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Abstract
In this study, using density functional theory, we calculated the band structure and photoelectric properties in a series of 12.5% B-doped (B = Ge, Sn, Ca, and Sr) CsPbI3 perovskite systems. It is found that Ge doping can improve the structural stability and is more conducive to applications under high-pressure or by applying stress via calculating the bond length, formation energy, elastic properties, and electronic local function. In addition, the optimal direction for applying stress is achieved according to the elastic properties. Furthermore, in terms of electronic properties, the reason of energy band variation and the influence of chemical bond on the structural stability of doped α-CsPbI3 are investigated. The possibility of the applications of the CsPb0.875B0.125I3 perovskite is explored based on the optical properties. Thus, the theoretical study of the CsPb0.875B0.125I3 perovskite provides novel insights into the design of next-generation photoelectric and photovoltaic materials.
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1. Introduction
As a new semiconductor material, cesium lead halide perovskite CsPbX3 (X = Cl, Br, or I) has attracted considerable attentions owing to its excellent photoluminescence quantum yield (PLQY), adjustable band gap, and excellent charge transport characteristics [1–5]. CsPbI3 has four polymorphs: cubic (α-CsPbI3), tetragonal (β-CsPbI3), and orthorhombic (γ-CsPbI3 and δ-CsPbI3). In particular, α-CsPbI3 has a narrow direct band gap (1.73 eV); thus, it is an ideal candidate for designing photoelectric devices in the visible range [6]. However, the high-temperature phase instability and Pb toxicity considerably limit the wide application of α-CsPbI3 [7]. Therefore, the improvement in the stability and the reduction in toxicity are the internal requirements of enhancing the applications of α-CsPbI3 perovskite in different fields. For this purpose, doping engineering is proposed to replace the Pb atom with one or more nontoxic or low-toxic elements in experimental and theoretical studies [8,9].
Multiple nontoxic or less toxic elements have been successfully doped in α-CsPbI3 [10–13]. First, Ge and Sn are selected for doping because their electronic structures are similar to that of Pb. α-CsPb0.8Ge0.2I3 was synthesized and annealed at 90 °С; this temperature was considerably lower than that required to produce the α-CsPbI3 perovskite (320 °С) [10]. The α-CsPb0.8Ge0.2I3 perovskite demonstrated a power conversion efficiency (PCE) of 3.97% and good external quantum efficiency values of 40%–70%, indicating it had good photovoltaic properties. At room temperature, the CsPb0.95Sn0.05I3-based perovskite solar cells with SnO2 as the electron transport material and CuI as the transport material had a maximum PCE of 6.71%, which was higher than that of the pure δ-CsPbI3 based perovskite solar cells [11]. Moreover, Ca and Sr are considered as dopants because they have stable bivalent states and are easy to synthesize. Wu et al. demonstrated that α-CsPbI3 nanocrystals doped with Ca had an excellent PLQY of 96.6% [12]. Furthermore, it exhibited excellent stability under ambient conditions for nine months and UV illumination for 32 h. The Sr-doped α-CsPbI3 quantum dots were able to retain high photoluminescence, and the fabricated red light-emitting diodes exhibited high brightness (1250 cd m−2 at 9.2 V) and good operational stability (half time > 2 h driven by 6 V) [13]. The above-mentioned experiments demonstrated that the doping of non-toxic or low-toxic elements can not only improve the photovoltaic and photoelectronic properties of α-CsPbI3 but also enhance their potential applications.
To examine the influence of doping elements on the properties of perovskites, multiple theoretical studies have been conducted using the first-principles method based on density functional theory (DFT). Yang et al. investigated the structural and electronic properties of alkaline-earth metal (Ba, Sr, Ca, and Mg)-doped α-CsPbI3 and demonstrated that Mg doping decreased the band gap of α-CsPbI3 and was suitable for the improved solar cell systems [14]. Wang et al. theoretically calculated the dopant concentration in the mixed Pb/Sn perovskites, CsPb1−xSnxI3 (x = 0-1), and discovered that with increase in x, the band gaps of mixed perovskites had a monotonous decrease and the absorption demonstrated a redshift [15]. The above-mentioned results provide theoretical guidance for experiments.
