1 Introduction

Environmental contamination is one of the biggest problems in the world, as it represents a constant threat to human health and ecological balance. Therefore, green technologies are a source of sustainable resources, in the photocatalysis process is one of the most used and promising, serving mainly to capture, convert, and store pollutants [1].

In particular, zinc oxide is a semiconductor material that has many applications in medicine, the ceramics industry, the manufacture of ultraviolet radiation shields, coatings, electronics, and spintronics [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Therefore, it is acquiring great interest due to its photocatalytic activity for the treatment of environmental pollution due to its oxidation and degradation capacity, an interest that has been increasing considerably in recent years. This semiconductor is one of the best photocatalysts due to its photochemical stability, low dielectric constant, high chemical stability, high optical activity, and above all its photocatalytic activity at room temperature and low cost [17]. However, zinc oxide has a relatively large band gap (\(\sim \)3.3 eV [18]), which does not allow it to absorb visible light and for this reason, the photocatalytic properties of zinc oxide could be limited.

Three crystalline structures can be found for zinc oxide, which are hexagonal wurtzite type, cubic zinc blende, and rock salt (or Rochelle salt). Under ambient conditions, the thermodynamically stable phase is that of wurtzite symmetry [19]. Each zinc atom is surrounded by 4 oxygen atoms at the corners of a tetrahedron (typical coordination of bonds with \(sp^{3}\) hybridization) and vice versa to form the wurtzite-type structure belonging to the P63mc space group which is made up of alternating layers of atoms along the Z axis [20].

Fig. 1
figure 1

a Study of the total energy as a function of the cutoff energy. b Total energy as a function of the k points

Full size image

Zinc oxide shows four preferential growth surfaces: (101\(\overline{0}\)), (112\(\overline{0}\)), (0001), and (000\(\overline{1}\)), the latter two being categorized as polar surfaces and playing an important role in the applications of this material. These two structures grow along the C axis and are found in the literature as Zn-polar (0001) and O-polar (000\(\overline{1}\)) [21]. Furthermore, quantized zinc oxide, with several alternating Zn-polar (0001) and O-polar (000\(\overline{1}\)) facets, is a typical polar crystal, and many extensive studies have indicated that zinc oxide with a large proportion of 0001 planes exhibits enhanced photocatalytic, such as degradation of organic contaminants [22,23,24].

Studies such as that of Yufei et al. [25] show that the energy of the polar Zn surface is higher than that of its counterpart, which means that it is more unstable and active. However, the (0001) surface has been shown to have the highest photocatalytic activity of all four surfaces.

McLaren et al. [24] discovered that OH ions have preferential adsorption on the (0001) surface due to the positive charge, which reacts with the holes of the semiconductor and generates OH radicals, promoting the photocatalytic reaction. E. Cerrato et al. [26] studied the properties of zinc oxide by doping it with different rare earth ions (lanthanum, erbium, praseodymium, ytterbium, and cerium), where they observed that the cations of lanthanum, erbium, praseodymium, and ytterbium could be within the crystalline structure of zinc oxide, while cerium creates a new phase of dioxide cerium. Furthermore, this type of action generated an influence on the optical absorption of pure zinc oxide, since by incorporating lanthanide ions in its structure there is a small absorption of visible light.

On the other hand, it is known that the properties of materials can be improved by doping or adding impurities [27], therefore, it is valid to ask if it is possible to improve the photocatalysis properties of zinc oxide surfaces by doping or addition of cerium impurities. To answer this question, we carried out a theoretical study of the structural and electronic properties of the pure zinc oxide 0001 surface and the cerium-doped system using density functional theory to determine possible improvements in the photocatalytic activity that cerium produces to zinc oxide.

In this study, we found that by adding cerium impurities to zinc oxide, the structural parameters slightly changed, changes were also presented in the electronic properties, which consist of intermediate states in the energy bandgap, located around the Fermi energy. The above may suggest that the zinc oxide system doped with cerium under a concentration of 6.25% can probably absorb visible light, which could lead to possible improvements in the photocatalytic properties of the material. It was also found that when carbon dioxide is absorbed on the surfaces of zinc oxide and cerium-doped zinc oxide, the bond lengths of this molecule increase and its bond angle decreases, which may signify a start in the process of reduction of this polluting gas.

In the next section, the computational methods are described, then the results are presented and discussed. Finally, a summary closes the article.

