Electronic Band Structure Variations in the Ceria Doped Zirconia: A First Principles Study

Using first principle calculations, the effect of Ce with different doping concentrations in the network of Zirconium dioxide (ZrO2) is studied. The ZrO2 cell volume linearly increases with the increasing Ce doping concentration. The intrinsic band gap of ZrO2 of 5.70 eV reduces to 4.67 eV with the 2.08% Ce doping. In 4.16% cerium doped ZrO2, the valence band maximum and conduction band minimum come closer to each other, about 1.1 eV, compared to ZrO2. The maximum band gap reduction of ZrO2 is observed at 6.25% Ce doping concentration, having the value of 4.38 eV. No considerable shift in the band structure is found with further increase in the doping level. The photo-response of the ZrO2 is modulated with Ce insertion, and two distinct modifications are observed in the absorption coefficient: an imaginary part of the dielectric function and conductivity. A 2.08% Ce-doped ZrO2 modeled system reduces the intensities of peaks in the optical spectra while keeping the peaks of intrinsic ZrO2. However, the intrinsic peaks related to ZrO2 completely vanish in 4.16%, 6.25%, 8.33%, and 12.5% Ce doped ZrO2, and a new absorption hump is created.


Introduction
Recently, zirconia (ZrO 2 ) based ceramic materials got increasing attention from researchers due their wide range of applications, including thermal barrier coatings (TBC), solid oxide fuel cells, catalysis, and energy conversion [1][2][3]. In thermal barrier coatings, zirconia in its pure form faces two main problems. The first one is its phase transformation from tetragonal to monoclinic, leading to volume expansion, cracking, and failure. Secondly, its thermal conductivity is not sufficiently low, and it could be lowered by mixing it with other oxides, including CeO 2 , Sc 2 O 3 , and In 2 O 3 . Moreover, the mixing of ZrO 2 with aforementioned oxides stabilizes ZrO 2 at high temperature [4,5].
Ceria (CeO 2 ) is widely used in the modern catalytic industry, automotive exhaust catalysis, solid oxide fuel cells, and water-gas shift (WGS) reactions [6,7]. For an oxygen storage material, it is used as a component in automotive three-way catalysts. The oxygen storage capabilities of CeO 2 are found to degrade at high temperature, which strongly limits its applications. It is reported that the thermal stability of CeO 2 can be improved by mixing it with zirconium oxide [8][9][10].
Charge compensation is essential in the case of substitutional doping. Ce 4+ and Zr 4+ both are tetravalent ions, and the substitution of Zr 4+ by Ce 4+ would not lead to any charge imbalance. Thus, the cerium insertion in the network of ZrO 2 would reduce the thermal conductivity while creating minimum structure distortion. Experimentally, it is proven that Ce mixing with ZrO 2 can lead to improved thermal stability at higher temperature, along with lowering thermal conductivity [11]. On the other hand, the addition of Zr into the bulk of CeO 2 can improve the oxygen storage capacity of a ceria-zirconia solid solution, and it can broaden the application spectrum of CeO 2 . Zr doping in the structure of CeO 2 is widely studied. Andersson et al. [10] used ab-initio calculations to calculate the redox thermodynamics and kinetics of CeO 2 mixed with ZrO 2 . It was found that Zr 4+ doping decreased the vacancy formation energy and the migration barrier in CeO 2 [10]. Yang [6] and his co-workers studied the effect of Zr doping on the redox properties of CeO 2 . Zr doping substantially lowered the formation energy of an O vacancy when the vacancy was created next to the Zr dopant [6].
With the Ce doping concentration Ce 1−x Zr x O 2 (x = 0.25, 0.5, 0.75, 1), Tian et al. [12] reported the replacement of Ce by Zr, leading to the formation of a pseudo-cubic fluorite-type structure. Moreover, increasing the Zr doping concentration linearly decreased the lattice parameters and cell volume of CeO 2 [12]. Because it is considered a solid solution, it would be important to increase the doping concentration of Ce in the cubic ZrO 2 and investigate its effect on the structure and properties. Moreover, Ce doping in the structure of cubic ZrO 2 should be studied in detail.

