Effects of strains on the electronic structure and optical properties of Ce-doped ZnO with interstitial H

Effects of strains on the electronic structure and optical properties of Ce-doped ZnO with interstitial H

Computational Materials Science 169 (2019) 109120 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.el...

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Computational Materials Science 169 (2019) 109120

Contents lists available at ScienceDirect

Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci

Effects of strains on the electronic structure and optical properties of Cedoped ZnO with interstitial H

T



Zhenchao Xua, Qingyu Houa,b,c, , Feng Guoa,c, Yong Lia, Cong Lia a

College of Materials Science and Engineering, Inner Mongolia University of Technology, Hohhot 010051, PR China College of Science, Inner Mongolia University of Technology, Hohhot 010051, PR China c Inner Mongolia Key Laboratory of Thin Film and Coatings, Hohhot 010051, PR China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Ce-doped ZnO with interstitial H Strain Electronic structure Optical property First-principles

The electronic structure and optical properties of Ce-doped ZnO systems have been widely studied, but the effects of different strains of Ce-doped ZnO or Ce- doped ZnO with interstitial H systems remain unclear. To solve these problems, this study identified the effects of biaxial strain on the electronic structure and absorption spectrum of Ce-doped ZnO with interstitial H systems through a generalized gradient approximation + U (GGA + U) with plane wave pseudopotential. The formation energy of Zn15CeHiO16 decreased with the distance between Ce and H. At a close distance between Ce atom and H atom (i.e., 0.1876 nm), Zn15CeHiO16 showed the lowest formation energy and best stability among the doping systems. The formation energy of Zn15CeHiO16 decreased when the compressive strain increased but increased when the tensile strain increased. All doping systems did not change the ZnO direct band gap. Zn15CeO16 band gap without strain decreased, and the absorption spectrum red shifted compared with that of Zn16O16. Zn16HiO16 and Zn15CeHiO16 band gaps without strain increased, and the absorption spectrum blue shifted. Zn15CeHiO16 band gap increased as the compressive strain increased. The static dielectric constant decreased, and the absorption spectrum blue shifted. These findings were valuable for the design and preparation of new ZnO-based short-wavelength light-emitting diodes. The band gap of Zn15CeHiO16 decreased as the tensile strain increased; the static dielectric constant increased, and the absorption spectrum red shifted. Trap effect was significant regardless of the compressive strain or the tensile strain and was beneficial for prolonging the electron lifetime. These findings are valuable for the design and preparation of novel ZnO-based photocatalysts.

1. Introduction The direct band gap of pure ZnO is 3.40 eV [1], and its exciton binding energy is 60 meV at room temperature [2]. Doping different elements in ZnO crystals can improve their properties. The valence electrons of rare-earth (RE) atoms are located in the 4f orbit surrounded by the filled 5s and 5p orbits. Temperature and crystal field exert a small effect on 4f electron transition due to the shield effect of 5s and 5p orbits. Consequently, RE optical transition is stable, especially in strong electric fields [3]. The magnetic and optical properties of RE-doped ZnO showed promising results [4–7]. The optical and electrical properties of Ce-doped ZnO are widely investigated. Bechambi et al. [8] studied the photocatalytic effect of hydrothermally synthesized Ce-ZnO. The results showed that Ce-doping shifts the absorption edge and reduces the electron-hole recombination. Lee et al. [9] studied the optical properties of Ce-doped ZnO



synthesized using a sol–gel process. Ce doping strengthens the absorption spectrum of ZnO system in the visible region. Sinha et al. [10] studied the optical and electrical properties of Ce-doped ZnO synthesized using the wet chemical solution route. The results show that Cedoped ZnO exhibits good application in dielectric, ferroelectric, and piezoelectric properties at the Ce doping concentration of 1 mol%. Iqbal et al. [11] studied the optical properties of Ce-doped ZnO synthesized using low-temperature soft chemical method. The band gap of Cedoped ZnO system is narrowed, and a significant red shift occurs in the ultraviolet region. Wen et al. [12] studied the electronic, optical, and magnetic properties of Ce-doped ZnO by using first-principles calculations, and results show that the Ce-doped ZnO system is a direct band gap semiconductor, with red-shifted absorption peak. Zhang et al. [3] studied the electronic structure and optical properties of Ce-doped ZnO by using first-principles calculations, and results show that the band gap of Ce-doped ZnO

Corresponding author at: College of Materials Science and Engineering, Inner Mongolia University of Technology, Hohhot 010051, PR China. E-mail address: [email protected] (Q. Hou).

https://doi.org/10.1016/j.commatsci.2019.109120 Received 26 April 2019; Received in revised form 27 June 2019; Accepted 6 July 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.