2 Methodology

Density functional theory was used to study the structural and electronic properties of the pure zinc oxide 0001 surface and the doped system. The Quantum-Espresso computational package implementing the Perdew-Burke-Ernzerhof Generalized Gradient Approximation was used to optimize the input parameters for the construction of the pure zinc oxide 0001 surface and the cerium-doped zinc oxide system.

To create our surface, the atomic positions and network parameters were taken, where the convergence of the total energy for the Bulk of zinc oxide, which was achieved using a cutoff energy of 85 and 850 Ry for the wave functions and a k-point mesh (6 \(\times \) 6 \(\times \) 3) as seen in Fig. 1.

After having the optimal parameters, we created the structure of the bulk of zinc oxide in the Wurtzite phase. Where the (0001) surface of zinc oxide has been modeled with a vacuum study as a function of the total energy as shown in Fig. 2.

Fig. 2
figure 2

Study of total energy as a function of vacuum

Full size image

Where the vacuum was increased by one angstrom by one angstrom until a vacuum of 10 \({\text{\AA }}\) was determined, thus guaranteeing that there is no atomic interaction between periodic images.

Subsequently, a study of the surface energy is carried out as a function of the number of layers as shown in Fig. 3, where 4 layers were taken, because the variation is no greater than 200 \(eV/A^2\), which is little compared to the average value, then it can be taken that from the fourth layer a trend towards the stability value is seen.

Fig. 3
figure 3

Study of total energy as a function of vacuum

Full size image

After optimizing the vacuum and the number of layers, we proceeded to create the four-layer \(2\times 2\) supercell, where we fixed the bottom layer, and a relaxation calculation was made. This \(2\times 2\) supercell has a thickness of 8.306 \({\text{\AA }}\) consisting of 32 atoms, where 16 atoms are zinc (gray color) and 16 oxygen atoms (red color) as shown in Fig. 4.

Fig. 4
figure 4

Supercell \(2\times 2\) of the zinc oxide surface

Full size image

3 Results and discussion

This section focuses on the detailed characterization of the structural and electronic properties, as well as the adsorption phenomenon in the system under study. Through techniques such as Density Functional Theory within the Perdew-Burke-Ernzerhofl generalized gradient approximation implemented in the Quantum-ESPRESSO package, bond lengths and angles are measured; thus evidencing the structural response to the presence of cerium impurities. Simultaneously, electronic parameters, such as density of states, are explored. Additionally, adsorption processes are analyzed, providing crucial information on how impurities and structure affect the interaction of the material with the adsorbate.

3.1 Structural properties

The structural properties of the surface (0001) of ZnO are studied, as shown in Fig. 5a, which is a \(4-\)layer \(2\times 2\) supercell with a thickness of 8.306 \({\text{\AA }}\) consisting of 32 atoms, where 16 atoms are zinc. (Gray color) and 16 oxygen atoms (red color). oxygens and zinc are presented three times coordinated with bond lengths \(Zn-O\), \(O-Zn\), and \(Zn-Zn\); also, an angle \(\alpha \) formed by \(Zn-O-Zn\).

Fig. 5
figure 5

Surface 001 of zinc oxide (ZnO) from a side view (a) and a top view (b)

Full size image
Fig. 6
figure 6

Surface of zinc oxide doped with Ce (ZnCeO) in the top layer from a side (a) view and a top view (b)

Full size image
Fig. 7
figure 7

Zinc oxide surface doped with Ce (ZnCeO) in the middle layer from a side (a) view and a top view (b)

Full size image
Table 1 Bond lengths and angles for the zinc oxide surface, cerium-doped zinc oxide in the top layer, and cerium-doped zinc oxide in an intermediate layer
Full size table

Next, the structural properties of the ZnCeO surface doped in the top layer are studied as shown in Fig. 6a, which is a (\(2\times 2\)) \(4-\)layer supercell with a thickness of 8.948 \({\text{\AA }}\), consisting of 32 atoms, where 15 atoms are zinc (gray color), 16 oxygen atoms (red color), and one cerium atom (blue color), three times coordinated oxygens with bond lengths \(Zn-O\), \(O-Zn\), \(Zn-Zn\), \(O-Ce\), and \(Zn-Ce\) where the zincs are located at the same distance; there is also an angle \(\alpha \) formed by \(Zn-O-Zn\) and an angle \(\beta \) formed by \(Zn-O-Ce\).

