Dielectric screening in semiconductors.

Abstract

Intra-atomic and interatomic Coulomb interactions are incorporated into bond-orbital theory, based upon universal tight-binding parameters, in order to treat the effects of charge redistribution in semiconductor bonds. The dielectric function \ensuremath{\epsilon}(q) is obtained for wave numbers in a [100] direction. The screening of differences in average hybrid energy across a heterojunction is calculated in detail, indicating that the decay length for the potential depends upon the relative values of Madelung and intra-atomic Coulomb terms. The parameters used here predict an imaginary decay length and thus an oscillating potential near the interface. The same theory is applied to point defects by imbedding a cluster in a matrix lattice, taking charges in that lattice to be consistent with continuum theory. Illustrating the theory with a phosphorus impurity in silicon, it is seen that the impurity and its neighboring atoms have charges on the order of only one-tenth of an electronic charge, alternating in sign from neighbor to neighbor as for planar defects. Although there are shifts in the term values on the order of a volt, the difference in these shifts for neighboring atoms is much smaller so that the effect on the bonds is quite small. This behavior is analogous to the response of a dielectric continuum to a point charge: The medium is locally neutral except at the center of the cluster and there are slowly varying potentials ${e}^{2}$/\ensuremath{\epsilon}r. Because of this slow variation, free-atom term values should ordinarily suffice for the calculation of bond properties and bond lengths at impurities. Corrections are larger for homovalent substitutions such as carbon in silicon.