Abstract
We apply the Thomas-Fermi theory to the problem of dielectric screening in a semiconductor when the external perturbation is given by an extended charge distribution. We introduce a boundary condition on the electric field at the origin. This is in contrast with the condition on the potential imposed by Resta in his original analysis of a point-charge perturbation. We then proceed to study three typical examples of external pseudopotentials and their associated pseudocharge distributions. The corresponding linearized Thomas-Fermi equations are solved both analytically and numerically. The exact nonlinear Thomas-Fermi equations are then solved numerically and compared with the linear results.
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