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system is narrowed, the electronic transition in the system is easy, and the imaginary part of the dielectric function moves toward the low energy direction. Tan et al. [13] investigated the magnetic properties of RE-doped ZnO and found that Ce-doped ZnO systems have magnetic properties, and the 4f states of the Ce atoms form the magnetic moment. Strain has an effect on the optical properties and magnetic properties of the system [14–17]. In ZnO systems, doping changes the lattice constant, which results in strained lattice. The lattice also can be strained by thermal expansion coefficient and lattice constant mismatch between the sample and the substrate. The strain can cause changes in the electronic structure and band gap of the doping system, resulting in changes in optical and magnetic properties. In experiments, films are obtained via non-equilibrium means, such as epitaxial growth. The growth of films is only affected by the biaxial strains in a and b axes and is not affected by the same strain in the c axis. The bond length does not change isotropically. Experimentally prepared films can be investigated as bulk structures under biaxial strain (i.e., relaxation in the vertical direction) [18–20]. Triaxial strain only causes the energy level to move, whereas biaxial strain causes the energy band to split. A large amount of NH4+ [21] and NH2+ [9] is present during Ce-doped ZnO sample preparation and processing. As such, interstitial H atoms are formed in the ZnO lattice [22–24]. However, previous studies have neglected the influence of interstitial H atoms on the physical properties of ZnO. In the current study, the effects of strains on the electronic structure and optical properties of Ce-doped ZnO with interstitial H were investigated using first-principle calculations. ZnO systems with doping Ce and interstitial H exhibited a significant trap effect, and the impurity level was near the Fermi level regardless of the compressive or tensile strain and is beneficial for prolonging electron lifetime. These results might help in the design and fabrication of novel ZnO-based short-wavelength light-emitting diodes or photocatalysts.

Fig. 1. Models: (a) Zn16HiO16; (b) Zn15CeO16; (c) Zn16HiO161-4; (d) Zn15CeHiO16a-h with different distance between the Ce atom and H atom.

2. Models and calculation method

pseudopotential. The valence electron configurations for constructing pseudopotential were Zn3d104s2, Ce4f15s25p65d16s2, and O2s22p4. The U values of Zn-3d and O-2p were set to 10.00 and 7.00 eV, respectively [27]. The calculated band gap of undoped ZnO cells was 3.40 eV in accordance with the experimental value [28]. The U value of Ce-4f was set to 6.00 eV [3] as the default value of the Materials Studio software.

2.1. Models

3. Results and discussion

Undoped ZnO exhibits a hexagonal wurtzite structure with a space group P63mc and C64υ symmetry. In the current work, the doping concentration of all systems was 6.25 mol%, and the structure of the doped ZnO systems was hexagonal wurtzite [25]. To investigate the effects of doping Ce and interstitial H atoms on the optical properties and electronic structure of ZnO systems, we built the following: undoped bulk Zn16O16 supercell as shown in Fig. 1(a); bulk Zn15CeO16 supercell for one Ce atom substituting one Zn atom as shown in Fig. 1(b); four kinds of bulk Zn16HiO161-4 supercells for one interstitial H atom as shown in Fig. 1(c), in which the interstitial H atoms were located at (0.5, 0.5, 0.5)、(0.6, 0.5, 0.6)、(0.5, 0.5, 0.75) and (0.4, 0.5, 0.875), respectively; and eight kinds of bulk Zn15CeHiO16a-h supercells for one Ce atom substituting one Zn atom and one interstitial H atom as shown in Fig. 1(d), in which the interstitial H atoms were located at (0.5, 0.5, 0.5) and the Ce atoms were located at a–h, respectively. To investigate the effects of different strains on the stability, optical properties, and electronic structure of ZnO with coexistence of doping Ce and interstitial H atoms, we set the strain amount ε applied to the a and b axes of Zn15CeHiO16a-h supercells as −5%, −4%, −3%, −2%, −1%, 0%, 1%, 2%, 3%, 4%, and 5%, respectively. Strain was defined as ε = (a − a0)/ a0, where a0 is the optimal lattice constant without strain, a is the lattice constant that corresponds to different strains, ε is a positive value for tensile strain and a negative value for compressive strain, and c-axis was relaxed. The stability, electronic structure, and optical properties of Zn15CeHiO16 systems with different strains were calculated.

