Predicted Lead-Free Perovskites for Solar Cells - Chemistry of

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Cite This: Chem. Mater. 2018, 30, 718−728

Predicted Lead-Free Perovskites for Solar Cells Roshan Ali,† Guo-Jiao Hou,† Zhen-Gang Zhu,*,†,‡,⊥ Qing-Bo Yan,§,‡ Qing-Rong Zheng,‡ and Gang Su*,‡,∥,⊥ †

School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, College of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China § College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China ∥ Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China ⊥ CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China ‡

S Supporting Information *

ABSTRACT: Organic−inorganic halide perovskites are quite promising in applications of large scale photovoltaic technology. However, toxicity is one of the crucial issues in these materials, and searching for environmentally friendly perovskite materials for green energy applications is in high demand. Here we present a systematic ab initio study on the replacement of toxic Pb in the perovskite CH3NH3PbI3 (MAPbI3) with possible mono- and a few binary replacements. In the mono-replacements study, Ge and Sn are the best alternatives to Pb. In the binary replacements, we replace Pb by mixing Ca/Si and Zn/Si. In case of Ca/Si, a monotonic decrease in band gaps with a monotonic increase in the optical absorption was observed with increasing the Ca concentration. It is observed for the first time that the substitution of Ca/Si (or Zn/Si) at the B-site with various ratios would lead to remarkably high device absorption efficiencies. The band gaps of the studied mixed replacements are in the ideal ranges for single-junction solar cell and one cell in tandem architecture. As a result of the smaller effective masses, the mixed replacements could have better carrier mobility. An ab initio molecular dynamic simulation demonstrates the stability of the mixed replacements. More importantly, the mixed substituting elements are highly abundant in the earth. This work is helpful to gain further insights into developing green solar cells with low cost and high performance and would lead to wide applications in the future.

I. INTRODUCTION

perovskites has been extended toward other optoelectronic applications, for instance, LEDs,15 lasers,16 and optical cooling,17 etc. MAPbI3 is a direct-gap semiconductor, with experimental bandgap of 1.55 eV.18 It has strong and very sharp absorption, almost 25 times higher than that of Si yet better than GaAs.19−21 They have long-lived photogenerated electrons and holes and have long charge diffusion length.22−25 Due to the small electron−hole effective masses, the ambipolar transport is high.26 In MAPbI3, dissipationless absorption and emission of photons were observed, which enable photons to recycle, leading to utilization of photons within the active layer.27 One of the main issues of these materials is its stability, which is relevant to (i) structural stability; (ii) thermal stability; (iii) atmospheric stability (moisture, oxygen); and (iv) encapsula-

The discovery of organic−inorganic halide perovskites, especially, methylammonium lead triiodide, CH3NH3PbI3 (MAPbI3), and formamidinium lead triiodide, HC(NH2)2PbI3 (FAPbI3), as light absorbers has brought a rapid development in photovoltaics (PV) technology.1−11 These perovskites contain earth-abundant essential elements, making them highly promising for low-cost and large-scale PV applications. In 2009, Kojima et al.1 for the first time investigated a MAPbI3-based solar cell with power conversion efficiency of 3.8%. Later, Lee et al.12 and Kim et al.3 improved the efficiencies remarkably up to 10.9% and 9.7%, respectively. These works arouse a great passion of studying these materials and the techniques to promote the performance and efficiency. The record efficiency for perovskite solar cells now stands at 22.1%,13 which is somehow comparable to the crystalline silicon, today’s leading PV technology (25.3%).14 It is reasonable to expect that the efficiency of perovskites can surpass the highest certified value soon. One may also notice that the research on halide © 2018 American Chemical Society

Received: September 22, 2017 Revised: January 2, 2018 Published: January 18, 2018 718

