Abstract
Though perovskite solar cells have good prospects, they also have some disadvantages, especially the impact of Pb on the environment and the use of expensive elements, which makes their production difficult to industrialize. Using first-principle density functional theory, we have investigated the geometric structures, electronic structures, and optical absorption coefficients of non-toxic and earth-abundant 1B-based perovskite solar cell absorbers. Our results show that Cs2AgAuI6, a toxin-free and inexpensive AgAu-based perovskite solar cell absorber, is suitable for use. It has a suitable HSE bandgap (1.289 eV) and a sharp absorption coefficient (~105 cm−1). Meanwhile, it is beneficial to the average electron and hole effective masses are 0.346 and 0.316 m0 respectively. The phonon spectra show that it is stable. Because the d-orbital energy of Cu is higher than those of Ag and Au, CuAu-based perovskite is not stable. This can be seen from the phonon spectra. Therefore, our calculations could provide strong evidence for the experimental synthesis of lead-free and low-cost perovskite solar cell absorber materials.
Introduction
In the space of <10 years, Perovskite solar cell (PSCs) material has gradually become a star material in the field of solar photovoltaic conversion. It has excellent photoelectric conversion efficiency (PCE), which has grown from 3.8 to 25.2% (Kojima et al., ; NREL Efficiency Chart Vol, ). The structural formula of a perovskite solar cell is AMIVXVII3. Nowadays, A can be not only a small organic molecule [A1 = CH3, CH(NH2)] but also a low-valent group-IA metal cation (A2 = Cs+, Na+, and Rb+), MIV represents a divalent group-IVA metal cation (MIV = Pb2+, Sn2+), and X is a halogen (X = Cl, Br, and I). This tremendous progress is because of its superior optoelectronic properties: suitable band gaps, a high tolerance factor (Gao et al., ), long carrier diffusion length (Stranks et al., ), low exciton binding energy (Lee et al., ; Burschka et al., ), and balanced electron and hole mobility (Stoumpos et al., ; Ponseca et al., ). These advantages make us more confident in researching and exploring perovskite solar cell materials.
Although the current perovskite solar cells have seen great success in theoretical research, there are still some great challenges in their practical application and large-scale commercial production. The first urgent problem to be solved is the stability of devices using perovskite material, especially devices that are under high temperature or a humid environment. This may be due to the loose chemical bonds between the organic cations and their inherent instability (Kulbak et al., ; Niu et al., ; Sutton et al., ). Recently, studies have shown that partial replacement of MA by FA can significantly improve the thermal stability of hybrid perovskite (Hu et al., ; Pellet et al., ; Binek et al., ). Therefore, in this paper, we will use the element Cs to replace the organic cation and research the various properties of the resulting perovskite solar cell materials. The second is the use of Pb in the perovskite materials, because it is a toxic element and is very harmful to our living environment. Therefore, we need to replace it but without affecting the photovoltaic conversion efficiency. Many researchers have used Sn to replace Pb, but Sn2+ is easily oxidized in air to Sn4+, and compared with lead-containing perovskite solar cells, devices with Sn-based perovskite materials have lower PCEs, e.g., that of MASnI3 is only about 6% and that of CsSnI3 is only about 3.5% (Hao et al., ; Noel et al., ). Therefore, researchers have considered converting two Pb2+ into IB group (Ag+, Au +, and Cu+) and IIIA group (In3+, Bi3+, and Ga3+) elements to keep the same valence number at MIV sites (Du et al., ; Meng et al., ; Slavney et al., ; Volonakis et al., ; Wei et al., ; Zhao et al., ) and design lead-free halide double-perovskite A2M+M3+. This work provides us with an idea to guide our exploration of inorganic non-toxic halide double-perovskite solar cells.
Recently, research has focused on the non-toxic inorganic mixed-valence double-perovskite solar cell absorption layer material Cs2Au2I6 (Matsushita et al., ; Castro-Castro and Guloy, ; Debbichi et al., ; Giorgi et al., ), where the Au element has a mixed valency of +1 and +3 (Liu et al., ). This material has a direct bandgap (~1.3 eV) and good stability and photoelectric conversion efficiency. However, a disadvantage is that Au is an expensive metal element, so this material is difficult to commercialize and industrialize.
