Theoretical Design for the Non-Toxic and Earth-Abundant Perovskite Solar Cell Absorber Materials

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., 2009;NREL Efficiency Chart Vol, 2019). The structural formula of a perovskite solar cell is AM IV X VII 3 . Nowadays, A can be not only a small organic molecule [A 1 = CH 3 NH + 3 , CH(NH 2 ) + 2 ] but also a low-valent group-IA metal cation (A 2 = Cs + , Na + , and Rb + ), M IV represents a divalent group-IVA metal cation (M IV = Pb 2+ , Sn 2+ ), 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 , long carrier diffusion length (Stranks et al., 2013), low exciton binding energy (Lee et al., 2012;Burschka et al., 2013), and balanced electron and hole mobility (Stoumpos et al., 2013;Ponseca et al., 2014). 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., 2015;Niu et al., 2015;Sutton et al., 2016). Recently, studies have shown that partial replacement of MA by FA can significantly improve the thermal stability of hybrid perovskite (Hu et al., 2014;Pellet et al., 2014;Binek et al., 2015). 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 Sn 2+ is easily oxidized in air to Sn 4+ , and compared with lead-containing perovskite solar cells, devices with Sn-based perovskite materials have lower PCEs, e.g., that of MASnI 3 is only about 6% and that of CsSnI 3 is only about 3.5% (Hao et al., 2014;Noel et al., 2014). Therefore, researchers have considered converting two Pb 2+ into IB group (Ag + , Au + , and Cu + ) and IIIA group (In 3+ , Bi 3+ , and Ga 3+ ) elements to keep the same valence number at M IV sites Meng et al., 2017;Slavney et al., 2017;Volonakis et al., 2017;Wei et al., 2017;Zhao et al., 2017) and design lead-free halide double-perovskite A 2 M + M 3+ X VII 6 . 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 Cs 2 Au 2 I 6 (Matsushita et al., 2005;Castro-Castro and Guloy, 2010;Debbichi et al., 2018;Giorgi et al., 2018), where the Au element has a mixed valency of +1 and +3 (Liu et al., 1999). 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 Cs 2 AgAuI 6 , 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 (∼10 5 cm −1 ). Meanwhile, it is beneficial to the average effective masses of electron and hole carriers, 0.346 and 0.316 m 0 , respectively. This is almost the same as that of MAPbI 3 . 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, 1996) and the standard frozen-core projector augmented-wave (PAW) methods (Kresse and Joubert, 1999). In the calculation, we used the generalized gradient approximation of Perdew, Burke, and Ernzerhof (PBE) (Perdew et al., 1996) 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., 2006). 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, 2015), 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, 1985) 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., 2019).

