Photovoltaic Performance of Lead-less Hybrid Perovskites From

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Photovoltaic Performance of Lead-Less Hybrid Perovskites From Theoretical Study Diwen Liu, Qiaohong Li, Jinyu Hu, Rongjian Sa, and Kechen Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02705 • Publication Date (Web): 03 May 2019 Downloaded from http://pubs.acs.org on May 4, 2019

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The Journal of Physical Chemistry

Photovoltaic Performance of Lead-less Hybrid Perovskites From Theoretical Study Diwen Liu,a,c Qiaohong Li,a Jinyu Hu,d Rongjian Sa*b,e and Kechen Wu*b a

State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, P. R. China b Center for Advanced Marine Materials and Smart Sensors, Minjiang University, Fuzhou 350116, P. R. China c University of Chinese Academy of Sciences, Beijing 100049, P. R. China d Laboratory of Functional Materials and Devices for Informatics, Department of Physics, Fuyang Normal University, Fuyang 236032, P. R. China e Institute

of Oceanography Ocean College, Minjiang University, Fuzhou 350108, P. R. China

ABSTRACT In recent years, organic-inorganic hybrid halide perovskites have attracted great attentions. In view of the toxicity of lead, lead-free perovskites have been developed in order to obtain comparable or better photovoltaic performance than that of MAPbI3. In this study, the structural, electronic and optical properties of the pure and mixed perovskite systems were investigated by using density functional theory calculations. The results reveal that three Pb-Sn-Ge perovskites are predicted to preserve improved structural stabilities over MAPbI3. The band gaps of hybrid perovskites can be tuned by means of the Sn/Ge doping. The band gap of MAPb0.50Sn0.25Ge0.25I3 is in the optimum

range

of

1.31.4

eV.

Optical

property

analysis

implies

that

MAPb0.50Sn0.25Ge0.25I3 possesses the comparable absorption ability in the visible light region compared with the MAPbI3 structure. In addition, the results indicate that MAPb0.50Sn0.25Ge0.25I3 with the highest PCE of 23.65% can be chosen as a potential candidate for the light absorption layer. The amount of lead will decline to a certain extent due to the partial substitution of Pb by Sn and Ge. These results are expected to 1

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be helpful for further experiments to find new kind of possible lead-less or lead-free perovskite materials. 1. INTRODUCTION Hybrid organic-inorganic halide perovskite solar cells have attracted intense attention in the past few years.1-4 The first exploration of methylammonium lead iodide (CH3NH3PbI3) as a potential light harvesting material in 2009,2 exhibiting a significant leap in the power conversion efficieny (PCE) from 3.8%2 to 23.7%.5 Hence, organic-inorganic hybrid halide perovskites are considered to be the most potential materials for the light absorption layers. However, the instability of lead-based perovskites and toxic lead element will hinder their wide use. Therefore, there is a necessity to explore stable lead-less or lead-free photovoltaic material as a substitution to obtain the same efficiency as the traditional CH3NH3PbI3 compound. Organic-inorganic hybrid perovskite materials are described by a general formula ABX3. A is a monovalent organic cation such as methylammonium (MA) or formamidinium (FA). B is a bivalent metal cation such as Pb2+, Sn2+ or Ge2+, and X is a halogen such as I, Br or Cl. The structural compositional variation of ABX3 can largely affect the configuration, band gap, and optical property in hybrid perovskites.6 In fact, in view of the toxicity of Pb, to replace Pb with a less toxic metal is considered to be an efficient tool of reducing the potential environmental impact of lead-based perovskites. The most viable replacement is Sn because Pb and Sn belong to the same group and have similar ionic radius. Sn is considered to be one of possible alternative candidates for lead. The band gap of MASnI3 is 1.30 eV.7 However, the 2


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MASnI3 structure is unstable due to the oxidation of Sn2+ to Sn4+.8 The measured PCE of the pure tin-based perovskite is only 6%,9-10 which is much lower than that of MAPbI3. The photovoltaic performance of mixed Pb and Sn hybrid perovskites have been reported.7, 11-12 It has demonstrated that partial replacement of Pb2+ with Sn2+ can tune the band gap from 1.55 eV to 1.17 eV according to the Pb-Sn ratios and extend the absorption spectra towards the mid-infrared region.7 Another suitable candidate is the Ge element. Methylammonium germanium iodide (MAGeI3) was synthesized by Kanatzidis’s group and exhibited remarkable optical property.13 However, the larger band gap of 1.9 eV for MAGeI3 is not expected to produce good performance in perovskite solar cells. The obtained maximum efficiency of the pure Ge-based perovskite is only 0.2%.14 Furthermore, the photovoltaic performance of mixed Pb and