DOI: 10.1021/acs.chemmater.7b04036 Chem. Mater. 2018, 30, 718−728

Article

Chemistry of Materials tion and electrodes. To optimize the absorption and stability of MAPbI3, replacement of cations or anion is a powerful way.18,28,29 The cation MA has been replaced by formamidinium (FA), double cation mixes MA/FA and FA/Cs, and triple cation mixes Cs/MA/FA, while triple anion (I3) is replaced by Br3.30−32 Saliba et al.33 replaced MA by rubidium cation (Rb+) and achieved a stable efficiency of 21.6% on small areas and 19.0% on a cell of 0.5 cm2 area. These mixes exhibit unexpected properties, for instance, Cs/FA mixes may suppress halide segregation.31 Mixes of Cs/MA/FA solar cells are more reproducible and thermally stable than MA/FA.32 For perovskite/perovskite tandem device architecture mixing of cation Pb with Sn is also a successful attempt.34 From these studies, we may conclude that adding more elements would increase the entropy of mixing, which can further stabilize the unstable system. Another important and serious issue is the presence of lead in these solar cell materials. As PV panels are normally placed in open field or on the roof of houses, their exposure to rainfall is unavoidable. In the presence of rain and moisture, PbI2 degrades as a substance that may cause severe health problems, i.e., from cardiovascular and developmental diseases to neurological and reproductive damages, increasing oxidative stress.35 Furthermore, lead pollution has serious impacts on soil and water resources, greenhouse gas emissions, and abundance of material inputs.36−38 To remove the toxicity of Pb in solar cells, one may either develop an effective method of encapsulation and recycling all components of the PV panels at the end of their lifetime or replace Pb by other nontoxic elements in halide perovskites. For the latter one, the Pb-free perovskites should have excellent absorption, having suitable and direct band gaps comparable to MAPbI3. Also the alternative Pb-free perovskite must exist in the range of tolerance factor (0.81−1.11)39,40 to ensure the structural stability of the perovskite solar cell. Recently, replacing Pb by suitable single elements, especially Sn, has attracted a lot of attention. The Sn-based perovskite shows strong absorption in the infrared spectral region and excellent charge-carrier mobilities.28 MASnI3 and MASn(I3−xBrx) have been shown to reach the efficiencies of 6.4%41 and 5.73%,42 respectively. Although Sn-based materials are excellent players, they are unstable due to the oxidation from Sn2+ to Sn4+, upon exposure to air.41,42 Besides, Sn is not a safer alternative to Pb.41,42 Hence, to make Sn-based perovskites more stable, Eperon et al. mixed Sn with Pb, forming FA0.75Cs0.25Sn0.5Pb0.5I3.34 Very recently, Klug et al.43 partially replaced Pb in MAPbI3 film by nine other elements, i.e., divalent metal species, MA(Pb:B)I3 (B = Co, Cu, Fe, Mg, Mn, Ni, Sn, Sr, and Zn), and found that the new materials possess excellent optical properties. They concluded that MAPbI3 lattice is highly tolerant to almost all homovalent elements. Excellent electronic properties of Pb-based perovskites are disturbed but not completely disrupted, and almost all alkaline earth metals can achieve a stable divalent oxidation state, which makes them suitable candidates for producing new mixed-metal perovskite compositions. At 63Pb:1Co molar ratio they achieved remarkable open-circuit voltage of 1.08 V and 17.2% champion device efficiency.43 The Pb replacement by Ca and Sr in MAPbI3 films has also been recently studied with remarkable long carrier lifetimes and devices with filling factors reaching 85%.44