3.1. Crystal structure, stability, and formation energy The equivalent lattice parameters and formation energies of Zn16O16, Zn15CeO16, Zn16HiO161-4, and Zn15CeHiO16a-h after geometry optimization without strains are shown in Table 1. Mulliken method was used to calculate the orbital charges. The sum of the charge transfer on the f-state and d-state orbits of the Ce atom approached + 3 in Zn15CeO16 and Zn15CeHiO16a-h supercells. Thus, the valence of the doped Ce in ZnO was + 3, which is consistent with previous experimental results [29]. The sum of the charge transfer of the H atom in the valence–electron approached + 1 in Zn16HiO161-4 and Zn15CeHiO16a-h supercells. Thus, the valence of the interstitial H atom was + 1, which was consistent with previous experimental results [22]. In Table 1, the equivalent lattice parameters a and c and volume Zn15CeO16 were larger than those of Zn16O16, which was attributed to the larger ionic radius of Ce3+ (i.e., 0.103 nm) [30] than that of Zn2+ (i.e., 0.074 nm) [13]. This result is in agreement with experimental results [31]. The equivalent lattice parameters a and c and volume Zn16HiO161-4 were larger than those of Zn16O16 because interstitial H atom increased the repulsive interaction of the excess positive charges of H + ion. The equivalent lattice parameters a and c and volume Zn15CeHiO16a-h were also larger than those of Zn16O16 because both Ce atom doping and interstitial H atom increased the volume of doped system. Formation energy is a physical variable that indicates the stability of a doped system and the degree of difficulty of atomic doping. The impurity formation energy (Ef) is defined as follows [32]: for Zn15CeO16 system,

2.2. Calculation method

Ef (Ce ) = EZn15 CeO16 − EZn16 O16 + nZn μZn − nCe μCe

All calculations were performed on the basis of a generalized gradient approximation + U (GGA + U) [26] with plane wave

for Zn16HiO16 2

1-4

system,

(1)

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Table 1 The lattice parameters, volume, distance between Ce and H (dCe-H), bond length and formation energies of all systems after geometry optimized without strains. The upper abbreviations 1–4 correspond to the four kinds of Zn16HiO161-4 systems with different location of interstitial H in Fig. 1(c), and the upper abbreviations a-h correspond to the eight kinds of Zn15CeHiO16a-h system with different distance between Ce and H in Fig. 1(d). Models

a, c/nm

V/nm3

dCe-H/nm

Bond length (//c)/nm

Ef (Ce + Hi)/eV

Zn16O16

a = 0.3282 [31] c = 0.5318 [31] a = 0.3305 [31] c = 0.5364 [31] a = 0.3290 c = 0.5344 a = 0.3292 c = 0.5347 a = 0.3295 c = 0.5351 a = 0.3291 c = 0.5345 a = 0.3308 c = 0.5389 a = 0.3316 c = 0.5396 a = 0.3318 c = 0.5391 a = 0.3322 c = 0.5443 a = 0.3336 c = 0.5453 a = 0.3336 c = 0.5454 a = 0.3351 c = 0.5504 a = 0.3370 c = 0.5503