Ge

hybrid

perovskites

were

reported.15

The

results

indicated

that

MAPb0.25Ge0.75I3 can beome a potential candidate for perovskite solar cells due to the lower effective masses, better optical absorption and proper band gap.15 A variety of theoretical studies have been reported about the electronic and optical properties of mixed Pb-Sn and Pb-Ge perovskites by using density functional theory (DFT) methods.8,

11, 15-16

The partial or full substitution of Pb2+ with other metals such as

Mg2+,17 Ca2+,18 Sr2+,19-20 Ba2+,21 Cd2+,22-23 Mn2+,24 Fe2+,25 or Pd2+,26 have widely been studied to understand their effect on the electronic and optical properties. Moreover, Ge is not easy oxidation compared with the same group as Sn,27 which is a drive for us to replace Pb with Sn and Ge in order to explore the photovoltaic properties of Pb-Sn-Ge ternary-metal perovskites. 3



In this work, the photovoltaic properties of Pb-Sn, Pb-Ge binary-metal, and Pb-Sn-Ge ternary-metal perovskites were systematically investigated based on the MAPbI3 structure with a tetragonal phase (I4/mcm).28 To our knowledge, the investagation of Pb-Sn-Ge ternary-metal perovskites applied the photovoltaic field are rarely studied based on the first-principles calculations.29 Therefore, it is necessary to investigate the structures and electronic properties of Pb-Sn-Ge ternary-metal perovskites and further understand their photovoltaic properties. Meanwhile, the photovoltaic performance of the mixed Pb-Sn and Pb-Ge perovskites were explored. 2. COMPUTATIONAL METHODS Density functional theory (DFT) calculations were carried out by means of the Vienna Ab initio Simulation Package (VASP).30 The projector-augmented wave function (PAW) method31 was used to denote the electron–ion interactions. The Pb 5d6s6p, Sn 4d5s5p, Ge 3d4s4p, I 5s5p, N 2s2p, C 2s2p, and H 1s states were considered for valence configurations. The structural optimization was performed using the exchange and correlation described by the generalized gradient approximation (GGA).32 The Brillion zone sampling was performed using 6 × 6 × 6 k-points. More denser 8 × 8 × 8 k-point grid was used for the electronic and optical properties of hybrid perovskites. The energy cutoff of 550 eV was employed in the calculation. The total energy was converged to 105 eV. The atom coordinates were fully optimized until the residual forces were less than 0.01 eV Å1 on each atomic site. Van der Waals interactions can play an important role in the current system involving organic molecules.33-34 Therefore, in order to get a precise theoretical understanding of weak interactions in 4


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hybrid perovskites, we optimize geometric structure of MAPbI3 using a series of van der Waals density functionals to descibe depersion interaction between the organic cations and inorganic framework. According to the reported results,35 the GGA method can give a accurate bandgap of MAPbI3 without considering the spin-orbital coupling (SOC) effect. However, it is known that the accuracy may be accidental since we have not included the SOC effect. In

order

to

obtain

Heyd-Scuseria-Ernzerhof

more

accurate

(HSE06)

band

hybrid

gaps

of

functional

hybrid

perovskites,

calculations

were

performed.36-37 The HSE06 calculations are quite time-consuming. Therefore, considering the calculation cost, -centered 4 × 4 × 4 k-point grids were used for k-point sampling in the Brillouin zone. For all the perovskite systems, the density of states (DOS) and partial DOS were calculated at the HSE06 level. In addition, to futher evaluate the photovoltaic performance of the pure and mixed perovskites, we calculated the short circuit current density (JSC), open circuit voltage (VOC), and theoretical PCE (η) based on the band gap Eg. The maximum short circuit current density JSC can be calculated by assuming that all the incident photons will be absorbed when their energies are larger than the band gap of the mixed perovskites. JSC can be calculated with the following equation:38-39 J SC  e 