Some interesting computational efforts are also made on replacement of toxic Pb by suitable elements in the last two years. Sun et al.45 used a 2 × 2 × 2 supercell of a tetragonal MAPbX3 (X = I, Br, Cl) and explored the possibilities of a splitanion method, in which they replaced Pb by nontoxic element (Bi) and one anion X atom by S, Se, and Te. They discovered stable pervoskites, MABiSeI2 and MABiSI2, with band gaps of 1.29 and 1.38 eV, respectively, with strong optical absorption. Wang et al.46 investigated cubic phase of MAMI3 (M = Pb, Sn, Ge, Sr) and suggested that simply replacing Pb with these elements will not lead to higher power conversion efficiencies. Korbel et al. made a computational search on possible cubic perovskites (ABX3) stabilized at high temperature, predicted more than 32 000 hypothetical perovskites,47 and claimed that only halide perovskites with Pb, Sn, and Ge are promising for PV technology. 47 Giorgi et al. replaced Pb by TlBi (MATl0.5Bi0.5I3) and InBi (MAIn0.5Bi0.5I3) and found that these systems are firmly equivalent to MAPbI3 and can be good alternatives for perovskite solar cells.48 MAGeI3 has the tendency to crystallize in the polar space group and, thus, has strong and stable absorption comparable to MAPbI3. Furthermore, MAGeI3 has an excellent hole and electron conductive behavior and stability as compared to MAPbI3.49 Sun et al.50 investigated a mixed Ge/Pb perovskites (MAGexPb1−xI3) with lower band gaps than those of the pure Pb and Ge based perovskites. According to their findings, the lattice distortion plays an important role on the positions of both conduction band minimum and valence band maximum, giving rise to a reduction on the bandgap. With increasing Ge proportion a red-shifted absorption with strong optical spectra has been observed. Among all the mixed systems they investigated MAGe0.75Pb0.25I3 with the best absorption, strongest peak, large peak area, and highest theoretical efficiency of 24.24%. The present work is the first systematic search for alternatives to lead-free perovskite materials that preserve the remarkable optoelectronic properties of the Pb-based perovskites. We consider the replacements of Pb2+ by single and mixed elements. In the former, we replace Pb by almost all elements from groups I−VIII, except the lanthanide−actinide series and some toxic elements (like Cs, Ra, Hg, Cr, As, Tl, Os, V, Tc, and Co) from the periodic table. Suitable single element replacements give 12 candidates. In the latter, we particularly study systematical replacements of Pb by mixing Ca (Zn) with Si for all 12 candidates with different ratios. To the best of our knowledge, this is the first ever attempt in which Pb has been replaced by two mixed nontoxic elements. The ratios which we have chosen for our mix study are 1:7, 3:5, and 4:4 for Ca/Si. In case of mixing Ca (Zn) and Si almost all the molar ratios show excellent optical absorption (ε2) and high device absorption efficiencies in almost entire solar spectra. Further experimental investigation is called for to confirm its suitability and photovoltaic performance.

II. METHODS We adopted first-principles calculations based on the density functional theory (DFT), implemented in the Vienna ab initio simulation package (VASP).51 The generalized gradient approximation of Perdew, Burke, and Ernzerhof (PBE)52 has been used for the exchange-correlation functional. For accurate band structure calculations we applied hybrid functional (HSE06)53 for our mixed alloys (Pb replacements by binary elements) and a few mono-replacement materials. It is noted that HSE-SOC gives highly accurate band structures (Eg is smaller than the one derived by using HSE06) in the 719


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Chemistry of Materials type of MAPbI3 materials. However, we did not apply it because only light elements (Ca, Zn, Si) are studied in our targeted mixed alloys and the spin orbit coupling is negligible for light elements. At room temperature, MAPbI3 stabilizes in a tetragonal structure with space group I4/mcm. We used the same supercell 2 × 2 × 2 structure of Zhang et al.45 of MAPbI3 containing total 96 atoms, in which there are 8-Pb atoms, as shown in Figure 1a. Structural parameters, e.g., lattice