To explore the effects of doping elements (Ge, Sn, Ca, and Sr) on the stability and photoelectric properties of perovskites, we systematically studied the doping systems (CsPb0.875B0.125I3, B = Ge, Sn, Ca, and Sr) using the first-principles method. The structural stability is investigated by calculating the bond length, formation energy, elastic properties, and electronic local function. By studying the electronic properties, the change in energy band before and after B-doping and the influence of electron distribution on its stability are discussed. In addition, the applications under high pressure or applying stress are studied according to the elastic properties. Finally, we also analyze the application of different doping systems (CsPb0.875B0.125I3, B = Ge, Sn, Ca, and Sr) by calculating optical properties. This work provides theoretical guidance for doping experiments in future.
2. Computational model and method
Herein, the first-principles calculation was based on DFT [16]. The calculation method was the all-electron-like projector augmented wave method and the exchange-correlation potential realized by Perdew–Burke–Ernzerhof (PBE) in the Vienna Ab Initio Simulation Package (VASP) [17]. The generalized gradient approximation (GGA) and PBE functions were used to calculate the structure, and the optimized crystal structure, electronic properties, and optical properties were obtained. The cut-off energy of the plane wave was set to 500 eV. All atoms can relax until the Hellmann–Feynman forces reach the convergence criterion of < 0.01 eV Å−1. The convergence threshold of energy was set at 10−5 eV. For structural optimization, the k-points were set to 3 × 3 × 3. All the calculated band structures are along five symmetry k-points: X (0 0.5 0), R (0.5 0.5 0.5), M (0.5 0.5 0), Γ (0 0 0), and X (0 0.5 0). The band structures were determined considering the spin-orbit coupling (SOC) interaction. For the mechanical properties, elastic constants have been calculated using stress-strain method [18]. Moreover, the crystal structure was visualized using VESTA.
3. Results and discussion
3.1 Structural properties
First, we calculated the protocell structure of CsPbI3. The calculated lattice constant of α-CsPbI3 is 6.375 Å, almost equal to the experimental value of 6.289 Å [19]. GGA calculations always overestimate structural optimization by ∼1%, and therefore these slight differences are within the acceptable range. Then, the α-CsPbI3 protocell structure was expanded to construct the CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr) supercell, as shown in Fig. 1. The ionic radii of the doped elements increase in the order of Ge, Ca, Sn, and Sr with the values of 0.73, 1.00, 1.12, and 1.18 Å, respectively. Because the radius of the doped ion differed from that of the Pb ion (1.19 Å), the crystal structure changed somewhat after doping. Thus, we calculated the lattice constants of α-CsPbI3 before and after doping. As shown in Table 1, the lattice constants of doping systems (B = Ge, Sn, Ca, and Sr) are 6.34, 6.374, 6.371, and 6.40 Å. In general, the smaller the ionic radius of the doped element, the more the lattice constant decreases. When the size of the doping ions is similar to the radius of the Pb ion, the lattice constant changes by a small magnitude and vice versa. This phenomenon has already been experimentally proved [10–13].
Table 1. Lattice parameters, calculated tolerance (t), and octahedral factors (μ) of α-CsPbI3 and CsPb0.875B0.125I3 (B = Ge, Ca, Sn, and Sr).
To explore the influence of doped elements on the internal crystal structure, we calculated the change in the bond length and octahedron before and after doping. Before doping, the Pb–I bond length was 3.19 Å and PbI6 had a regular octahedral structure. After elemental doping, we calculated the octahedron structures of BI6 and PbI6 at different positions in CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr). For the doped BI6 octahedral structure, all the B–I bond lengths are identical, and therefore it has a regular octahedral structure. However, the PbI6 octahedral structure changes at different positions. We calculated the PbI6 octahedral structure and Pb–I bond length at bit 1, bit 2, and bit 3 (labeled 1, 2, and 3 in Fig. 1). The calculation results are demonstrated in Fig. S1 and S2 in the Supplement 1. The octahedron closest to the doping point is squeezed because the doping elements affect the orbital overlap of the B–X bond. With the increase in the distance from the doped point, the octahedral structure returns to the regular octahedral structure. Moreover, the doping element affects the length change of Pb–I. The Pb–I bond lengths of the doping systems (Ge, Sn, Ca, and Sr) at position 3 are 3.175, 3.186, 3.187, and 3.20 Å, respectively. The reduction in bond length confirms the enhancement of bond strength and stability. Hence, the results show that Ge doping improves the stability of α-CsPbI3 among the four doped elements.
