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Article

Electronic Structure and Optical Properties of Inorganic Pm3m and Pnma CsPbX3 (X = Cl, Br, I) Perovskite: A Theoretical Understanding from Density Functional Theory Calculations

by
Hamid M. Ghaithan
1,*,
Saif M. H. Qaid
1,
Zeyad A. Alahmed
1,
Huda S. Bawazir
1 and
Abdullah S. Aldwayyan
1,2,*
1
Physics and Astronomy Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
2
King Abdullah Institute for Nanotechnology, King Saud University, Riyadh 11451, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Materials 2023, 16(18), 6232; https://doi.org/10.3390/ma16186232
Submission received: 21 July 2023 / Revised: 19 August 2023 / Accepted: 29 August 2023 / Published: 15 September 2023
(This article belongs to the Section Energy Materials)
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Abstract

:
In this study, we investigated the optoelectronic properties of cubic (Pm3m) and orthorhombic (Pnma) CsPbX3 (X = I, Br, and Cl). We utilized the full potential linear augmented plane wave method, which is implemented in the WIEN2k code, to facilitate the investigation. Different exchange potentials were used to analyze the optoelectronic behavior using the available density functional theory methods. Our findings revealed that CsPbX3 perovskites display direct band gaps at the R and Г points for cubic (Pm3m) and orthorhombic (Pnma) structures, respectively. Among the exchange potentials, the mBJ-GGA method provided the most accurate results. These outcomes concurred with the experimental results. In both Pm3m and Pnma structures, interesting changes were observed when iodide (I) was replaced with bromine (Br) and then chlorine (Cl). The direct band gap at the R and Г points shifted to higher energy levels. Similarly, when I was replaced with Br and Cl, there was a noticeable decrease in the absorption coefficient, dielectric constants, refractive index, and reflectivity, in addition to a band gap shift to higher energy levels.

Graphical Abstract

1. Introduction

Organic–inorganic perovskites have become a focal point in research related to photovoltaics, light-emitting diodes, lasers, and photodetectors [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. The chemical formula for an inorganic halide perovskite is ABX3, where A represents an inorganic monovalent cation (such as Cs), B signifies an inorganic divalent cation (Pb or Sn), and X denotes a halogen anion (I, Br, or Cl) [21]. Numerous researchers have utilized various density functional theory (DFT) methods to understand the optoelectronic properties of organic–inorganic perovskites [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. Local density approximation (LDA) and Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) are the most commonly used methods. These models are preferred because of their low computational cost [37,38,44,45]. However, they struggle to calculate the energy band gap (Eg) and lattice parameters of the studied perovskite owing to the self-interaction error and the lack of a derivative discontinuity for comparing the Kohn–Sham (KS) band gap with the experimental band gap. The Engel–Vosko (EV-GGA) functional, on the other hand, is designed to reproduce the exchange correlation potential rather than the total energy and is useful for calculating band gaps and optical properties while overestimating lattice parameters [35,36,37,38,39,40,41]. An alternative method, the (screen) hybrid functional, offers superior accuracy in terms of Eg but at a higher computational cost [46,47].
Previous research has demonstrated that the modified Becke–Johnson GGA (mBJ-GGA) yields accurate Eg values for a wide range of materials, such as wide-band-gap insulators, semiconductors, and 3d transition-metal oxides. This is due to its additional dependence on kinetic energy density [25,42,43,48,49,50,51,52,53,54,55]. The mBJ-GGA method has been applied to study the optoelectronic properties of cubic (Pm3m), tetragonal (P4mm), and orthorhombic Pnma CsPbBr3 perovskite. The calculated Eg aligns well with the experimental values. Moreover, the modified Becke–Johnson generalized gradient approximation (mBJ-GGA) potential can be used to study the optoelectronic properties of Pm3m and Pnma CsPbX3. The systematic DFT investigation of Pm3m and Pnma CsPbX3 perovskites provides a deep understanding of their crystal structure–property relationships, as well as their potential applications in optoelectronics.
In our study, we investigated the optoelectronic properties of Pm3m and Pnma CsPbX3 (X = I, Br, and Cl) using the accurate mBJ-GGA method, both with and without spin–orbit coupling (SOC). Along with LDA [35], the PBE-GGA [37], Engel–Vosko GGA (EV-GGA) [56], new modified Becke–Johnson GGA (nmBJ-GGA), and unmodified Becke–Johnson GGA (umBJ-GGA) methods were used. These methods were implemented in the WIEN2k code. To validate the DFT calculation, the Eg values were compared with previous experimental and theoretical results. The mBJ-GGA method yielded values that aligned well with the experimental data. This study endeavors to delve into the cubic and orthorhombic crystal systems with a renewed perspective, taking advantage of recent advancements in characterization techniques and computational modeling. The calculated electronic and optical properties show tunable absorption coefficients, dielectric constants, refractive indices, and reflectivity values, as well as charge transport properties, when iodide is replaced with bromine and chlorine within the visible light range. As a result, our findings are critical for furthering research into CsPbX3 perovskite materials’ potential applications in optoelectronic devices such as solar cells, light-emitting diodes, and photodetectors.