0.05000



0.201243



0.05170



0.200441

−7.7082

0.05001



0.203757

−0.9585

0.05010



0.203766

−0.9570

0.05014



0.203771

−0.9563

0.05007



0.203769

−0.9572

0.05173

0.1876

0.202593

−10.4703

0.05180

0.3208

0.202607

−9.9760

0.05192

0.3208

0.202612

−9.6780

0.05199

0.3752

0.202614

−9.6170

0.05221

0.4566

0.202619

−9.5150

0.05238

0.4566

0.202624

−9.3047

0.05347

0.5533

0.202631

−3.8764

0.05345

0.6417

0.202630

−3.2116

Zn15CeO16 Zn16HiO16

1

Zn16HiO162 Zn16HiO163 Zn16HiO16

4

Zn15CeHiO16a Zn15CeHiO16b Zn15CeHiO16

c

Zn15CeHiO16

d

Zn15CeHiO16e Zn15CeHiO16f Zn15CeHiO16

g

Zn15CeHiO16h

in Table 1. The formation energy of all systems was negative, indicating that substituting Ce atoms and interstitial H atoms can be present in ZnO, and system stability was increased. For the four kinds of Zn16HiO161-4 systems with different location of interstitial H, the system Zn16HiO161 showed the lowest formation energy and best stability when the interstitial H atoms were located at (0.5, 0.5, 0.5), and doping was the easiest among the four systems. Thus, for the four kinds of Zn16HiO161-4, the Zn16HiO161 system (simplified to Zn16HiO16) was used to study the effect of strain on the stability, optical properties, and electronic structure. Furthermore, the interstitial H atoms in the eight kinds of Zn15CeHiO16a-h systems were also located at (0.5, 0.5, 0.5). For the eight kinds of Zn15CeHiO16a-h systems with different distances between Ce and H, formation energy decreased as the distance between Ce and H decreased. At a close distance between Ce atom and H atom (i.e., 0.1876 nm), Zn15CeHiO16a showed the lowest formation energy and best stability, and doping was the easiest among the eight systems. Thus, for the eight kinds of Zn15CeHiO16a-h, Zn15CeHiO16a (simplified to Zn15CeHiO16) was used to study the effect of strain on the stability, optical properties, and electronic structure. The effects of strains on formation energy were investigated by calculating the formation energy of Zn15CeO16, Zn16HiO16, and Zn15CeHiO16 with different strains. EZn15 CeO16 , EZn16 Hi O16 , EZn15 CeHi O16 , and EZn16 O16 in Formula (1), (2), and (3) were used as the total energy of Zn15CeO16, Zn16HiO16, Zn15CeHiO16, and Zn16O16 with different strains, respectively. The results are shown in Fig. 2. The formation energy of Zn15CeO16, Zn16HiO16, and Zn15CeHiO16 decreased as compressive strain increased. Thus, the stability of the doped systems was enhanced, and doping became easy. The formation energy of Zn15CeO16, Zn16HiO16, and Zn15CeHiO16 increased as tensile strain increased. Thus, the doped systems became unstable, and doping became increasingly difficult.

Fig. 2. Formation energy of Zn16HiO16, Zn15CeO16 and Zn15CeHiO16 with different strains.

Ef (H ) = EZn16 Hi O16 − EZn16 O16 − nH for

Zn15CeHiO16a-h

μ H2 (2)

2

system,

Ef (Ce + H ) = EZn15 CeHi O16 − EZn16 O16 + nZn μZn − nCe μCe − nH

μ H2 2

(3)

where EZn15 CeO16 is the total energy of Zn15CeO16, EZn16 Hi O16 is the total energy of each Zn16HiO161-4, EZn15 CeHi O16 is the total energy of each Zn15CeHiO16a-h, EZn16 O16 is the total energy of Zn16O16, nZn is the number of Zn atoms substituted by Ce atoms, nCe is the number of doping Ce atoms, nH is the number of interstitial H atom, μZn and μCe are the chemical potentials of Zn and Ce, and μ H2 is the chemical potential of the crystalline phase hydrogen molecule. The formation energy of each doped system without strain is shown

3.2. Band structure and total density of states The band structure and total density of states (TDOS) of Zn16O16, 3

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Fig. 3. Band structure of Zn16O16, Zn15CeO16, Zn16HiO16 and Zn15CeHiO16 without strains.

