Structure-dependent electronic properties of nanocrystalline cerium oxide films

We investigate the electronic properties of nanocrystalline cerium oxide $\left({\mathrm{CeO}}_x\right)$ films, grown by various techniques, and we establish universal relations between them and the film structure, composition, and morphology. The nanocrystalline ${\mathrm{CeO}}_x$ films mainly consist of ${\mathrm{CeO}}_2$ grains, while a considerable concentration of trivalent ${\mathrm{Ce}}^{3+}$ is distributed at the ${\mathrm{CeO}}_2$ grain boundaries forming amorphous ${\mathrm{Ce}}_2{\mathrm{O}}_3.$ A small portion of ${\mathrm{Ce}}^{3+}$ is also located around O-vacancy sites. The optical properties of the ${\mathrm{CeO}}_x$ films are considered, taking into account the reported band-structure calculations. The fundamental gap $E_g$ of ${\mathrm{CeO}}_x$ is due to the indirect $\mathrm{O}2\overrightarrow{p}\mathrm{Ce}4f$ electronic transition along the L high-symmetry lines of the Brillouin zone and it is correlated with the $\left[{\mathrm{Ce}}^{3+}\right]$ content, explaining the redshift of $E_g$ in nanostructured ${\mathrm{CeO}}_x,$ which is due to the ${\mathrm{Ce}}^{3+}$ at the grain boundaries and not due to the quantum-size effect itself. We also correlate the energy position of the $\mathrm{O}2\overrightarrow{p}\mathrm{Ce}4f$ electronic transition, which varies up to 160-meV wide, with the lattice constant of the ${\mathrm{CeO}}_2$ grains. We also show that the higher-order transitions are more sensitive to film composition. The refractive index, far below $E_g,$ is explicitly correlated with the film density, independently of the ${\mathrm{Ce}}^{3+}/{\mathrm{Ce}}^{4+}$ and O concentrations, grain size, and lattice parameter. The density is also found to be the major factor affecting the absolute value of the ${\varepsilon }_2$ peak, which corresponds to the $\mathrm{O}2\overrightarrow{p}\mathrm{Ce}4f$ electronic transition.