Lead Replacement in CH 3 NH 3 PbI 3 Perovskites

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Lead Replacement in CH 3 NH 3 PbI 3 Perovskites

Kan Wang , Ziqi Liang , Xinqiang Wang , and Xudong Cui *

K. Wang, Prof. X. Cui Science and Technology on Plasma Physics Laboratory Research Center of Laser Fusion CAEP Mianyang , Sichuan 621900 , China E-mail: [email protected] K. Wang, Prof. X. Wang Department of Physics Chongqing University Chongqing 401331 , China Prof. Z. Liang Department of Materials Science Fudan University Shanghai 200433 , China

DOI: 10.1002/aelm.201500089

The advantages of APbI 3 perovskites in the solar cells fi eld are prominent in their optical and electronic properties. The small direct band gap of 1.55–1.61eV leads to a very board absorption range almost over the entire visible light region. [ 8,9 ] The direct band gap p–p transition, which was reported from a series of ab initio cal-culations, [ 9–11 ] makes these perovskites with better light absorption abilities than that of common p–s transition type thin-fi lm solar cells materials such as CdTe. Moreover, the excitons generated by light absorption in perovskite are easy to be dis-sociated into free carriers at room temper-ature (the binding energy of exciton is few meV). [ 12,13 ] In addition, small carrier effec-tive mass estimated from density function theory (DFT) calculations [ 14,15 ] is competi-tive to monocrystal silicon, with experi-mentally obtained long carrier lifetime and long carrier diffusion lengths exceeding a micrometer [ 16,17 ] Such long carrier diffu-

sion lengths enable the solar cell application of thin APbI 3 fi lm with thickness of ≈500 nm by further improving their optical absorption effi ciency.

To further explore the potentials of such materials, work on the underlying mechanisms of those advantages are still ongoing. [ 18–21 ] These work mainly focused on the investigations of functionalities for each part consisting of AMX 3 , namely, A, M, X, and/or their interactive behaviors. For instance, DFT calculations were employed to investigate the role of the organic cations A + in APbI 3 perovskites. [ 9,22 ] It was found that by choosing molecular cations A + with different ionic radius, the lattice volume can be easily altered, thus making the band gap tuning of perovskites more fl exible. [ 22,23 ] Also, the random orientation of polar molecular cation A + in APbI 3 will bring out nanoscale charge localization in the two band extremes according to Ma and Wang. [ 24 ] The charge localization in valance band maximum (VBM) and conduction band minimum (CBM) have no overlapping, suggesting that two separated “high-ways” for electrons and holes are responsible for the long carrier life-time observed in the experiments. [ 25 ] Rensmo and co-workers showed that a shift of the valence band edges will occur for the APbBr 3 perovskite due to an intrinsic binding energy difference of the halide ions. [ 26 ] Besides, the solar cells using mixed-halide perovskites exhibited long carrier diffusion distances and high effi ciencies. By different mixture ratio of halide, the band gap of perovskites can be dramatically changed. [ 27 ]

As for the role of metal M, attentions are placed on the replacement of Pb in APbI 3 , since Pb compounds are highly toxic and would result in environmental problems if mass

Superior photovoltaic performance in organic–inorganic hybrid perovskite is based on the unique properties of each moiety contined within it. Identifying the role of metal atoms in the perovskite is of great importance to explore the low-toxicity lead-free perovskite solar cells. By using the fi rst-principle calculations, four types of AMX 3 (A = CH 3 NH 3 , M = Pb, Sn, Ge, Sr, X = I) per-ovskite materials are investigated and an attempt is made to understand the structural and electronic infl uences of the metal atoms on the properties of perovskites. Then, the solutions to the replacement of Pb are discussed. It is found that for the small radius metal atoms as compared with Pb, the strong geometry distortion will result in a less p–p electron transition and larger carrier effective mass. The outer ns 2 electrons of the metal ions play critical roles on the modulation of the optical and electronic properties for perovskite materials. These fi ndings suggest that the solutions to the Pb replacement might be metal or metallic clusters that have effective ionic radius and outer ns 2 electrons confi guration on the metal ions with low ionization energy similar to Pb 2+ . Based on this, lead-free perovskite solar cells are expected to be realized in the near future.