Eg

S (E) dE E

(1)

where the parameters of e, E, and S(E) are the electronic charge, an incident photon energy, and the incident spectral power per unit area, respectively. JSC is a function only of Eg and the incident spectrum. It is clear from Eq. 1 that the lower the Eg value, 5



the greater will be JSC. Herein, we use the solar spectrum data provided by the National Renewable Energy Laboratory to calculate the short circuit current density. The open circuit voltage can be estimated based on the Eg of perovskites and a variable parameter loss-in-potential Eloss. The open circuit voltage VOC can be calculated as follows:38-39 eVOC  E g  Eloss

(2)

where Eloss can be adopted with two values 0.7 eV and 0.5 eV from a previous report.38 The maximum theoretical PCE of hybrid perovskites can be obtained by using the results of JSC and VOC estimated in the above two equations:38-40

 (E g ) 

FF  J SC  VOC Psun

(3)

where the fill factor FF, we take the FF with 80% to match the reported PCE based on MAPbI3 single crystals with the Eloss of 0.7 eV.41 Psun is the total incident power, it can be calculated as follows:38-40 

Psun   S ( E )dE 0

(4)

In order to further investigate the stabilities of the pure and mixed perovskite systems, we calculated the formation energies of a series of the pure and mixed perovskite systems. The crystal structure of MAI was derived from reference.42 We chose the most stable BI2 compounds as the reference states with space group: PbI2 _

(P63mc), SnI2 (C2/m), and GeI2 (P3m1). The energies of MAI, PbI2, SnI2, and GeI2 were calculated using the same computational paramerters. 3. RESULTS and DISCUSSION 6


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3.1 Geometric Structures To obtain more insight into the structures of hybrid perovskites, the concept of the tolerance factor was initially introduced by Goldschmidt.43-44 The tolerance factor was usually used to estimate the formation of a stable perovskite crystal-phase, and use the following formula:1 t

RA  RX 2 ( R  RX )

(5)

The octahedral factor  is an another important parameter which was proposed by Li et al. in 2008, given by45



RB RX

(6)

where RA, RB, and RX are the effective ionic radius for the A, B and X position, respectively. The research’s results suggest that the value of the tolerance factor should be wave between 0.813 and 1.107.46 As a matter of fact, in order to get a stable perovskite, the ideal t should be close to 1. In addition, the value of the octahedral factor µ was expected to locate in the range of 0.440.90.45 The radii of the organic cation MA+ is about 1.8 Å, the radii of the iodine anion I is 2.2 Å and the radius of the metal cations are 1.19 Å, 1.12 Å, and 0.73 Å for Pb2+, Sn2+, and Ge2+, respectively.47 Two kinds of the tolerance and octahedral factors of the pure and mixed perovskite systems are presented Table 1. The results reveal that the tolerance factors of all the perovskite materials are consistent with the relevant conclusions.46 However, when the concentration of Ge reaches at 50%, perovskite materials don’t meet the lowest boundary value of the octahedral factors, thus indicating that this kind 7



Page 8 of 37

of perovskites are less stable. As a result, the Kanatzidis’s group had reported the structure of MAGeI3 with highly distorted inorganic framework.13 Table 1 Calculated the tolerance and octahedral factors of the pure and mixed perovskites. Series MAPbI3 MAPb0.75Sn0.25I3 MAPb0.5Sn0.5I3 MAPb0.25Sn0.75I3 MASnI3 MAPb0.75Ge0.25I3 MAPb0.5Ge0.5I3 MAPb0.25Ge0.75I3 MAGeI3 MAPb0.5Sn0.25Ge0.25I3 MAPb0.25Sn0.5Ge0.25I3 MAPb0.25Sn0.25Ge0.5I3

t



0.834 0.839 0.843 0.848 0.852 0.864 0.895 0.929 0.965 0.868 0.873 0.900

0.541 0.533 0.525 0.517 0.509 0.489 0.436 0.384 0.332 0.481 0.473 0.428

Accurate structural characteristics plays an important impact in predicting the electronic and optical properties of hybrid perovskites. We employ seven exchange and

correlation

functionals,

GGA/PBE,32

GGA/PBEsol,48

optB86b-vdW,49

optPBE-vdW,49 vdW-DF,50 vdW-DF2,51 and DFT-D352 to calculate the lattice parameters and volumes of MAPbI3. The results are listed in Table 2. From these results it can be seen that the AAPE values for the lattice constants of MAPbI3 are all smaller than 5% under a series of functionals. If it takes the lattice constants and volumes into consideration, optB86b-vdW yields the best results. The optB86b-vdW functional can give satisfied agreement between calculated and experimental structural parameters of hybrid perovskites.28 Therefore, optB86b-vdW is chosen for the structural optimization, electronic and optical properities of the pure and mixed perovsiktes in all calculations. Note that the formation energies of the pure and mixed perovsiktes are also calculated by using the optB86b-vdW functional. 8