Methodology
The Kohn-Sham density functional theory (DFT) calculations were performed with Materials Studio 8.0 [13]. The valence electronic states were expanded in a basis of plane waves, and the oscillating wave function of core electrons were represented by a projected augmented wave approach. Moreover, the special Perdew-Burke-Ernzerhof functional for solids (PBEsol) [14,15] was used as an exchange correlation functional with ultrasoft pseudopotential [16]. For the plane-wave set, a cut-off energy of 400 eV and 3 × 3 × 3 k-points mesh was utilized. Simulated models were optimized with respect to cell parameters and atomic positions using the Broyden, Fletcher, Goldfarb, Shanno (BFGS) minimization scheme under the maximum force of 0.01 eV/Å. Furthermore, the stress tensor on the cell was less than 0.02 GPa [17,18].
A conventional 12 atoms cubic unit cell of zirconia (space group Fm-3m), extended to 2 × 2 × 1 repetition forming a 48 atom supercell, was utilized. Cerium (Ce) doped zirconia models were introduced by replacing a regular lattice Zr atom with a Ce atom. The cerium doping concentration can be increased by increasing the number of Ce atoms substituting the Zr sites. The Ce doped zirconia modeled systems and their corresponding Ce doping concentration and Ce/Zr ratio are summarized in Table 1. The CeZr-1 and CeZr-6 models are visualized in Figure 1.

The Effect of Ce Inclusion on the ZrO2 Structure
The optimized lattice parameters and cell volumes of the zirconia structure are summarized in Table 2. The pure ZrO2 system has a = 10.158 Å , b = 10.158 Å (double values because of 2 × 2 × 1 supercell), and c = 5.0796 Å . The optimized lattice parameters are in close agreement with the available calculated data [12,19] and experimental values [20]. Substituting Ce at Zr sites induces slight change in the lattice parameters in the form of elongation. Table 2 depicts that as the content of Ce increases, the elongation in the lattice parameters increases. The higher ionic radii of Ce 4+ = 0.97 Å in comparison to Zr 4+ = 0.84 Å is responsible for this change [6]. Furthermore, the cell volume of zirconia gradually increased with the increasing Ce concentration. The behavior of the cell volume with the Ce doping concentration is displayed in Figure 2. A linear increase in the unit cell volume is found with the increasing Ce doping concentration. Cerium (0.97 Å ) insertion at Zr (0.84 Å ) sites is responsible for the increase in cell volume.

The Effect of Ce Inclusion on the ZrO 2 Structure
The optimized lattice parameters and cell volumes of the zirconia structure are summarized in Table 2. The pure ZrO 2 system has a = 10.158 Å, b = 10.158 Å (double values because of 2 × 2 × 1 supercell), and c = 5.0796 Å. The optimized lattice parameters are in close agreement with the available calculated data [12,19] and experimental values [20]. Substituting Ce at Zr sites induces slight change in the lattice parameters in the form of elongation. Table 2 depicts that as the content of Ce increases, the elongation in the lattice parameters increases. The higher ionic radii of Ce 4+ = 0.97 Å in comparison to Zr 4+ = 0.84 Å is responsible for this change [6]. Furthermore, the cell volume of zirconia gradually increased with the increasing Ce concentration. The behavior of the cell volume with the Ce doping concentration is displayed in Figure 2. A linear increase in the unit cell volume is found with the increasing Ce doping concentration. Cerium (0.97 Å) insertion at Zr (0.84 Å) sites is responsible for the increase in cell volume. The average bond lengths of the optimized Ce doped ZrO2 modeled systems are summarized in Table 3. The zirconia system is optimized with the O-Zr and O-O bond lengths of 2.1993 Å and 2.5395 Å , respectively. The calculated data is in good agreement with the theoretical [12] and experimental [21] findings. Substituting Ce at Zr sites elongates the O-Zr and O-O bond lengths. Table 3 depicts that the O-Zr and O-O bond lengths linearly increase with an increasing Ce doping concentration. The increasing trend of the O-Zr and O-O bond lengths is ascribed to the difference in the ionic radii of Ce 4+ and Zr 4+ . It is interesting to note that the O-Ce bond length initially showed an increasing trend, which became nearly constant for CeZr-2, CeZr-3, CeZr-4, and CeZr-6. Table 3. Bond lengths (averaged) of the simulated systems.

