Impurities in covalent crystals: Exchange-correlation and local-field effects

A many-body investigation is presented for the screening of a pointlike impurity at a substitutional and at an interstitial site in diamond and silicon. Along the lines of previous work on the optical response and on the quasiparticle properties, the induced electronic charge density is obtained within the linear-response theory by adopting successively improved approximations for the polarizability matrix, namely, the random-phase approximation without ($\overline{\mathrm{RPA}}$) and with (RPA) the inclusion of local-field effects, and the time-dependent screened—Hartree-Fock approximation (TDSHF) with the inclusion of excitonic and local-field effects. It is shown that for diamond, both excitonic and local-field corrections introduce changes in the density profile comparable in magnitude to the commonly used zeroth-order ($\overline{\mathrm{RPA}}$) screening result. Thus, both many-body corrections are indispensable in a realistic description of impurity screening in a covalent insulator. For silicon the combined corrections are still of comparable size as the $\overline{\mathrm{RPA}}$, with the dominance of RPA local-field corrections. The charge flux towards the impurity in diamond is preferentially directed along the bonds; in silicon this asymmetry is less pronounced, in agreement with empirical bond-charge models. Changing the impurity position from a substitutional to an interstitial site shows that the screening is more efficient for the substitutional than for the interstitial case. Our findings should strongly influence binding-energy calculations of shallow impurities and should also be important for interpretations of experiments where charged particles such as muons and positrons probe the electronic many-particle system.