2. DFT Methods

In this study, we employed the full potential linear augmented plane wave (FP-LAPW) method within the framework of DFT. This method is incorporated in the WIEN2k code [30,57,58,59] as outlined in our previously published research [42,54,60,61,62]. Our primary focus was to investigate the optoelectronic properties of Pm3m and Pnma CsPbX3 (X = I, Br, and Cl). Therefore, we used the following methods: LDA [44], PBE-GGA [37], mBJ-GGA [48], nmBJ-GGA, umBJ-GGA, and EV-GGA, as shown in Figure 1. The PBEsol method was used to investigate the lattice parameters of the structures. This method more accurately reproduces experimental values, as evidenced by its low relative error values [36]. Considering the heavy lead element present, we included the SOC effect [42,63,64] in the calculation with the mBJ-GGA method. The basis function was expanded to Rmt × Kmax = 9 for all structures. We sampled the Brillouin zones using 12 × 12 × 12 and 14 × 9 × 14 k-point meshes for Pm3m and Pnma CsPbX3, respectively. The total energy converged until it reached <10−4 Ry. Additionally, we introduced the Fourier expansion of the charge density with a maximum of Gmax = 12 (a.u.)−1. Ultimately, we set the RMT of Cs, Pb, I, Br, and Cl atoms at 2.2, 2.5, 2.5, 2.2 and 2.2 a.u., respectively.

3. Results and Discussion

3.1. Structural Properties

The structural properties of Pm3m and Pnma CsPbX3 (X = I, Br, and Cl) perovskites were calculated using the PBEsol approximation method. The lattice parameters of these structures were determined by fitting the Murnaghan equation [65]. Figure 2 shows the variation of energy E(Ry) versus the volume of the studied structures, as per the Murnaghan equation of state [65]. For comparison, Table 1 displays the calculated lattice parameters (a, b, and c), pressure derivatives (B′), and bulk modulus values (B), alongside previously measured and predicted values. For cubic CsPbI3, CsPbBr3, and CsPbCl3, we found the lattice parameters to be 6.262, 5.875, and 5.734 A0, respectively. For orthorhombic CsPbI3, CsPbBr3, and CsPbCl3, the calculated lattice parameters are (a = 8.856, b = 8.576, c = 12.472 A0), (a = 8.161, b = 11.617, c = 8.115 A0), and (a = 7.902, b = 11.248, c = 7.899 A0), respectively. Our calculated data align well with previous measurements and predictions, thus reinforcing the reliability of our computational scheme [22,29,30,33,61,62,66,67,68,69,70].
Visualization for Electronic and Structural Analysis (VESTA 3) was used to obtain the theoretical X-ray diffraction (XRD) [82], as illustrated in Figure 3. When substituting iodide with bromine, and then with chlorine, the diffraction peaks of Pm3m and Pnma CsPbX3 shifted toward higher 2-theta values. Figure 3a shows the XRD pattern of CsPbI3 (Pm3m) with diffraction peaks at 13.89°, 19.62°, 23.97°, 31.33°, 34.19°, 39.79°, 42.37°, 44.69°, 46.99°, and 49.32°. These peaks shifted to 15.80°, 22.34°, 27.52°, 31.87°, 35.84°, 39.40°, 45.77°, 48.69°, 51.64°, and 56.88° for CsPbCl3 (Pm3m). The peaks for orthorhombic CsPbX3 (Pnma) shifted to higher 2-theta values, as depicted in Figure 3b. This shift was also evident when I was replaced with Br and Cl. This shift is caused by a decrease in the unit cell volume of the crystal structure.