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Table 2 Calculated and experimental structural parameters for MAPbI3. Functionals

a/Å

b/ Å

c/ Å

V/ Å3

PBE 8.92 8.92 13.17 1048.23 PBEsol 8.70 8.70 12.82 970.22 optB86b-vdW 8.76 8.75 12.88 986.31 optPBE-vdW 8.88 8.88 13.10 1032.84 vdW-DF 9.03 9.03 13.36 1090.25 vdW-DF2 8.82 8.82 12.98 1010.25 DFT-D3 8.76 8.76 12.95 993.74 b Exp. 8.85 8.85 12.64 990.00 a AAPE: Average Absolute Percentage Errors for lattice constants. b From ref. 28.

AAPEa (%) 1.93 1.60 1.35 1.44 3.25 1.12 1.50 /

The investigated unit cell contains four MAPbI3 primitive units, so we can simulate three values of the Pb-Sn ratio, Pb-Ge ratio, and Pb-Sn-Ge ratio, respectively. For the cases of x(y) = 0.25, 0.50, and 0.75, all the possible substitution sites have approximately the same stability in the mixed MAPb1-xSnxI3 and MAPb1-yGeyI3 perovskite systems, which have been verified by recent calculation results.7,

15

Geometric optimization of the mixed perovskite systems have been carried out at the optB86b-vdW level with considering the MAPbI3 experimental parameters. The optimized structures of the pure and Pb-Sn-Ge perovskite systems are displayed in Fig. 1. Meanwhile, by performing a variable cell relaxation, we find a slight decrease of the volume with increasing the Sn/Ge percentage, as shown in Figure 1, which is in good agreement with the characteristics of the metal ionic radius, RPb2+  RSn2+  RGe2+. For the pure Sn-based perovskite, we performed geometric optimization using the MASnI3 tetragonal I4cm β-phase.28 Moreover, the experimental structure of MAGeI3 with the space group R3m was considered.13

9



Page 10 of 37

Figure 1. The optimized structures of the pure and Sn-Ge-doped perovskites at the optB86b-vdW level are shown in (100) view. Pb: black; Sn: green; Ge: yellow; I: purple; C: brown; N: light blue; H: light pink.

To further estimate the stabilities of the pure and mixed perovskites, we calculate the formation energies of these perovskite systems through the following definition:

H  E (MAPb1 x  ySn x Ge y I 3 )  [ E (MAI)  (1  x  y ) E (PbI 2 )  xE (SnI 2 )  yE (GeI 2 )]

(7)

where x and y represent the doped ratio of Sn and Ge metal cations, respectively. The calculated formation energies (H) of all the systems are shown in Figure 2. For the 10


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prototype perovskite MAPbI3, the calculated H is 0.01 eV/f.u., indicating a marginal instabilty. This result is in accord with the reported calculations.53-54 It can be seen that the structural stabilities of the Sn-doped perovskite systems are more stable than that of MAPbI3. Meanwhile, we find that Sn-doping is a better choice with respect to Ge-doping in view of the stabilities of the mixed perovskite systems. In the case of MAGeI3, our calculated result is positive and quite close to zero, which is good agreement with the previous calculated data.54 All the Pb-Sn-Ge perovskites are predicted to preserve improved structural stabilities over MAPbI3. Furthermore, considering the partial substitution of Pb by Sn and Ge, the toxicity of lead can be alleviated to a certain extent.

Figure 2. Calculated the formation energies and volumes of the pure and mixed perovskite systems.

