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Article

Effect of Vacancy Defects on the Electronic Structure and Optical Properties of Bi4O5Br2: First-Principles Calculations

1
School of Physics and Electronic Information, Yan’an University, Yan’an 716000, China
2
School of Physics and Electronic Engineering, Xianyang Normal University, Xianyang 712000, China
3
College of Electrical and Mechanical Engineering, Nanchang Institute of Technology, Nanchang 330044, China
*
Author to whom correspondence should be addressed.
Coatings 2024, 14(11), 1361; https://doi.org/10.3390/coatings14111361
Submission received: 4 September 2024 / Revised: 11 October 2024 / Accepted: 24 October 2024 / Published: 25 October 2024

Abstract

:
First-principles calculations based on density functional theory are employed to investigate the impact of vacancy defects on the optoelectronic properties of Bi4O5Br2. The results indicate that vacancy defects induce minimal lattice distortion in Bi4O5Br2 without compromising its structural stability. Oxygen or bromine vacancies are more likely to occur than bismuth vacancies. The introduction of a bismuth vacancy leads to n-type semiconductor behavior in the Bi4O5Br2 system, while the creation of an oxygen vacancy reduces the bandgap and enhances the light absorption capacity. Bi4O5Br2 with three coordinated oxygen vacancies exhibits a higher effective electron–hole pair mass ratio, which is advantageous for the efficient separation of electron–hole pairs. Bi4O5Br2 with three coordinated oxygen vacancies exhibits enhanced absorption and reflection coefficients in the visible-light region compared to other systems, indicating that oxygen vacancy defects significantly promote visible-light absorption and electron–hole separation. This research provides new theoretical insights for understanding and optimizing the performance of photocatalysts based on Bi4O5Br2.

1. Introduction

With the rapid acceleration of human industrialization, a substantial amount of petrochemical energy has been consumed, leading to severe air pollution. Environmental degradation and energy scarcity have emerged as two pressing issues that demand immediate attention [1]. Semiconductor photocatalysts can efficiently harness solar energy to degrade organic pollutants, eradicate microorganisms, and mitigate environmental pollution effectively. However, conventional photocatalysts like TiO2 and ZnO have limited light absorption capabilities because of their wide band gaps, resulting in low utilization rates of solar energy. Therefore, it is essential to explore semiconductor photocatalysts with an enhanced light absorption performance [2].
In recent years, bismuth oxide halides (BimOyXn, where X = Cl, Br, I) have been found to exhibit a graphene-like lamellar structure, consisting of alternating X-Bi-O-Bi-O-X layers arranged along the (001) direction. The formation of this lamellar morphology is attributed to the covalent bonds within the layers and the van der Waals forces between them. The presence of dipole moments, generated by the polarization of atomic orbitals between layers, creates an internal electric field that enhances the efficiency of charge carrier separation and boosts photocatalytic activity [3,4]. Moreover, increasing the Bi/X ratio can enhance the optical absorption and hybridization of the conduction band, thereby promoting electron migration and facilitating photogenerated electron–hole pair separation [5]. Among the various compositions in the BimOyXn system, Bi4O5Br2, an n-type semiconductor photocatalyst, has attracted significant attention. This attention is due to its suitable band gap, tunable morphology, good chemical stability, and satisfactory performance in visible light-driven photocatalysis. Moreover, the conduction band (CB) of Bi4O5Br2 has a negative position relative to normal hydrogen electrode, which can effectively activate molecular oxygen to generate O2- active groups. Bi4O5Br2-based photocatalysts are being developed to address increasingly complex energy and environmental problems. The applications of Bi4O5Br2-based photocatalysts include pollution degradation [6], hydrogen evolution [7], CO2 reduction [8], N2 fixation [9], etc. It shows promising potential for applications in environmental purification and energy conversion fields. However, despite these advantages mentioned above, there are still challenges associated with the high recombination rates of photogenerated carriers and differences in active sites that limit the overall photocatalytic performance of Bi4O5Br2-based materials [10]. To address these issues effectively, researchers have conducted a series of rational designs and modification studies, including element doping [11,12], carbon material modification [13], morphology control [14], construction of heterojunctions [15,16], and defect engineering [17].
Surface defect engineering is a regulatory method that can adjust the surface properties, band structure, and charge carrier concentration of photocatalysts. Surface defects play various positive roles, such as lowering activation energy, directly participating in reactions as active sites, improving light harvesting and charge carrier concentration, and promoting surface charge separation as separation centers [18]. The presence of point defects and impurities can significantly alter the electrical and optical properties of semiconductors. Therefore, understanding the role of defects and controlling them is crucial for developing semiconductor photocatalysis [19]. Oxygen vacancies (OVs) are typical defects that promote photogenic electron–hole transfer by broadening the range of light absorption [17,20]. Cai demonstrated that OVs synergistically enhance the piezoelectric catalytic performance with ultra-thin structures in Bi4O5Br2 [21], while Dong showed that halogen vacancies serve as electron trap centers to activate inert N2 molecules effectively [9]. Jin found that increasing the bismuth (Bi) content affects the electric potential by making the conduction band more negative in bismuth-rich photocatalysts, which increases the absorption range but reduces the capacity [4]. Chen believes that introducing OVs can adjust the position between the conduction band and valence band, thereby improving the gap value excited by visible light and increasing the utilization rate [22]. However, some viewpoints suggest OVs could increase electron–hole recombination, which reduces carrier mobility [23]. Currently, there is a lack of comprehensive theoretical research on the formation mechanism of vacancy defects in Bi4O5Br2 and the influence mechanism on optical properties is particularly unclear.
First principles provide a robust approach to investigate defects in semiconductors, facilitating the identification and comprehension of defect characteristics [24]. To offer theoretical guidance for the efficient design of Bi4O5Br2 photocatalysts, it is crucial to thoroughly explore the influence of vacancy defects on the properties of Bi4O5Br2. In this study, we employ density functional theory within the framework of the first-principles method to construct vacancy defect models for bismuth, oxygen (O), and bromine (Br) atoms. The formation energy calculations are performed to ascertain their structural stability. Additionally, an extensive investigation is conducted on the electronic structure, optical properties, and photocatalytic performance of the defect system.