In this paper, our results show that Cs2AgAuI6, a non-toxic and inexpensive AgAu-based perovskite solar cell absorber, is a suitable alternative. It has a suitable HSE bandgap (1.289 eV) and a sharp absorption coefficient (~105 cm−1). Meanwhile, it is beneficial to the average effective masses of electron and hole carriers, 0.346 and 0.316 m0, respectively. This is almost the same as that of MAPbI3. The phonon spectra show that it is stable. Because the d-orbital energy of Cu is higher than those of Ag and Au, CuAu-based perovskite is not stable. This can be seen from the phonon spectra. Therefore, our calculations could provide strong evidence for the experimental synthesis of lead-free and low-cost perovskite solar cell absorber materials.
Computational Methods
Our first-principles calculations were performed on the basis of density-functional theory (DFT) methods by using the Vienna Ab Initio Simulation Package (VASP) code (Kresse and Furthmüller, ) and the standard frozen-core projector augmented-wave (PAW) methods (Kresse and Joubert, ). In the calculation, we used the generalized gradient approximation of Perdew, Burke, and Ernzerhof (PBE) (Perdew et al., ) as the exchange-correlation functional to optimize the structures and calculate band gaps. In order to reduce the self-interaction error of DFT in bandgap calculation, we used the Heyd-Scuseria-Ernzerhof (HSE) of the standard hybrid density functional with 25% exact Fock exchange (Krukau et al., ). The cutoff energy for the plane wave function was 400 eV. The structures are relaxed until total energies are converged to 10−8 eV, and the k-point meshes have a grid spacing of 2π × 0.02 Å−1. The force on all atoms was <3 × 10−3 eV·Å−1. The 6 × 6 × 6 k-grid was used for density of states (DOS) and optical absorption coefficient calculation of halide perovskite. For the calculation of the phonon spectrum, the finite difference method was implemented in Phonopy code (Togo and Tanaka, ), and we constructed a 2 × 2 × 2 supercell of perovskite structures. The force constant was obtained by considering phonon-phonon interaction with the calculation of VASP. The phonon spectrum was acquired by processing the data in Phonopy. MD simulations of a 3 × 3 × 3 supercell with 270 atoms were implemented at room temperature (300 K) with VASP code using the canonical ensemble with a Nose–Hoover thermostat (Hoover, ) under an energy cutoff of 300 eV with 1,000 steps under a time step of 1.0 fs. The properties of the electronic structure and optics were obtained using the VASPKIT program (Wang et al., ).
Results and Discussion
Firstly, we established the most stable crystal structure. Here, we choose ABX3 of four different crystal structures belonging to the space groups Pm-3m, I4/mmm, P63/mmc, and Pnma, respectively. The different total energies referring to the most stable configuration (I4/mmm) are 0.376, 0, 0.671, and 0.110 eV. In our DFT calculation, we thus use the structure with the I4/mmm space group, shown in Figure 1a. The most stable one, with the cell parameter 8.647 Å, is consistent with the previous experimental result (Debbichi et al., ).
Figure 1
Then, we established a suitable double perovskite crystal structure. We see that Cs2M+M3+ has four different crystal structures because there are four different cation sites in Au-based perovskite. In our calculation, the most stable ones can be seen in Figures 1b,c. Both of them have the same perovskite structure symmetry and it should be easier to form for junctions with low non-radiative recombination.
The Goldschmidt tolerance factor (t) can be used as an empirical index to evaluate the structural stability of the perovskite (Kieslich et al., ; Shi et al., ; Travis et al., ), and for AMIVXVII3 perovskite, t is defined as:
where RA, RM, and RX represent the effective ion radii of the A, M site cation and X site anion, respectively. For double perovskite A2M+M3+ the Goldschmidt tolerance factor t for the M site . Generally speaking, the lower the symmetry index of the structure, the lower the Goldschmidt tolerance factor t. When t = 1, it is an ideal cubic perovskite structure; the range 0.9 ≤ t ≤ 1 is generally considered to be very suitable of perovskite, indicating the possibility of a cubic structure; in the range of 0.71 ≤ t ≤ 0.9, it indicates that due to the inclination of the MX6 octahedron, a rhombohedral or orthorhombic structure may be formed; when t < 0.71, it will change the unstable perovskite structure. In our results, the tolerance factor is 0.827, 0.906, and 0.932 for Cs2Au2I6, Cs2AgAuI6, and Cs2CuAuI6, respectively. This means that it is possible to form the cubic perovskite structure for all of them. This is consistent with our calculation, as shown in Figure 1. In addition, we performed ab initio molecular dynamics (AIMD) simulations to evaluate the thermal stability of Cs2AgAuI6. As shown in Figure S1, the structures during 1.0ps AIMD simulation maintain the perovskite structure, indicating that Cs2AgAuI6 is thermally stable.