1. Introduction

Organic–inorganic perovskites materials (AMX 3 , A = organic molecule, M = metal, X = halide) have shown great potentials in thin-fi lm solar cells, due to their unique optical and electronic properties, and low cost with simple synthetic methods. [ 1–4 ] The representative perovskites are APbI 3 (A = CH 3 NH 3 ) and the power conversion effi ciencies (PCEs) have already reached ≈20 % [ 5 ] or even more in few years since it was fi rst reported in 2009, [ 6 ] with an incredibly increasing rate which is never seen in other solar cells materials. [ 7 ] Based on these outstanding per-formances, the perovskites solar cells are expected to become a major type of solar energy conversion devices in the future.

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productions are realized. [ 1,28,29 ] Recently, Kanatzidis and co-workers [ 30 ] and Snaith and and his group [ 31 ] have synthesized ASnI 3 perovskite by using SnI 2 as the precursor solution under inert atmosphere. In this work, Pb was replaced with Sn and it seems that aforementioned problem caused by Pb was relieved, but the low PCE of 5.73 ≈ 6% , and low stability of Sn 2+ in oxygen atmosphere [ 29–31 ] bring new issues. Essentially, this arises from the differences of ionic radius of metal ions, intrinsic ionization energy and even electron shell structure between Sn and Pb. To explore lead-free perovskite solar cells with high PCEs, one must get deep insights into the effects of the metal ion on the perovskite materials.

Bearing these in minds, we studied four kinds of AMX 3 (A = CH 3 NH 3 , M = Pb, Sn, Ge, and Sr, X = I, denoted as AMI 3 ) perovskites (high temperature cubic phases), with special focus on the role of metal M by fi rst-principles calculations. The selection of such metals is based on the following considera-tions: (1) Pb and Sr both have the +2 valence state and similar ionic radius but different electron shell structures. By com-paring APbI 3 with ASrI 3 perovskite, we then could investigate the infl uence of electronic nature of metal atoms on perovskite (note that Sr is chemically active and might not be appropriate for the solution method, and here we just use it as an example); (2) For Sn and Ge, since Pb, Sn, and Ge have the similar outer electron shell structure but different ionic radius, we could study the infl uence of lattice distortion and intrinsic ioniza-tion energy of metal atoms on the properties. Our investiga-tions suggest that a suitable ionic radius for metal atoms will make the crystal more stable, and the outer ns 2 electrons con-fi guration on the metal ions with low ionization energy will be helpful to obtain better optical absorption and carrier diffusion in AMI 3 structures.

2. Methods

Previous studies have shown that the properties of AMX 3 -type perovskites are prone to be affected by the lattice symmetry of the crystal, which is determined by the ionic size of each atom in the perovskites. [ 10,22 ] Such lattice symmetry modulation is indicated by a Goldschmidt factor [ 32 ] = + +( ) / 2( )A X M Xt R R R R , where R A , R M , and R X is the ionic radius for the organic cation A + , metal cation M 2+ and halide anion X − , respectively. Typically, the perovskite is cubic when the value of t is close to unity. t lower than ≈0.9 indicates the tendency of losing the ideal cubic symmetry and will move toward low-symmetry tetragonal, orthorhombic or other structures characterized by cooperative octahedra rotations. [ 33 ] Taking the ionic size for each ion in the perovskites into considerations, [ 34 ] the t values for our four per-ovskites are listed in Table 1 . We can see that the t values for all four perovskites AMI 3 (M = Pb, Sn, Ge, Sr) are well between 0.9 and 1.1, suggesting the cubic lattice can be retained under certain conditions. In our calculations, a simple cubic unit cell is then considered as the initial confi guration for all four perovskites. In addition, researches showed that the perovs-kite with a C–N bond oriented along the ⟨111⟩ direction is the most stable one, [ 19 ] although the small energy barrier (usually within 0.04 eV) for the organic cations rotation will lead to a large uncertainty in the prediction of the thermodynamic phase

stability for these halides, resulting in several possible thermo-dynamic metastable states. Here we then set the initial confi gu-rations for all four perovskites with the dipole of A + along the ⟨111⟩ direction.