The Effect of Ce Inclusion on the Electronic Band Structure of Zirconia
The band structures of Ce doped ZrO2 modeled systems are shown in Figure 3. Generalized gradient approximation (GGA) calculations underestimate the band gap due to the well-known shortcoming of density functional theory (DFT) [22]. For cubic ZrO2, the calculated band gap is 3.307 eV, which is underestimated compared to the experimental value of 5.70 eV. A constant scissor operator is applied for all investigated structures for making the band structure comparable to the experimental value [23]. Intrinsic insulating behavior is clarified from Figure 3a  The average bond lengths of the optimized Ce doped ZrO 2 modeled systems are summarized in Table 3. The zirconia system is optimized with the O-Zr and O-O bond lengths of 2.1993 Å and 2.5395 Å, respectively. The calculated data is in good agreement with the theoretical [12] and experimental [21] findings. Substituting Ce at Zr sites elongates the O-Zr and O-O bond lengths. Table 3 depicts that the O-Zr and O-O bond lengths linearly increase with an increasing Ce doping concentration. The increasing trend of the O-Zr and O-O bond lengths is ascribed to the difference in the ionic radii of Ce 4+ and Zr 4+ . It is interesting to note that the O-Ce bond length initially showed an increasing trend, which became nearly constant for CeZr-2, CeZr-3, CeZr-4, and CeZr-6.

The Effect of Ce Inclusion on the Electronic Band Structure of Zirconia
The band structures of Ce doped ZrO 2 modeled systems are shown in Figure 3. Generalized gradient approximation (GGA) calculations underestimate the band gap due to the well-known shortcoming of density functional theory (DFT) [22]. For cubic ZrO 2 , the calculated band gap is 3.307 eV, which is underestimated compared to the experimental value of 5.70 eV. A constant scissor operator is applied for all investigated structures for making the band structure comparable to the experimental value [23]. Intrinsic insulating behavior is clarified from Figure 3a   The density of states is calculated for elaborating the electronic structure of the modeled systems in detail. As verified from Figure 5, the recent calculations show no gap states between the valence and conduction band. The only modification that Ce doping performed is the shifting of the valence band edge and conduction band closer to each other. The band gap is modified due to Ce insertion in the ZrO2 network, and all Ce doped ZrO2 modeled systems depict a reduced band gap. The density of states findings are consistent with the reported data [12].

The Effect of Ce Inclusion on the Photo-Response of Zirconia
The photo-response of zirconia originates from the interactions of photons with the electrons in ZrO2, leading to the transition of electrons between the occupied and unoccupied states. CASTEP calculates the real and imaginary part of the dielectric function, which are further used to calculate the other optical properties like absorption, reflectivity, and conductivity [24,25]. The imaginary part of the dielectric function given in Equation (1) is used to calculate the optical absorption (Equation (2)).
( ) The density of states is calculated for elaborating the electronic structure of the modeled systems in detail. As verified from Figure 5, the recent calculations show no gap states between the valence and conduction band. The only modification that Ce doping performed is the shifting of the valence band edge and conduction band closer to each other. The band gap is modified due to Ce insertion in the ZrO 2 network, and all Ce doped ZrO 2 modeled systems depict a reduced band gap. The density of states findings are consistent with the reported data [12]. The density of states is calculated for elaborating the electronic structure of the modeled systems in detail. As verified from Figure 5, the recent calculations show no gap states between the valence and conduction band. The only modification that Ce doping performed is the shifting of the valence band edge and conduction band closer to each other. The band gap is modified due to Ce insertion in the ZrO2 network, and all Ce doped ZrO2 modeled systems depict a reduced band gap. The density of states findings are consistent with the reported data [12].