2. Computational Details

All first-principles calculations were performed using density functional theory (DFT) implemented in the Cambridge sequential Total Energy Package (CASTEP) software package 2020 [25]. The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) was adopted for electron exchange and correlation [26]. A cut-off energy of 500 eV was set for the plane-wave expansion of electron wave functions of all atoms. Pseudo-atomic calculations were performed for Bi (6s26p3), for O (2s22p4), and for Br (4s24p5). Vacancy defect models were created by changing atoms in the primitive cell. The first Brillouin zone was sampled with a 2 × 6 × 2 Monkhorst–Pack k-point grids for the primitive cell. Although a higher cut-off energy and k-point were tested, they did not lead to significant improvements. Self-consistent field (SCF) calculations were performed with a tolerance of 1.0 × 10−6 eV/atom to ensure convergence. The atoms in the cell were completely relaxed, and the convergence criterion of the force was set at 0.01 eV/A.

3. Results and Discussion

3.1. Crystal Structure

Bi4O5Br2 belongs to the monoclinic system with the Hermann–Mauguin symbol space group of P1211 [27]. Its lattice parameters are: a = 14.539 Å, b = 5.605 Å, c = 10.782 Å, α = γ = 90°, and β = 97.75° [28]. The pristine Bi4O5Br2 has an emblematic layered structure with -[Br-Bi-O-Bi-Br]- layers stacked along the orientation through weak van der Waals interactions, as shown in Figure 1a.
Before introducing vacancy defects, the geometric structure and electronic properties of the pristine Bi4O5Br2 were investigated. The model consists of a unit cell containing 16 Bi atoms, 20 O atoms, and 8 Br atoms (Figure 1b). Within the cell, there are two distinct Bi atoms and two distinct O atoms. For clarity, Bi atoms with three coordination bonds are depicted in blue, those with four coordination bonds in purple, O atoms with three coordination bonds in red, and O atoms with two coordination bonds in green. The bond lengths of Bi1-O2, Bi1-O1, Bi2-O1, and Bi2-O2 are 2.09 Å, 2.13 Å, 2.11 Å, and 2.12 Å, respectively. The formation of vacancies at any equivalent lattice site for Bi and O atoms is energetically equivalent, with a fixed formation energy. The vacancy defect model is represented by V, and the lower corner mark represents the defect atom. Therefore, the five vacancy defect models constructed can be expressed as VBi1, VBi2, VO1, VO2, and VBr, respectively. The calculated lattice parameters are shown in Table 1. The lattice parameters of the geometrically optimized Bi4O5Br2 system are a = 14.595 Å, b = 5.651 Å, c = 10.938 Å, α = γ = 90°, and β = 97.93°, which are similar to the results of previous experiments [29]. The geometric optimization outcomes for the defective system indicate that, in comparison to the pristine Bi4O5Br2 structure, the presence of vacancies induces lattice distortion. However, the variations in all parameters remain within an acceptable threshold.