3.2 Electronic Properties In order to better explore the electronic properties of the pure and mixed MAPb1-x-ySnxGeyI3 series, we employ two kinds of different DFT methods to gain their band gaps. The results indicate that the prototype perovskite MAPbI3 is a direct 11



band gap semiconductor with both the conduction band minimum (CBM) and valence band maximum (VBM) located in the  point. The band gap of MAPbI3 with the optB86b-vdW method is 1.49 eV, which is consistent with the previous theoretical and experimental values.47, 55 It can be seen that the mixed perovskite systems also possess the direct band gaps as shown Figure 3 and Figure S1-S2. Besides, The calculated band gaps of MASnI3 and MAGeI3 with the optB86b-vdW functional are 0.64 eV and 1.08 eV, respectively, which are in good agreement with the previous theoretical results.47, 56 However, the results from the optB86b-vdW method seriously underestimates their band gaps compared with the experimental values of 1.30 eV and 1.90 eV.7, 13 It is well known that the PBE method usually underestimates the band gaps of hybrid perovskites. For MAPbI3, it is regarded as an accidental case, which was reported by Even et al.57 In order to obtain more accurate band gaps, we use HSE06 calculations.

Figure 3. Calculated band structures of the pure and Sn-Ge-doped perovskite systems at the optB86b-vdW level.

The calculated band gaps of the pure and mixed perovskite systems are shown in Figure 4. For MAPbI3, the HSE06 method will give an overestimated band gap of 12


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1.97 eV without considering the SOC effect. The calculated band gap of MAPbI3 with the combination of HSE06 and SOC shows a lower band gap (1.05 eV)47 compared with its experimental value (1.55 eV).7,

12

The calculated band gaps by the HSE06

method of MASnI3 and MAGeI3 are 0.91 eV and 1.41 eV, respectively, which are closer to their experimental values than those of the optB86b-vdW results. As shown in Fig. 4, the calculated band gaps of Sn-doped and Ge-doped MAPbI3 both will reduce with the increase proportion of Sn or Ge from two kinds of the DFT methods. The band gaps of MAPb1-xSnxI3 for x increased from 0.25 to 0.75 with the HSE06 method are 1.57 eV, 1.36 eV, and 1.04 eV, respectively. Particularly, the HSE06 method can give accuate band gaps of MAPb0.50Sn0.50I3 and MAPb0.25Sn0.75I3, which are in good agreement with their theoretical and experimental values.7, 11-12 The SOC effect for Pb-based perovskites is strong, the SOC effect for Ge-based perovskites is weak, and the SOC effect for Sn-based perovskites locates between Pb-based and Ge-based perovskites.58 This means that the HSE06 method can give accuate band gaps of the mixed perovskites when the Pb content falls in between 25% and 50% regardless of the SOC effect. The band gap variation of MAPb1-yGeyI3 perovskite systems with the HSE06 and HSE06-SOC methods will become smaller when the Pb content gradually reduces, which has been verified by Sun et al.15 The band gaps of MAPb1-yGeyI3 for y increased from 0.25 to 0.75 with the HSE06 method are 1.77 eV, 1.75 eV, and 1.54 eV, respectively. Moreover, the band gaps trend of MAPb1-xGexI3 perovskite systems with the SOC effect show an upward behavior, which is an opposite behavior to both the PBE and HSE06 methods.15 Based on the above results, the HSE06 method can also give accuate band gaps of the mixed Pb-Sn-Ge perovskite systems. The calculated band gaps of MAPb0.50Sn0.25Ge0.25I3, MAPb0.25Sn0.50Ge0.25I3, and MAPb0.25Sn0.25Ge0.50I3 are 1.37 eV, 1.26 eV, and 1.56 eV, respectively. 13



According to the Shockley-Queisser theory, the optimal band gap for single junction solar cells is in the range of 1.31.4 eV.40 Among three mixed perovskites, MAPb0.50Sn0.25Ge0.25I3 and MAPb0.25Sn0.50Ge0.25I3 both possess the suitable band gaps and can be chosen as potential candidates in perovskite solar cells. Besides, MAPb0.25Sn0.25Ge0.50I3 is also quite promising for perovsikte solar cells compared with MAPbI3.

Figure 4. Experimental and Calculated band gaps for the pure and (a) Sn-doped MAPbI3, (b) Ge-doped MAPbI3 and (c) Sn-Ge-doped MAPbI3.

To further undertand the electronic structure, the density of states (DOS) of the pure and Pb-Sn-Ge-doped perovskite series are analyzed. The DOS structures of the pure and Pb-Sn-Ge-doped compounds are simulated with the HSE06 method as shown in Figure 5, and the DOS with Pb-Sn and Pb-Ge mixed perovskites are shown in the Supporting Information (Figure S3-S4). As for the prototype perovskite 14


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MAPbI3, the VBM is mainly occupied by the I-5p orbital, while the CBM is occupied by Pb-6p orbital. With regard to the Sn-Ge-doped perovskites, the main contribution of the VBM still derives from the I-5p orbital, but the main contribution of the CBM derives from the Pb-6p, Sn-5p, and Ge-4p orbitals, which is different from that of MAPbI3. Besides, the organic cations have little contribution to the CBM and VBM around the Fermi energy level. The DOS structures of Sn-doped and Ge-doped perovskites are similar to those of Sn-Ge-doped perovskites.