As we know, the thermodynamic stability of photovoltaic materials should be stable under all possible decomposition pathways. The decomposition pathways of Cs2Au2I6, Cs2AgAuI6, and Cs2CuAuI6 can be seen in Table S1. The enthalpy of decomposition (ΔHd) is the amount of energy that a substance gains during a reaction, which is the difference between the sum of the energies of each substance that is obtained after the reaction and the energies of the reactants themselves. A positive ΔH means that the reaction is endothermic; it means that the reactant itself is very stable and needs to absorb energy from the outside to react, which results in suppressed decomposition of Cs2Au2I6, Cs2AgAuI6, and Cs2CuAuI6 and shows that the structure is stable.
As can be seen in Table S1, we would be able to synthesize Cs2Au2I6 much more easily than MAPbI3 because the dissociation energy of the former is larger than that of the latter (Yin et al., ; Debbichi et al., ). We also find that we should avoid forming the secondary phase AuI3 by carefully controlling the growth conditions. Although some of the decomposition enthalpies of Cs2CuAuI6 are larger than that of Cs2AgAuI6, it would be difficult to form the former if we found the secondary phases (for example CuI2, CsCuI3) in the experiment. Meanwhile, we should also be much more careful to control the experimental conditions to form Cs2CuAuI6 and Cs2AgAuI6 so as to avoid any of the secondary phases (for example, CuI, AgI, CsCu2I3, CsAg2I3, CsCuI3, and CsAuI3) forming. Also, it is more important to avoid the secondary phase Cs2Au2I6 forming in the experiment if we would want to synthesize Cs2CuAuI6 and Cs2AgAuI6.
In solar cell devices, the photo-generated carriers can be effectively collected along the electrodes. The effective mass of carriers is one of the important factors that determine the carrier mobility. Therefore, we choose the ideal semiconductor materials, which should have light effective masses of the electron () and hole (). The effective mass of the photo-generated carrier can be approximately fitted around the band edge by:
where k represents the wave vector along different directions and ε(k) represents the eigenvalue of energy on the band.
From our results, the effective masses of the electron () and hole () are clearly comparable among various semiconductor materials. Cs2Au2I6 is more suitable as a perovskite solar cell material, as it has heavy effective masses of the electron () and hole () at point N in Figure 2 of 0.362m0 and 0.371m0. In previous research, MAPbI3 perovskite solar cells have been shown to have good electronic and optical properties. It was found that the effective mass of its electron () is 0.32 m0 and of the hole () is 0.36 m0 (Giorgi et al., ; Yin et al., ). This further indicates that when perovskite solar cells have lower effective masses of electrons and holes, their photo-generated carriers will be better collected by the electrodes and have higher photoelectric conversion efficiency. For Cs2AgAuI6, the heavy effective masses of the electron () and hole () are 0.548 and 0.494 m0, while for Cs2CuAuI6, the effective masses of the electron () and hole () are heavier, 0.754 and 0.572 m0. It is clear that the effective masses of the electron and hole in Cs2AgAuI6 and Cs2CuAuI6 are much larger than those in CsAuI3. This is because the d orbital of Ag and Cu is higher than that of Au, so the VBM is much more localized in Cs2AgAuI6 and Cs2CuAuI6 than in Cs2Au2I6, and the VBM is much more dispersive in Cs2Au2I6 than in Cs2AgAuI6 and Cs2CuAuI6. This can be seen in Figure 2.