system causes electrons near the conduction band minimum to undergo considerable energy level splitting, which narrows down the band gap [33]. The bond length parallel to the c-axis of Ce-O in Zn15CeO16 was shorter than that of Zn-O in Zn16O16. Thus, the attraction between the valence band maximum and the conduction band minimum was enhanced leading to band gap narrowing. These two functions made the band gap of the system narrow. In accordance with renormalization theory, the multibody effect of Zn15CeO16 was greater than Burstein–Moss effect, and the system band gap narrowed [34,35]. The band structure and TDOS of Zn16HiO16 without strains are shown in Fig. 3(c). The interstitial H atom did not change the direct band gap of ZnO, and the spin-up and spin-down TDOS were symmetric. Thus, Zn16HiO16 did not exhibit magnetic property. An impurity level appeared at the middle of the band gap. Zn16HiO16 band gap was

Zn15CeO16, Zn16HiO16, and Zn15CeHiO16 without strains were calculated to determine the effects of different doping methods on band structure of doping systems as shown in Fig. 3. The mechanism of band gap variation was discussed by calculating the bond lengths of each system without strains as shown in Table 1. Zn32O32 band gap without strain in Fig. 3(a) is 3.40 eV, which is consistent with that in a previous study [28]. The band structure and TDOS of Zn15CeO16 without strains is shown in Fig. 3(b). Doping Ce atom did not change the direct band gap of ZnO, and the spin-up and spin-down TDOS in the conduction band were asymmetric. Thus, Zn15CeO16 exhibited magnetic property, while the total magnetic moment was 1.001 μB . The band gap of Zn15CeO16 was 3.229 eV, which was narrower than that of Zn16O16 and is consistent with a previous report [31]. The magnetic moment of the doping 4

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Fig. 3. (continued)

trap effect that blocked the electron-hole pair complex in the system. The probability that the electrons on the impurity level were excited to the conduction band was rapidly increased. This will be discussed in detail in Section 3.3. Zn15CeHiO16 band gap was 3.467 eV, which was wider than that of Zn16O16 because the magnetic moment of the doping system caused electrons near the conduction band minimum to undergo a significant energy level splitting, which narrowed the band gap. The bond length parallel to the c-axis of Ce-O in Zn15CeHiO16 was longer than that of Zn-O in Zn16O16. Thus, the attraction between the valence band maximum and the conduction band minimum was weakened, leading to band gap increase. The effect of the former was weaker than that of the latter, which led to increased band gap. In accordance with renormalization theory, the multibody effect of Zn15CeHiO16 was weaker than Burstein–Moss effect, and the system band gap increased. Without strains, the band gap was in the order

3.879 eV, which was wider than that of Zn16O16 because the bond length parallel to the c-axis of Zn-O in Zn16HiO16 was longer than that of Zn-O in Zn16O16. As such, the attraction between the valence band maximum and the conduction band minimum was weakened, leading band gap increase. In accordance with renormalization theory, the multibody effect of Zn16HiO16 was weaker than Burstein–Moss effect. Thus, the system band gap increased. The band structure and TDOS of Zn15CeHiO16 without strains are shown in Fig. 3(d). Doping Ce atom and interstitial H atom did not change the direct band gap of ZnO, and the spin-up and spin-down TDOS in the conduction band were asymmetric. Thus, Zn15CeHiO16 exhibited magnetic property, and the total magnetic moment was 1.001 μB . Otherwise, the band structure of Zn15CeHiO16 shifted toward the low energy, and the impurity level in the middle of the band gap was located at the Fermi level. This phenomenon created a significant 5

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Fig. 4. (continued)

Fig. 4. Band structure of Zn15CeHiO16 with different strain: −5%, −4%, −3%, −2%, −1%, 1%, 2% and 3%, 4%, 5%.