the outstanding mono-replaced materials to further mix them and investigate their performance for a better replacement of the MAPbI3. Next, we are presenting the structural and thermodynamic stability of the mono- and mixed-replacement materials. After that we will discuss the structural, electronic, optical, and device absorption efficiencies for our mono- and mixed-replaced perovskite materials. A. Structural and Thermal Stability. The main issues of the organic−inorganic perovskite material (MAPbI3) are the poor structural and chemical stability along with the serious issue of the lead (Pb) toxicity. Here in this section we are going to focus on alternative materials having comparable absorption and high structural and thermal stability. Structural stability could be defined as the ability of a material to exist in a perovskite phase suitable for PV performance within the limitations of temperature and pressure.39 According to Li et al.57 and Yang et al.,58 a material in the range of tolerance factor 0.81−1.11 (we call this tolerance factor range) exists in the perovskite structure, and out of this range alternative structures can form, such as orthorhombic, hexagonal, etc. It is noted that the tolerance factor gives a rough indication of its ability to form a perovskite or nonperovskite structure.39 It is because the ionic radii of the constituents are not fixed to consider it accurately.39,40 For the tolerance factor (t), we adopted the mean ionic radii for molar ratios 4 Ca:4 Si and 4 Zn:4 Si followed by the previous work48 (for example, rB = (rCa + rSi)/ 2), while in the case of other alloys, we just multiplied the ratios 0.125 (or 0.375) with Ca and 0.875 (or 0.625) with Si (for example, rB = 0.125(rCa) + 0.875(rSi)). To evaluate the chemical stability (thermodynamic stabilities) of the listed mono- and mixed-replaced perovskites we calculated the decomposition energies with respect to the possible decomposing pathways. Basically, MAPbI3 decomposes into the corresponding binary materials (MAI + PbI2).59 In a similar way we consider the decomposition of all mono-replacements (for example, MASnI3 → MAI + SnI2). The decomposition enthalpy for our mixed replacements can be calculated through the following decomposition relation (we select Ca/Si as an example)

Figure 1. Supercell structure of MAPbI3 is shown from a front view in (a) and a side view in (b). Supercells are shown for MA(Ca0.125Si0.875)I3 in (c), for MA(Ca0.375Si0.625)I3 in (d), and MA(Ca0.5Si0.5)I3 in (e). constants, unit cell volume, internal coordinates, etc. were obtained after successful optimization. For convergence criterion of the structural parameters, a cutoff energy of 520 eV for the plane wave basis set was selected. The k-points selected for the convergence of the structure were 3 × 3 × 3, and a force criterion of 0.025 eV Å−1 was used. For the self-consistent calculations and optical properties, kpoints of 4 × 4 × 4 have been used. For the well converged bandgap calculations, four special k-points, (0, 0, 0), (0.5, 0.5, 0), (0, 0.5, 0.5), and (0.5, 0, 0.5), were selected. The crystals for different mixedreplacement ratios are shown in Figure 1c−e. We have used the methods described in refs 54−56 to calculate the absorption efficiency of a realistic solar cell device (see Figure 4a), where 80 nm thick ITO (indium doped tin oxide) is placed on a flat glass, followed by 15 nm thick PEDOT:PSS (poly(3,4ethylenedioxythiophene):poly(styrenesulfonate)), 5 nm thick PCDTBT (poly(N-9′-heptadecanyl-2,7-carbazole-alt-5,5-(4′,7′-di(thien-2-yl)-2′,1′,3′-benzothiadiazole))), and a 350 nm thick layer of MAPbI3 or Pb-free materials we proposed in this work, 10 nm thick PC60BM ((6,6)-phenyl-C61-butyric acid methyl ester) and 100 nm thick Ag layer. In this cell, PEDOT:PSS and PC60BM are represented by HTL and ETL to obtain the excited carriers in MAPbI3 or other Pb-free materials. For better understanding the PV performance, this device architecture helps us to investigate and compare the total device absorption efficiency of the parental as well as our Pb-free materials.

ΔH = E(MACa1 − nSi nI3) − [E(MAI) + (1 − n)E(CaI 2) + nE(I 2) + nE(Si)]

(1)

where n represents the ratios 0.875, 0.625, and 0.5. According to eq 1, the negative value of ΔH means energy/heat loss (exothermic process) during formation of MACa1−nSinI3 or MAZn1−nSinI3, confirming the thermodynamic stability of these materials. The larger magnitude of the negative ΔH leads to higher thermodynamic stability of the product material and vice versa. Figure 2 (red dotted line) shows the formation enthalpy (ΔH) for all mixed and a few mono-replaced materials as a comparison to MAPbI3. Our calculated (ΔH) value for MAPbI3 (−0.01 eV/f.u.) is well consistent with the previous calculated values of −0.02 eV/f.u.58 and −0.1 eV/f.u.60 Similarly, our calculated ΔH value for MAPbBr3 (−0.18 eV/f.u.) is also well consistent with the previous calculated results of −0.25 eV/ f.u.60 Our results as well as the previous calculated results have discrepancies with the experimental values, ΔH300K = 0.36 and 0.07 for MAPbI3 and MAPbBr3, respectively.61 This inconsistency may be due to the calculations we performed at T = 0 K, while the experiment was performed at T = 300 K. For MAPbCl3, our result is −0.16 eV/f.u. which is closer to the

