The source of n-type conductivity in undoped transparent conducting oxides has been a topic of debate for several decades. The point defect of most interest in this respect is the oxygen vacancy, but there are many conflicting reports on the shallow versus deep nature of its related electronic states. Here, using a hybrid quantum mechanical/molecular mechanical embedded cluster approach, we have computed formation and ionization energies of oxygen vacancies in three representative transparent conducting oxides: In2O3,SnO2, and ZnO. We find that, in all three systems, oxygen vacancies form well-localized, compact donors. We demonstrate, however, that such compactness does not preclude the possibility of these states being shallow in nature, by considering the energetic balance between the vacancy binding electrons that are in localized orbitals or in effective-mass-like diffuse orbitals. Our results show that, thermodynamically, oxygen vacancies in bulk In2O3 introduce states above the conduction band minimum that contribute significantly to the observed conductivity properties of undoped samples. For ZnO and SnO2, the states are deep, and our calculated ionization energies agree well with thermochemical and optical experiments. Our computed equilibrium defect and carrier concentrations, however, demonstrate that these deep states may nevertheless lead to significant intrinsic n-type conductivity under reducing conditions at elevated temperatures. Our study indicates the importance of oxygen vacancies in relation to intrinsic carrier concentrations not only in In2O3, but also in SnO2 and ZnO.
Bibliographical noteFunding Information:
The authors acknowledge funding from EPSRC Grants No. EP/I01330X/1, No. EP/K016288/1, and No. EP/N01572X/1. The authors also acknowledge the use of the UCL Legion and Grace High Performance Computing Facilities (Legion@UCL and Grace@UCL) and associated support services, and the ARCHER supercomputer through membership of the UK's HPC Materials Chemistry Consortium, which is funded by EPSRC Grant No. EP/L000202, in the completion of this work. J.B. thanks P. Deák and O. Bierwagen for useful discussions. A.W. and D.O.S. acknowledge membership of the Materials Design Network.
All Science Journal Classification (ASJC) codes
- Materials Science(all)
- Physics and Astronomy (miscellaneous)