Thomas - Fermi-type dielectric screening of statistical atomic models of donor-specific impurities in a semiconductor-like valence electron gas at zero temperature

Abstract

Thomas - Fermi- (TF-) type theories are applied to the problem of static dielectric screening in a semiconductor at absolute zero when the impurity-charge-density distribution is given by a variational statistical approximation. This treatment of the external perturbation is consistent with the valence electron-gas formulation of the host crystal and in contrast with the point-charge probe and other donor-specific or pseudocharge distributions that have been previously studied in this context. One-parameter exponential bound-electron charge densities are employed in this report. For purposes of illustration, atomic parameters specifying the chemical identity of an impurity are characteristic of phosphorus (group V) and sulphur (group VI) substitutional single and double donors, respectively, and a reference silicon ion. Linearized TF and Thomas - Fermi - Dirac (TFD) screening equations for the exponential case and its point-charge limit are solved in closed analytical form with silicon as the host semiconductor. The corresponding nonlinear TF and TFD equations are solved numerically and nonlinear screened impurity potentials are compared with linear results. Dielectric screening of statistical impurities follows the same general trend as noted for a point charge, that is, the nonlinear theory is more effective than its linear approximation. Furthermore, for a given statistical impurity, with a given degree of ionization, the ion potential is more effectively screened in the following order: linear TF, linear TFD, nonlinear TF, and nonlinear TFD. Corresponding screening radii decrease in this order. Within the set of statistical ions under consideration, linear and corresponding nonlinear screening radii and their differences decrease as the degree of ionization decreases. Further development is planned to test the usefulness of this approach to donor and host potentials in conventional and generalized effective-mass calculations of isocoric and nonisocoric binding energies.