigenvalues for both the bulk and surface problem obtained from the first set of functions are presented, and numerical results for Si and Ge are given for each set of trail functions. Previously published bulk eigenvalues for Si and Ge were corrected for orthogonality. © 1969 The American Physical Society.