First-principles study of electronic properties of two-dimensional metal mixed perovskites solar cell and water resistance performance

Two-Dimensional (2D) layered hybrid organic-inorganic perovskite (HOIP) materials have been considered as potential photoconductive materials for solar cells owing to extraordinary conversion efficiency and easy preparation process. In this study, we perform first-principles design on metal mixed 2D HOIPs (BA2(Cs1-x Rb x )2Sn1.5Pb1.5I10 with different proportions of composition (x = 0, 0.5 and 1)) to investigate their electronic properties and stability against moisture. We find that the band gap and effective mass of BA2(Cs1-x Rb x )2Sn1.5Pb1.5I10 increases as the concentrations of mixed Rb atoms increases. Moreover, the result of calculated adsorption energy indicates that the metal mixed 2D HOIPs with different composition ratios of Rb atom exhibit better capacity on the resistance of water than the pure one (BA2MA2Sn3I10). The metal mixed 2D HOIPs shows great potential to be a new generation of solar cell with low-cost, suitable band gap, high thermal stability, and desirable power conversion efficiency.

For example, the recent study of 2D (CH 3 (CH 2 ) 3 NH 3 ) 2 (CH 3 NH 3 ) n−1 Pb n I 3n+1 film showed that a tunable bandgap and notably moisture-resistant can be engineered by controlled the number of inorganic layers [36].
Liu et al demonstrated that the properties of defects could be tuned by varying synthesis conditions in 2D perovskites [37].At the same time, first principle's based computational methods have also been studied in 2D HOIPs.Li et al have demonstrated that 2D (MA) 2 PbI 4 can be used as highly-efficient solar absorbers due to the excellent electronic and optical properties [38].Su et al found that the doped Mn 2+ in (C 8 H 20 N 2 )PbBr 4 can effectively promote the photoluminescence quantum yield [39].The recent study of Xie et al demonstrated the doped Li ions in (PEA) 2 PbBr 4 is capable of enhancing the intensity while broadening the x-ray luminescence [40].Sui et al found that the bandgap of PEA 2 Sn x Pb 1−x Br 4 showed special bending by changing metal atom from Pb to Sn, which can be used for versatile optoelectrical fields [41].Furthermore, many researchers explore the optoelectronic properties of Sn-or Ge-based 2D HOIPs, indicting the great potential for future large-scale applications of perovskite-based commercial production [42].Besides, the structures on the 2D HOIPs are also significant to take a comprehensive research and analysis on the material properties [43][44][45][46].Herein, we perform a systematically study in the crystal structure, electric property and stability of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 with different proportions of composition (x = 0, 0.5 and 1) applying the firstprinciples calculations.We demonstrate that the electronic properties and stability against moisture of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 strongly depend on composition ratios of atoms.We find the capacity of the metal mixed 2D HOIPs is better than the pure one (BA 2 MA 2 Sn 3 I 10 ) and 3D HOIPs in solar energy harvesting, especially for BA 2 Cs 2 Sn 1.5 Pb 1.5 I 10 holding high stability, high electron mobility and narrow band gap.

Computational methods
Perdew-Burke-Eznerhof generalized gradient approximation (PBE-GGA) and density-functional theory (DFT) based first-principles calculations have been conducted in studying the electronic and structural properties of BA 2 MA 2 Sn 3 I 10 (the pure one), BA 2 Cs 2 Sn 1.5 Pb 1.5 I 10 , BA 2 CsRbSn 1.5 Pb 1.5 I 10 and BA 2 Rb 2 Sn 1.5 Pb 1.5 I 10 , respectively.Here, we employ tetragonal crystal structure with three-layer thickness as shown in figure 1.A unit cell including more than 90 atoms is used.CH 3 (CH 2 ) 3 NH 3 + (BA) molecules is used as the organic terminal cations to cover the surfaces of 2D HIOPs.The projector augmented wave (PAW) scheme as incorporated in the Vienna ab initio simulation package (VASP) was used.3 × 3 × 1 k-point meshes have been generated for considering systems by the first Brillouin zone sampled by Monkhorst-Pack method.The nonlocal density functional, vdW-DF, was applied to meet up with the weak interaction between the inorganic matrix and organic molecule.A cut-off energy of 500 eV was used for the expansion of plane wave basis.These parameters achieve convergence in this study.

