Titanium in large silicon clusters

The application of molecular ab initio methods to investigate the electronic structure of localized impurities in semiconductors requires the study of the convergence of the results with increasing cluster size. Here we compare results for interstitial Ti in silicon, obtained with clusters of increasing size: TiSi 10 H 16 , TiSi 30 H 40 , and TiSi 66 H 64 . These clusters contain one, two, or three shells of silicon atoms, respectively, centered around Ti at a T d interstitial site. The hydrogen atoms serve as saturators of the dangling bonds. The Si core electrons are replaced by an effective potential. The calculations are based on open shell RHF theory and limited CI extensions. The charge distribution in the central part of the three clusters is very similar. In the clusters the partially occupied orbitals are much more delocalized than the 3 d orbitals in the free ions. The total impurity‐induced electronic charge, however, is quite localized, due to the compensating response of the Si closed shell density. Ionization of the impurity also causes a compensating response of the Si closed shells: only about 10% of the density difference is in the impurity region and the major part is behind the outermost shell of Si atoms. Transition metal associated (3 d ‐like) excitation energies are not very dependent on the cluster size, and the relative ordering of the lowest lying states remains unchanged. Impurity associated ionization energies decrease considerably due to the extra relaxation offered by the additional shells of Si atoms. Our results indicate that a reliable description of interstitial transition metals in silicon can be provided by calculations on reasonably small clusters: Si 30 H 40 is sufficiently large.