As per the calculated results of the bond lengths, introducing doping elements resulted in structural changes. The tolerance factor (t) and octahedral factor (μ) are generally calculated to predict structural stability [20]. In the inorganic Pb-based perovskite α-CsPbI3, B-site atom Pb and halogen atom I form an octahedral structure. Goldschmidt et al. proposed a tolerance factor (t) to evaluate whether site A can stabilize the framework that shares the octahedron [BI6]4−. The octahedral factor (μ) can then be used to evaluate the compatibility between the B cations of the I anions sublattice and the octahedral holes. The expressions of the tolerance factor and octahedral factor are $t = \frac{{({R_A} + {R_I})}}{{\sqrt 2 ({R_B} + {R_I})}}$, $\mu = \frac{{{R_B}}}{{{R_A}}}$, respectively, where RA, RB, and RI are the ionic radii of elements A (Cs), B (Ge, Sn, Ca, and Sr), and I, respectively. When t and μ meet the following conditions, 0.8 ≤ t ≤ 1.0 and 0.41 ≤ μ ≤ 0.73, we can predict whether CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr) can retain the perovskite structure [21]. The tolerance and octahedral factors of α-CsPbI3 were 0.807 and 0.541, respectively. When the tolerance factor tended to have high values, the structure tended to be considerably stable. Ge, Sn, Ca, and Sr doping increased the tolerance factor to a certain degree; Ge doping increased it the most. The tolerance factor of CsPb0.875Ge0.125I3 was 0.821. The doping of Ge, Sn, Ca, and Sr can retain the original structure of α-CsPbI3 perovskite, and Ge doping is more conducive to increase structural stability among the four doped elements.
3.2 Stability properties
The structural changes of the halide perovskites have been explored using lattice parameters and bonding lengths. The structural stability has been determined by the calculation of tolerance factor and octahedral structure; however, the structural stability changes and the application changes of materials cannot be completely evaluated. Therefore, we calculated the stability using the formation energy and the elastic constants to estimate the mechanical properties of the structures.
3.2.1 Formation energy
When designing a new material, material stability is first evaluated. If the material is unstable, the subsequent performance analysis will be meaningless. In this section, we calculated the stability of the material using the formation energy, which estimates whether the structure can be experimentally synthesized and whether it was stable. When the formation energy (Ef) is negative, the structure can be stable. A negative value of Ef indicates a stable perovskite. Thus, we calculated the formation energy before and after doping, respectively. The formulas for calculating the formation energy are as follows [22]:
where E(CsI), E(PbI2), and E(BI2) are the energies of CsI, PbI2, and BI2, respectively; E(CsPbI3) is the energy of α-CsPbI3 undoped system; and E(CsPb0.875B0.125I3) is the energy of α-CsPbI3 doped system where B (Ge, Sn, Ca, and Sr) is replaced with Pb. Because the temperature of VASP is 0 K, the contribution of structure entropy is little. Therefore, the contribution of entropy to the total formation energy is ignored in the calculation. Gibbs free energy is equal to enthalpy.The calculated results are shown in Table 2. The formation energy of α-CsPbI3 is −0.528 eV, and the energies of the doped CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr) are −0.745, −0.488, −0.577, and −0.458 eV, respectively. According to the calculated results, Ge has the lowest formation energy among the four doping elements. We then calculated the formation energies for different doping concentrations from 5.56% to 25%, as shown in Table S1 of the Supplement 1. All the formation energies of CsPb1−xBxI3 (B = Ge, Sn, Ca, and Sr) are negative, indicating that these structures are stable. Among them, the formation energy of Ge doping is smaller than that of the other dopants, which indicated that Ge doping is the most stable.
Table 2. Calculated formation energy Ef (eV), elastic constant (Cij), bulk modulus (B), shear modulus (G), Young’s modulus (E), Pugh’s ratio (B/G), and Poisson’s ratio of α-CsPbI3 and CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr).
