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In standard doping, adding charge carrier to a compound results in a shift of the Fermi level towards the conduction band for electron doping and towards the valence band for hole doping. We discuss the curious case of antidoping, where the direction of band movements in response to doping is reversed. Specifically, p-type antidoping moves the previously occupied bands to the principal conduction band resulting in an increase of band gap energy and reduction of electronic conductivity. We find that this is a generic behavior for a class of materials: early transition and rare earth metal (e.g., Ti, Ce) oxides where the sum of composition-weighed formal oxidation states is positive; such compounds tend to form the well-known electron-trapped intermediate bands localized on the reduced cation orbitals. What is less known is that doping by a hole annihilates a single trapped electron on a cation. The latter thus becomes electronically inequivalent with respect to the normal cation in the undoped lattice, thus representing a symmetry-breaking effect. We give specific theoretical predictions for target compounds where hole antidoping might be observed experimentally: Magnéli-like phases (i.e., CeO2-x and TiO2-x) and ternary compounds (i.e., Ba2Ti6O13 and Ba4Ti12O27), and note that this unique behavior opens the possibility of unconventional control of materials conductivity by doping.