Electronic structure of hydrogen- and alkali-metal-vacancy complexes in silicon

We have applied the self-consistent-field scattered-wave Xα cluster method to the substitutional group-I impurities (X) H, Li, Na, K, H₄, and Li₄ (Td symmetry) in silicon using the cluster XSi₄H₁₂. We find that for the neutral alkali-metal impurities the electronic structure of the vacancy is essentially preserved except that the t₂ gap state is now occupied by the appropriate number of alkali-metal-atom valence electrons plus the normal neutral-vacancy complement of two electrons. This means that the Li₄ impurity, for example, is better described as a vacancy V^4- charge compensated by four Li⁺ ions. Hence this suggests that alkali-metal impurities do not passivate vacancy dangling bonds. The electronic structures of the H and H₄ impurities, on the other hand, are found to be quite different from those of their alkali-metal-impurity counterparts. The single-hydrogen impurity (on-center substitutional hydrogen) is found to have vacancylike a₁ states but crystalline siliconlike t₂ states. Four hydrogen atoms in a vacancy do appear to passivate the vacancy dangling bonds; thus in this case the electronic structure of crystalline silicon is recovered.