In Fig. 4(a)–(e), the band gap of the system became wider as the compressive strain increased from −1% to −5%. According to Fig. 5, the valence band maximum and conduction band minimum moved toward the high energy level, but the movements of conduction band minimum was significantly larger than that of valence band maximum. As such, the band gap of the system became wider. The bond length parallel to the c-axis direction of Ce-O in Zn15CeHiO16 lengthened as the compressive strain increased from −1% to −5% as shown in Fig. 6. Thus, the attraction between the valence band maximum and conduction band minimum was weakened leading to band gap increase. From the perspective of renormalization theory, the multibody effect of Zn15CeHiO16 was weaker than Burstein–Moss effect as compressive strain increased from −1% to −5%. Thus, the band gap of the system

Zn15CeO16 < Zn16O16 < Zn15CeHiO16 < Zn16HiO16. The effect of strain on the band structure of Zn15CeHiO16 system was analyzed by calculating the band structure of Zn15CeHiO16 with different strains as shown in Fig. 4. The different strains did not change the direct band gap of ZnO, and the impurity level in the middle of the band gap was still located at the Fermi level. The total magnetic moment of Zn15CeHiO16 with different strains was unchanged, which was 1.001 μB . The mechanism of band gap variation were discussed by calculating the valence band maximum and conduction band minimum (core level alignment [36–40]) as shown in Fig. 5 and bond lengths as shown in Fig. 6 of Zn15CeHiO16 with different strains. 6

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Fig. 4. (continued)

Fig. 5. Shifts of VBM and CBM of Zn15CeHiO16 with different strain.

Fig. 4. (continued)

increased. In Fig. 4(f)–(g), the system band gap became narrower as the compressive strain increased from 1% to 5%. According to Fig. 5, as the compressive strain increased from 1% to 4%, the valence band maximum and the conduction band minimum moved toward the low energy level, but the movements of conduction band minimum was significantly larger than that of valence band maximum. As such, the band gap of the system became narrower. Furthermore, the valence band maximum of Zn15CeHiO16 moves toward the high energy level, but the conduction band minimum moves toward the low energy level while the strain was 5%. As such, the band gap of the system became narrower. The bond length parallel to the c-axis of Ce–O in Zn15CeHiO16 became short as tensile strain increased from 1% to 5% as shown in

Fig. 6. Bond length of Zn15CeHiO16 with different strains.

Fig. 6. Thus, the attraction between the valence band maximum and conduction band minimum was enhanced, leading to band gap increase. From the renormalization theory perspective, the multibody effect of Zn15CeHiO16 was stronger than the Burstein–Moss effect as tensile strain increased from 1% to 5%. Thus, the band gap of the system increased.

7

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3.3. Trap effects The accumulation of non-equilibrium carriers on the impurity level is called trap effect. In accordance with semiconductor physics, the concentration of non-equilibrium electrons accumulated at the impurity level can be expressed formulas follows [41]:

Δnt =

Nt n1 Δn (n 0 + n1)2

(4)

where Δnt is the concentration of non-equilibrium electrons accumulated at the impurity level, Nt is the concentration of composite centers, n 0 is the concentration of equilibrium electrons, Δn is the concentration of non-equilibrium electrons, and n1is the concentration of equilibrium electron when the Fermi level coincides with the composite center level. Δnt has the maximum when n1 = n 0 :

(Δnt )max =

Nt Δn 4n 0

(5)

The impurity level coincides with the Fermi level, which is most beneficial to the trap effect and greatly prolongs the relaxation time of electron recovery from the non-equilibrium state to the equilibrium state [42–44]. To visually analyze the effect of strain on the trap effect in the Zn15CeHiO16 system, the TDOS of Zn15CeHiO16 with different strains were calculated as shown in Fig. 7. The impurity level was still near the Fermi level regardless of the compressive strain or the tensile strain. The trap effect was still significant, which was beneficial in prolonging the relaxation time and electron lifetime. These findings were consistent with the results of the band structure analysis. While the impurity level overlaps with Fermi level, the electrons need the lowest energy to transition from the impurity level to the conduction band. The energy gap from deep impurity level to conduction band of Zn15CeHiO16 with different strains were calculated and shown in Fig. 8. The energy gap from deep impurity level to conduction band of Zn15CeHiO16 increased as compressive strain increased but decreased as tensile strain increased.

Fig. 8. The energy gap from deep impurity level to conduction band of Zn15CeHiO16 with different strains.