Figure 2
Figure 3
Although PBE or HSE+SOC calculations sometimes give a bandgap result that approaches experimental values (Yin et al., ; Du, ), the most recent calculation shows that the HSE calculation of the Cs2Au2I6 system approaches the experiment results. As shown in Figure S2, the relative band gap between PBE and PBE+SOC calculations is only around 0.1 eV. From Figure 2, the bandgap of Cs2Au2I6 obtained with HSE calculation is 1.167 eV; this is consistent with recent theoretical reports (~1.3 eV) (Giorgi et al., ) and is close to a previous experimental result, which gave a value of 1.31 eV (Debbichi et al., ). This indicates that Cs2Au2I6 lacks strong exciton binding energy, so it is easier to produce a free election and hole after photoexcitation; at the same time, the G → M band gap is relatively flat, which indicates that Cs2Au2I6 has two-dimensional or one-dimensional properties (Saparov et al., ; Xiao et al., ). At the same time, Figure 2 shows that the HSE band gaps of Cs2AgAuI6 and Cs2CuAuI6 are 1.289 and 1.344 eV, respectively. It is clearly seen that the band edge of Cs2Au2I6 is the d-orbital of the Au atom, while the band edge of Cs2AgAuI6 and Cs2CuAuI6 is the d-orbital of the Ag and Cu atoms, respectively. This is because the d electron energy of Ag and Cu atoms is higher than the d electron energy of an Au atom (Kojima and Kitagawa, ). This was also confirmed by the PDOS in Figure S3. In Figure 2, it can be seen at band edges along the G → M direction have flat conduction and valance bands, and the possibility of carrier mobility has huge anisotropy along out-of-plane and in-plane direction; this is due to Cs2Au2I6 having different 5d-orbital splitting of elongated Au3+(d8)I6 octahedra and compressed Au+(d10)I6 octahedra (Liu et al., ; Tang et al., ), and Cs2AgAuI6 at the band edge also has two different d metal cations, indicating that Cs2Au2I6 and Cs2AgAuI6 have 2D electronic properties in 3D materials (Tang et al., ). Meanwhile, the bandgap edges of the N → P direction shows an obvious dispersion band edge. We calculated that Cs2Au2I6 has light effective masses of the electron () and hole () of 0.145 and 0.137 m0 and that those of Cs2AgAuI6 are 0.310 and 0.218 m0, indicating that the carriers are easier to move. This is due to the Au and I orbitals forming an anti-bonding overlap so that there is larger dispersion. We found that the band gap of Cs2Au2I6 is almost the same as that of Cs2AgAuI6 is the ideal material that we were looking for.
It should be noted that the optimal solar cell absorbers should have a direct bandgap and high optical absorption with p-p optical transition (Yin et al., ). Although 1B-based perovskites have d-d optical transition, they also have comparatively high optical absorption (~105 cm−1) (Figure 3). This is consistent with previous research on semiconductors with d-d transitions (Heo et al., ). From our results, we found that the optical absorption of the 1B-based perovskites has strongly anisotropic properties. There is different optical absorption for the directions parallel and perpendicular to the z-axis. This is in good agreement with previous experimental and theoretical results (Debbichi et al., ; Giorgi et al., ). Our results show that the optical absorptions of Cs2Au2I6 and Cs2AgAuI6 are very similar. This is because both of them have a similar band structure. Meanwhile, we found that the optical absorption along the zz direction of Cs2AgAuI6 is stronger than that of Cs2Au2I6. This is because the bond length between the cation and I became longer when we use Ag atom substitution of an Au atom in Cs2Au2I6. As can be seen from Table 1, the lattice constant of Cs2AgAuI6 is a little larger than that of Cs2Au2I6. Then, the d-d transition became weaker in Cs2AgAuI6, so the optical absorption coefficient will become stronger in Cs2AgAuI6.
Table 1
| 1B-based PVSK | PBE lattice parameters (Å) | PBE band gap (eV) | HSE band gap (eV) | |
|---|---|---|---|---|
| Au-based PVSK | Cl | 7.808 | 0.931 | 1.591 |
| Br | 8.139 | 0.748 | 1.264 | |
| I | 8.647 | 0.770 | 1.167 | |
| AgAu-based PVSK | Cl | 7.804 | 0.812 | 1.566 |
| Br | 8.152 | 0.740 | 1.369 | |
| I | 8.687 | 0.763 | 1.289 | |
| CuAu-based PVSK | Cl | 7.657 | 0.647 | 1.982 |
| Br | 8.021 | 0.688 | 1.487 | |
| I | 8.561 | 0.838 | 1.344 | |
The structural parameters (Å), PBE band gap (eV), and HSE band gap (eV) of 1B-based perovskite solar cell absorbers.