3.2. Electronic Properties

The electronic properties of CsPbX3 perovskites can vary depending on their crystal structure [1,2,3,4,5,6,7,8,9,10]. The bandgap (Eg) can be tuned by adjusting the halide component. With increasing halogen atomic number (i.e., Cl < Br < I), the Eg of Pm3m and Pnma decreases. This tunability enables the optimization of solar cell absorption and LED light emission. Pnma CsPbX3 perovskite has a more complex crystal structure than cubic perovskite, and its electronic properties can differ due to structural changes [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. Figure 4a shows the band structure along the (X, R, and Γ) K-points of Pm3m CsPbX3 (X = I, Br, and Cl) using LDA, PBE-GGA, mBJ-GGA, nmBJ-GGA, umBJ-GGA, and EV-GGA, where the top of the valence band was set as 0 eV. The band structure indicated that the valence band maximum (VBM) and the conduction band minimum (CBM) were located at point R structures, resulting in a direct band gap. We also calculated the Pnma CsPbX3 band structure using the same methods as for CsPbBr3, where the VBM and CBM were located at the Γ point with a direct band gap as shown in Figure 4b. As shown in Table 2 and Figure 5, the mBJ-GGA method proved effective at yielding accurate Eg values for both Pm3m and Pnma CsPbX3 perovskite. Given the presence of the heavy lead element in CsPbX3, it was crucial to include the SOC effect to accurately describe the band structures [60,63,64]. The SOC effect caused a drastic change in the electronic band gap, resulting in band gaps of 0.952, 1.53, and 1.69 eV for Pm3m CsPbI3, CsPbBr3, and CsPbCl3, respectively. The band gaps with the SOC effect for Pnma CsPbI3, CsPbBr3, and CsPbCl3 were reduced to 1.189, 1.482, and 2.167 eV, respectively.
The total density of states (TDOS) of both Pm3m and Pnma CsPbX3 was examined to gain insights into the factors influencing Eg trends. We began by calculating the TDOS of CsPbX3 compounds to observe the effect of replacing I with Br and Cl on the Eg trend, as shown in Figure 6. Despite these substitutions, the overall TDOS feature remained consistent, with the DOS edges shifting upward for both the Pm3m and Pnma CsPbX3 compounds. Figure 7 shows the TDOS of the investigated compounds using the mBJ-GGA method, which is known for its accuracy. Furthermore, an upward shift in TDOS was observed for both the Pm3m and Pnma CsPbX3 compounds.
To provide a more detailed analysis, we calculated the partial density of states (PDOS) for Pm3m CsPbI3 as an example. As shown in Figure 8, Cs + does not influence the VBM but instead contributes to maintaining overall load neutrality and structural stability [22,26,28,42,63,102,103,104]. The VBM primarily stems from I p orbitals, supplemented by contributions from Pb s orbitals. The CBM is formed primarily by Pb p states, with minor contributions from I s and p states.

3.3. Optical Properties

The optical properties of perovskites, specifically Pm3m and Pnma CsPbX3, play a crucial role in determining their performance in solar cells, light-emitting diodes (LEDs), and photodetector devices. The dielectric functions ε1(ω) and ε2(ω), which describe a material’s response to incident photons as a function of energy, are depicted in Figure 9. The static frequency ε1(0) represents the real part of the dielectric function ε1(ω) value at zero frequency, and it ranges between 3.02 and 4.60. The radiation absorbed by the compound [105] is represented by ε2(ω), with main peaks appearing between 3.51 and 5.50 eV. Notably, ε2(ω) remains at zero until photon energy reaches the band gap energy, indicating the onset of direct optical transition between the VBM and the CBM.
Figure 10 depicts the calculated absorption coefficient α(ω) using the mBJ-GGA method, which determines a light absorber’s ability to harvest solar energy. Moreover, α(ω) is plotted against energy (0–10 eV) for the Pm3m and Pnma CsPbX3 compounds. The absorption edge shifted upward to a higher energy side when I was replaced with Br and Cl for both Pm3m and Pnma CsPbX3. A complex absorption and dielectric spectrum with multiple peaks can result from the combination of excitonic effects, band-to-band transitions, quantum confinement, phonon modes, defects, and anharmonic effects in CsPbX3 perovskite materials. The specific energies and intensities of these peaks can provide important information about the material’s electronic and structural properties, which are important for understanding its behavior and optimizing its performance in various applications. These perovskites exhibit strong light absorption across a broad range of energy, including the visible and near-infrared regions. This high absorption coefficient is attributed to the strong interaction between the lead (Pb) and halogen (X) atoms, which leads to efficient absorption of photons [24,25,26,27,28,29,30,31,32,33,34]. The broad absorption range of these compounds indicates their potential applications in various optical and optoelectronic devices operating within this range.
The refractive index n(ω) was calculated using the mBJ-GGA method as shown in Figure 11. n(ω) is a critical feature of semiconductors, indicating the degree to which light is refracted or bent [105]. As the energy increases, the value of n(ω) increases until it reaches 2.74, 2.34, and 2.14 eV for Pm3m, CsPbI3, CsPbBr3, and CsPbCl3, respectively, and 2.72, 2.40, and 2.14 eV for Pnma CsPbI3, CsPbBr3, and CsPbCl3, respectively. Beyond this point, it starts to fluctuate, exhibiting nonlinear behavior. The calculated n(0) values were 2.138, 1.88, and 1.74 eV for Pm3m CsPbI3, CsPbBr3, and CsPbCl3 and 2.14, 1.96, and 1.76 eV for Pnma CsPbI3, CsPbBr3, and CsPbCl3, respectively.
The calculated reflectivity R(ω) in relation to incident energy is shown in Figure 12. At zero frequency, Pm3m CsPbI3 has a static reflectivity R(0) value of 0.132, which then decreases to 0.096 and 0.073 for Pm3m CsPbBr3 and CsPbCl3, respectively. Similarly, the R(0) value of Pnma CsPbI3 decreases from 0.132 to 0.106 and 0.077 for Pnma CsPbBr3 and CsPbCl3, respectively. By increasing the energy, R(ω) starts to increase in the 3–5 eV range before beginning to fluctuate and decrease at higher energies. The optical properties of Pnma CsPbX3 perovskites are clearly similar to those of cubic perovskites. They also have tunable optical bandgaps due to their halide composition [24,25].