The original lattice and atomic position for the four perovs-kites AMI 3 (M = Pb, Sn, Ge, and Sr) are fully optimized and without using constraints. In order to study the effect of lat-tice distortion, we compare the optimized ASnI 3 and AGeI 3 structures with the structure fi xed into the geometry of APbI 3 perovskite, which will be denoted as f-ASnI 3 and f-AGeI 3 per-ovskites in the latter contents. In other words, for those two perovskites f-ASnI 3 and f-AGeI 3 , we simply replace the Pb atom in the optimized APbI 3 perovskite with Sn and Ge atoms, and no further geometry optimization will be carried out in the simulations. Meanwhile, by comparing APbI 3 with f-ASnI 3 and f-AGeI 3 perovskite, we also examine the infl uence of the nature of the metal ions.

The calculations were performed using the VASP code in the framework of DFT. [ 35,36 ] The PAW pseudopotential was used with an energy cutoff of 500 eV for the plane-wave basis functions. [ 37 ] Also, 5d 10 6s 2 6p 2 , 4d 10 5s 2 5p 2 , 3d 10 4s 2 4p 2 , and 4s 2 4p 6 5s 2 valence electron potential were used for the Pb, Sn, Ge, and Sr atom, respectively, to explicitly study the effects of the outer electron shell of metal atoms. The × ×9 9 9 Γ-centered k -point mesh is employed in structure optimization and electronic properties calculations. The lattice vectors and atomic positions are optimized according to the guidance of atomic forces, with a criterion that requires the force on each atom smaller than × −5 10 3 eV Å −1 . In the whole calculations, the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) is used as the exchange-correlation functional. [ 38 ] The calculated bulk moduli for four perovskites are computed by fi tting the energy-volume dependence with the Murnaghan expression.

3. Results and Discussion

Figure 1 shows the optimized structure of APbI 3 , ASnI 3 , AGeI 3 , and ASrI 3 perovskite, the main optimized structural param-eters for the four AMI 3 crystals are given in Table 1 . After full optimization for the lattice and atomic position, APbI 3 and ASnI 3 perovskites exhibit a quasi-cubic phase with little lattice distortion (bond angle of 89.48° and 89.01°, respectively). The AGeI 3 perovskite has a relatively large lattice distortion with a bond angle of 87.62°, deviating much from the exact 90° of cubic phase. The ASrI 3 perovskite still remains the cubic phase after optimization. Since various phases of perovskites can be

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Table 1. The Goldschmidt factor t , lattice constants and bulk moduli for the four perovskites.

Perovskite Goldschmidt factor t

Lattice constant Bond length of M–I [Å]

Bulk modulus [GPa]

a = b = c [Å] α = β = γ [°]