III. RESULTS AND DISCUSSION We systematically and carefully explore almost all possibilities of single-element replacements (briefly called mono-replacements) and a number of binary-element replacements (briefly called bi-replacements or mixed replacements) as presented below. For mono-replacements, a few lead-free alternative perovskites (MASnI341,42 and MAGeI349) have been successfully synthesized and investigated. However, the investigation still lacks a full spectrum. Therefore, one of our aims is to give such a scanning to study the possible applications in solar cell devices by using Pb-free perovskite materials. Moreover, for mono-replacements, we show the structural, electronic band gaps, and optical properties in detail. Another aim was to select 720


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Although we describe the thermodynamic stability by calculating the enthalpy formations, it is not very reliable to predict the stability. Therefore, we perform the ab initio molecular dynamic (AIMD) simulations through PWmat simulation package.62 We have used the Nose−Hoover thermostat63 and controlled the temperature at 300 K. The time step was taken as 2 fs; while the total simulation time used was 8 ps for MA(Ca0.5Si0.5)I3 and 4 ps for MA(Zn0.5Si0.5)I3. We present the AIMD simulation only for MA(Ca0.5Si0.5)I3 and MA(Zn0.5Si0.5)I3 and give the potential energy vs time graph in the Supporting Information (Figure S2). It is clear from Figure S2 that MA(Ca0.5Si0.5)I3 undergoes a large fluctuation in a very short interval of time (0.2 ps) and tends to an equilibrium state from 0.2 ps until 8 ps. Similarly, we used the total time of 4 ps for MA(Zn0.5Si0.5)I3 and found that it is stable until the end of 4 ps. B. Structural Properties. Our simulations start from the tetragonal MAPbI3 supercell. For lead (Pb) replacement we mixed calcium and silicon (Ca/Si) with different ratios by dividing the proportion into 1:7 (12.5%, 87.5%), 3:5 (37.5%, 62.5%), and 4:4 (50%, 50%). In the case of Zn/Si we choose only the ratio 4:4 (50%, 50%). In Ca/Si with ratio 1:7, we have replaced the 1-Pb atom with Ca at the core (111 direction) of the supercell; while the remaining the 7-Pb atoms are replaced by Si. For ratio 3:5, we replaced the 3-Pb atoms with Ca at the core (111), (010), and (112) directions, while the remaining 5Pb atoms were replaced with Si. Furthermore, in case of the ratio 4:4, we keep the three Ca atoms unchanged as in the case of the ratio 3:5, and replace the fourth Pb atom in the direction (011) by Ca (or Zn); the remaining 4-Pb atoms (behind the Ca) are replaced by Si, as shown in Figure 1e. In the Supporting Information (Table S1), the lattice parameters for our mixed and mono-replaced materials (24-total in number) in a comparison to MAPbX3 (X = I, Br, Cl) are shown. We started from the initial unrelaxed supercell structure of MAPbI3 with lattice constants a = b = 12.52 Å and c = 12.66 Å and angles α = β = γ = 90°. After a successful relaxation, the lattice constants for MAPbI3 are a = b = 12.7 Å and c = 12.95 Å with lattice angles of α = γ = 90°, β = 89.0°. Replacing I3 by Br3 and Cl3, lattice constants decrease in the angle β < 89°. The above trend is also observed in all our mixed-replaced materials, except MA(1Ca:7Si)Br3 and MA(4Zn:4Si)I3 where elongation is observed as compared to the relaxed MAPbI3, which may be due to the weak ionic bond interaction between the organic cations and halogen ions. This trend has also been observed in most of the cases in mono-replaced materials. The deviations of the lattice angles from 90° for all our mixed and mono-replaced materials are also observed (Figure S2). The angles deviation is basically the results of distortion of the structures. In the case of Zn/Si replacements, all the angles are below 90°, and this means that more distortion produced in these perovskites materials; this high distortion may be the reason for their second direct and high dispersive band valleys at Γ- and K-symmetry points in both VB and CB. In case of monoreplaced materials except a few, almost all α = γ = 90°, while for β a decrease is observed below 90°. As a consequence of the change of the lattice constants and angles, the system volume is largely affected (Figure S2). In the mixed perovskites materials, volume contraction has been observed as we move from I3 to Br3 and Cl3 which has also been observed in the present study for MAPbX3 (X = I, Br, Cl) and confirmed by previous calculations.64 This volume contraction is basically due to the lattice constriction almost in all the three directions. In