Figure 5. Calculated the density of states for the pure and Sn-Ge-doped perovskite systems.

It is known that the band gap of a perovskite is related to the structural distortion. Therefore, it is quite necessary to understand the reason for the decreases and increases of the band gaps in the mixed perovskites. The previous results have indicated that the band gaps of perovskites can be affected by the structural distortion and the key factor is the Pb-I-Pb bond angle.59 The B-I-B bond angles (B = Pb, Sn, or Ge) can be decomposed into two categories: in ab plane and along with c axis. The B-I-B bond angles of the pure and mixed perovskite systems are listed in Table 3. The B-I-B bond angles (B = Pb, Sn, or Ge) with ab plane in the mixed perovskite systems 15



Page 16 of 37

gradually become larger and in turn their band gaps reduce when the Sn or Ge content increases. The results indicate that the ab plane distortion may play a greater role in tuning the band gap. The greater distortion in the B-I-B bond angles of MAPb0.25Sn0.25Ge0.50I3 gives rise to an increased band gap of 1.56 eV compared with other two Pb-Sn-Ge perovskites. In fact, the effects of two kinds of the distortions should be considered together. Therefore, it can be seen that the effects of distortion of the B-I-B bond angles can provide an explanation for the discrepancy in band gaps among the mixed perovskite systems. Table 3 The B-I-B (B = Pb, Sn or Ge) bond angles for the pure and Sn/Ge-doped MAPbI3. B-I-B bond angles () In ab plane

Along c axis

150.5 151.7 152.8 155.3 156.3 153.4 155.8 158.4 166.1 154.4 156.0 156.3

176.0 176.1 176.3 175.7 175.0 172.9 174.7 168.4 166.1 176.5 171.7 168.5

MAPbI3 MAPb0.75Sn0.25I3 MAPb0. 50Sn0.50I3 MAPb0.25Sn0.75I3 MASnI3 MAPb0.75Ge0.25I3 MAPb0. 50Ge0.50I3 MAPb0.25Ge0.75I3 MAGeI3 MAPb0.50Sn0.25Ge0.25I3 MAPb0.25Sn0.50Ge0.25I3 MAPb0.25Sn0.25Ge0.50I3

To get more insight into the electronic properties, we next examine the Bader charge analysis for the pure and mixed perovskite systems. Note that the Bader charge analysis of all the perovskite systems are calculated at the optB86b-vdW level. In view of the different chemical environments of the iodine ions in the inorganic framework, it can be divided into two categories, Ia (apical iodide ions) and Ie (equatorial iodide ions), which is well consistent with the reported theoretical 16


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analysis.34 As shown in Table 4, it is obvious that the charge transfer of the organic cations keeps almost unchanged. However, the charge transfer of the iodine ions gradually reduces, especially in the mixed Ge-based perovskite systems. Meanwhile, the charge transfer of three metal cations changes apparently when the Sn/Ge content gradually increases. Table 4 The Bader charge analysis for the pure and Sn/Ge-doped MAPbI3.

MAPbI3 MAPb0.75Sn0.25I3 MAPb0. 50Sn0.50I3 MAPb0.25Sn0.75I3 MASnI3 MAPb0.75Ge0.25I3 MAPb0. 50Ge0.50I3 MAPb0.25Ge0.75I3 MAGeI3 MAPb0.50Sn0.25Ge0.25I3 MAPb0.25Sn0.50Ge0.25I3 MAPb0.25Sn0.25Ge0.50I3

MA

Pb/Sn/Ge

I

Ia

Ie

0.721 0.720 0.719 0.721 0.727 0.719 0.716 0.716 0.740 0.717 0.720 0.718

0.924 0.917/0.923 0.906/0.917 0.901/0.904 0.897 0.910/0.722 0.901/0.706 0.889/0.689 0.651 0.897/0.909/0.719 0.895/0.902/0.694 0.898/0.904/0.684