APbI 3 0.92 6.47 89.48 3.18, 3.28 16.2

ASnI 3 0.96 6.41 89.01 3.07, 3.31 11.5

AGeI 3 1.07 6.30 87.62 2.77, 3.56 7.86

ASrI 3 0.93 6.55 90.00 3.26, 3.30 16.1

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synthesized under different conditions, it is worth to check the stability of our structures. The calculated phonon spectrums for all four perovskites are shown in Figure 2 a–d. We can see that in these four perovskites, the phonons mainly concen-trated on three energetic regions: (i) a low-frequency band from 0 to 150 cm −1 , corresponding to the fundamental vibra-tion modes of all elements; (ii) a middle-frequency band from 350 to 1600 cm −1 , attributed to the vibration modes of organic cation; and (iii) a high-frequency band from 2900 to 3200 cm −1 , due to the vibration modes of hydrogen atoms. Some imaginary low frequencies are found around the R (0.5 0.5 0.5) and M (0.5 0.5 0.0) points in APbI 3 , ASnI 3 , and ASrI 3. Intuitively, this suggests that these three structures are unstable. Nevertheless, numerous simulations show that such imaginary modes in phonon spectrum are a common feature, which are also found in cubic, orthorhombic, and tetragonal phases of APbI 3 . [ 39,40 ] This might be the reason why the phase of APbI 3 is easy to transform under different temperatures. To further verify the structural stabilities, we calculate the total energy versus volume

curve ( E – V curve) for our quasi-cubic APbI 3 structure and com-pared with the exact cubic phase of APbI 3 (which has been found experimentally. [ 23,28 ] The results are shown in Figure 2 e. We can see that our quasi-cubic APbI 3 structure is much more energetically stable than the original cubic phase, suggesting the reliability of our calculations (the E – V curves for other three structures are similar so the data are not shown here). Note that there are no such imaginary frequencies for the AGeI 3 perovs-kite (Figure 2 c). Due to larger lattice distortion in AGeI 3 after optimization, AGeI 3 is transformed into a new stable rhombo-hedral phase and then lose its original cubic phase.

Table 1 lists the Goldschmidt factor t , lattice constants, and bulk moduli for the four perovskites. It is clear to see that APbI 3 , ASnI 3 , and ASrI 3 perovskites keep almost the same cubic form like the initial confi gurations; while AGeI 3 has a large lattice distortion due to the small radius of Ge. Typically, the Ge–I bond length in AGeI 3 perovskite has a strong long-short alteration of 0.79 Å, implying a large migration of the metal atom Ge from the center of the cells. Such large



Figure 1. The optimized geometry: a) APbI 3 , b) ASnI 3 , c) AGeI 3, and d) ASrI 3 , respectively. Large dark gray in (a): lead; large light gray in (b): tin; large gray in (c): germanium; green in (d): strontium; purple: iodine; brown: carbon; small light gray: nitrogen; white: hydrogen atoms.

Figure 2. The phonon density of states for relaxed a) APbI 3 , b) ASnI 3 , c) AGeI 3 , and d) ASrI 3 with their phonon dispersion of the low frequency modes inset in each panel. Total energy (eV/unit cell) versus volume (Å 3 /unit cell) is also given between our structure and the exact cubic phases for e) APbI 3 .

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displacement makes the electrons hard to transfer from Ge 2+ ions to I − . To verify this, Bader charge analysis are performed and results are listed in Table 2 . We can fi nd only 0.68 electrons on Ge have been taken to the halide, much smaller than that of other three metal atoms. Such small electron transfer indicates a weak interaction between Ge 2+ and I − , leading to a small bulk modulus of 7.86 GPa (Table 1 ). ASnI 3 seems to have a larger bulk modulus of 11.5 GPa, while the much active 5s 2 electrons on Sn (due to the low 3th and 4th ionization energy of 30.5 and 40.7 eV, respectively) are easy to be oxidized to Sn 4+ , resulting in a fast decomposition for ASnI 3 under ambient conditions as reported experimentally. [ 30,31 ] Meanwhile, APbI 3 and ASrI 3 show relatively high stability with a bulk modulus of 16.2 and 16.1 GPa, respectively, due to their small lattice distortion and relatively high ionization energy for metal ions. Especially, the Sr 2+ ion cannot be further oxidized since there are only two 5s valance electrons in Sr with the low 1st (5.7eV) and 2nd ioni-zation energy (11.0 eV). As a result, a large charge transfer of 1.49 e is found between Sr 2+ and I − ions, leading to a strong Sr–I interaction. For the cubic phases of perovskite ( t value in the range between 0.9 and 1.1), we can see that the bulk mod-ulus decreases with the increasing of the Goldschmidt factor t and APbI 3 perovskite have the largest stability with the smallest t value of 0.92 among these four perovskites. On the basis of these fi ndings, we can envision that metals atoms or clusters with a suitable ionic radius and specifi c outer electron confi g-uration (such as ns 2 np 2 or ns 2 nd 2 etc.) with low 1st and 2nd ionization energy will help to stable these hybrid perovskite crystals.