Figure 2. Tolerance factor (t), black in color, represents the perovskite phase stability for all mono- and mixed-replaced materials. The two dotted black lines represent the tolerance factor range. The red curve represents our calculated formation enthalpy. The blue and magenta color triangles represent the previous calculated enthalpy formation values, while the green square represents the experimental formation enthalpy for MAPbI3. Materials below the horizontal red-dotted line show thermodynamic stability.

experimental value of −0.094 eV/f.u.61 and better than the previous calculated value of −0.7 eV/f.u.60 It is shown in Figure 2 that MAPbI3 is marginally stable as compared to MAPbBr3 and MAPbCl3. It is also obvious that the thermodynamic stability of these perovskites increases in the order of I, Br, and Cl, which has also been confirmed by previous calculations.60,61 For MASnI3 our derived formation enthalpy is well satisfied with previous results. In the case of MAGeI3 our calculated enthalpy is positive while the previous calculated data is negative, but both are quite close to zero.58 In our mixed replacements, except MACa0.5Si0.5I3 (ΔH = 0.07 eV/f.u.), all other alloys are negative and, hence, very stable. Since MAI, CaI2, Si, and I2 are all known materials, the synthesis of the perovskite product may be performed by mixing all these components in solid or in solution at room temperature or under heating. Figure 2 (black dotted line with square symbols) shows the tolerance factor (t) for mono- (MASnI3 and MAGeI3) and mixed-replaced materials in comparison to MAPbX3 (X = I, Br, Cl). Horizontal black dotted lines represent the borders of the tolerance factor range, i.e., t = 0.81 and t = 1.11. Our calculated tolerance factors (t = 0.93, 0.942, 0.95) for MAPbX3 (X = I, Br, Cl) are well consistent with the previous results.57,58,61 Furthermore, our calculated tolerance factors (1.02, 0.9) for MASnI3 and MAGeI3 are also well consistent with previous calculations.40,58 In our mixed replacements, materials with triiodides (I3) are found in the tolerance factor range due to its larger ionic radius. And the tolerance factors for MA(Ca0.125Si0.875)I3 and MA(Zn0.5Si0.5)Br3 exist at the edge of the tolerance factor range. When I3 was replaced by Br3 or Cl3, some materials go out of the tolerance factor range due to its smaller ionic radius, such as MA(Ca0.125Si0.875)Br3, MA(Ca0.125Si0.875)Cl3, MA(Ca0.375Si0.625)Cl3, and MA(Zn0.5Si0.5)Cl3, which may or may not be in the perovskite structure. In conclusion most mixed-replaced materials are structurally and thermally very stable (see Figure 2). The tolerance factor (t) and thermodynamic stability (ΔH) for other mono-replaced materials are given in the Supporting Information (Figure S1). 721


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Chemistry of Materials principle, this is due to the variation of the ionic radii of the substituting atoms. More specifically, the structure deformation is also due to the changes of bonding lengths and angles between the inorganic metal atoms (Ca−Si, Zn−Si) as well as with the anions (I, Br, Cl). Furthermore, there is also a weak bonding interaction between hydrogen and anion atoms (H−I) which causes structural distortion and volume variations. Notably, for all lattice parameters, a very small (∼2%) deviation has been observed in all our studied materials. C. Replacement of Pb with Single Elements. We studied almost all groups in the periodic table except lanthanide−actinide series and the top toxic elements (Cs, Cd, Hg, Cr, As, Tl, Po, Os, V, Tc, and Co). Furthermore, hydrogen, carbon, nitrogen, phosphorus, oxygen, and sulfur replacements are not considered due to their smaller ionic radii. The smaller the radius of the substituting element, the greater will be the distortion of the structure, leading to less stability and symmetry of the structure, which may not be able to maintain good PV performance. In this study we did not consider the noble group elements (group 18). It is found that elements of the 2nd, 12th, 13th, and 14th groups are suitable and feasible to replace Pb, while the elements of the remaining groups show metallic nature, as summarized in Table 1 and Figure 3. From the mono-replacements we may conclude that elements having valency 2+ or 4+ are the possible replacements for Pb.