3.2.2 Elastic properties
The elastic constant describes the stiffness of a crystal in response to external strain, which can reflect the mechanical stability of the structure [23,24]. Within the linear deformation range of the material (when the strain is small), the stress and strain of the system agree with Hooke’s law. The law states that for a sufficiently small deformation, the stress is proportional to the strain; i.e., the stress component is a linear function of the strain component, and the elastic stiffness constant of 3D materials is 6 × 6 matrix (Cij, i and j = 1–6), which is related to the structural symmetry (Eqs S1 and S2 in the Supplement 1). The cubic crystal system α-CsPbI3 has only three required constants: C11, C12, and C44. We calculated the elastic constants and elastic modulus of the structures using GGA. Table 2 shows the values of the elastic constant and elastic modulus. The structure is stable when the elastic constants meet Born’s stability restrictions. Born’s stability restrictions of the cubic phase are as follows [25]:
As per the elastic constant, we calculated the elastic modulus that can measure the toughness and brittleness of the material structure, including the bulk modulus (B), shear modulus (G), Young’s modulus (E), Pugh’s ratio (B/G), and Poisson’s ratio (ν) (see Eqs S3–S8 in the Supplement 1). By calculating the elastic modulus, CsPb0.875Ge0.125I3 has the strongest strength and certain compressive resistance. Compared with the other three doped perovskite structures, the Ge-doped structure is more conducive to applications under high-pressure or by applying stress. The specific analysis is as follows.
The bulk modulus is an index to determine the strength or hardness of the crystal, representing the strength of the crystal against brittleness. The smaller the bulk modulus, the easier the crystal is to compress. As per the volume modulus listed in Table 2, the bulk moduli of doped crystals are reduced, and CsPb0.875Sr0.125I3 has the smallest bulk modulus. Thus, the crystal compressibility order is CsPb0.875Ge0.125I3 < CsPb0.875Ca0.125I3 < CsPb0.875Sn0.125I3 < CsPb0.875Sr0.125I3. This shows that CsPb0.875Ge0.125I3 has the strongest anticompressibility. The shear modulus proves the strength of the crystal to the plastic deformation. We can use the ratio of the volume modulus to the shear modulus, Pugh’s ratio, to evaluate the softness or brittleness of the substance. When B/G > 1.75, the crystal is ductile; when B/G < 1.75, the crystal is brittle [26]. The Pugh’s ratio of α-CsPbI3 is 2.31, indicating the toughness of α-CsPbI3. After doping the four elements, the Pugh’s ratio varied from 2.18 to 2.26, indicating that the doped material could maintain toughness.
Young’s modulus indicates the degree of resistance a material offers to longitudinal tension. We calculated Young’s modulus (E) of undoped α-CsPbI3 according to Equation S5 in the Supplement 1 and compared it (17.75 GPa) with the result of others (17.79 GPa) [23]. Moreover, we calculated the 3D and 2D Young’s modulus, as shown in Fig. 2. Figure 2 shows the 3D and 2D Young’s modulus of α-CsPbI3, which presents that the mechanical properties of α-CsPbI3 are anisotropic. To examine the situation of the Young’s modulus of α-CsPbI3, we chose the [−0.58 −0.58 0] and [1 0 0] planes for projection. The Young’s modulus of α-CsPbI3 has a maximum and minimum value of 34.8 and 10.1 GPa, respectively. According to the results of Fig. S3 in the Supplement 1, the minimum value of Ge-doped Young’s modulus is 10.9 GPa, larger than the other three doped structures. Therefore, Ge doping improved the stiffness of α-CsPbI3. Figure 2(c) shows the projection of Fig. 2(a). We can be found that the maximum is along the direction of Pb-I bond. The other four doping systems also show this phenomenon in the Supplement 1. This is because the value of Young’s modulus is related to the strength of bonds between atoms. The Pb-I bond is the strongest, the Young’s modulus in this direction is the largest. Therefore, when applying stress in the experiment, we can choose along the direction.
Fig. 2. (a) 3D surfaces of Young’s modulus (E) of undoped α-CsPbI3. 2D polar plots of E for α-CsPbI3 projected normal to (b) the [−0.58 −0.58 0] plane and (c) [1 0 0] plane.