The band structures of these four confi gurations are shown in Figure 3 . In APbI 3 , ASnI 3 , and AGeI 3 perovskites, the inves-tigated band-structures are characterized by a direct band gap at R point in the Brillion zone with a band gap of 1.60, 0.78, and 1.33 eV, respectively. For ASrI 3 , the band gap is characterized

between R and X since it is with an indirect band gap (3.77 eV). We fi rst look at the band structure between APbI 3 and ASrI 3 perovskites (They are considered as no distortion due to sim-ilar ionic radius between Pb and Sr). For the APbI 3 perovskite, since the Pb atoms locate at the center of the cubic APbI 3 lat-tice, the major orbital characters of Pb 6p x , 6p y , and 6p z orbitals at the CBM ( Figure 4 a) only couple with the I 5p x , 5p y , and 5p z , respectively; while in other two directions, there remain nonbonding character with I p orbitals, and thus, leading to a small directive band gap of 1.60 eV at R point. However, for ASrI 3 , the VBM is still mainly occupied by I 5p orbitals while the CBM is mainly occupied by Sr 4d orbitals (Figure 4 d) since Sr has a different outer electron confi guration of 5s 2 4d 0 5p 0 . Besides the d 2z and −d 2 2x y orbitals which can couple with I 5p orbitals along the axes, the d xy , d yz , and d xz orbitals which devi-ated from the coordinate axes can also form antibonding with the I 5p orbitals. Therefore, the energy level of the CBM state for ASrI 3 will be raised to generate a large band gap of 3.77 eV. For APbI 3 , ASnI 3 , and AGeI 3 , the metal atoms (Pb, Sn, Ge) have the same ns 2 np 2 electrons shell structure, resulting in similar band-structure for three perovskites (Figure 3 ). The CBM of APbI 3 and ASnI 3 is composed of a nearly threefold degenerated Pb–p or Sn–p state while it is split into a twofold degenerated states ±1/ 2, 1/ 2 and a fourfold degenerated states ±3/ 2, 3/ 2 and ±3/ 2, 1/ 2 in AGeI 3 with a separation of ≈0.52 eV, resulting in a decreasing in band gap. Such energy state splitting may be attributed to the large lattice distortion of AGeI 3 since energy rise for short Ge–I bond and drop for the long Ge–I bond. Note that the calculated band gap of ASnI 3 and AGeI 3 (0.78 and 1.33 eV) with DFT are smaller than their experimental values (1.20 and 1.6 eV). [ 42 ] We attributed this to the inherent shortage of DFT-GGA methods in band gap calcu-lation. More accurate band gaps can be reproduced by higher-level methods such as HSE, GW calculations, [ 11,14 ] in which



Table 2. The Bader charge on each atom in all four AMI 3 (A = Pb, Sn, Ge, Sr) perovskites. The data of ionization energy for metal atoms are taken from ref. [ 41 ] .

Perovskite Bader charge on metal ion [e]

Bader charge on I − anion [e]

Bader charge on A + cation [e]

The 1st, 2nd, 3th, 4th order ionization potential for metal atoms [eV]

APbI 3 0.90 −0.55 0.75 7.4, 15.0, 31.9, 42.3

ASnI 3 0.87 −0.54 0.75 7.3, 14.6, 30.5, 40.7

AGeI 3 0.68 −0.47 0.73 7.9, 15.9, 34.2, 45.7

ASrI 3 1.49 −0.75 0.76 5.7, 11.0, 42.9, 57.0

Figure 3. The band structure for APbI 3 , ASnI 3 , AGeI 3 , and ASrI 3 obtained by DFT calculations.