Figure 3. Pb-replaced (12 in total), unreplaced (due to smaller ionic radii; 17 in total), metallic (30 in total), highly toxic (12 in total), and mixed (Ca/Si, Zn/Si) Pb-replaced elements are tabulated in the periodic table.

point except MAAlI3 and MAGaI3 (indirect at Γ−K). From the calculated band structures we found that MASiI3, MASnI3, and MAGeI3 are highly dispersive, which may exhibit excellent electronic transport properties compared to MAPbI3. The other materials with single-element replacements have very low dispersions in the valence as well as the conduction bands. The highly dispersive MASiI3 inspires us to further investigate the mixed combination of Si with other suitable elements for the purpose of excellent PV performance and electronic properties. Our calculated PBE band gap for MAPbI3 is 1.63 eV, while by HSE06 its band gap value is 2.20 eV, which overestimates the experimental band gap value of 1.55 eV18 but is well consistent with other theoretical values 1.67,59 1.59,65 1.6,46 and 1.62 eV48 by PBE potential while 2.02 eV64 by HSE06 as shown in Table 1. It is noted that the band gap of 1.55 eV is not quite suitable for stronger and excellent absorption due to the relatively short absorption limited to 800 nm. Hence, further investigations are required to find a suitable candidate having optimum band gap with strong optical absorption. Figure 4b,c

Table 1. Band Gap Values (HSE, PBE) for Our MonoReplaced Materials along with Previous Theoretical and Experimental Results Are Presented, in a Comparison to MAPbI3a materials

PBE (this)

HSE06 (this)

MAPbI3

1.63

2.20

MASnI3 MAGeI3

0.81 0.87

1.23 1.28

1.67,b 1.62,c 1.6,d 1.59,e 1.37f 0.78,g 0.61,h 0.37f 1.17,i 1.33,d 0.96f

MASiI3 MABI3 MAAlI3 MAGaI3 MAZnI3 MABeI3 MAMgI3 MACaI3 MASrI3 MABaI3

0.14 0.40 1.44 0.72 2.72 0.41 1.39 3.89 3.94 3.97

0.51 − − − 3.77 − − − − −

− − − − − − − − 3.77d −

PBE (prev.)

HSE (prev.)

exp.

2.02j

1.55k

0.75f 2.16,j 1.41f − − − − − − − − − −

1.20i 1.90i − − − − − − − − − −

Figure 4. (a) Schematic structure of the simulated device, with a single layer perovskite. (b) The dielectric function ϵ2 and (c) the absorption efficiency of the simulated device with the active Pb-free perovskite layer of MAPbI3, MAGeI3, and MASnI3.

is the imaginary part of the dielectric function (ε2) and device absorption efficiency single layer of MASnI3, MAGeI3, and MAPbI3, which show a strong absorption in the energy range of 1.6−3.5 eV, mostly in the visible and partial UV spectral region. Alkaline earth metals (group 2) have a stable divalent oxidation state, which makes them suitable candidates for the replacement of divalent Pb2+. We observed that the band gap monotonically increases as we go from top to bottom in the periodic table. Such an increase of band gap is consistent with the tendency of the increase of the ionic radius. The band gap of MAMgI3 is 1.39 eV, which is close to the band gap of MAPbI3 and even closer to the band gap of FAPbI3 (Eg = 1.47 eV). MAMgI3 shows a broader and strong absorption at higher energies 4.5−9.5 eV in the UV spectral region, and hence it would be a promising material in solar cell in this region. Other replacements of Pb in this group are Ca, Sr, and Ba, which have wider band gaps of 3.85, 3.94, and 3.97 eV, respectively. These

