Dielectric theory of impurity binding energies. III. Group-III acceptors in Si and Ge

Chemical shifts of ground-state energies and g factors of acceptors X in Si or Ge host crystals are analyzed within the framework of effective-mass theory. The unit cell centered on the impurity is regarded as a unit cell of a hypothetical SiX of GeX crystal. The differences in energy levels of valence and conduction bands of this hypothetical crystal at Gamma, X, and L are calculated according to the semiempirical spectroscopic rules developed by Phillips and Van Vechten to describe levels of zinc-blende crystals. These energy differences are compared with those of the host crystal and are used to renormalize effective masses in the impurity unit cell. Rough estimates then show that this approach yields chemical trends in good agreement with experiment and explains several quantitative features of the data that cannot be explained by qualitative models based on ionic radii or electronegativity differences.