3.2. Vacancy Formation Energy

A vacancy is an important type of point defect in a crystal. The emergence of a vacancy disrupts its periodic binding state, resulting in an increase in the local energy. The energy difference between the presence of a vacancy and its absence is known as the vacancy formation energy. This energy is a critical parameter that reflects the ease and stability of vacancy formation and plays a pivotal role when evaluating the rationality of crystal structure models. A lower formation energy indicates that the material system is more likely to develop vacancy defects. By determining the vacancy formation energy, one can identify the sites with the least energy and, accordingly, position vacancies in the crystal. Defect formation energies are defined as [30,31]:
E f = E d e f e c t E b u l k + i n i μ i
where E(defect) represents the total energy of the supercell in which the defect is formed, E(bulk) denotes the total energy of the bulk material, and μ i represents the chemical potentials. The chemical potentials of oxygen and bromine atoms are represented by half the energy of an oxygen molecule and a bromine molecule, respectively. The chemical potential of a bismuth is the energy of a single Bi atom in the rhombohedral structure. Here, i represents the different types of atoms and n represents the number of vacancy atoms in the perfect crystal (i n = 1 in the work). Table 2 presents formation energies for various atomic vacancy defects. Bismuth atom vacancy defects with three and four coordination bonds have formation energies of 9.03 eV and 12.68 eV, respectively, significantly higher than those for oxygen and bromine vacancies. This indicates a low probability for bismuth vacancy defects to form in the Bi4O5Br2 system. Formation energies for oxygen atom vacancy defects with two and three coordination bonds are 5.60 eV and 2.26 eV, respectively. This suggests that it is more favorable to form oxygen defects, indicating that oxygen with two coordination bonds is comparatively more stable within the crystal structure. The formation energy of VBr is only 0.65 eV higher than that of VO1, which indicates a high likelihood for the occurrence of defects in the form of VO1 and VBr in the Bi4O5Br2 system. As a result, this study specifically concentrated on vacancy defects related to oxygen and bromine. Furthermore, to better understand the relationship between different supercell sizes and defect formation energy, we calculated the defect formation energy for the O1 defect in both the 2 × 1 × 1 and 2 × 2 × 1 supercells. The calculations revealed that, in the 2 × 1 × 1 supercell, the defect formation energy is smaller than that of the defect in the primitive cell, while in the 2 × 2 × 1 supercell, the formation energy is almost the same as that in the 2 × 1 × 1 supercell. The calculations suggest that, as the supercell size increases, the calculated defect formation energy tends to stabilize. This value is closer to the actual defect formation energy in real materials, which aids in our better understanding of the behavior of defects in practical materials.

