Vacancy complexes with oversized impurities in Si and Ge

In this paper we examine the electronic and geometrical structure of impurity-vacancy complexes in Si and Ge. Already Watkins suggested that in Si the pairing of Sn with the vacancy produces a complex with the Sn-atom at the bond center and the vacancy split into two half vacancies on the neighboring sites. Within the framework of density-functional theory we use two complementary ab initio methods, the pseudopotential-plane-wave method and the all-electron Kohn-Korringa-Rostoker method, to investigate the structure of vacancy complexes with 11 different $sp$-impurities. For the case of Sn in Si, we confirm the split configuration and obtain good agreement with EPR data of Watkins. In general we find that all impurities of the $5sp$ and $6sp$ series in Si and Ge prefer the split-vacancy configuration, with an energy gain of 0.5--10.3em0exeV compared to the substitutional complex. On the other hand, impurities of the $3sp$ and $4sp$ series form a (slightly distorted) substitutional complex. Al impurities show an exception from this rule, forming a split complex in Si and a strongly distorted substitutional complex in Ge. We find a strong correlation of these data with the size of the isolated impurities, being defined via the lattice relaxations of the nearest neighbors.