The Effect of Ce Inclusion on the Photo-Response of Zirconia
The photo-response of zirconia originates from the interactions of photons with the electrons in ZrO2, leading to the transition of electrons between the occupied and unoccupied states. CASTEP calculates the real and imaginary part of the dielectric function, which are further used to calculate the other optical properties like absorption, reflectivity, and conductivity [24,25]. The imaginary part of the dielectric function given in Equation (1) is used to calculate the optical absorption (Equation (2)). ( )

The Effect of Ce Inclusion on the Photo-Response of Zirconia
The photo-response of zirconia originates from the interactions of photons with the electrons in ZrO 2 , leading to the transition of electrons between the occupied and unoccupied states. CASTEP calculates the real and imaginary part of the dielectric function, which are further used to calculate the other optical properties like absorption, reflectivity, and conductivity [24,25]. The imaginary part of the dielectric function given in Equation (1) is used to calculate the optical absorption (Equation (2)).
The Ω, v, c, ω, and k in Equation (1) represent the volume of the elementary cell, valence band, conduction band, frequency, and the vector defining the polarization direction of the electric field. Absorption coefficient (Equation (2)) is represented by α(ω).
The optical properties of Ce doped ZrO 2 modeled systems are displayed in Figure 6. Due to the intrinsic wide band gap (5.70 eV for ZrO 2 ), pure ZrO 2 is found to absorb high energy photons. As clarified from Figure 6a, pure zirconia has a strong absorption peak, around 38.6 nm and 54.9 nm. Moreover, a wide absorption band is observed starting from 101 nm and ending at 224.1 nm. These peaks might originate from the transitions of electrons between O 2p and Zr 3d states. Ce doping modified the optical response of ZrO 2 . Increasing Ce doping concentration created substantial change in the absorption curves of ZrO 2 . The CeZr-1 depicted an absorption peak at 39.4 and 54.0 nm, with less intensity compared to pure zirconia. The broad absorption band in case of CeZr-1 is shifted to longer wavelengths ending at 274.8 nm. The changes induced in the optical absorption spectra of CeZr-1 are attributed to the insertion of Ce 4f states in the band structure. It is interesting to note that the models CeZr-2, CeZr-3, CeZr-4, and CeZr-6 exhibit different behavior to upcoming photons. The peaks around 39 nm and 54 nm completely disappeared. Moreover, the broad peak is shifted to longer wavelengths starting at 122.7 nm and ending at 290.2 nm. One should note from Figure 6a that there is very small difference between the absorption spectra of CeZr-2, CeZr-3, CeZr-4, and CeZr-6. The shifting of the absorption peaks and the creation/disappearance of new/existing peaks are ascribed to the states introduced due to Ce doping. The imaginary of dielectric function is shown in Figure 6b. Peaks for Zr-0 and relatively smaller peaks for CeZr-1 are found at 38.6 nm, 54.0 nm, and 176.1 nm attributed to the excitations of electrons from O 2p to Zr 3d states. The optical absorption drastically changed in CeZr-2, CeZr-3, CeZr-4, and CeZr-6 modeled systems. The peaks around 38.6 nm and 54 nm disappeared, and the absorption hump is found centering at around 225 nm. Electronic transitions are responsible for the optical spectra. One should note that the band structure of the doped systems changed due to the creation of Ce 4f states, leading to modification in the optical spectra. The peak hump around 225 nm is attributed to excitations of electrons between O 2p to Ce 4f and Zr 3d states. The absorption spectra and the imaginary part of the dielectric function verify the band structure findings. Figure 6c summarizes the conductivity of the simulated models. Computational results of the conductivity of Zr-0, as seen from Figure 6c, show peaks at 38.6 nm and 54 nm. Following the peaks, a broad absorption is found starting at 99.2 nm and ending at 227.7 nm. The 2.08% Ce doped ZrO 2 displays peaks with less intensity compared to Zr-0 at 38.6 nm and 54 nm. Moreover, the broad absorption hump is also found with reduced intensity. It is interesting to note that the hump starting at 101 nm for CeZr-1 is shifted to higher wavelengths ending at 275.7 nm. CeZr-2, CeZr-3, CeZr-4, and CeZr-6 demonstrate a single absorption band starting at 124.5 nm and ending at around 300 nm.
The Ω, v, c, ω, and k in Equation (1) represent the volume of the elementary cell, valence band, conduction band, frequency, and the vector defining the polarization direction of the electric field.
The optical properties of Ce doped ZrO2 modeled systems are displayed in Figure 6. Due to the intrinsic wide band gap (5.70 eV for ZrO2), pure ZrO2 is found to absorb high energy photons. As clarified from Figure 6a, pure zirconia has a strong absorption peak, around 38.6 nm and 54.9 nm. Moreover, a wide absorption band is observed starting from 101 nm and ending at 224.1 nm. These peaks might originate from the transitions of electrons between O 2p and Zr 3d states. Ce doping modified the optical response of ZrO2. Increasing Ce doping concentration created substantial change in the absorption curves of ZrO2. The CeZr-1 depicted an absorption peak at 39.4 and 54.0 nm, with less intensity compared to pure zirconia. The broad absorption band in case of CeZr-1 is shifted to longer wavelengths ending at 274.8 nm. The changes induced in the optical absorption spectra of CeZr-1 are attributed to the insertion of Ce 4f states in the band structure. It is interesting to note that the models CeZr-2, CeZr-3, CeZr-4, and CeZr-6 exhibit different behavior to upcoming photons. The peaks around 39 nm and 54 nm completely disappeared. Moreover, the broad peak is shifted to longer wavelengths starting at 122.7 nm and ending at 290.2 nm. One should note from Figure 6a that there is very small difference between the absorption spectra of CeZr-2, CeZr-3, CeZr-4, and CeZr-6. The shifting of the absorption peaks and the creation/disappearance of new/existing peaks are ascribed to the states introduced due to Ce doping. The imaginary of dielectric function is shown in Figure 6b. Peaks for Zr-0 and relatively smaller peaks for CeZr-1 are found at 38.6 nm, 54.0 nm, and 176.1 nm attributed to the excitations of electrons from O 2p to Zr 3d states. The optical absorption drastically changed in CeZr-2, CeZr-3, CeZr-4, and CeZr-6 modeled systems. The peaks around 38.6 nm and 54 nm disappeared, and the absorption hump is found centering at around 225 nm. Electronic transitions are responsible for the optical spectra. One should note that the band structure of the doped systems changed due to the creation of Ce 4f states, leading to modification in the optical spectra. The peak hump around 225 nm is attributed to excitations of electrons between O 2p to Ce 4f and Zr 3d states. The absorption spectra and the imaginary part of the dielectric function verify the band structure findings. Figure 6c summarizes the conductivity of the simulated models. Computational results of the conductivity of Zr-0, as seen from Figure 6c, show peaks at 38.6 nm and 54 nm. Following the peaks, a broad absorption is found starting at 99.2 nm and ending at 227.7 nm. The 2.08% Ce doped ZrO2 displays peaks with less intensity compared to Zr-0 at 38.6 nm and 54 nm. Moreover, the broad absorption hump is also found with reduced intensity. It is interesting to note that the hump starting at 101 nm for CeZr-1 is shifted to higher wavelengths ending at 275.7 nm. CeZr-2, CeZr-3, CeZr-4, and CeZr-6 demonstrate a single absorption band starting at 124.5 nm and ending at around 300 nm.