4. Conclusions

In summary, this study investigated the optoelectronic properties of Pm3m and Pnma CsPbX3 (X = I, Br, and Cl) perovskite, using different approximation methods in DFT. We used the PBEsol method to calculate the lattice parameters, which were found to align well with the measured and previously predicted values, demonstrating the reliability of our computational scheme. We also calculated the electronic band structure and optical properties of CsPbX3 perovskite using different density functional theory methods. The band gap values obtained using the mBJ-GGA method were closely aligned with experimental values. Both Pm3m and Pnma CsPbX3 presented direct band gaps at the R and Г points. When I was replaced with Br and then Cl in Pm3m and Pnma CsPbX3, the direct band gap located at the R and Г points shifted to higher energy levels. This replacement also resulted in a decrease in the absorption coefficient, dielectric constant, refractive index, and reflectivity, along with a band gap shift to higher energy.

Author Contributions

Conceptualization, H.M.G. and Z.A.A.; methodology, H.M.G. and Z.A.A.; software, H.M.G. and Z.A.A.; validation, Z.A.A. and A.S.A.; formal analysis, H.M.G., Z.A.A., S.M.H.Q. and A.S.A.; investigation, H.M.G., Z.A.A., H. S. B., S.M.H.Q. and A.S.A.; writing—original draft preparation, H.M.G.; writing—review and editing, H.M.G., Z.A.A., A.S.A., H.S.B. and S.M.H.Q.; supervision, A.S.A. and Z.A.A.; funding acquisition, A.S.A. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Ministry of Education” in Saudi Arabia (IFKSUDR_E166).

Acknowledgments

The authors extend their appreciation to the Deputyship for Research & Innovation, “Ministry of Education” in Saudi Arabia for funding this research work through the project number (IFKSUDR_E166).

Conflicts of Interest

The authors declare no conflict of interest.

