First-Principles Calculations of the Electronic Structure and Optical Properties of Yttrium-Doped ZnO Monolayer with Vacancy

The electronic structures and optical characteristics of yttrium (Y)-doped ZnO monolayers (MLs) with vacancy (zinc vacancy, oxygen vacancy) were investigated by the first-principles density functional theory. Calculations were performed with the GGA+U (generalized gradient approximation plus U) approach, which can accurately estimate the energy of strong correlation semiconductors. The results show that the formation energy values of Y-doped ZnO MLs with zinc or oxygen vacancy (VZn, VO) are positive, implying that the systems are unstable. The bandgap of Y-VZn-ZnO was 3.23 eV, whereas that of Y-VO-ZnO was 2.24 eV, which are smaller than the bandgaps of pure ZnO ML and Y-doped ZnO MLs with or without VO. Impurity levels appeared in the forbidden band of ZnO MLs with Y and vacancy. Furthermore, Y-VZn-ZnO will result in a red-shift of the absorption edge. Compared with the pure ZnO ML, ZnO MLs with one defect (Y, VZn or VO), and Y-VZn-ZnO, the absorption coefficient of Y-VO-ZnO was significantly enhanced in the visible light region. These findings demonstrate that Y-VO-ZnO would have great application potential in photocatalysis.


Introduction
Since the third scientific and technological revolution, energy has become essential for economic development. At present, fossil energy, such as oil, natural gas, and coal, is the most consumed energy in the world. However, the energy resources on earth are limited, and these fossil fuels will rapidly run out in the first half of the 21st century. Therefore, the vigorous development of renewable energy is not only conducive for sustainable economic development but also for alleviating the increasingly serious energy and environmental problems. As a potential renewable energy source, solar energy, especially visible light (which accounts for most of the solar energy), is believed to contribute to mitigating these problems through photocatalytic technology (also known as semiconductor-based photocatalytic technology) [1]. Semiconductor-based photocatalysis has attracted considerable attention due to its direct conversion of solar energy to easily stored hydrogen, as well as free secondary pollution [2,3]. The basic principle of semiconductor-based photocatalytic technology is the energy band theory of solids. Under visible light of ZnO (0001) layers is reduced, due to the depolarization of the surface. Experimentally, Deng et al. [41] synthesized a ZnO ML by reactive deposition of Zn on Au (111), which confirmed the existence of a ZnO ML graphite-like structure. Tan et al. [42] investigated the structural, electronic, and magnetic properties of RE metals (RE = Y, Ce, Eu, Gd, and Dy) doped ZnO ML using the DMol 3 package. The ZnO ML with Ce, Eu, Gd, or Dy was magnetic, but Y-doped ZnO ML was a nonmagnetic semiconductor. ZnO ML undergoes a transition from semiconductor to metal with the presence of Y doping. Although the electronic and optical properties of ZnO ML with yttrium (Y) or vacancies have been described, the structural and optical properties of yttrium-doped ZnO ML with vacancy defect (V Zn or V O ) have not been investigated yet.
In this work, the first-principles calculations of yttrium (Y)-doped ZnO ML with zinc vacancy (V Zn ) or oxygen vacancy (V O ) are performed. For comparison, pristine ZnO ML and ZnO MLs with Y or vacancy are also calculated. The crystal structures and formation energies of pure ZnO ML and ZnO ML with Y or vacancy are studied to ensure the rationality of the models. The electronic structures and optical properties of the ZnO ML doping systems are obtained, analyzed, and compared. This work also analyzes the possible photocatalytic reaction mechanism to further understand the photocatalytic principle of Y doping with vacancy on ZnO MLs.