3.3. Electronic Structure

Accurately estimating the electronic band gap, directly calculating the type of band gap (direct or indirect), and the contributions of various substances to the density of electronic states (DOS) are crucial for assessing the suitability of materials in optoelectronic and photocatalytic applications. The calculated band structure of the intrinsic Bi4O5Br2 is shown in Figure 2a. It can be observed from the figure that the band gap value of the intrinsic Bi4O5Br2 is 2.38 eV, which is close to the experimental value (2.32 eV) and consistent with the calculated value (2.38 eV) [32,33].
The valence band maximum (VBM) of intrinsic Bi4O5Br2 is located at the F point of the Brillouin zone, while the conduction band minimum (CBM) is at the G point. This indicates that Bi4O5Br2 is an indirect bandgap semiconductor. Due to the difference in momentum between positions in k-space, an indirect bandgap can effectively inhibit the recombination of excited electrons with holes, which is beneficial for photocatalytic activity applications. Figure 3a presents the total density of states (TDOS) and partial density of states (PDOS) for intrinsic Bi4O5Br2 to further analyze its composition. From the figure, it can be observed that near the VBM, hybrid states composed mainly of O 2p and Br 4p are present in intrinsic Bi4O5Br2, while near CBM, contributions from Bi 6p states dominate. Therefore, photogenerated holes primarily appear at O and Br sites, while electrons mainly appear at Bi sites.
In the vacancy defect system, there are unbonded electrons that lead to defect energy levels. Figure 2b illustrates the band structure of VO1. Compared to the intrinsic Bi4O5Br2, two defect energy levels appear in the VO1 band structure, and one defect energy level appears in the VO2 band structure. Under the influence of vacancy defects, the band gap values of VO1 and VO2 are reduced to 2.25 eV and 2.31 eV, respectively. By analyzing Figure 3b,c, it can be observed that the defect energy levels appearing in the band gap are mainly contributed by the Bi 6p states. This is primarily because oxygen atoms bond with bismuth atoms in this system. When oxygen atoms are missing, some outer electrons of bismuth remain unbonded and exist as dangling bonds, resulting in defect energy levels near the Fermi level. It can be concluded that the formation of defect energy levels is due to the introduction of oxygen vacancy defects, which disrupts the periodic potential field generated by atomic arrangement. The introduction of oxygen vacancy causes electrons in the valence band to first transfer to defect energy levels and then to the conduction band, shifting the absorption edge towards the red region and expanding the light absorption range for improved light utilization efficiency and enhanced carrier separation promotion. Additionally, defect energy levels capture photo-induced carriers, promoting their separation and enhancing the material’s photocatalytic activity.
The band structure of the VBr is shown in Figure 2d, where the Fermi level enters the conduction band, indicating that a low concentration of Bi defects will make the Bi4O5Br2 system an n-type semiconductor. As the defect concentration increases, the Fermi level continues to move towards and eventually enters the conduction band. By analyzing the combined density of states in Figure 3d, it can be observed that there is no change in the composition of the conduction and valence bands; near the valence band maximum, hybrid states of O 2p and Br 4p still dominate, while near the conduction band minimum, Bi 6p states contribute to these states. When the Fermi level enters or comes close to the conduction band, the conductivity is enhanced, which affects photocatalysis by increasing its likelihood for occurrence. The enhancement occurs because, when the Fermi level enters or approaches the conduction band, it introduces more conductive electrons and holes into this region, thereby increasing the rate of electron–hole pair generation and migration. Consequently, this promotes the better separation and utilization of photogenerated carriers, which leads to an improved efficiency and rate for photocatalytic reactions. Therefore, when the Fermi level enters or becomes close to the conduction band, it enhances the photocatalytic activity within semiconductors.