Poisson’s ratio is another index to examine the ductility and brittleness of a material. Generally, a solid is ductile when Poisson’s ratio is > 0.26. The larger the Poisson’s ratio, the higher the ductility. The Poisson’s ratio of undoped α-CsPbI3 is 0.311, indicating that these materials have certain ductility. Compared with Poisson’s ratio of the four elements, Ca doping improved the ductility of the material, namely, toughness.
3.3 Electronic properties
3.3.1 Band structure
Because doping will change the electronic level, we calculated the energy band, the density of states (DOS), and the electronic localization function. For a solar cell absorber, a suitable band gap to completely absorb photons in the visible light of the solar spectrum is a very important criterion. Therefore, we calculated the energy band before and after doping of α-CsPbI3. Because of the spin effect of the Pb atom, we considered the SOC effect, which greatly reduces the band gap, as shown in Table 3. The doping of Ca and Sr increases the band gap of α-CsPbI3, whereas the doping of Ge and Sn shows the opposite trend. Furthermore, Rongjian et al. demonstrated the variation of the calculated bandgap using HSE06 [27], confirming that our calculation is credible. These changes have been experimentally confirmed [10–13]. Based on previous studies, semiconductor solar cells with an optimum band gap of 1.34 eV may have the greatest efficiency. Based on the previous studies, semiconductor solar cells with an optimum band gap of 1.34 eV may have the great efficiency14. Therefore, the proper doping of Ge or Sn can improve the efficiency of α-CsPbI3 solar cells by reducing the band gap. Figure 3 shows the band structures without considering the SOC. The changes in the band structures demonstrate that the highly symmetric point of the band changes from R to Γ after doping. Energy bands are then formed by splitting energy levels, reflecting the interaction between atomic orbitals. The change in the energy band with high symmetry points shows that the atomic orbitals overlap of CsPb0.875B0.125X3 (B = Ge, Sn, Ca, and Sr) is different from undoped α-CsPbI3. In the following, we calculated DOS to explain this difference.
Table 3. Calculated band gaps using PBE (GGA) and PBE (SOC) methods
3.3.2 Density of states
To investigate the change in the band structure, we calculated the DOS of the structure. DOS reflects the contribution of atomic orbitals at different energies in the energy band. Figure 4 shows the calculated total DOS (TDOS) and partial DOS (PDOS). Cs element just donates one electron to neutralize the charge in materials and contributes little to DOS. The DOS diagram of α-CsPbI3 demonstrates that the top of the valence band is contributed by the orbitals of I-p and Pb-s, and the bottom of the conduction band is primarily contributed by the orbitals of Pb-p. The orbital contribution of each element after doping shows that the contribution of Ge and Sn is similar to that of Pb. The orbital coupling between Ge-p/Sn-p and Pb-p occurs at the bottom of the conduction band (CBM), thus causing a reduction in the CBM. The contribution of alkaline-earth metals Sr and Ca to CBM and the top of the valence band is very weak, but the d orbitals of alkaline-earth metals contribute at ∼4 eV, which is large, indicating that they affect the atomic orbital overlap at a local location of the conduction band. Thus, it makes the conduction band move up, increasing the band gap value.
Fig. 4. The state density of (a) protocell CsPbI3 and (b–e) supercell CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr).
3.3.3 Charge analysis
The changes in charge density can explore the change in chemical bonds in the structure to understand the macrochange of the structure. First, Fig. 5(a–e) shows the differential charge density diagram of α-CsPbI3 and CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr), thus demonstrating the charge accumulation and depletion before and after doping. Yellow and blue are the accumulation and dissipation of charges, respectively. Charge accumulation occurs near the Pb, B-doped, and I atoms, while charge dissipation occurs near the Cs atom. In α-CsPbI3, the strength of the binding force between Pb and I is greater than that of other positions in space. Furthermore, this explains the reason for the largest Young’s modulus in the Pb–I bond direction. To examine the electron variation, we calculated the electron local function diagram of the structure.
Fig. 5. Charge density diagram of (a) CsPbI3 and (b–e) CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr), the electron local function diagram of (f) CsPbI3 and (g–j) CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr).