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Materials 16 06232 g001
Figure 1. DFT approximation methods used to calculate the optoelectronic properties of Pm3m and Pnma perovskite structures.
Figure 1. DFT approximation methods used to calculate the optoelectronic properties of Pm3m and Pnma perovskite structures.
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Materials 16 06232 g002
Figure 2. Variation of the energy E(Ry) versus the volume for Pm3m and Pnma CsPbX3(X = I, Br, and Cl) using the PBEsol method.
Figure 2. Variation of the energy E(Ry) versus the volume for Pm3m and Pnma CsPbX3(X = I, Br, and Cl) using the PBEsol method.
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Materials 16 06232 g003
Figure 3. X-ray diffraction patterns for (a) cubic and (b) orthorhombic CsPbX3 (X = I, Br, and Cl) perovskites. Inset: crystal structures of perovskites.
Figure 3. X-ray diffraction patterns for (a) cubic and (b) orthorhombic CsPbX3 (X = I, Br, and Cl) perovskites. Inset: crystal structures of perovskites.
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Materials 16 06232 g004
Figure 4. Band structure of Pm3m and Pnma CsPbX3 (X = I, Br, and Cl) perovskites obtained using LDA, PBE, mBJ, umBJ, and nmBJ potentials.
Figure 4. Band structure of Pm3m and Pnma CsPbX3 (X = I, Br, and Cl) perovskites obtained using LDA, PBE, mBJ, umBJ, and nmBJ potentials.
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Materials 16 06232 g005
Figure 5. Band gaps (Eg) of cubic and orthorhombic CsPbX3 calculated using various functional methods and compared to experimental Eg values.
Figure 5. Band gaps (Eg) of cubic and orthorhombic CsPbX3 calculated using various functional methods and compared to experimental Eg values.
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Materials 16 06232 g006
Figure 6. Total density of states of Pm3m and Pnma CsPbX3 perovskite in the range −0.7 to 2.5 eV using the LDA, PBE-GGA, mBJ-GGA, nmBJ-GGA, umBJ-GGA, and EV-GGA methods.
Figure 6. Total density of states of Pm3m and Pnma CsPbX3 perovskite in the range −0.7 to 2.5 eV using the LDA, PBE-GGA, mBJ-GGA, nmBJ-GGA, umBJ-GGA, and EV-GGA methods.
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Materials 16 06232 g007
Figure 7. Total density of states of Pm3m (left) and Pnma (right) CsPbX3 perovskite in the range −0.7 to 2.5 eV using the mBJ-GGA method.
Figure 7. Total density of states of Pm3m (left) and Pnma (right) CsPbX3 perovskite in the range −0.7 to 2.5 eV using the mBJ-GGA method.
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Materials 16 06232 g008
Figure 8. Calculated PDOS of Pm3m CsPbI3 with various doping concentrations (x) using the mBJ-GGA method.
Figure 8. Calculated PDOS of Pm3m CsPbI3 with various doping concentrations (x) using the mBJ-GGA method.
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Materials 16 06232 g009
Figure 9. Calculated real dielectric function (left) and imaginary dielectric function (right) of Pm3m and Pnma CsPbX3 using the mBJ-GGA method.
Figure 9. Calculated real dielectric function (left) and imaginary dielectric function (right) of Pm3m and Pnma CsPbX3 using the mBJ-GGA method.
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Materials 16 06232 g010
Figure 10. Absorption coefficient α(ω) of Pm3m and Pnma CsPbX3 using the mBJ-GGA method.
Figure 10. Absorption coefficient α(ω) of Pm3m and Pnma CsPbX3 using the mBJ-GGA method.
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Materials 16 06232 g011
Figure 11. Calculated refraction index values of Pm3m and Pnma CsPbX3 using the mBJ-GGA method.
Figure 11. Calculated refraction index values of Pm3m and Pnma CsPbX3 using the mBJ-GGA method.
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Materials 16 06232 g012
Figure 12. Calculated reflectivity of Pm3m and Pnma CsPbX3 using the mBJ-GGA method.
Figure 12. Calculated reflectivity of Pm3m and Pnma CsPbX3 using the mBJ-GGA method.
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Table 1. Lattice parameters (a, b, and c), pressure derivatives (B′), and bulk modulus values (B, GPa) for the studied halide perovskites using the PBEsol method.
Table 1. Lattice parameters (a, b, and c), pressure derivatives (B′), and bulk modulus values (B, GPa) for the studied halide perovskites using the PBEsol method.
Lattice ParametersCsPbI3CsPbBr3CsPbCl3
Pm3m
a = b = c		PnmaPm3m
a = b = c		PnmaPm3m
a = b = c		Pnma
This study6.262a = 8.856
b = 8.576
c = 12.472		5.875
5.740 [71]		a = 8.161
b = 11.617
c = 8.115		5.734a = 7.902
b = 11.248
c = 7.899
Other DFT6.25 [33]
6.39 [29]
6.38 [30]
6.05 [23]
6.40 [33,72]		a = 8.87 [31]
b = 8.54 [31]
c = 12.45 [31]		5.8445 [73]
5.874 [74]		a = 8.376 [67]
b = 11.497 [67]
c = 7.617 [67]
a = 8.251 [66]
b = 11.753 [66]
c = 8.203 [66]
a = 8.250 [68]
b = 11.70 [68]
c = 8.210 [68]		5.61 [70]
5.73 [24]
5.49 [23]
5.605 [75,76]		7.973 [61]
11.355 [61]
7.916 [61]
Other exp.6.177 [77]
6.28 [78]
6.33 [30]
6.297 [79]		a = 8.856 [80]
b = 8.576 [80]
c = 12.472 [80]
a = 8.646 [81]
b = 8.818 [81]
c = 12.520 [81]		 a = 8.260 [73]
b = 11.765 [73]
c = 8.212 [73]		 7.90193 [66]
11.24778 [66]
7.89928 [66]
7.97613 [61]
11.35674 [61]
7.91729 [61]
B (GPa) 17.8520.74
20.73 [62]		22.6524.21
22.59 [69]
25.447 [22]
26.33 [70]		25.62
B′ 4.3574.88
4.9 [62]		5.5915.01
4.33 [69]
4.4 [22]		5.654
Table 2. Band gaps (Eg) of Pm3m and Pnma inorganic perovskites calculated using the LDA, PBE-GGA, EV-GGA, PBEsol-GGA, and umBJ-GGA methods and compared to those from previous experimental and theoretical studies.
Table 2. Band gaps (Eg) of Pm3m and Pnma inorganic perovskites calculated using the LDA, PBE-GGA, EV-GGA, PBEsol-GGA, and umBJ-GGA methods and compared to those from previous experimental and theoretical studies.
DFT Approximation MethodCsPbI3CsPbBr3CsPbCl3
Pm3mPnmaPm3mPnmaPm3mPnma
LDA1.38--1.591.652.01--
PBE1.39
0.207mBJ+ SOC		1.651.751.782.212.19
umBJ-GGA1.65--1.992.002.49--
EV-GGA1.71--2.102.162.69--
nmBJ-GGA1.99--2.682.583.61--
mBJ-GGA1.93
0.952mBJ + SOC		2.11
1.189mBJ + SOC		2.43
1.53mBJ + SOC		2.44
1.482mBJ + SOC		3.22
1.69mBJ + SOC		3.29
2.167mBJ + SOC
Others_DFT1.45_PBE [54]
1.90_mBJ [54]
1.56 [33]
1.48 [83]
1.11 [23]
1.359 [30]
1.831 [31,84]		1.983_mBJ [60]
1.831 [31,84]
1.48 [83]		1.77_PBE [54]
2.50_mBJ [54]
1.79 [26]
2.00 [85]
1.75 [25]
2.35 [25]
1.12 [23]
1.76 [30]
2.63 [30]		2.32 [86]
2.40 [84]
2.420_mBJ [60]		2.20_PBE [26,87]
2.829_KTB-mBJ [28]
2.92_HSE [24]
3.406_PBE [22]
2.88_GW [71]		3.05 [29]
3.325 [60]
Others_Exp.1.87 [88]
1.792 [89]
1.85 [61]
1.75 [68]		1.75 [68]
1.85 [61]		2.30 [90]
2.36 [20]
2.32 [91]
2.282 [92]		2.38 [93]
2.479 [61]
2.25 [94]
2.252 [95]
2.36 [96]
2.24 [96]
2.20 [97]
2.32 [98]		3.00 [90]
2.97 [99]
3.04 [100]
2.98 [96]		2.91 [66]
2.78 [101]
3.132 [61]
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MDPI and ACS Style

