Multivalency of Group 15 Dopants in SnO2

The multivalent behavior of group 15 elements P, As, Sb, and Bi, on the cation site in SnO₂ has been studied via first-principles calculations. Through accurate calculation of the energy position of the defect transition energy levels with respect to the host conduction band minimum using a combination of hybrid functional and GW calculations, we found that As and Bi will change their oxidation state from +5 to +3 when the Fermi level approaches the conduction band minimum, while P and Sb will stay in the +5 state until the Fermi level rises to an energy well above the conduction band minimum. The change of the oxidation state is associated with the occupation of an electron-compensating defect state resulting from the antibonding s-p hybridization between the group 15 dopant and the ligands. Thus, only P and Sb are good electron-dopants (donors). As is a borderline case allowing only limited n-type doping, whereas Bi is a deep defect that pins the Fermi level within the band gap and causes insulating behavior. We discuss the chemical trends with the atomic energy of the valence s state and the ionic radii of the dopants.