3.4. The Effective Mass Changes in Charge Carriers

The efficiency of the diffusion and migration of photogenerated carriers in semiconductors is an important factor that affects the activity level of photocatalytic reactions [34]. When a semiconductor photocatalyst absorbs photons with energy greater than its band gap, it excites electrons from the valence band to the conduction band, generating photogenerated carriers. During migration from the interior of the semiconductor material to the active site on its surface, a significant number of these carriers undergo recombination due to Coulomb interactions between the photogenerated electrons and holes, resulting in a reduced quantum efficiency for photocatalysis. A higher migration rate for photogenerated carriers decreases their likelihood of recombining, making it more advantageous for efficient photocatalysis. The average velocity at which photogenerated carriers migrate is related to their effective mass [33]:
v = k m *
The effective mass of photogenerated carriers can be calculated based on the dispersion relationship near the maximum of the valence band and the minimum of the conduction band in the band structure [35]:
m * = ± 2 d 2 E / d k 2
where m* is the effective mass of charge carrier, and d 2 E / d k 2 is the coefficient of the second-order term in a quadratic fit of E(k) curves for the band edge.
The charge separation efficiency of charge carriers was evaluated via the relative effective mass of electrons and holes. The relative ratio (D) of the effective masses plays a significant role in photocatalysis, which is evaluated via the following equation [35]:
D = m h * m e *
By definition, a higher D value indicates a greater tendency for the separation of photogenerated electron–hole pairs, thereby enhancing the photocatalytic activity. To further clarify the impact of vacancy defects on the photocatalytic activity of Bi4O5Br2, we calculated the effective mass of electrons at the bottom of the conduction band and holes at the top of the valence band using the results from the band structure analysis, according to Equation (3). The calculation results are shown in Table 3.
The effective mass of electrons for the intrinsic Bi4O5Br2 is 0.140, as shown in Table 3, while the effective mass of holes is 0.432. The effective mass of photogenerated electrons is much smaller than that of photogenerated holes, which characterizes Bi4O5Br2 as a typical semiconductor photocatalyst with light electrons and heavy holes. The D value of the intrinsic Bi4O5Br2 reaches 3.086, higher than that of the traditional TiO2 photocatalyst but lower than that of the g-C3N4 photocatalyst. In defective systems, compared to the intrinsic Bi4O5Br2, the D values for the VBi2, VO1, and VBr systems increases with the VBr system, having the highest D value at 6.871. On the premise of similar effective masses of electrons, the vacancy defect in a bromine atom significantly increases the effective mass of holes. The vacancy defect in the bromine atom introduces new energy levels near the valence band maximum, as shown in Figure 2d. The mixing of these levels with the valence band states results in changes to the curvature of the valence band, making it more compact and flatter. As a result, this increases the effective mass of valence band holes. A further analysis reveals a significant difference in effective masses between photogenerated electrons and holes in the VBr system, indicating notable disparities in their migration rate and diffusion efficiency. This substantial difference enhances asynchronization between photogenerated electrons and holes, effectively reducing recombination probability and improving carrier separation efficiency. The calculation results demonstrate that vacancy defects of Bi2, O1, and Br atoms all contribute to enhancing the carrier separation efficiency.

3.5. The Optical Properties

The calculations of optical properties are based on the imaginary part of the dielectric function, which arises from direct inter-band transitions as described by the following expression [37]:
ε 2 ω = 2 e 2 π Ω ε 0 k , v , c ψ k c u · r ψ k v 2 δ ( E k c E k v ω )
where Ω is the protocell volume; u is the vector defining the polarization of the incident electric field; k is the reciprocal lattice vector; the superscripts c and v represent the conduction band and the valence band, respectively; ω is the frequency of the incident photon; and ψ k c u · r ψ k c is the momentum transition matrix. Since the dielectric function shows a causal response, the real part (ε1) of the dielectric function can be obtained from the imaginary part via the Kramers–Kroning relation. The absorption coefficient α(ω) can be obtained with ε1(ω) and ε2(ω) [37]:
α ω = 2 ω ε 1 2 ω + ε 2 2 ω ε 1 ( ω ) 1 2
The optical properties of the studied systems are depicted in Figure 4. Figure 4a illustrates the real part of the dielectric function. When the x-axis value is zero, the corresponding value on the y-axis represents the static dielectric constant. The static dielectric constant values for Bi4O5Br2, VO1, VO2, and VBr are 6.39, 9.02, 6.63, and 21.85, respectively. Compared to the intrinsic semiconductor Bi4O5Br2, VO2 shows almost no change in its dielectric constant, while VO1 and VBr exhibit an increase in their respective values. Notably, VBr has a significantly high dielectric constant value. According to Lin’s Equation, a higher permittivity of a photocatalyst corresponds to a longer photoelectron lifetime in its conduction band, which suggests that VO1 and VBr may possess better charge separation and transport abilities, thereby enhancing the photocatalytic efficiency. The imaginary part of the complex dielectric function describes the light absorption properties of the material, which can be calculated using the occupied and unoccupied momentum matrix elements. The calculated imaginary dielectric function and absorption coefficient are shown in Figure 4b,c. As shown in Figure 4c, with the introduction of vacancy defects, the absorption edges of all defect systems are redshifted. Among them, the VBr system exhibits the largest redshift and has its first absorption peak at 0.95 eV, located in the infrared region, while other systems’ absorption peaks are in the ultraviolet region. No absorption peaks were generated in the visible light region for any of these systems. However, it is worth noting that the VO1 system exhibits a relatively high light absorption rate in the visible light region. Figure 4d displays the reflectivity of each system, which determines the penetration depth of light in the semiconductor material. A lower reflectivity is beneficial for the deeper propagation of light in the material, thereby increasing the possibility of interaction between light and the material. In the visible light region, the VO1 system exhibits the highest reflectivity, while the VBr system has the lowest. These results indicate that an O1 vacancy has a significant impact on the Bi4O5Br2 material’s photocatalytic performance. Specifically, an O1 vacancy on its surface can significantly enhance visible light absorption, thereby improving Bi4O5Br2’s photocatalytic performance. On contrast, an O1 vacancy inside the material not only fails to increase light absorption but also increases the recombination probability of electrons and holes, which hinders carrier transport and reduces Bi4O5Br2’s photocatalytic efficiency.