Figure 5(f–j) shows the electron local function (ELF) diagram of α-CsPbI3 and CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr). The ELF diagram shows the distribution of electrons in space and can distinguish the covalent, ionic, and metallic bonds. The formula for ELF is as follows [28]:
3.4 Optical properties
The optical properties of perovskite materials can provide theoretical guidance for their applications in solar cells and other photoelectronic fields. Moreover, based on the optical properties, the structure of the materials and the electron transition between different bands can be analyzed.
Important optical properties were calculated, including the real and imaginary parts of complex dielectric functions, light absorption, reflectivity, refractive index, and extinction coefficient. The expression of light absorption coefficient, reflectivity, refractive index, and extinction coefficient of the material is as follows:
Fig. 6. Calculated optical constants of undoped α-CsPbI3 and CsPb0.875B0.125I3 (B = Ge, Sn, Ca, and Sr). (a) The imaginary parts of complex dielectric functions, (b) absorption coefficient, (c) extinction coefficient, (d) the real parts of complex dielectric functions, (e) reflectivity, and (f) refractive index.
In Fig. 6(d), the real part of the complex dielectric function ${\varepsilon _1}(\omega )$ is shown. In the real part, the most important property is the static dielectric function ${\varepsilon _1}(0)$, which is a fundamental parameter related to the carrier regeneration rate in solar cells [29]. A high value of the dielectric function results in a low recombination rate. Therefore, the doping of Ge and Sn may decrease the recombination rate, whereas the doping of Sr and Ca will increase the recombination rate. The increase in the recombination rate benefits applying the material to light-emitting devices. Therefore, Sr and Ca-doped perovskites can be considered to light-emitting devices.
To some extent, the reflectivity of the material is related to the refractive index and the real part of the complex dielectric function. Therefore, we plotted the changes in the reflectivity and refractive index before and after doping in Fig. 6(e) and (f). The reflectivity increases with the decrease of the complex dielectric function value. This is because, when ${\varepsilon _1}(\omega )$ is at negative values, the material exhibits metallic properties. The reflectivity of the material will increase with the metal abundance. The Ge and Sn elements increase the metallic properties of the material when the value of ${\varepsilon _1}(\omega )\; $ tends to be negative, demonstrating an increasing trend in the reflectance. This trend is consistent with the results of Afsari et al. [23].
The refractive index can be used to probe the propagation of electromagnetic waves through a material. As shown in Fig. 6(f), we calculated the refractive index as a function of the incident photon energy. The change in the refractive index shows the similar trend as the real part of the complex dielectric function. In the visible range, i.e., at the first peak position, the refractive index of undoped α-CsPbI3 is 3.02, and the refractive index values of Ge doping increased to 3.08. Sn, Sr, and Ca doping decreased the peak value to 2.98, 2.93, and 2.94, respectively.
4. Conclusion
In summary, we studied the structural stability, electronic and optical properties of CsPb0.875B0.125I3 (B = Ge, Ca, Sn, and Sr) using first-principles calculations and compared them with those of undoped CsPbI3. The structure analysis shows that the doping of Ge results in the largest reduction of the Pb–I bond length. The formation energy values demonstrate that Ge doping can improve the stability of the material. The calculation of elastic properties demonstrates that the Ge-doped CsPb0.875Ge0.125I3 perovskite can be applied under high pressure or by applying stress. Furthermore, the electronic properties show a change in the band gaps for CsPb0.875B0.125I3 (B = Ge, Ca, Sn, and Sr) perovskite, which are attributed to the influence of the doped element orbitals on the original orbitals. Moreover, the calculation of charge density shows that the chemical bonding of the B–I is different from that of the Pb–I bond. Finally, the optical properties indicates that Ge or Sn doping is conducive to applying in the photovoltaic field, whereas Sr or Ca doping is conducive to applying in the photoelectric field. This change provides a specific idea for the subsequent design of photovoltaic and photoelectric materials.
Funding
National Natural Science Foundation of China (11904212); Natural Science Foundation of Shandong Province (ZR2018BA031, ZR2019MA037, ZR2020MA081).
