Size-dependent lattice expansion of nanoparticles is observed for many ionic compounds, including metal oxides, while lattice contraction prevails for pure metals. However, the physical origin of this effect, which is of importance for the thermodynamic, chemical and electronic properties of nanoparticles, is discussed controversially. After a survey of the experimental literature, revealing a wide variety of materials with size-dependent lattice expansion, we show that the negative surface stress is the key reason for lattice expansion, while the excess of lattice sums or point defects of various charge states can be excluded as general explanations. Ab initio calculations of surface stresses for various surface structures of metal oxides confirm the model of a surface-induced lattice expansion.

Intrinsic point defects in indium oxide, including vacancies, interstitials as well as antisites, are studied by means of first-principles calculations within density functional theory using the generalized gradient approximation together with on-site corrections. Finite-size effects are corrected by an extrapolation procedure in order to obtain defect formation energies at infinite dilution. The results show that all intrinsic donor defects have shallow states and are capable of producing free electrons in the conduction band. This applies in particular to the oxygen vacancy. Since it has also a low formation energy, we find that the oxygen vacancy should be the major donor in this material explaining the n-type conductivity as well as the non-stoichiometry of indium oxide. In addition, we show that there are a wealth of oxygen dumbbell-like defects which are thermodynamically relevant under oxidizing conditions. Finally, we discuss defect induced changes of the electronic structure.

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail.

We present a comparative study of oxygen vacancies in In2O3, SnO2, and ZnO based on the hybrid-functional method within the density-functional theory (DFT). For In2O3 and SnO2, our results provide strong evidence of shallow donor states at oxygen vacancies. In comparison with the (semi)local exchange-correlation approximations in DFT, the hybrid-functional method strongly lowers the formation energy of the positive charge state and keeps that of the neutral state nearly intact. The trend is analyzed in terms of changes in lattice relaxation energies and in electron energy levels near the band gap. The existence of shallow donor states at oxygen vacancies and the consequent n-type conductivity are in line with experimental findings. The results invalidate some former theoretical interpretations based on standard DFT calculations.

No abstract