Finally, the structural properties of the ZnCeO surface doped in the middle layer are studied as shown in Fig. 7a, which is a \(4-\)layer \(2\times 2\) supercell with a thickness of 8.908 \({\text{\AA }}\), consisting of 32 atoms, where 15 atoms are zinc (grey color), 16 oxygen atoms (red color), and one cerium atom (blue color), there are three times coordinated oxygens with \(O-Zn\) bond lengths of 1.9604 \({\text{\AA }}\) in the doping, \(O-Zn\) of 3.3762 \({\text{\AA }}\) in the Z direction, \(Zn-O\), \(Zn-Zn\), \(O-Ce\), and \(Zn-Ce\); there is also an angle \(\alpha \) formed by \(Zn-O-Zn\).

It can be seen in Table 1 the bond lengths and angles between the atoms reported.

We decided to make a comparison of the data obtained for the Hubbard value \(U=0\,eV\) and \(U=7\,eV\) since in the literature we do not find work on zinc oxide surfaces doped with cerium and by making this comparison we can see that in Table 1, The values of the bond lengths and angles vary a little, this may be due to the small difference in covalent radius that the zinc atom has with respect to the cerium atom, the covalent radius of the zinc atom is 1.417 \({\text{\AA }}\) and the of cerium is 1.627 \({\text{\AA }}\), these covalent radii are those reported by the program used Quantum ESPRESSO.

3.2 Electronic properties

Next, we present the electronic properties for the systems studied with a Hubbard value \(U=0 \, eV\) and \(U=7 \, eV\).

3.2.1 Electronic properties for Hubbard (U=0 eV)

The electronic properties of the surface (0001) of ZnO are studied. Figure 8 shows the density of states (DOS) and PDOS contributions, where the fermi level is located at the origin of the plot.

Fig. 8
figure 8

DOS and PDOS for the ZnO surface

Full size image

From Fig. 8, we can see that there is an overlap between the bands, which indicates that it is a conductor, where the orbitals that contribute the most are the p orbitals of the oxygen atom and the d orbitals of the zinc atom, it also presents a small 0.21 Bohr mag/cell magnetization.

Next, the electronic properties of the ZnCeO surface doped in the top layer are studied. Figure 9 shows the density of states (DOS) and PDOS contributions, where the fermi level is located at the origin of the plot.

Fig. 9
figure 9

DOS and PDOS forthe ZnCeO surface for the first layer

Full size image

From Fig. 9, we can see that there is an overlap between the bands, which indicates that it is a conductor, where the orbitals that contribute the most are the 2p orbitals of the oxygen atom and the 5d orbitals of the cerium atom, where it presents symmetry for the spin up and spin down which indicates that it does not have magnetic properties.

Finally, the electronic properties of the ZnCeO surface doped in the penultimate layer are studied. Figure 10 shows the density of states (DOS) and PDOS contributions, where the fermi level is located at the origin of the plot.

Fig. 10
figure 10

DOS and PDOS for the ZnCeO surface for the middle layer

Full size image

In the same way, we can see that in Fig. 10 there is an overlap between the bands, which indicates that it is a conductor, where the orbitals that contribute the most are the d orbitals of the cerium atom and the p orbitals of the oxygen atom, where it presents symmetry for spin up and spin down which indicates that it does not have magnetic properties.

Because in the literature we only found studies of monolayers of zinc oxide doped with cerium, we decided to make a comparison between the electronic properties of the zinc oxide surface when it is doped with cerium in the upper layer and when it is doped in an intermediate layer, thus finding that there is little difference between the layers, since it continues to present the same symmetry for the up and down spin, thus indicating that it does not have magnetic properties. Furthermore, the orbitals that contribute the most to the valence band and the conduction band remain the same for both shells.

3.2.2 Electronic properties for Hubbard (U=7 eV)

From Fig. 11, we can see that there is an overlap between the bands, which indicates that it is a conductor, where the orbitals that contribute the most are the p orbitals of the oxygen atom and the p orbitals of the zinc atom, where not presents symmetry for the spin up and spin down which indicates that it has a small magnetization of −0.11 Borh mag/cell.

Fig. 11
figure 11

DOS and PDOS for the ZnO surface

Full size image

Next, the electronic properties of the ZnCeO surface doped in the top layer are studied. Figure 12 shows the density of states (DOS) and PDOS contributions, where the fermi level is located at the origin of the plot.