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many body effects and spin orbital coupling (SOC) are consid-ered together. We stress here that individually using DFT-SOC or DFT with many body effects will still not have band gap values that being close to the experiments for these four per-ovskites. To get a clear picture for this, Figure 1 S presents the comparison of the band gap values from pure DFT and DFT-SOC calculations (Figure S1, Supporting Information). In latter contents, the band gap values from DFT computations are used for discussion. In addition, the calculated electronic char-acters of the band edge states are in good agreement with those methods, indicating that our results about electronic properties are still reliable.

To fi gure out the infl uence of metal nature and lattice dis-tortion on the properties due to ionic radius differences of metal atoms, we perform band gap calculations for f-ASnI 3 and f-AGeI 3. As we stated before, they are fi xed into the con-fi guration of APbI 3 perovskite by simply replacing Pb atom in the structure without optimization, and thus, the infl uence of lattice distortion can be neglected in this case. Compared with optimized ASnI 3 and AGeI 3 (the band gap for ASnI 3 is 0.78eV, for AGeI 3 is 1.33eV), the calculated band gaps for f-ASnI 3 and f-AGeI 3 are 0.78 and 1.21 eV, respectively. The band gap of f-ASnI 3 remains unchanged since only little distortion in ASnI 3 perovskite (Table 1 ). While the band gap of f-AGeI 3 has decreased by 0.12 eV with AGeI 3 due to the lattice distortion in AGeI 3 perovskite, in agreement with previous reports (Table 1 ). Although the calculations of f-ASnI 3 and f-AGeI 3 are without optimizations, we can see that lattice distortion caused by metal atoms with small ionic radius (such as Ge) will not only affect the lattice stability of the perovskites (geometry dependent), but also their optical absorption properties (this is directly refl ected from band gaps). Therefore, choosing metal atoms with an ionic radius matching with organic cations and halide anions might be a compromised option for crystal stability and large optical absorption. Recently, a type of C 7 H 7 PbI 3 perovskite [ 43 ] contained the optoelectronically active tropylium exhibits a

broad spectral absorption and improved carrier mobility is reported, further supporting this conclusion.

It is well known that carrier mobility is another key factor for the perovskite solar cells. In semiconductor physics, this is characterized by the effective mass of carriers. A small effective mass of carriers would be helpful to improve the device perfor-mance. The relationship between photocarrier effective masses and their mobility can be expressed as: τ⎛

⎝⎜⎞⎠⎟= *m

q

m, where q is

the elementary charge and τ is the average scattering time. Considering a constant τ value, we can see that a large carrier mobility of perovskite can be obtained by a small carrier effec-tive mass. By using the parabolic approximation for the band extremes, [ 15 ] we estimated the effective mass ( m * ) of carriers existing around the bottom of the conduction band and the top of the valence band, shown in Table 3 . We found that for APbI 3 and ASnI 3 perovskite, the effective mass for electrons and holes are quite similar, agreeing well with the ambipolar transferring behavior that already confi rmed in experiments. [ 17 ] Comparing with the conventional silicon solar cells (which the *me and *mh is estimated to be 0.19 and 0.16 m 0 ), the car-rier effective mass in both APbI 3 ( = =0.23, 0.25* *m me h ) and ASnI 3 ( = =0.23, 0.13* *m me h ) are quite competitive. The small carrier effective masses in APbI 3 and ASnI 3 imply that these two perovskites have good carrier transferring ability. In con-trast, AGeI 3 and ASrI 3 perovskites have larger carrier effective mass, meaning that the carriers in the lattice are much heavier and hard to transfer. Besides, the effective masses of holes in these two perovskites are found to be much larger than that of electrons, suggesting an imbalance carrier transferring process in these structures. Note that if the spin-orbit coupling (SOC) effects are taking into considerations in the simulations, the calculated values for carrier effective mass will get closer to the experimental values. [ 15 ] For this reason, we also list the values with DFT-SOC calculations in Table 3 .