Calculation Method
First-principles calculations were performed on the basis of the density functional theory (DFT) [43]. Compared with LDA (local density approximation) functionals, GGA (generalized gradient approximation) functionals (including PW91 , PBE [Perdew-Burke-Ernzerhof] and RPBE [Revised-Perdew-Burke-Ernzerhof]) have more precise energy and structure and are more suitable for open systems. PW91 was first proposed by Perdew et al. in 1991 [44]. PBE was first proposed by Perdew and Burke in 1996. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential [45]. RPBE was first proposed in 1998 with improvements in the chemisorption energy of atoms and molecules [46]. Therefore, we adopted the GGA with PBE function as the correlation function [47], and the exchange-correlation interaction between ions and electrons was described by ultrasoft pseudopotentials [48]. The valence electron orbitals for Zn, O, and Y were chosen as Zn 3d 10 4s 2 , O 2s 2 2p 4 , and Y 4d 1 5s 2 , respectively. In this work, all the calculations of structural stability, electronic, and optical properties of ZnO ML with and without Y or vacancy were performed by CASTEP (Cambridge Sequential Total Energy Package). Geometry optimization was performed with all atoms moving freely and cells optimized fully. In order to investigate the impact of Y and vacancy doping concentration on the stability of ZnO ML, models of 2 × 2 × 1, 3 × 3 × 1, and 4 × 4 × 1 supercells were considered. The co-existence of Y and vacancy in ZnO ML was investigated in the most stable doping models. The plane-wave cutoff energy was 400 eV, the Monkhorst-Pack grid of k-point sampling was set to 4 × 4 × 2 in the Brillouin zone (BZ) [49]. In the self-consistent field calculation, the convergence precision of the energy charge was 1.0 × 10 −5 eV/atom, the maximum displacement convergence criterion was 1.0 × 10 −3 Å, the maximum force acting on each atom was 0.03 eV/Å, and the maximum stress was 0.05 GPa. A vacuum region of 15 Å was applied along the z-direction above the ZnO ML to avoid the interactions caused by periodic boundary conditions. The intrinsic coordinates and crystal parameters were completely relaxed in the geometric optimization. The GGA+U method was adopted to optimize the energy of systems and correct the bandgap value of ZnO ML [50]. The Hubbard parameters U d,Zn of 10 eV [51], U p,O of 7 eV [51], and U d,Y of 2 eV [23] were employed. Besides this, all the calculations were performed under spin polarization and the same U parameters.