Ghaithan, H.M.; Qaid, S.M.H.; Alahmed, Z.A.; Bawazir, H.S.; Aldwayyan, A.S. Electronic Structure and Optical Properties of Inorganic Pm3m and Pnma CsPbX3 (X = Cl, Br, I) Perovskite: A Theoretical Understanding from Density Functional Theory Calculations. Materials 2023, 16, 6232. https://doi.org/10.3390/ma16186232

AMA Style

Ghaithan HM, Qaid SMH, Alahmed ZA, Bawazir HS, Aldwayyan AS. Electronic Structure and Optical Properties of Inorganic Pm3m and Pnma CsPbX3 (X = Cl, Br, I) Perovskite: A Theoretical Understanding from Density Functional Theory Calculations. Materials. 2023; 16(18):6232. https://doi.org/10.3390/ma16186232

Chicago/Turabian Style

Ghaithan, Hamid M., Saif M. H. Qaid, Zeyad A. Alahmed, Huda S. Bawazir, and Abdullah S. Aldwayyan. 2023. "Electronic Structure and Optical Properties of Inorganic Pm3m and Pnma CsPbX3 (X = Cl, Br, I) Perovskite: A Theoretical Understanding from Density Functional Theory Calculations" Materials 16, no. 18: 6232. https://doi.org/10.3390/ma16186232

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