Through Figure 4, we can clearly see that Cs2Au2I6 and Cs2AgAuI6 are stable, even if the system of Cs2Au2I6 and Cs2AgAuI6 has a lower virtual frequency; this may be due to the strong Coulomb interaction between metal elements, and the virtual frequency is within reasonable limits. In this study, we tried to dope with other elements the reduce the amount of Au needed. The phonon spectra calculation from our research indicates that Cs2AgAuI6 is very stable, contrary to Cs2CuAuI6, and so a Cu-based perovskite solar cell absorber would be difficult to synthesize. This is clearly shown in Figure 2 the d band energy of the Cu atom is higher than that of the Ag and Au atoms. This result is consistent with the previous calculation (Xiao et al., ).
Figure 4
The calculated bandgaps and the geometric parameters are summarized in Table 1. The picture painted by our results could provide practical guidance for choosing the appropriate compositions to harvest good solar-to-solar cell absorbers. For example, for a two-junction tandem solar cell configuration that obtains the best conversion efficiency, the top and bottom cell should be made of semiconductors with bandgaps of 1.9 and 1.0 eV. Table 1 suggests that Cs2CuAuCl6 could be chosen for the top cell and Cs2Au2I6 could be chosen for the bottom cell. For a three-junction configuration, the semiconductors for the top, middle, and bottom cells should have bandgaps of 2.3, 1.4, and 0.8 eV, respectively. Accordingly, Table 1 suggests Cs2Au2(Br1−xClx)6 and Cs2AgAu(Br1−xClx)6 for the middle cell and Cs2Au2I6 for the bottom cell, though there is no optimal composition for the top cell. Our results show that all of the compositions in Table 1 with the same perovskite structure should be easier to form for junctions with low non-radiative recombination.
Conclusions
In the paper, we researched the crystal structures, electronic structures, and optical properties of 1B-based perovskite solar cell absorbers by using the density-functional theory. Our results show that Cs2AgAuI6, a non-toxic and inexpensive AgAu-based perovskite solar cell absorber, may be a good choice. It has a suitable HSE band gap (1.289 eV) and a sharp absorption coefficient (~105 cm−1). Meanwhile, it is beneficial to the average effective masses of the electron and hole carrier, 0.346 and 0.316 m0, respectively. The phonon spectra show that it is stable. Because the d-orbital energy of Cu is higher than those of Ag and Au, CuAu-based perovskite is not stable. This can be seen from the phonon spectra. Therefore, our calculations could provide strong evidence for experimental synthesis of lead-free and low-cost perovskite solar cell absorber materials.
Statements
Data availability statement
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation, to any qualified researcher.
Author contributions
CF conceived the idea and performed the calculations. All authors analyzed the results and wrote the paper.
Funding
This work was supported by funding from the National Natural Science Foundation of China (under Grant No. 11604035).
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmats.2020.00168/full#supplementary-material
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Summary
Keywords
perovskite solar cell, lead-free, earth-abundant, first-principles calculation, high absorption coefficient
Citation
Feng C, Feng G, Zhao Q, Li S and Li D (2020) Theoretical Design for the Non-Toxic and Earth-Abundant Perovskite Solar Cell Absorber Materials. Front. Mater. 7:168. doi: 10.3389/fmats.2020.00168
Received
26 February 2020
Accepted
06 May 2020
Published
16 June 2020
Volume
7 - 2020
Edited by
Zhenyu Li, University of Science and Technology of China, China
Reviewed by
Youyong Li, Soochow University, China; Yafei Li, Nanjing Normal University, China
Updates
Copyright
© 2020 Feng, Feng, Zhao, Li and Li.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Chunbao Feng fengcb@cqupt.edu.cnDengfeng Li lidf@cqupt.edu.cn
This article was submitted to Computational Materials Science, a section of the journal Frontiers in Materials
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