Nonlinear screening of positive point charges in diamond, silicon, and germanium

Abstract

In the present paper we have formulated a variational principle for obtaining approximate analytical solutions of a nonlinear differential equation established by Cornolti and Resta for the potentials of positive point charges embedded in pure diamond, silicon, and germanium. We have considered the cases of charges $Z=+1, +2, +3, +4$ (in atomic units) in these semiconductors, while Cornolti and Resta considered the cases of $Z=+1, +4$. We find that our approximate analytical results for the spatial dielectric functions of diamond, silicon, and germanium, depending on $Z$, are in excellent agreement with the numerical results of Cornolti and Resta, who have presented their results in the form of graphs.