Conclusions
Ce doping significantly modified the electronic band structure and photo-response of ZrO2. The cell volume of the basic unit cell of ZrO2 exhibited linear variations with the Ce doping concentration. The electronic band gap of ZrO2 was reduced considerably by doping ZrO2 with Ce. A maximum reduction of about 1.32 eV was found for the CeZr-3 model, with a Ce doping concentration of 6.25%. The optical properties investigation revealed that the intrinsic peaks of ZrO2 were maintained at low doping levels, and these peaks completely vanished at high doping levels, leading to the creation of a new absorption band. The Ce inclusion in ZrO2 is expected to reduce the thermal conductivity, which would widen the utilization of Ce doped ZrO2 in thermal barrier coating applications.

Conclusions
Ce doping significantly modified the electronic band structure and photo-response of ZrO 2 . The cell volume of the basic unit cell of ZrO 2 exhibited linear variations with the Ce doping concentration. The electronic band gap of ZrO 2 was reduced considerably by doping ZrO 2 with Ce. A maximum reduction of about 1.32 eV was found for the CeZr-3 model, with a Ce doping concentration of 6.25%. The optical properties investigation revealed that the intrinsic peaks of ZrO 2 were maintained at low doping levels, and these peaks completely vanished at high doping levels, leading to the creation of a new absorption band. The Ce inclusion in ZrO 2 is expected to reduce the thermal conductivity, which would widen the utilization of Ce doped ZrO 2 in thermal barrier coating applications.