RESULTS AND DISCUSSION
Firstly, we established the most stable crystal structure. Here, we choose ABX 3 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., 2018).
Then, we established a suitable double perovskite crystal structure. We see that Cs 2 M + M 3+ X VII 6 has four different crystal structures because there are four different cation sites in Aubased 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., 2015;Shi et al., 2016;Travis et al., 2016), and for AM IV X VII 3 perovskite, t is defined as: where R A , R M , and R X represent the effective ion radii of the A, M site cation and X site anion, respectively. For double perovskite A 2 M + M 3+ X VII 6, 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 MX 6 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 Cs 2 Au 2 I 6 , Cs 2 AgAuI 6 , and Cs 2 CuAuI 6 , 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 Cs 2 AgAuI 6 . As shown in Figure S1, the structures during 1.0ps AIMD simulation maintain the perovskite structure, indicating that Cs 2 AgAuI 6 is thermally stable.
As we know, the thermodynamic stability of photovoltaic materials should be stable under all possible decomposition pathways. The decomposition pathways of Cs 2 Au 2 I 6 , Cs 2 AgAuI 6 , and Cs 2 CuAuI 6 can be seen in Table S1. The enthalpy of decomposition ( H d ) 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 H 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 Cs 2 Au 2 I 6 , Cs 2 AgAuI 6 , and Cs 2 CuAuI 6 and shows that the structure is stable.
As can be seen in Table S1, we would be able to synthesize Cs 2 Au 2 I 6 much more easily than MAPbI 3 because the dissociation energy of the former is larger than that of the latter (Yin et al., 2014a;Debbichi et al., 2018). We also find that we should avoid forming the secondary phase AuI 3 by carefully controlling the growth conditions. Although some of the decomposition enthalpies of Cs 2 CuAuI 6 are larger than that of Cs 2 AgAuI 6 , it would be difficult to form the former if we found the secondary phases (for example CuI 2 , CsCuI 3 ) in the experiment. Meanwhile, we should also be much more careful to control the experimental conditions to form Cs 2 CuAuI 6 and Cs 2 AgAuI 6 so as to avoid any of the secondary phases (for example, CuI, AgI, CsCu 2 I 3 , CsAg 2 I 3 , CsCuI 3 , and CsAuI 3 ) forming. Also, it is more important to avoid the secondary phase Cs 2 Au 2 I 6 forming in the experiment if we would want to synthesize Cs 2 CuAuI 6 and Cs 2 AgAuI 6 .
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 (m * e ) and hole (m * h ). 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 (m * e ) and hole (m * h ) are clearly comparable among various semiconductor materials. Cs 2 Au 2 I 6 is more suitable as a perovskite solar cell material, as it has heavy effective masses of the electron (m * e ) and hole (m * h ) at point N in Figure 2 of 0.362m 0 and 0.371m 0 . In previous research, MAPbI 3 perovskite solar cells have been shown to have good electronic and optical properties. It was found that the effective mass of its electron (m * e ) is 0.32 m 0 and of the hole (m * h ) is 0.36 m 0 (Giorgi et al., 2013;Yin et al., 2014b). This further indicates that when perovskite solar cells have lower effective masses of electrons and holes, their photogenerated carriers will be better collected by the electrodes and have higher photoelectric conversion efficiency. For Cs 2 AgAuI 6 , the heavy effective masses of the electron (m * e ) and hole (m * h ) are 0.548 and 0.494 m 0 , while for Cs 2 CuAuI 6 , the effective masses of the electron (m * e ) and hole (m * h ) are heavier, 0.754 and 0.572 m 0 . It is clear that the effective masses of the electron and hole in Cs 2 AgAuI 6 and Cs 2 CuAuI 6 are much larger than those in CsAuI 3 . This is because the d orbital of Ag and Cu is higher than that of Au, so the VBM is much more localized in Cs 2 AgAuI 6 and Cs 2 CuAuI 6 than in Cs 2 Au 2 I 6 , and the VBM is much more dispersive in Cs 2 Au 2 I 6 than in Cs 2 AgAuI 6 and Cs 2 CuAuI 6 . This can be seen in Figure 2.
Although PBE or HSE+SOC calculations sometimes give a bandgap result that approaches experimental values (Yin et al., 2014a;Du, 2015), the most recent calculation shows that the HSE calculation of the Cs 2 Au 2 I 6 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 Cs 2 Au 2 I 6 obtained with HSE calculation is 1.167 eV; this is consistent with recent theoretical reports (∼1.3 eV) (Giorgi et al., 2018) and is close to a previous experimental result, which gave a value of 1.31 eV (Debbichi et al., 2018). This indicates that Cs 2 Au 2 I 6 lacks strong exciton binding energy, so it is easier to produce a free election and FIGURE 2 | The HSE band structures of 1B-based perovskite solar cell absorbers. Blue and red shapes indicate the dz 2 and dx 2 -y 2 orbitals of 1B atoms, respectively. Circles, triangles, and inverted triangles represent Au, Ag, and Cu atoms contributions, respectively. hole after photoexcitation; at the same time, the G→M band gap is relatively flat, which indicates that Cs 2 Au 2 I 6 has twodimensional or one-dimensional properties Xiao et al., 2016). At the same time, Figure 2 shows that the HSE band gaps of Cs 2 AgAuI 6 and Cs 2 CuAuI 6 are 1.289 and 1.344 eV, respectively. It is clearly seen that the band edge of Cs 2 Au 2 I 6 is the d-orbital of the Au atom, while the band edge of Cs 2 AgAuI 6 and Cs 2 CuAuI 6 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, 1994). 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 Cs 2 Au 2 I 6 having different 5d-orbital splitting of elongated Au 3+ (d 8 )I 6 octahedra and compressed Au + (d 10 )I 6 octahedra (Liu et al., 1999;Tang et al., 2019), and Cs 2 AgAuI 6 at the band edge also has two different d metal cations, indicating that Cs 2 Au 2 I 6 and Cs 2 AgAuI 6 have 2D electronic properties in 3D materials . Meanwhile, the bandgap edges of the N→P direction shows an obvious dispersion band edge. We calculated that Cs 2 Au 2 I 6 has light effective masses of the electron (m * e ) and hole (m * h ) of 0.145 and 0.137 m 0 and that those of Cs 2 AgAuI 6 are 0.310 and 0.218 m 0 , 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 Cs 2 Au 2 I 6 is almost the same as that of Cs 2 AgAuI 6 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., 2014b). Although 1Bbased perovskites have d-d optical transition, they also have comparatively high optical absorption (∼10 5 cm −1 ) (Figure 3). This is consistent with previous research on semiconductors with d-d transitions (Heo et al., 2017). From our results, we found that FIGURE 4 | Calculated phonon spectra of Cs 2 Au 2 I 6 , Cs 2 AgAuI 6 , and Cs 2 CuAuI 6 , respectively. 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., 2018;Giorgi et al., 2018). Our results show that the optical absorptions of Cs 2 Au 2 I 6 and Cs 2 AgAuI 6 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 Cs 2 AgAuI 6 is stronger than that of Cs 2 Au 2 I 6 . This is because the bond length between the cation and I became longer when we use Ag atom substitution of an Au atom in Cs 2 Au 2 I 6 . As can be seen from Table 1, the lattice constant of Cs 2 AgAuI 6 is a little larger than that of Cs 2 Au 2 I 6 . Then, the d-d transition became weaker in Cs 2 AgAuI 6, so the optical absorption coefficient will become stronger in Cs 2 AgAuI 6 .
Through Figure 4, we can clearly see that Cs 2 Au 2 I 6 and Cs 2 AgAuI 6 are stable, even if the system of Cs 2 Au 2 I 6 and Cs 2 AgAuI 6 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 Cs 2 AgAuI 6 is very stable, contrary to Cs 2 CuAuI 6 , 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 .
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 Cs 2 CuAuCl 6 could be chosen for  Table 1 suggests Cs 2 Au 2 (Br 1−x Cl x ) 6 and Cs 2 AgAu(Br 1−x Cl x ) 6 for the middle cell and Cs 2 Au 2 I 6 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 nonradiative 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 Cs 2 AgAuI 6 , 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 (∼10 5 cm −1 ). Meanwhile, it is beneficial to the average effective masses of the electron and hole carrier, 0.346 and 0.316 m 0 , 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 lowcost perovskite solar cell absorber materials.

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).