Crystal Structure and Structural Stability
To better study the properties of the ZnO ML with Y or vacancy, the crystal structure and stability of the ZnO ML should be investigated first. ZnO ML was acquired by cutting the bulk wurtzite ZnO with (0001) polar surface. The top view of the optimized ZnO ML is shown in Figure 1a, which illustrates a graphene-like structure. Each atom in the ZnO ML was three-fold coordinated, which is different from the four-fold coordinate Zn and O atoms in the bulk wurtzite structure [52]. Figure 1b shows the side view of the original and optimized ZnO MLs. The side view of the original ZnO ML was a ripple surface [53] because it retained the wurtzite structure of bulk ZnO (α = 90 • , β = 90 • , γ = 120 • ). However, the side view of the optimized ZnO ML became flat, the O-Zn-O bond angle was 120 • , and the bond length between Zn and O atoms was 1.895 Å, which agrees well with the previous theoretical values [54,55]. The Zn-O bond length in the ZnO ML was smaller than the corresponding bond length in bulk ZnO (2.01 Å). This discrepancy is due to the stronger sp 2 orbital hybridization of ZnO in the 2D structure than the sp 3 orbital hybridization in bulk ZnO [43]. To assess the stability of the ZnO ML with and without Y or vacancy, the formation energies of the ZnO MLs were calculated. The formation energy (E f ) can be calculated by the following [56]: Here, E defect is the total energy of ZnO ML with defect (Y, V Zn , V O ), E perfect is the total energy of the pristine ZnO ML without any impurity or vacancy, n i is the number of atoms of type i added to (n i > 0) or removed from (n i < 0) the initial system, and µ i is the chemical potential of an atom of type i [15]. The µ i is the chemical potential obtained from the energy of one zinc or yttrium atom in a large 2D supercell (i.e., µ Y = −188.521 eV, µ Zn = −1708.148 eV, µ O = −429.571 eV). Figure 2 shows the formation energies of ZnO MLs with and without Y or vacancy. As shown in the figure, all formation energy values of Y single-doped ZnO ML were negative, indicating that Y-doped ZnO ML can spontaneously form in the experiment. The formation energy value of Y single-doped ZnO ML changed from −1.428 eV to −0.188 eV with increasing Y concentration. Hence, ZnO ML can be inferred to be the most stable system when the doping concentration of Y is 6.25 at.%. Besides this, the formation energy of V Zn -ZnO was close to that of V O -ZnO, which were both positive. This finding indicates that the systems are unstable, and V O -ZnO seems less unstable than V Zn -ZnO. Hussain et al. [57] Table 1), whereas the Zn-O bond lengths closest to V O in Figure 3b increased slightly. The charge effect can be used to explain the changes in bond lengths and bond angles associated with the vacancies. A zinc atom is removed from the monolayer to form V Zn , and two negative charges are left in the monolayer. Therefore, other positively-charged zinc atoms would move toward V Zn . By contrast, the neighbouring oxygen atoms with negative charges would not be attracted by static electricity and would move further away. Therefore, the Zn-O bond lengths near the V Zn would be shortened, explaining the changes in the bond angle. For V Zn , both zinc and oxygen moved closer to an oxygen site when the oxygen was removed [58]. In addition, the lattice parameters of ZnO ML, Y-ZnO, V Zn -ZnO, V O -ZnO, Y-V Zn -ZnO, and Y-V O -ZnO were 3.282, 3.329, 3.281, 3.282, 3.282, and 3.290 Å, respectively. The results indicate that the lattice constant of ZnO increased by Y doping, the lattice constant of ZnO decreased slightly by the presence of V Zn , and V O had little effect on the lattice constant of ZnO. The ionic radius of Y 3+ (0.9 Å) was larger than that of Zn 2+ (0.74 Å), which increased the lattice parameter a of ZnO ML. The removal of the zinc and oxygen atoms resulted in a small change in the lattice parameters of ZnO ML. Table 1. Bond length d and bond angle θ of ZnO ML, V Zn -ZnO, and V O -ZnO (the atomic number is labeled in Figure 3).