In order to further understand why there is such a large difference in carrier transferring ability, the density of states (DOS) for all four perovskites are analyzed and shown in Figure 5 . It is clear to see that in APbI 3 , ASnI 3 , and AGeI 3 , the upper valence band are mostly occupied by the p orbitals of I atoms, along with few s orbitals of metal atoms; the lower conduction band are mostly occupied by the p orbitals of metal atoms, along with few s and p orbitals of I atoms. In addition,



Figure 4. The charge density (yellow isosurfaces) of the band extremes for AGeI 3 a) for VBM and c) for CBM) and f-AGeI 3 b) for VBM and d) for CBM perovskite.

Table 3. The effective mass of carriers for the four perovskites esti-mated from the calculated band structures at DFT level along the R–Γ direction. *me is the effective mass for electron, *mh is the effective mass for hole. For comparison, we also list the values with DFT-SOC calcula-tions in the bracket.

/*0m me /*

0m mh

APbI 3 0.30 (0.16) 0.25 (0.14)

ASnI 3 0.23 (0.16) 0.13 (0.17)

AGeI 3 0.33 (0.34) 0.35 (0.56)

ASrI 3 0.44 (0.46) 1.40 (1.82)

f-ASnI 3 0.27 (0.18) 0.11 (0.11)

f-AGeI 3 0.29 (0.23) 0.21 (0.31)

Silicon 0.19 0.16

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a signifi cant carrier transition from the p orbitals of metal atoms to the p orbitals of I atoms can be seen and enables a strong optical absorption (shown in Figure 6 ). The organic cation A + has almost no contribution to the electronic proper-ties near the Fermi level, agreeing with the previous reports [ 19 ] although the random orientation of polar organic molecules in nanoscale will bring out a charge localization and reduce the carrier recombination. [ 24 ] However, the DOS in ASrI 3 perovs-kite is much different from other three perovskites because Sr has a different outer electron shell structure with Pb, Sn, and Ge. Since Sr 2+ ion has no outer electrons after the 5s 2 electrons being taken away by the high electron affi nity I atom (although it is still mostly occupied by the p orbitals of I ions, the valence band for ASrI 3 becomes much narrow, resulting in a very large hole effective mass); while the p–d carrier transition from I − ion to Sr 2+ ion enables a very strong optical absorption at

ultraviolet range (Figure 6 ). In the cases of ASnI 3 and AGeI 3 , we fi nd that the DOS is almost unchanged except the conduc-tion band having translation, consisting with the band gap vari-ations (Figure 3 ). However, a signifi cant splitting appears in the middle of valance band for AGeI 3 (Figure 5 c). This unwished splitting makes the extension of the valance band nearly half reduced, leading to a large effective mass of 0.35 m 0 for the holes as discussed previously (Table 3 ). In addition, there is no such splitting can be found in f-AGeI 3 perovskite (Figure 4 f), suggesting the splitting may be caused by the high distortion of AGeI 3 perovskite. From Figure 4 b,e we can see that both ASnI 3 and f-ASnI 3 perovskite also show no splitting in their valance bands since the lattice distortion is much less for the ASnI 3 perovskite. The Ge-p orbitals in AGeI 3 perovskite have a much stronger contribution to VBM than that of in APbI 3 and ASnI 3 , indicating that a large amount of p electrons still remain on Ge 2+ ions and a much weak p–p transition (Figure 4 a). This fi nding is consistent with our Bader charge analysis (Table 2 ) that only 0.68 electrons on Ge has been given to the halide I due to the high ionization energy of Ge. Besides, we can clearly see that around Ge atom the charge density in the VBM (Figure 4 a) has some overlap with that in the CBM (Figure 4 c) due to the remaining electrons on Ge. This overlap between VBM and CBM increases chances for electrons and holes to meet each other, and thus may lxead to a high carrier combi-nation in the carrier transfer process. By contrast, for f-AGeI 3 perovskite (Figure 4 b,d), such overlap between VBM and CBM disappears. This implies the electrons have less possibility to recombine with holes, indicating a lower carrier combina-tion. Such large difference between these two cases can be attributed to the large displacement of Ge from lattice center (which is caused by the undersized ionic radius). We then sug-gest that metal atoms or clusters with a suitable ionic radius to the lattice will be benefi cial for a better carrier transferring performance.