ε (ω) = ε1 (ω) + i ε2 (ω)

whereε1 (ω) is real part of complex dielectric function and ε2 (ω) is the imaginary part of complex dielectric function. The effect of different doping methods on the complex dielectric function of the system was discussed by calculating the real and imaginary parts of Zn16O16, Zn15CeO16, Zn16HiO16, and Zn15CeHiO16 as shown in Fig. 9. The electrical constant in the absence of incident light is called the static dielectric constant, which is the intercept of the real part of the dielectric function on the ordinate [45]. In Fig. 9(a), the static dielectric constants of Zn16O16, Zn15CeO16, Zn16HiO16, and Zn15CeHiO16 without strains were 1.68, 1.59, 1.87, and 1.84, respectively. The static dielectric constant of Zn15CeO16 decreased compared with that of Zn16O16, which indicated that system polarization weakened, the intensity of the photo-generated electric field of the system became small, and the ability of the system to bind the charge weakened. The static dielectric constants of Zn16HiO16 and Zn15CeHiO16 increased compared with that of Zn16O16, which indicated that system polarization strengthened, the intensity of the photo-generated electric field of the system was heightened, and the ability of the system to bind the charge was enhanced. The imaginary part of the complex dielectric function characterizes the energy consumed by the formation of the electric dipole, which is related to the transition between the bands and reflects the degree of electronic stimulated transition of the material. The larger the value of the imaginary part, the greater the probability that electrons absorb photons; the greater the number of electrons in the excited state, the greater the probability of transition [45]. To discuss in detail the electronic stimulated transition in the system, the partial density of states (PDOS) of Zn16O16, Zn15CeO16, Zn16HiO16, and Zn15CeHiO16 without strains are shown in Fig. 10. The imaginary part of the complex dielectric function of the Zn16O16 system had three dielectric peaks at 3.82, 5.36, and 8.40 eV in the energy range of 0–10 eV as shown in Fig. 9(b). Compared with Fig. 10(a), the first peak, second, and third peaks were from the electronic transitions from the O-2p state to the Zn4s state, from the Zn-3d state to the O-2p state, and from the Zn-3d state to the O-2s state, respectively. The imaginary part of the complex dielectric function of the Zn15CeO16 system had two dielectric peaks at 1.24 and 8.32 eV in the energy range of 0–10 eV as shown in Fig. 9(b). Compared with Fig. 10(b), the first and second peaks were from the electronic transitions from the Ce-4f state to the Zn-4s state and the Zn3d state to the O-2s state. The imaginary part of the complex dielectric function of the Zn16HiO16 system had four dielectric peaks at 2.99, 4.41, 5.95, and 8.85 eV in the energy range of 0–10 eV as shown in Fig. 9(b). Compared with that in Fig. 10(c), the first, second, third, and last peaks

3.4. Dielectric function analysis Dielectric constant characterizes the degree of polarization of the medium under the action of an external electric field, that is, the ability of the medium to bind to the charge. The larger the dielectric constant, the stronger the binding ability to charge, which indicates that material polarization is strong. The dielectric constant of a medium can be described by a complex dielectric function as follows: 20

-5% -4% -3% -2% -1% 0%

15

5

-1

DOS (eV )

10

0

1% 2% 3% 4% 5%

-5 -10 -15 -20

-8

-6

-4

-2

0

2

4

6

(6)

8

Energy (eV) Fig. 7. TDOS of Zn15CeHiO16 with different strain. 8

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Fig. 9. Dielectric Function of Zn16O16, Zn15CeO16, Zn16HiO16 and Zn15CeHiO16 without strains: (a) real part, (b) imaginary part.

