Gap narrowing in charged and doped silicon nanoclusters

The gap narrowing in charged Si35H36 and n-type doped Si34DH36 (D=P, As, Sb, S, Se, and Te) clusters is studied within the GW approximation, including energy dependence of the dielectric matrix and local-field effects. It is shown that the density functional theory does not properly describe the gap narrowing in clusters, as it was found earlier in bulk Si. The main mechanisms of this effect in clusters are the same as in bulk Si: (i) the screened exchange interaction between additional electrons and (ii) the extra screening of the Coulomb interaction by additional electrons. At the same time, our calculations show that the carrier-induced gap narrowing has peculiar features in the clusters. A much weaker screening of the electron-electron interaction strongly increases the first and decreases the second mechanism of gap narrowing in Si clusters as compared to bulk Si. We find also that the gap-narrowing effect is more pronounced in doped clusters than in charged ones due to the charge localization near impurity ions. The electronic spectrum of the charged and doped Si clusters with one electron is spin split. The local-density approximation calculation greatly underestimates the value of the spin splitting. A calculation performed with the screened Hartree-Fock method shows that the splitting is large. It considerably narrows the gap and brings important spin effects into cluster properties.