4. Conclusions

Utilizing the DFT theory, we employed the first-principles method to compute the formation energy, electronic structure, effective mass, and optical properties of the Bi4O5Br2 system in the presence of Bi, O, and Br vacancy defects. Following geometric optimization, it was observed that, when vacancy defects were introduced into the pristine Bi4O5Br2 system, a slight crystal lattice distortion occurred. The formation energy calculation revealed that all elemental vacancy defects could exist stably, with the difficulty of forming VBi2, VBi1, VO2, VBr, and VO1 vacancies decreasing in sequence. In its intrinsic state, Bi4O5Br2 exhibited a bandgap of 2.38 eV. The introduction of OVs defects led to the disruption of the Bi-O bond and resulted in a new defect level at the Fermi level due to the 6p orbital of Bi, consequently narrowing the bandgap and enhancing visible light absorption capability. Notably for the VO1 system, the electron effective mass was determined as 0.172, while the hole effective mass was found to be 0.668; this significant difference between electron and hole effective masses aids in reducing the recombination probability, thereby improving the charge carrier separation efficiency. From an optical perspective, the analysis revealed that, within the visible light range, the VO1 system exhibited the highest absorption coefficient and reflectivity, indicating that the presence of surface VO1 defects in the Bi4O5Br2 material can significantly enhance its visible light catalytic performance. In conclusion, our theoretical study not only lays a foundational framework for the design of Bi4O5Br2-based photocatalysts but also significantly advances its potential applications in the field of photocatalysis.

Author Contributions

Conceptualization, B.H. and Y.L.; methodology, Y.Z.; software, F.Z.; validation, Y.Y.; formal analysis, B.H.; writing—original draft preparation, Y.L. and J.L.; writing—review and editing, B.H.; visualization, Y.Y.; supervision, F.Z.; funding acquisition, F.Z., Y.Z. and B.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (No: 62264015), the Basic Research Program of Natural Science of Shaanxi Province (No: 2023-JC-QN-0748), Innovation and entrepreneurship training program for students of Yan’an University (No: D2023202), Doctoral Scientific Research Startup Project of Yan’an University (No: YDBK2021-04), and 2024 Innovation and Entrepreneurship for Undergraduates (No: 202410719052).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

There are no conflicts of interest to declare.

