Exchange correlation in the X alpha approximation and shallow-donor impurity ionization energy.

Abstract

The Thomas-Fermi-Dirac (TFD) theory of dispersive valence screening of an ionized impurity in a semiconductor is extended to include exchange correlation in the X\ensuremath{\alpha} approximation. Linearization of the resulting screening equation yields a closed analytical expression for the spatial dielectric function of the electron-gas model semiconductor. The exchange-correlation potential of a shallow-donor impurity and the exchange interaction of the donor electron with the valence electrons are used in an effective-mass, three-parameter, variational calculation of the donor ionization energy. A single-band model and electronic constants appropriate to silicon are used for illustration. Marked differences are noted between the results of this application of linearized TFD screening and those reported previously by another author, who calculated the ionization energy on the basis of an incomplete formulation of the basic nonlinear screening equation in the X\ensuremath{\alpha} approximation.