0.548 0.546 0.543 0.541 0.541 0.527 0.506 0.485 0.464 0.524 0.523 0.504

0.543 0.541 0.538 0.534 0.547 0.521 0.489 0.478 0.462 0.515 0.517 0.504

0.551 0.548 0.546 0.545 0.539 0.531 0.515 0.489 0.464 0.528 0.526 0.503

3.3 Optical Properties To evaluate the optical performance of the mixed perovskites, we calculate the optical absorption coefficient of each structure. The absorption coefficient I() is given as below:60 I ( )  2

  ( )   ( ) 2

1

2

2

  1 ( )



1/ 2

(8)

where 1() and 2() represent the real and imaginary parts of the dielectric function depending on the light frequency . The results are obtained by using the optB86b-vdW functional with a scissor operator applied to obtain the band gap calculated by HSE06 except for MAPbI3. For comparison, the optical absorption of 17



MAPbI3, MASnI3, and MAGeI3 were also calculated. Figure 6 displays the optical absorption coefficient of the pure and mixed perovskites. The optical absorption of MAPbI3, MASnI3, and MAGeI3 agree well with the previous results.47 The optical absorption of MAPbI3 shows a red shift with respect to those of all the mixed perovskites. Besides, the optical absorption coefficient of MAGeI3 is apparently weaker than those of the other Ge-based perovskites in the 350400 nm. In the range of 350450 nm, the absorption ability of MAPbI3 is stronger than those of the mixed perovskite systems. The mixed Pb-Sn-Ge perovskites show good absorption for high energy visible light and ultraviolet light because of the blue shift of the mixed perovskites compared with the MAPbI3 structure.

Figure 6. The optical absorption spectra of (a) Sn-doped MAPbI3, (b) Ge-doped MAPbI3 and (c) Sn-Ge-doped MAPbI3.

18


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In addition, in order to estimate the photovoltaic performance of hybrid perovskites, we calculate the open circuit voltages, short circuit current densities, and theoretical PCE (η) of the pure and mixed perovskite systems by using eqn (1)(4). The obtained results are listed in Table 57. The short circuit current density (JSC) shows a increase trend with the decreasing band gap. MASnI3 has the largest JSC (47.25 mA/cm2), which is attributed to the lowest band gap. The calculated band gap of MASnI3 is lower than its experimental value 1.30 eV.7 However, the estimated PCE of MASnI3 is the lowest among all the perovskite systems due to a lower VOC. Besides, the perovskites with the suitable band gaps improve their short circuit current densities and open circuit voltages. Moreover, a reduced Eloss value will promote increasing the VOC and impove the PCE. MAPb0.50Sn0.50I3 possesses good efficiency over 23% higher than those of MAPbI3 and MASnI3, and showes better electron and hole transport properties.7 The estimated PCE of MAGeI3 reaches up to 23.55%, which is attributed to the underestimated band gap. The results reveal that MAPb0.50Ge0.50I3 with the higher efficinecy of 22.73% in the mixed Pb-Ge perovskite systems. Among the mixed perovskite systems, MAPb0.50Sn0.25Ge0.25I3 with the largest PCE is superior to the other systems. MAPb0.50Sn0.25Ge0.25I3 is predicted to be more stable than the corresponding MAPb0.50Sn0.50I3 due to the less oxidizable Ge. These results indicate that MAPb0.50Sn0.25Ge0.25I3 with the highest PCE of 23.65% can be chosen as a potential candidate for the light absorption layer. MAPb0.25Sn0.50Ge0.25I3 and MAPb0.25Sn0.25Ge0.50I3 are shown to preserve the photovoltaic performance of MAPbI3. From the above results, we can conclude that perovskite with the suitable 19



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band gap and wider optical absorption spectra are the main factors to obtain the higher PCE. Table 5 The calculated band gaps, short-circuit current densities, open-circuit voltages and PCE for the MAPb1-xSnxI3 perovskite systems.