Doping System
Bond  Figure 4. From Figure 4a,b, both valence band maximum (VBM) and conduction band minimum (CBM) were situated at the G point, indicating a direct bandgap. In Figure 4a, the bandgap of pure ZnO ML (4.03 eV) is greater than bulk ZnO (3.37 eV) [12], which can be explained by the quantum confinement effects, and it was confirmed theoretically and experimentally [59]. In addition, the energy band structures of the spin-up and spin-down components were symmetrical, indicating that the pristine ZnO ML is a non-magnetic semiconductor. From Figure 4b, Y-ZnO is a direct bandgap semiconductor with a bandwidth of 4.56 eV, which is larger than that of ZnO ML. It was noted that the Fermi level of Y-ZnO moved up and located approximately at the CBM, which produced a degenerate n-type semiconductor. This degenerate n-type semiconductor showed the Burstein-Moss effect [20]. A new impurity level appeared because of Y doping, and this impurity was located near the Fermi level in the energy band structure of the spin-up channel. The impurity level can serve as an effective recombination center and increases the separation rate of eand h + when ZnO is illuminated by a light source. In addition, the energy band structures of the spin-up and spin-down channels were asymmetrical, implying that Y-ZnO is a magnetic semiconductor. Figure 4c clearly shows that the Fermi level of V Zn -ZnO moved slightly to the lower energy level, indicating that V Zn -ZnO is a degenerate p-type semiconductor, and shallow acceptor states were created around the Fermi level in the VBM, increasing the carrier concentration. For V O -ZnO, the forbidden bandgap increased, and the Fermi level shifted towards the higher energy region compared with the intrinsic ZnO ML, as shown in Figure 4d. Thus, the VB may be inferred to be completely occupied by electrons. On the other hand, the spin-up and spin-down components of V Zn -ZnO and V O -ZnO were symmetrical, indicating the absence of magnetism for the ZnO ML with vacancy.    Figure 5a, the VB consisted of two parts: the lower part was composed of Zn-3d and O-2p states, whilst the upper part was mainly dominated by O-2p states. The hybridization of the Zn-3d and O-2p states occurred in the VB, and the bonding states were formed in this energy region [18]. The CB was mainly ascribed to Zn-4s and O-2p states. Therefore, the antibonding states in the CB of ZnO ML comprised Zn-4s and O-2p states [18]. From Figure 5b, the VB mainly consisted of O-2p and Zn-3d states, the VBM was determined by O-2p states, and the CB was mainly composed of Y-4d and Zn-4s states, with limited contribution from O-2p states. In addition, the chemical bonding of Zn, O, and Y atoms caused orbital hybridization between the Y atom and adjacent Zn and O atoms, and the electron density overlaps will increase with Y doping, which plays a crucial role in controlling the chemical properties of Y-ZnO. This process will also lead to the splitting of the donor energy level and expansion into an impurity band. Therefore, Y doping has a great impact on ZnO ML conductivity. In addition, the TDOS was asymmetrical, indicating that the spin-polarization mainly originated from the 4d electrons of the Y atom. For V Zn -ZnO and V O -ZnO, the bandgap of ZnO ML was mainly determined by Zn-4s states in the CB and O-2p states in the VB. For oxygen vacancy, the VBM and CBM moved to a lower energy region, the presence of V O resulted in the splitting of the VB into two narrower bandgaps (−2 eV and 0 eV), as shown in Figure 5d. The upper energy level was located in the forbidden band, which is induced by oxygen vacancy [31]. The new energy level is beneficial to the transition of electrons under low-energy incident light. Moreover, vacancy could change the conductivity of ZnO ML by changing the carrier concentration near the Fermi level, which is similar to that of Y doping.

Y-doped ZnO MLs with Vacancy
The effects of V Zn and V O on the electronic structure of Y-doped ZnO ML were investigated. Figure 6 shows the energy band structures of ZnO MLs with Y and vacancy (V Zn or V O ), which were calculated by the GGA+U method. From Figure 6a, the VBM and CBM of Y-V Zn -ZnO were located at the G point, suggesting that Y-V Zn -ZnO is a direct bandgap semiconductor. The bandgap of Y-V Zn -ZnO was reduced to 3.23 eV, which is smaller than those of ZnO ML and Y-ZnO. Chemical bonds can be formed between a zinc atom and three adjacent oxygen atoms, so the V Zn induced holes provided by three surrounding O atoms. The increase in hole concentration hindered the transition of electrons and the recombination of eand h + . In addition, the position of the Fermi level in Y-V Zn -ZnO was substantially consistent with that of ZnO ML, which was located near the VBM. From Figure 6b, the VBM of Y-V O -ZnO was situated at the G point, whereas the CBM was located between the Z and H points. Thus, Y-V O -ZnO is an indirect bandgap semiconductor. The bandgap of Y-V O -ZnO (2.24 eV) was smaller than that of Y-V Zn -ZnO. The Fermi level of Y-V O -ZnO lay near the CBM, which produced typical n-type metallic characteristics [23]. This means that shallow donor states were created near the CBM, thus leading to an increase in carrier concentration. Besides this, some new impurity levels were found near the CBM. The appearance of the impurity levels indicates that electrons were introduced, which is conducive to the separation of electron-hole pairs when the incident light is irradiated.  The spin-up and spin-down components of the Y-V O -ZnO DOS were asymmetrical, suggesting that the spin-polarization mainly came from the 4d and 5s electrons of the Y atom. In summary, the forbidden band width of ZnO ML with Y and vacancy is reduced, and the introduced impurity level will act as a "springboard" for electrons to jump into the CB, which may result in a stronger optical absorption coefficient in the visible light region [60]. The value of DOS near the Fermi level increases because of Y doping, which is also advantageous to the transition of electrons.