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. J. Chen, J. Wang, X. Xu, J. Li, J. Song, S. Lan, S. Liu, B. Cai, B. Han, and J.T. Precht, “Efficient and bright white light-emitting diodes based on single-layer heterophase halide perovskites,” Nat. Photonics 15(3), 238–244 (2021). [CrossRef]
2. J. Guo, Y. Fu, M. Lu, X. Zhang, S.V. Kershaw, J. Zhang, S. Luo, Y. Li, W.W. Yu, and A.L. Rogach, “Cd-Rich Alloyed CsPb1-xCdxBr3 Perovskite Nanorods with Tunable Blue Emission and Fermi Levels Fabricated through Crystal Phase Engineering,” Adv. Sci. 7(15), 2000930 (2020). [CrossRef]
3. J. Li, L. Xu, T. Wang, J. Song, J. Chen, J. Xue, Y. Dong, B. Cai, Q. Shan, and B. Han, “50-Fold EQE improvement up to 6.27% of solution-processed all-inorganic perovskite CsPbBr3 QLEDs via surface ligand density control,” Adv. Mater. 29(5), 1603885 (2017). [CrossRef]
4. L. Protesescu, S. Yakunin, M.I. Bodnarchuk, F. Krieg, R. Caputo, C.H. Hendon, R.X. Yang, A. Walsh, and M.V. Kovalenko, “Nanocrystals of cesium lead halide perovskites (CsPbX3, X = Cl, Br, and I): novel optoelectronic materials showing bright emission with wide color gamut,” Nano Lett. 15(6), 3692–3696 (2015). [CrossRef]
5. Y. Xu, Q. Chen, C. Zhang, R. Wang, H. Wu, X. Zhang, G. Xing, W.W. Yu, X. Wang, and Y. Zhang, “Two-photon-pumped perovskite semiconductor nanocrystal lasers,” J. Am. Chem. Soc. 138(11), 3761–3768 (2016). [CrossRef]
6. G.E. Eperon, G.M. Paternò, R.J. Sutton, A. Zampetti, A.A. Haghighirad, F. Cacialli, and H.J. Snaith, “Inorganic caesium lead iodide perovskite solar cells,” J. Mater. Chem. A 3(39), 19688–19695 (2015). [CrossRef]
7. B. Jeong, H. Han, Y.J. Choi, S.H. Cho, E.H. Kim, S.W. Lee, J.S. Kim, C. Park, D. Kim, and C. Park, “All-Inorganic CsPbI3 Perovskite Phase-Stabilized by Poly (ethylene oxide) for Red-Light-Emitting Diodes,” Adv. Funct. Mater. 28(16), 1706401 (2018). [CrossRef]
8. Y. Zhao, Y. Wang, J. Duan, X. Yang, and Q. Tang, “Divalent hard Lewis acid doped CsPbBr3 films for 9.63%-efficiency and ultra-stable all-inorganic perovskite solar cells,” J. Mater. Chem. A 7(12), 6877–6882 (2019). [CrossRef]
9. H. Zhao, J. Xu, S. Zhou, Z. Li, B. Zhang, X. Xia, X. Liu, S. Dai, and J. Yao, “Preparation of Tortuous 3D γ-CsPbI3 Films at Low Temperature by CaI2 as Dopant for Highly Efficient Perovskite Solar Cells,” Adv. Funct. Mater. 29(27), 1808986 (2019). [CrossRef]
10. A. Kogo, K. Yamamoto, and T.N. Murakami, “Germanium ion doping of CsPbI3 to obtain inorganic perovskite solar cells with low temperature processing,” Jpn. J. Appl. Phys. 61(2), 020904 (2022). [CrossRef]
11. A. Dehingia, U. Das, and A. Roy, “Compositional Engineering in α-CsPbI3 toward the Efficiency and Stability Enhancement of All Inorganic Perovskite Solar Cells,” ACS Appl. Energy Mater.5(10), 12099–12108 (2022). [CrossRef]
12. X. Wu, H. Shao, Y. Zhong, L. Li, W. Chen, B. Dong, L. Xu, W. Xu, D. Zhou, and Z. Wu, “Synergistic Regulation Effect of Nitrate and Calcium Ions for Highly Luminescent and Robust α-CsPbI3 Perovskite,” Small 18(9), 2106147 (2022). [CrossRef]