Optimized structures, formation energies and layer distance
The 2D HOIPs can be conceptually obtained by cutting their bulk counterpart along the 〈100〉-oriented layers.
In this work, we employ Cs and Rb atoms to replace MA molecules on metal mixed (Sn-Pb-based) 2D HOIPs with three inorganic sheets (n = 3), which is BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 with different proportions of composition (x = 0, 0.5 and 1).Geometry optimization has been carried out using the tetragonal phase, as shown in figure 1.The empirical factor of Goldschmidt tolerance (t) is usually adopted to evaluate which perovskite compounds can be formed respect to the ionic radius of each component.It is defined as follows: where R A , R B , and R X means the effective ionic radii of A, B, and X, respectively.Ideally, the favourable t value is between 0.8 and 1.0 for form-stable 2D/3D perovskite structures.In this paper, the calculated t value is in the range of 0.92 < t < 0.99, which can form stable crystal structures for these metal mixed 2D HOIPs.We also optimized these geometry of the crystal structures.The optimized lattice constants show that the lattice constants in x and y directions (a and b, a = b) for the pure one turn to small with the doped Cs and Rb atoms (table 1).Meanwhile, the lattice constants a and b trend to small as the concentration of Rb atoms increases.While for lattice constant c, it has an upward tendency and reaches a maximum value (26.73 Å) at x = 0.5.Once Cs atoms are totally replaced by Rb atoms (x = 1), the c dramatically decrease to the minimum value (26.44 Å).We see that the lattice constant of BA 2 (Cs 1-x Rb x )Sn 1.5 Pb 1.5 I 10 is strongly depend on the concentration of Rb atom.We investigate formation energy of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 at x = 0, 0.5 and 1, respectively.The following formular is used for the calculation of formation energy: Here E tot (mixture) and E tot (pure) are total energies of the mixed 2D HOIPs (BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 ) and the pure one (BA 2 MA 2 Sn 3 I 10 ), respectively.m x is the contained energy in Cs + , Rb + , or Pb2 + atom.m y is the contained energy in MA + molecule or Sn 2+ atom.The result of calculated energies on equation (2) are presented in figure 2. We find the formation energies of BA 2 (Cs 1-x Rb x )Sn 1.5 Pb 1.5 I 10 at x = 0, 0.5 and 1 are below zero, it means that to involve an exothermic chemical reaction to form a stronger binding force.There is also a tendency of rising, as the composition ratio of Rb atoms increase.The calculated result shows that Cs and Rb could replaced the respective MA molecule in 2D HOIPs under the moderate condition owing to the negative substitutional energy.
Meanwhile, the composition ratio of the mixed Rb atoms act a crucial role in the distance of layer (d) (figure 3).The layer distances of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 is obviously larger than the pure one (d = 13.20 Å).In particular, BA 2 (Cs 0.5 Rb 0.5 ) 2 Sn 1.5 Pb 1.5 I 10 exhibits the largest layer distance among these four systems, which   We find that the band gap with SOC effect is 0.6 eV narrower averagely than those calculated by PBE-GGA method for x = 0, x = 0.5, and x = 1, respectively.Similar to the result of PBE-GGA method, the bandgaps of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 with SOC increases as x increases (1.06 eV, 1.13 eV and 1.17 eV for x = 0, 0.5 and 1, respectively), which are still larger than that of BA 2 MA 2 Sn 3 I 10 (1.02 eV) (figures 4(e)-(h)).In addition, regarding the spin-splitting states at the valence-band maximum along the Γ→X  To further explore the origins of band edge states, we also calculated partial density of states (figure 5).For the pure one (BA 2 MA 2 Sn 3 I 10 ), its VBT are dominantly contributed to the s electrons and partially to the p electrons of Sn atoms, and its CBB is determined by the p states of Sn atoms (figure 5

Carrier effective mass
Carrier effective mass is crucial for conversion efficiency of solar harvesting.To further systematically investigate the effect, We combined with the calculated band structures to obtain the carrier effective masses, electron (m e * ) and hole (m h * ) of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 (x = 0, 0.5, and 1) as the following equation where k is the wavevector and ( ) e k are the band edges eigenvalues close to the top or bottom.The calculated results clearly show that the hole effective mass ( ) ⁎ m h of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 is obviously heavier than the pure one, while the electron effective mass ( ) ⁎ m e is much lighter than the pure one (figure 6).As the concentrations of mixed Rb atoms increased, ⁎ m h slightly decrease from −0.22 to 0.29, while ⁎ m e have an increase trend until the value for 0.53 converges.As a result, it is clearly visible that BA 2 Cs 2 Sn 1.5 Pb 1.5 I 10 exhibit the lightest effective mass, and BA 2 Rb 2 Sn 1.5 Pb 1.5 I 10 has the heaviest effective mass.Our calculations demonstrate that by adjusting the concentration of mixed Rb atoms can effectively achieve a light effective mass in BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1. 5I 10 .
Compare with the 3D HOIPs, the stability of 2D HOIPs exhibit a good advantage.To better demonstrate 2D HOIPs have a good water resistance, we calculated their adsorption energies on physisorption and dissociation.To ensure the calculated adsorption energies are reliable, we constructure a 40.95 Å vacuum layer in the z direction.We select four different adsorption positions of water molecules in crystal structure is as follow:

Conclusions
In this paper, we present a first-principles study based on DFT in the crystal structures (including relaxed structure, formation energy and layer distance) and electronic properties of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 with different composition ratios (x = 0, 0.5, 1).The results show that the structures of these mixed metal 2D HOIPs are stable due to the reasonable Goldschmidt tolerance factor and the negative substitutional energy.In other words, MA molecules and Sn atoms can be easily replaced in 2D HOIPs by Cs or Rb atoms, and Pb atoms, respectively.We also clearly show that the lattice constants and the layer distances can be effectively tuned by changing the concentration of Rb atom.Furthermore, the doped Rb atom has a significantly influence on the bandgap.As the composition ratio of the mixed Rb atom increases, the bandgap of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 also increases.Similarly, the effective mass can also be changed with different concentrations of mixed Rb atoms.It can be effectively reduced at the low concentration of Rb atoms.As a result, BA 2 Cs 2 Sn 1.5 Pb 1.5 I 10 (x = 0) exhibits the smallest bandgap and the lightest effective mass in these studied mixed 2D HOIPs systems.For the stability against water, we clearly demonstrate that BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 can more effectively prevent the  corrosion of water molecules than the pure one and 3D HOIPs because of the high positive adsorption energy.BA 2 Cs 2 Sn 1.5 Pb 1.5 I 10 exhibit the strongest adsorption energy.We predict that BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 are more efficient in solar-energy harvesting due to suitable band gap, strong optical absorption, high carrier mobility and high stability.It is expected that BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 with different composition ratios (x = 0, 0.5, and 1), especially BA 2 Cs 2 Sn 1.5 Pb 1.5 I 10 , may be excellent potential alternatives to the 3D HOIPs on solar-energy harvesting materials.

Table 1 .
Calculated lattice constants (Å) of the pure SnI-based 2D HOIPS and the metal mixed 2D HOIPS with different composition ratios (x = 0, 0.5 and 1).34% than the pure one.Because of the van der Waals forces decay in 2D HOIPs, a considerable increase of the layer distance can be obverved with the concentration of MA molecule decreases and that of Rb atom increases.As a result, the layer distances of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 materials could be tuned up by changing the composition ratio of mixed Rb atoms.Based on the relaxed crystal structures, the electronic and stability properties of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 with different proportions of composition (x = 0, 0.5 and 1) are investigated.
(a)).Different from the pure one, the VBT of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 is mainly determined by the s electrons of Sn atoms and that of Pb atoms with partial contribution from p electrons of I and Pb atoms (figures 4(b)-(d)).The CBB of TETP phase is attributed to the p states of Pb and Sn atoms.Similar to the pure one, Cs and Rb atoms have little effect on the band edges states.Meanwhile, the concentration of Rb atoms have a slightly effect on the band edges states.

Figure 7 .
Figure 7. (a) Initially adsorption positions of water molecules.(b) Calculated adsorption energies of water molecule with different proportions of composition of Rb atom.
3.2.Electronic properties of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 As the same to BA 2 MA 2 Sn 3 I 10 , the calculated band structures (figure4) show that BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 with different concentrations of mixed Rb atoms are also direct band-gap semiconductors.The bottom of the conduction band (CBB) and the top of valence band (VBT) are found at Γ points in the Brillouin zone.The band gaps of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 are greatly larger than the pure one (1.19 eV), which is 1.63 eV, 1.68 eV, and 1.74 eV for x = 0, x = 0.5, and x = 1, respectively.As the concentrations of mixed Rb atoms increases, the bandgaps of BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 also gradually increases.To ensure that the results of this study is reliable, we calculate the band structures based on the spin-orbit coupling (SOC).It is well known that SOC is strong in halide perovskites due to presence of heavy element Iodine (Pb) elements.Strong SOC effects in hybrid perovskites significantly reduce the band gap by inducing a large splitting of the first degenerated conduction level.As a result, considering SOC effect in the standard generalized gradient approximation (GGA) is very important for DFT calculation that predicts the accurate band gap of hybrid halide perovskites.Figures4(e)-(h)show our calculated band gap with SOC effect for BA 2 MA 2 Sn 3 I 10 and BA 2 (Cs 1-x Rb x ) 2 Sn 1.5 Pb 1.5 I 10 with different concentrations of mixed Rb atoms.