Double-Hole-Mediated Coupling of Dopants and its Impact on Band Gap Engineering in TiO2

A double-hole-mediated coupling of dopants is unraveled and confirmed in TiO₂ by density-functional theory calculations. We find that when a dopant complex on neighboring oxygen sites in TiO₂ has net two holes, the holes will strongly couple to each other through significant lattice relaxation. The coupling results in the formation of fully filled impurity bands lying above the valence band of TiO₂, leading to a much more effective band gap reduction than that induced by monodoping or conventional donor-acceptor codoping. Our results suggest a new path for semiconductor band gap engineering.