Role of oxygen vacancies on the structure and density of states of iron-doped zirconia

In this paper, we study the effect of iron doping in zirconia using both theoretical and experimental approaches. Combining density functional theory (DFT) simulations with the experimental characterization of thin films, we show that iron is in the ${\mathrm{Fe}}^{3+}$ oxidation state and, accordingly, the films are rich in oxygen vacancies ($V_{\mathrm{O}}^{{}^{••}}$). $V_{\mathrm{O}}^{{}^{••}}$ favor the formation of the tetragonal phase in doped zirconia (${\mathrm{ZrO}}_2$:$\mathrm{Fe}$) and affect the density of states at the Fermi level as well as the local magnetization of $\mathrm{Fe}$ atoms. We also show that the $\mathrm{Fe}\left(2p\right)$ and $\mathrm{Fe}\left(3p\right)$ energy levels can be used as a marker for the presence of vacancies in the doped system. In particular, the computed position of the $\mathrm{Fe}\left(3p\right)$ peak is strongly sensitive to the $V_{\mathrm{O}}^{{}^{••}}$ to $\mathrm{Fe}$ atoms ratio. A comparison of the theoretical and experimental $\mathrm{Fe}\left(3p\right)$ peak positions suggests that in our films this ratio is close to $0.5$. Besides the interest in the material by itself, ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$ constitutes a test case for the application of DFT on transition metals embedded in oxides. In ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$, the inclusion of the Hubbard $U$ correction significantly changes the electronic properties of the system. However, the inclusion of this correction, at least for the value $U=3.3$ eV chosen in the present work, worsen the agreement with the measured photoemission valence band spectra.

Figure 1

DFT (GGA) formation energy of oxygen vacancies [see Eq. (1)] in ${\mathrm{ZrO}}_2$:Y, ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$, and ${\mathrm{ZrO}}_2$ in the two extrema case of (a) oxygen-rich and (b) oxygen-poor conditions in both the tetragonal and the monoclinic structures. The doped systems are considered in the charge compensated configuration (i.e., $y_{V_{\mathrm{O}}^{{}^{••}}/X}=0.5$ for $X=\mathrm{Fe},\mathrm{Y}$). The values are computed for different oxygen vacancies concentrations and also varying, for some concentrations, the position of the oxygen vacancies. In (a) and (b), histograms are presented in the same order (and colors).

Figure 2

DFT (GGA) total energy difference per formula unit between the tetragonal against the monoclinic phase for (a) ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$ and (b) ${\mathrm{ZrO}}_2$:Y. Total energies are computed for the charge compensated system (dots, $y_{V_{\mathrm{O}}^{{}^{••}}/X}=0.5$ for $X=\mathrm{Fe},\mathrm{Y}$) changing the atomic configurations for each given concentrations. The shadowed areas are guides for the eyes while the continuous lines are a linear fit of the data. Also the results for the systems without oxygen vacancies (crosses, $y_{V_{\mathrm{O}}^{{}^{••}}/X}=0$) are shown for comparison. The zero level is shifted by (i) $-46$ meV/f.u. to align the energy difference at zero doping with the experimental value, and (ii) $-5$ meV/f.u. to include the computed zero-point-energy difference of the two lattices.

Figure 3

Total (full line) and $d$-orbital projected (dashed line) density of states (DOS) at the GGA level of ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$ at $x_{\mathrm{Fe}}=25\%$ with $y_{V_{\mathrm{O}}^{{}^{••}}/\mathrm{Fe}}$ equal to (a) 0, (b) $0.5$, and (c) 1, respectively. The vertical dashed line marks the Fermi level. The Fermi level in (b) is the zero of the energy axis, while in (a) and (c), the zero is obtained aligning the bottom of the valence band at $\approx$$-6.5$ eV as in (b).

Figure 4

Total (full line) and $d$-orbital projected (dashed line) density of states (DOS) at the GGA+$U$ level of ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$ at $x_{\mathrm{Fe}}=25\%$ with $y_{V_{\mathrm{O}}^{{}^{••}}/\mathrm{Fe}}$ equal to (a) 0, (b) $0.5$, and (c) 1, respectively. The vertical dashed line marks the Fermi level. The Fermi level of (b) is the zero of the energy axis, while in (a) and (c), the zero is obtained by aligning the top of the conduction band at $\approx$5 eV as in (b).

Figure 5

Tof–SIMS depth profile of ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$ at $x_{\mathrm{Fe}}\approx 20\%at$.

Figure 6

XRD patterns of ${\mathrm{ZrO}}_2$ (blue) and ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$ (red) ($\mathrm{Fe}$ doping $\approx$$20\%\mathrm{at}.$) films evidencing Fe doping is effective in suppressing the monoclinic phase. t(${\mathrm{ZrO}}_2$) and m(${\mathrm{ZrO}}_2$) indicates the reflections from reference tetragonal and monoclinic ${\mathrm{ZrO}}_2$, respectively.[38] (Right) Relaxed DFT structure for m(${\mathrm{ZrO}}_2$), t(${\mathrm{ZrO}}_2$), and t(${\mathrm{ZrO}}_2$:$\mathrm{Fe}$) at $x_{\mathrm{Fe}}=25\%\mathrm{at}.$ represented with the xcrysden package (see Ref. 39); Zr atoms in blue, $\mathrm{Fe}$ atoms in red, and the smaller O atoms in black.

Figure 7

(a) The $\mathrm{Fe}\left(2p\right)$ core level photoemission spectra in ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$. (b) $\mathrm{Fe}\left(3p\right)$ and $\mathrm{Zr}\left(4s\right)$ photoemission spectra and computed DOS for ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$ with $y_{V_{\mathrm{O}}^{{}^{••}}/\mathrm{Fe}}$ equal to 0 (green dashed), $0.5$ (red continuous), and 1 (black dot-dashed). The $\mathrm{Fe}\left(3p\right)$ majority-spin level is in light gray. (c) Measured and computed valence band (VB) for pure ${\mathrm{ZrO}}_2$. (d) Measured VB for ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$. Computed VB for ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$ with $\mathrm{Fe}$ doping substitutional at $y_{V_{\mathrm{O}}^{{}^{••}}/\mathrm{Fe}}=0.5$ (continuous red line) or interstitials (dashed maroon line). In (b)–(d), the experimental data (and fit) are vertically shifted with respect to the DFT-DOS. All DOS are obtained within the GGA. The experimental data were collected with the PHI 5600 instrument (see details in Sec. 2b).

Figure 8

Valence band of ${\mathrm{ZrO}}_2$:$\mathrm{Fe}$. The GGA+$U$ scheme at $x_{\mathrm{Fe}}=18.75\%$, $y_{V_{\mathrm{O}}^{{}^{••}}/\mathrm{Fe}}=0.5$, for the values of $U=0.0,1.0,2.0,3.3$, is compared against experimental data. The smearing parameter used for the plot is $0.06$ Ry. The experimental data were collected with the PHI 5600 instrument (see details in Sec. 2b).