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Figure 1. (a) Side view of the Bi4O5Br2 supercell. (b) Unit cell of Bi4O5Br2. The blue, purple, red, green, and yellow balls represent Bi1 (with a coordination bond of 3), Bi2 (with a coordination bond of 4), O1 (with a coordination bond of 3), O2 (with a coordination bond of 2), and Br atoms, respectively.
Figure 1. (a) Side view of the Bi4O5Br2 supercell. (b) Unit cell of Bi4O5Br2. The blue, purple, red, green, and yellow balls represent Bi1 (with a coordination bond of 3), Bi2 (with a coordination bond of 4), O1 (with a coordination bond of 3), O2 (with a coordination bond of 2), and Br atoms, respectively.
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Figure 2. Band structure: (a) Bi4O5Br2, (b) VO1, (c) VO2, (d) VBr.
Figure 2. Band structure: (a) Bi4O5Br2, (b) VO1, (c) VO2, (d) VBr.
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Figure 3. Calculated total DOS and partial DOS: (a) Bi4O5Br2, (b) VO1, (c) VO2, (d) VBr. The vertical dashed line denotes the Fermi level.
Figure 3. Calculated total DOS and partial DOS: (a) Bi4O5Br2, (b) VO1, (c) VO2, (d) VBr. The vertical dashed line denotes the Fermi level.
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Figure 4. Optical properties: (a) real part of the dielectric function, (b) imaginary part of dielectric function, (c) absorption coefficient, (d) reflection coefficient. The colors of the rainbow correspond to regions of visible light.
Figure 4. Optical properties: (a) real part of the dielectric function, (b) imaginary part of dielectric function, (c) absorption coefficient, (d) reflection coefficient. The colors of the rainbow correspond to regions of visible light.
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Table 1. The calculated structural parameters of Bi4O5Br2 and Bi4O5Br2 with vacancy.
Table 1. The calculated structural parameters of Bi4O5Br2 and Bi4O5Br2 with vacancy.
Modela/Åb/Åc/Åαβγ
Experiment [29]14.5395.60510.78290.0097.7590.00
Unit cell14.5955.65110.93890.0097.9390.00
VBi114.6065.64510.94390.0098.0090.00
VBi214.5945.65110.94190.0098.0190.00
VO114.6215.66010.90290.0097.7990.00
VO214.6005.64710.94390.1698.0090.10
VBr14.5925.65110.93989.9997.9089.98
Table 2. Total energies and formation energies of Bi4O5Br2 with vacancy.
Table 2. Total energies and formation energies of Bi4O5Br2 with vacancy.
ModelEbulk/eVEdefect/eVEf/eV
VBi1 (1 × 1 × 1)−18,819.348−18,020.2199.03
VBi2 (1 × 1 × 1)−18,819.348−18,016.57212.68
VO1 (1 × 1 × 1)−18,819.348−18,383.0482.26
VO1 (2 × 1 × 1)−37,570.360−37,134.0762.24
VO1 (2 × 2 × 1)−75,140.223−74,703.9412.24
VO2 (1 × 1 × 1)−18,819.348−18,379.7055.60
VBr (1 × 1 × 1)−18,819.348−18,353.4092.91
Table 3. The calculated electron effective mass ( m e * ) at the conduction band minimum, the hole effective masses ( m h * ) at the valence band maximum, and the relative ratio of effective masses (D).
Table 3. The calculated electron effective mass ( m e * ) at the conduction band minimum, the hole effective masses ( m h * ) at the valence band maximum, and the relative ratio of effective masses (D).
Species m e * m h * D
Perfect0.1400.4323.086
VBi10.6380.9211.444
VBi20.2250.8813.916
VO10.1720.6683.884
VO20.1840.4822.620
VBr0.1471.0106.871
g-C3N4 [34]3.9297.4
TiO2 [36]0.621.702.74
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Huang, B.; Liu, Y.; Zhang, Y.; Zhang, F.; Yang, Y.; Li, J. Effect of Vacancy Defects on the Electronic Structure and Optical Properties of Bi4O5Br2: First-Principles Calculations. Coatings 2024, 14, 1361. https://doi.org/10.3390/coatings14111361

AMA Style

Huang B, Liu Y, Zhang Y, Zhang F, Yang Y, Li J. Effect of Vacancy Defects on the Electronic Structure and Optical Properties of Bi4O5Br2: First-Principles Calculations. Coatings. 2024; 14(11):1361. https://doi.org/10.3390/coatings14111361

Chicago/Turabian Style

Huang, Baorui, Yeqi Liu, Yanni Zhang, Fuchun Zhang, Yanning Yang, and Jiaxin Li. 2024. "Effect of Vacancy Defects on the Electronic Structure and Optical Properties of Bi4O5Br2: First-Principles Calculations" Coatings 14, no. 11: 1361. https://doi.org/10.3390/coatings14111361

APA Style

Huang, B., Liu, Y., Zhang, Y., Zhang, F., Yang, Y., & Li, J. (2024). Effect of Vacancy Defects on the Electronic Structure and Optical Properties of Bi4O5Br2: First-Principles Calculations. Coatings, 14(11), 1361. https://doi.org/10.3390/coatings14111361

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