Figure 5. The PDOS of a) APbI 3 , b) ASnI 3 , c) AGeI 3 , d) ASrI 3 , e) f-ASnI 3 , and f) f-AGeI 3 , respectively. The Fermi levels have been set to zero eV.

Figure 6. The optical absorption coeffi cient for these four perovskites AMI 3 (M = Pb, Sn, Ge, and Sr).

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The optical absorption spectra for these four perovskites are shown in Figure 6 . We can see that APbI 3 dominates the absorption spectrum at the wavelength between 300 to 450 nm. While in the wavelength range between 450 and 800 nm, the absorption for ASnI 3 becomes the largest. Although the calcu-lated band gap for ASnI 3 (0.78 eV) has an underestimate due to the inherent shortage of DFT calculations, its experimental value (1.20 eV) is still smaller than that of APbI 3 (1.60 eV). It seems that the ASnI 3 perovskite has a better optical absorp-tion performance in the spectrum range of interest. While at short wavelength (200–300 nm), ASnI 3 , AGeI 3 , and ASrI 3 have much higher absorptions than that of APbI 3 . This absorption shift can be refl ected from band gap variations (see Figure 3 ) and might be considered as a way to extend energy input by the replacement of Pb with other metals (such as Sn) within APbI 3 . Note that in the work of ASnI 3 , [ 30,31 ] the obtained effi ciency is low compared with the state-of-the-art APbI 3 perovskites. More experimental efforts on ASnI 3 perovskites are still needed to verify this. From Figures 3 and 6 , we can see that a larger band gap for ASrI 3 makes the optical absorption spectrum deviates from visible to ultraviolet range, indicating very low optical absorption effi ciency for solar light. Furthermore, the band gap of ASrI 3 appears to be indirect with the VBM at R point and CBM at Γ point (Figure 3 ), which means that the phonons will be generated when the photogenerated carriers are created, and then lead to a large thermal radiation effect (also indicating a low effi ciency for the light absorption). The large difference of performance in optical absorption between APbI 3 and ASrI 3 perovskites suggests that the outer 6s 2 electrons in the Pb 2+ ions are much important for band gap modulation and for better optical absorption. By doping with different metals into the structures and optimizing both the band gap and absorp-tion together, one can extend the optical absorption ranges and realize high absorption effi ciency.

4. Conclusions

In summary, the fi rst-principles are performed within the framework of DFT to investigate the effects of metal atoms (Sn, Pb, Ge, Sr) on the electronic and optical properties of four perovskites, aiming to identify the solution to the replacement of Pb. The selected metals either having similar ionic radius and/or outer electron shell structures allow us to investigate the infl uence of electronic nature of metal atoms, lattice distor-tion, as well as intrinsic ionization energy of metal atoms on perovskites. Our fi ndings suggest that simply replacing Pb with above-mentioned metals will not lead to higher PCEs. The alter-native solutions might be metals or metallic clusters that have similarly effective ionic radius and outer ns 2 electrons confi gu-ration on the metal ions with low ionization energy as Pb 2+ . In such a way, realizing high-effi ciency lead-free perovskite solar cells would be feasible soon.

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements This work was funded by the Thousands Talents Programs of China at the Research Center of Laser Fusion, CAEP, and the Science and Technology on Plasma Physics Laboratory.

Received: March 8, 2015 Revised: July 24, 2015

Published online: August 22, 2015

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