Population Analysis and Charge Density Difference
To understand the bonding between atoms, the Mulliken charges for ZnO ML were calculated. Table 2 Table 3 shows the chemical bond lengths and bond populations of Y-doped ZnO MLs with and without vacancy. The bonding population indicates the degree of overlap of the two bonded atomic electron clouds, which can be used to obtain the properties of chemical bonds. The bond length of the Y-O bond revealed a linear relationship with the corresponding overlap population [61]. Table 3 shows that the degree of overlap of the electron cloud was inversely proportional to the bond length. The bond length of Y-O was larger than that of Zn-O (1.895 Å), because the radius of Y 3+ (0.09 nm) is larger than that of Zn 2+ (0.074 nm). In addition, the Y-O bond length of Y-V Zn -ZnO was shorter than that of Y-V O -ZnO, which indicates that the Zn and Y electron clouds were overlapping. Therefore, the transfer   Figure 8 depicts the charge density differences of ZnO ML and Y-doped ZnO ML with or without vacancy. As shown in Figure 8b, the charge density distribution changed obviously with Y doping. The electron densities around Zn 2+ (1.00 e) and Y 3+ (1.14 e) ions are different, which can be seen from the Mulliken charge in Table 2. The incorporation of Y and vacancy into a crystal induced modifications of the electron density distribution in the space between crystal lattice ions, as provided in Figure 8c,d [61]. This result indicates that the covalent bond characteristic between Y and adjacent O atoms in Y-V Zn -ZnO was stronger than that in Y-ZnO and Y-V O -ZnO because of the overlap of electron clouds and a strong interaction. In addition, the electron cloud overlap of Zn-O bonds near the V Zn in Figure 8c was significantly greater than that near the V O in Figure 8d. The Zn-O bond near the V Zn was more covalent, indicating that the electron transfer between the Zn atom and the adjacent O atom near the V Zn was less than that near the V O .

Optical Properties
To better understand the application of Y-ZnO, V Zn -ZnO, V O -ZnO, Y-V Zn -ZnO, and Y-V O -ZnO in nanodevices, the optical properties should be calculated. In this work, the optical properties of ZnO ML with impurity or defect were obtained by the GGA+U method. In the linear response range, the macroscopic optical response function of the solid is described by the complex dielectric function of light ε(ω)=ε 1 (ω)+iε 2 (ω). The dielectric function ε(ω) characterizes the linear response of the materials to electromagnetic radiation. The imaginary part ε 2 (ω) of the dielectric function is directly related to optical absorption coefficient, which can be calculated from the matrix element between the electronic wave functions of the occupied states and the unoccupied states according to the selection rule of the electronic transition [62]. The imaginary part ε 2 (ω) is expressed as follows [43]: where ω is the frequency of incident photons; Ω is the unit cell volume; ε 0 is the permittivity in free space; k is the reciprocal lattice vector; v and c stand for the VB and CB, respectively; u and r are the vector defining polarization of the incident electric field and the position vector; ϕ c k and ϕ v k are the wave functions of CB and VB, respectively [16].
The absorption coefficient α(ω) describes the percentage of light intensity attenuation at the unit distance of light wave propagation, which can be obtained from ε 1 (ω) and ε 2 (ω), as follows [63]: During the calculation of the imaginary part of the dielectric function and the absorption coefficient, the incident radiation is linearly polarized along the (100) direction. The energy range of the visible spectrum is 1.63-3.10 eV, and the corresponding wavelength is 760-400 nm. Figure 9 depicts the results of imaginary part and the absorption coefficient of Y-doped ZnO MLs with vacancy. The calculation results of the pure ZnO ML and ZnO MLs with Y or vacancy are also shown for comparison. The peak was determined by the electron transition, which followed the selection rules. Figure 9a shows two distinct peaks in the dielectric function of ZnO ML, which are located at 4.70 eV and 7.70 eV, respectively. For Y-ZnO, the position of the absorption peak gradually shifted toward the higher energy region with Y doping, which is known as a blue-shift. A new peak appeared near 0.75 eV, which was mainly attributed to Y doping. For V Zn -ZnO, one main peak was shown at 4.70 eV and moved to 5.10 eV, which is called a blue-shift. For V O -ZnO, the main peak shifted to lower energy with the existence of V O , which is known as a red-shift. For Y-V Zn -ZnO, three main peaks were observed, and they exhibited a blue-shift.    During the photocatalytic process, the hole in the VB diffuses to the photocatalyst surface and oxidises with H 2 O/OHto form hydroxyl radicals (·OH). The electrons in the CB move to the surface of the catalyst and react with O 2 to produce superoxide radical anions (·O − 2 ), which can be utilized as species for the degradation of organic pollutants by oxidation [64]. The surface reactions are given in Equations (4)- (9):

