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

Abstract

We have applied the self-consistent-field scattered-wave $X\alpha$ cluster method to the substitutional group-I impurities ($X$) H, Li, Na, K, ${\mathrm{H}}_4$, and ${\mathrm{Li}}_4$ ($T_d$ symmetry) in silicon using the cluster $X{\mathrm{Si}}_4{\mathrm{H}}_{12}$. We find that for the neutral alkali-metal impurities the electronic structure of the vacancy is essentially preserved except that the $t_2$ 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 ${\mathrm{Li}}_4$ impurity, for example, is better described as a vacancy $V^{4-}$ charge compensated by four ${\mathrm{Li}}^{+}$ ions. Hence this suggests that alkali-metal impurities do not passivate vacancy dangling bonds. The electronic structures of the H and ${\mathrm{H}}_4$ 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 $a_1$ states but crystalline siliconlike $t_2$ 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.