Band gap (eV) VOC (Vloss = 0.7 eV) VOC (Vloss = 0.5 eV) JSC (mA/cm2) η (%) (Vloss = 0.7 eV) η (%) (Vloss = 0.5 eV)

x = 0.25

x = 0.50

x = 0.75

x = 1.00

1.57 0.87 1.07 23.23 18.21 22.39

1.36 0.66 0.86 30.45 18.11 23.59

1.04 0.34 0.54 41.56 12.73 20.22

0.91 0.21 0.41 47.25 8.94 17.45

Table 6 The calculated band gaps, short-circuit current densities, open-circuit voltages and PCE for the MAPb1-yGeyI3 perovskite systems.


y =0.25

y =0.50

y =0.75

y =1.00

1.77 1.07 1.27 17.76 17.31 20.32

1.75 1.05 1.25 18.30 18.35 20.61

1.54 0.84 1.04 24.26 18.36 22.73

1.41 0.71 0.91 28.73 18.38 23.55

Table 7 The calculated band gaps, short-circuit current densities, open-circuit voltages and PCE for the pure and MAPb1-x-ySnxGeyI3 perovskite systems.


Pure

x = 0.25 y = 0.25

x = 0.50 y = 0.25

x = 0.25 y = 0.50

1.49 0.79 0.99 25.76 18.33 22.98

1.37 0.67 0.87 30.17 18.21 23.65

1.26 0.56 0.76 33.04 16.67 22.62

1.56 0.86 1.06 23.62 18.30 22.56

4. CONCLUSIONS In summary, the structural, electronic and optical properties of MAPb1-x-ySnxGeyI3 perovskites were investigated by using first principles calculations based on DFT. The results indicate that the structures of Sn-doped perovskite systems are more stable 20


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compared with the prototype perovskite MAPbI3. Moreover, the results also show that the Sn-doped series have a greater advantage than Ge-doped compounds in terms of the structural stability. All the Pb-Sn-Ge perovskites are shown to preserve improved structural stabilities over MAPbI3. The calculated band gaps of Sn-doped and Ge-doped MAPbI3 will reduce with the increase proportion of Sn or Ge. The HSE06 method can give accuate band gaps of the mixed Pb-Sn-Ge perovskite systems. The results reveal that MAPb0.50Sn0.25Ge0.25I3 with the highest PCE of 23.65% can be chosen as a potential candidate for the light absorption layer. Other two Pb-Sn-Ge perovskites are shown to perserve the photovoltaic performance of MAPbI3. Moreover, the mixed Pb-Sn-Ge perovskites show the comparable absorption ability in the visible light region compared with the MAPbI3 structure. The toxicity of lead can be alleviated to a certain extent in view of the partial substitution of Pb by Sn and Ge. The search for totally Pb-free materials still remains a great challenge in perovskite solar cells and our results reveal that MAPb0.50Sn0.25Ge0.25I3 can be chosen as a suitable candidate to reduce the Pb content in perovskite solar cells and show better photovoltaic performance compared with the prototype perovskite MAPbI3. We hope that our results will be helpful for further experiments to find new kind of possible lead-less or lead-free perovskite materials. Supporting Information The band structures and density of states for the mixed MAPb1-xSnxI3 and MAPb1-yGeyI3 perovskites.

21



AUTHOR INFORMATION Corresponding Author *E-mail: [email protected], [email protected].

Fax: +86 591 63173138

ORCID Diwen Liu: 0000-0001-8119-7666 Qiaohong Li: 0000-0001-9286-3580 Jinyu Hu: 0000-0002-5706-6209 Rongjian Sa: 0000-0002-8515-2438 Kechen Wu: 0000-0002-9531-2239 Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China (No. 21673240) and the Foreign Cooperation Project of Fujian Province (No. 2017I0019). The authors gratefully thank the Supercomputing Centre in Fuzhou for providing computer resources. REFERENCES (1) Snaith, H. J., Perovskites: The Emergence of a New Era for Low-Cost, High-Efficiency Solar Cells. J. Phys. Chem. Lett. 2013, 4, 3623-3630. (2) Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T., Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050-6051. (3) Noh, J. H.; Im, S. H.; Heo, J. H.; Mandal, T. N.; Seok, S. I., Chemical Management for Colorful, Efficient, and Stable Inorganic–Organic Hybrid Nanostructured Solar Cells. Nano Lett. 2013, 13, 1764-1769. (4) Green, M. A.; Ho-Baillie, A.; Snaith, H. J., The Emergence of Perovskite Solar Cells. Nat. Photonics 2014, 8, 506. (5)NREL, Best Research-Cell Efficiences chart, https://www.nrel.gov/pv/assets/pdfs/best-reserch-cell-efficiencies.pdf. (6) Wang, B.; Xiao, X.; Chen, T., Perovskite Photovoltaics: A High-Efficiency 22


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Photovoltaic Performance of Lead-less Hybrid Perovskites From

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