Photocatalytic Reaction Mechanism and Installation Scheme of Photocatalytic Oxidation
From the above photocatalytic reaction processes, the photocatalytic property of Y-V O -ZnO was improved compared with the original ZnO ML. The doping of Y and vacancy can effectively promote the separation of electron-hole pairs, thus prolonging carrier lifetime. More carriers jump to the ZnO ML surface and participate in the photocatalytic reaction under visible light irradiation, which improves the redox reaction efficiency. Finally, the organic pollutants are decomposed into non-toxic H 2 O and CO 2 , achieving the goal of pollutant degradation.
The photocatalytic oxidation of azo dye wastewater was performed in the equipment shown in Figure 11. The main component of the system was the flow reactor (Trojan Technologies, London, ON, Canada) with a refill covered with a titania-silica coating [65]. The solar reactor included one UV transparent glass tube as a receiver [66]. The photoactive refill was adhered to the inner walls of the reactor. The refill was composed of a thin Y-V O -ZnO layer mixed with a water solution of silicone binder. Before photocatalysis, the reactor was washed with excess immobilized photocatalyst to ensure that only a thin layer of the photocatalyst remained on the fabric. The azo dye wastewater was pumped from the feed tank into the reactor and circulated in the reactor. Samples were extracted termly for analysis until the azo dye wastewater was decomposed into a colorless, non-toxic liquid.

Conclusions
In summary, we explored crystal structure, structural stability, electronic structure, and optical properties of Y-doped ZnO ML with V Zn or V O by first-principles density functional theory. For comparison, a first-principles study of pure ZnO ML and ZnO MLs with Y or vacancy was calculated. The calculation results showed that the maximum formation energy value of Y-ZnO is −0.188 eV. The formation energies of ZnO MLs with vacancy and ZnO MLs with Y and vacancy (V Zn , V O ) were positive, indicating that ZnO MLs with vacancy are unstable with or without Y. The bandgap of ZnO ML increased with the presence of Y. Meanwhile, impurity levels appeared near Fermi level in Y-ZnO, which was attributed to Y-4d and Zn-4s states. In addition, the bandgap of Y-doped ZnO ML with vacancy was smaller than those of ZnO ML, Y-ZnO, and V O -ZnO, which suggests that the emission of Y-doped ZnO MLs with V Zn or V O would exhibit a red-shift from 4.03 eV to 3.23 eV, 2.24 eV, respectively. The impurity level could be induced by the doping of Y or V O , which is advantageous for the electronic transition. Population analysis and charge density difference showed the change in the electrons and the bonding situation of Zn, O, and Y atoms in the ZnO monolayer doping systems. Moreover, the light absorptions of Y-doped ZnO MLs with vacancy were enhanced in the visible light region compared with that of the pristine ZnO ML and ZnO ML with one defect (Y, V Zn , or V O ). In particular, the enhancement of the absorption coefficient of yttrium-doped ZnO ML in the VIS region became more pronounced with or without V O . This work can provide some references for the application of Y-V O -ZnO in the photocatalytic field.

Conflicts of Interest:
The authors declare no conflict of interest.