13. J.-S. Yao, J. Ge, K.-H. Wang, G. Zhang, B.-S. Zhu, C. Chen, Q. Zhang, Y. Luo, S.-H. Yu, and H.-B. Yao, “Few-nanometer-sized α-CsPbI3 quantum dots enabled by strontium substitution and iodide passivation for efficient red-light emitting diodes,” J. Am. Chem. Soc. 141(5), 2069–2079 (2019). [CrossRef]
14. W. Yang, Y. Tang, Q. Zhang, L. Wang, B. Song, and C. Wong, “Reducing Pb concentration in α-CsPbI3 based perovskite solar cell materials via alkaline-earth metal doping: a DFT computational study,” Ceram. Int. 43(16), 13101–13112 (2017). [CrossRef]
15. G.T. Wang, J.H. Wei, and Y.F. Peng, “Electronic and optical properties of mixed perovskites CsSnxPb(1− x) I3,” AIP Adv. 6(6), 065213 (2016). [CrossRef]
16. J.P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996). [CrossRef]
17. G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B 54(16), 11169–11186 (1996). [CrossRef]
18. M. Liao, Y. Liu, F. Zhou, T. Han, D. Yang, N. Qu, Z. Lai, Z.-K. Liu, and J. Zhu, “A high-efficient strain-stress method for calculating higher-order elastic constants from first-principles,” Comput. Phys. Commun. 280, 108478 (2022). [CrossRef]
19. D. Trots and S. Myagkota, “High-temperature structural evolution of caesium and rubidium triiodoplumbate,” J. Phys. Chem. Solids 69(10), 2520–2526 (2008). [CrossRef]
20. V. Goldschmidt, “Krystallbau and chemische Zusammensetzung,” Ber. Dtsch. Chem. Ges. 60(5), 1263–1296 (1927). [CrossRef]
21. Y. Zhao and K.J.C.S.R. Zhu, “Organic-inorganic hybrid lead halide perovskites for optoelectronic and electronic applications,” 45(3), 655–689 (2016).
22. S. Zhu, J. Ye, Y. Zhao, and Y. Qiu, “Structural, Electronic, Stability, and Optical Properties of CsPb1−xSnxIBr2 Perovskites: A First-Principles Investigation,” J. Phys. Chem. C 123(33), 20476–2048 (2019). [CrossRef]
23. M. Afsari, A. Boochani, and M.J.O. Hantezadeh, “Electronic, optical and elastic properties of cubic perovskite CsPbI3: Using first principles study,” Optik 127(23), 11433–11443 (2016). [CrossRef]
24. S. Tennakoon, Y. Peng, M. Mookherjee, S. Speziale, G. Manthilake, T. Besara, L. Andreu, and F. Rivera, “Single crystal elasticity of natural topaz at high-temperatures,” Sci. Rep. 8(1), 1–9 (2018). [CrossRef]
25. F. Mouhat and F.-X. Coudert, “Necessary and sufficient elastic stability conditions in various crystal systems,” Phys. Rev. B 90(22), 224104 (2014). [CrossRef]
26. A. Gencer and G. Surucu, “Properties of BaYO3 perovskite and hydrogen storage properties of BaYO3Hx,” Int. J. Hydrogen Energy 45(17), 10507–10515 (2020). [CrossRef]
27. R. Sa, B. Luo, Z. Ma, L. Liang, and D. Liu, “Revealing the influence of B-site doping on the physical properties of CsPbI3: A DFT investigation,” J. Solid State Chem. 309, 122956 (2022). [CrossRef]
28. L. Wang, W.-Y. Wang, R.-L. Zhong, Y.-Q. Qiu, and H.-M. Xie, “Second-Order Nonlinear Optical Responses and Concave-Convex Interactions of Size-Selective Fullerenes/Corannulene Recognition Pairs: The Effect of Fullerene Size,” J. Phys. Chem. C 120(45), 26034–26043 (2016). [CrossRef]
29. X. Liu, B. Xie, C. Duan, Z. Wang, B. Fan, K. Zhang, B. Lin, F. J. Colberts, W. Ma, and R. A. Janssen, “A high dielectric constant non-fullerene acceptor for efficient bulk-heterojunction organic solar cells,” J. Mater. Chem. A 6(2), 395–403 (2018). [CrossRef]