Fig. 10. PDOS of systems without strains: (a) Zn16O16, (b) Zn15CeO16, (c) Zn16HiO16, (d) Zn15CeHiO16.

were from the electronic transitions from the O-2p state to H-1s state, the H-1s state to the Zn-4s state, the Zn-3d state to the O-2p state, and the Zn-3d state to the O-2s state. The imaginary part of the complex dielectric function of the Zn15CeHiO16 system had three dielectric peaks at 2.85, 5.59, and 8.46 eV in the energy range of 0–10 eV as shown in Fig. 9(b). Compared with Fig. 10(d), the first, second, and third peaks were from the electronic transition from the O-2p state to H-1s state, the H-1s state to Ce-4f state, and the Zn-3d state to the O-2s state. The real and imaginary parts of complex dielectric function of the Zn15CeHiO16 system with different strains are shown in Fig. 11. Fig. 11(a) shows that the static dielectric constant of Zn15CeHiO16 decreased as compressive strain increased, which indicated that system polarization was weakened. The intensity of the photo-generated electric field of the system became small, and the ability of the system to bind the charge was weakened. The static dielectric constant of Zn15CeHiO16 increased with increasing tensile strain, which indicated that system polarization became strong, the intensity of the photogenerated electric field of the system became large, and the ability of the system to bind the charge was enhanced. In Fig. 11(b), the imaginary part of complex dielectric function of the Zn15CeHiO16 moved to the high energy level with the compressive strain increasing, and the dielectric peak became weak in the 0–10 eV energy range; the imaginary part moved to the low energy level with increasing tensile strain, and the dielectric peak became stronger in the 0–10 eV energy range.

3.5. Absorption spectrum The absorption spectra of Zn16O16, Zn15CeO16, Zn16HiO16, and Zn15CeHiO16 without strains are shown in Fig. 12. Compared with that of Zn16O16, Zn15CeO16 absorption peak moved to the low energy level, and the absorption spectra red shifted, which was consistent with that of the experimental result [31]. The absorption spectra of Zn16HiO16 and Zn15CeHiO16 moved to the high energy level and blue shifted. These results were consistent with the analysis of band structure of doped systems without strains. The absorption spectra of Zn15CeHiO16 different strains were calculated, as shown in Fig. 13. The absorption peak of Zn15CeHiO16 moved to the high energy level, and the absorption peak increased as the compressive strain increased. The absorption spectra of Zn15CeHiO16 blue shifted, and the minimum energy of the absorption spectrum moved toward high energy as the compressive strain increased. The absorption peak of Zn15CeHiO16 moved to the low energy level, and absorption peak decreased with increasing tensile strain. The absorption spectra of Zn15CeHiO16 red shifted, and the minimum energy of the absorption spectrum moved toward low energy as compressive strain increased. These findings were consistent with the analysis of the band structure and trap effect of Zn15CeHiO16 systems with different strain.

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Fig. 10. (continued)

Fig. 11. Dielectric Function of Zn15CeHiO16 with different strains: (a) real part, (b) imaginary part.

4. Conclusion Ce-doped ZnO with interstitial H showed a low formation energy and excellent stability at the 0.1876 nm distance between Ce atom and H atom. Zn15CeHiO16 formation energy decreased as compressive strain increased and doping became easy. The formation energy of Zn15CeHiO16 increased with tensile strain increase and the doping difficulty was increased. Zn15CeHiO16 band gap increased as compressive strain increased. The static dielectric constant decreased, and the imaginary part of the complex dielectric function and the absorption spectrum moved toward the high energy level. This finding was valuable for the design and preparation of new ZnO-based short-wavelength light-emitting diodes. Zn15CeHiO16 band gap decreased as tensile strain increased. The static dielectric constant increased, and the imaginary part of the complex dielectric function and the absorption spectrum moved toward the low energy level. The impurity level located at the Fermi level regardless of the compressive strain or the tensile strain. Thus, trap effect was significant, which was beneficial for prolonging electron lifetime. These findings were valuable for the design and preparation of novel ZnO-based photocatalysts.

Fig. 12. Absorption spectrum of Zn16O16, Zn15CeO16, Zn16HiO16 and Zn15CeHiO16 without strains.

CRediT authorship contribution statement

Cong Li: Data curation, Visualization.

Zhenchao Xu: Conceptualization, Methodology, Writing - , original draft, Data curation. Qingyu Hou: Writing - review & editing, Project administration, Funding acquisition. : . Feng Guo: Writing - review & editing, Project administration. Yong Li: Data curation, Visualization.

Acknowledgments This work was supported by the National Natural Science 10

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Fig. 13. Absorption spectrum of Zn15CeHiO16 with different strains.

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