From Fig. 12, we can see that there is an overlap between the bands, which indicates that it is a conductor, where the orbitals that contribute the most are the p orbitals of the oxygen atom and the d orbitals of the cerium atom, there is not symmetry for the spin up and spin down it, which indicates that it has a small magnetization of −0.12 Borh mag/cell

Finally, the electronic properties of the ZnCeO surface doped in the middle layer are studied. Figure 13 shows the density of states (DOS) and PDOS contributions, where the fermi level is located at the origin of the plot.

Fig. 12
figure 12

DOS and PDOS for the ZnCeO surface for the top layer

Full size image
Fig. 13
figure 13

DOS and PDOS for the ZnCeO surface for the middle layer

Full size image

In the same way, we can see that in Fig. 13 there is an overlap between the bands, which indicates that it is a conductor, where the orbitals that contribute the most are the d orbitals of the cerium atom and the p orbitals of the oxygen atom, there is no symmetry for the spin up and spin down it, which indicates that it has a small magnetization of 0.10 Borh mag/cell

Comparing the electronic properties of the cerium-doped zinc oxide surfaces in the upper layer and in an intermediate layer with different Hubbard values \(U=0\,eV\) and \(U=7\,eV\), we observe that for a value of \(U=0\,eV\) it does not present magnetization, while that when adding the value of \(U=7\,eV\), it does not present symmetry in the spin up and the spin down, which indicates that there is a magnetization.

3.3 Study of the adsorption of carbon dioxide on the surface of zinc oxide and zinc oxide doped with cerium

In Fig. 14, we show the configurations in which carbon dioxide adsorption occurred for the clean and doped systems in the top layer.

Fig. 14
figure 14

\(CO_2\) adsorption on the zinc oxide surface (\(ZnO/CO_2\)) 14a and \(CO_2\) adsorption on the cerium-doped zinc oxide surface \((ZnCeO/CO_2)\) 14b

Full size image

Thus, in the systems studied, the activation of carbon dioxide is observed, because it bends the carbon dioxide molecule. Where a charge transfer occurs towards the surface Table 2, and the lengths of the bonds increase Table 3, being in accordance with Reimers, W.G. [28]

Table 2 Löwdin charges for the carbon dioxide
Full size table

3.3.1 Electronic properties for carbon dioxide adsorption

For Fig. 15, we observe that there is an overlap between the bands, which indicates that they behave like a conductor, where the orbitals that contribute the most to the valence band are the p of oxygen while the orbitals that contribute the most to the conduction band are the p of titanium. We also note that the upward spin is not symmetrical with the downward spin, therefore it presents a magnetization of −0.60 Borh mag/cell.

For Fig. 16, we again observe an overlap between the bands, which indicates that they behave like a conductor, where the orbitals that contribute the most to the valence band are the p of oxygen while the orbitals that contribute the most to the band conduction are the p of titanium and the d orbitals of cerium. We also note that the upward spin is symmetrical with the downward spin, therefore it does not have magnetic properties.

Table 3 Structural parameters for the carbon dioxide
Full size table

4 Conclusion

A study on the effects of adding cerium impurities on the structural and electronic properties of the 0001 zinc oxide surface has been successfully carried out, from which the following conclusions can be made:

Cerium doping on the zinc oxide surface slightly distorts the lattice parameters and bond lengths due to the small difference in covalent radius that the cerium atom has concerning zinc.

Having a concentration of 6.25% of cerium on the zinc oxide surface, the orbitals that make the greatest contribution to the valence band are the p orbitals of the zinc atoms and the p orbitals of the oxygen atoms, obviously, in the conduction band presents a great change, this is due to the effect produced by the impurity of the cerium atom on the zinc oxygen surface, thus being the d orbitals of the cerium atom the one that makes the greatest contribution in the conduction band, where it presents symmetry for the spin up and the spin down which indicates that it does not have magnetic properties.

Fig. 15
figure 15

DOS and PDOS for the \(ZnO/CO_2\) surface

Full size image
Fig. 16
figure 16

DOS and PDOS for the \(ZnCeO/CO_2\) surface

Full size image

It was found that when adding cerium impurities to zinc oxide, there were changes in the electronic properties, which consist of intermediate states in the forbidden energy band, located around the Fermi energy. This may suggest that the \(Zn_{0,9375}\) \(Ce_{0,0625} O\) system can probably absorb visible light, which could lead to possible improvements in the photocatalytic properties of the material.

When dioxide of carbon is adsorbed on the surfaces of zinc oxide and zinc oxide doped of cerium, the bond lengths of this molecule increase, and its bond angle decreases, which can mean a beginning in the process of reduction of this polluting gas.