The unit of band gap is eV. “This” indicates this work, “prev.” means previous work, and “Expr.” represents experimental work. bReference 59. cReference 48. dReference 46. eReference 65. fReference 58. g Reference 66. hReference 67. iReference 49. jReference 64. k Reference 18. a

Table 1 shows the band gap values for MAPbI3 and all possible mono-replaced materials (12 in total) in comparison to previous calculated and experimental results. It is obvious from Table 1 that all our calculated band gap values are well consistent with the previous as well as experimental results. The elements of the 2nd, 12th, and 14th groups are homovalent to Pb2+; hence, they are the natural choices to replace Pb for possible better performance. We observed that all these possible replacements have direct band gaps at the Γ 722


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strong device absorption efficiencies for future high solar cell materials. The optical properties and device absorption efficiency for the remaining single-element replacements are given in the Supporting Information (Figure S3). For single element replacements, we can conclude that group 14 elements are the better replacements of Pb for high PV performance and carrier transfer. D. Mixed, Ca/Si, and Zn/Si Perovskite Materials. Before going into the details, we would like to pay more attention on some related works and correlate them to the present study. Boix et al. investigated that transition elements (like Cu, Mn, Fe, Co, and Ni) are promising alternatives to Pb due to their rich chemistry.66 We could not find such evidence in our present single-element replacement calculations. However, we expect better PV performance of these metals in a mixedreplacement study. A mixed study of the transition elements has recently been investigated by Klug et al.,43 MA(Pb:B)I3 (B = Co, Cu, Fe, Mg, Mn, Ni, Sn, Sr, and Zn), in which they found highest efficiency of 17.2% for the molar ratio of 63Pb:1Co. According to Pérez-del-Ray et al.44 almost all alkaline earth metals (such as Ca) can achieve a stable divalent oxidation state, which makes them suitable candidates for producing new mixed-metal perovskite compositions. Inspired by these works, we mixed Si (found highly dispersive and absorptive) with Ca and Zn with different specific ratios and found them highly efficient alternatives to MAPbI3. A single junction solar cell can only absorb partial light energies of the solar spectrum because photons with energies less than the band gap do not contribute at all. The absorption efficiency is thus limited by this cutoff. Hence, a narrow band gap around 1.0 eV is a suitable choice. The required band gap for the single junction solar cell is in the range of 1.10−1.40 eV, and the ideal bandgap is about 1.3 eV. A way to get a higher efficiency than that of a single junction solar cell is to build a solar cell by stacking different photoactive layers together. There are two common ways of stacking different layers in different architectures: multijunction solar cell and tandem solar cell. For multijunction solar cells the possible band gaps are from 1.55 to 2.30 eV, but the ideal band gap is between 1.7 and 1.8 eV. However, they are difficult to manufacture and design because the photocurrent generated in each layer needs to be matched; otherwise, electrons will be absorbed between layers. Tandem solar cell is easily achievable with high efficiency, which is composed of two stacking absorbers, i.e., top and bottom cells. For example, MAPbBr3/MAPbI3 and MAPbBr3/multicrystalline-screen-printed-Si are used as a top cell in the tandem architecture achieving the efficiencies of 13.4% and 18.8%, respectively.68 The ideal bandgap of the top cell should be in the range of 1.73−1.9 eV for absorbing the light of higher energy, while the bottom cell should have a band gap value in the range of 0.9−1.2 eV for absorbing the light of lower energy.34 This motivates us to search for new solar cell perovskite materials, especially toxic-free perovskite materials with narrow or wider band gaps having excellent absorption in application of different device architectures. The most studied materials, MAPbX3 and FAPbX3 (X = I, Cl, Br), have band gaps larger than 1.3 eV.45,46,49,65,66,69 Therefore, they are suitable for single junction solar cell and top cells in tandem architecture.18,41,70,71 In our present study we discovered Pb-free perovskite materials with high absorption efficiencies and different band gap values suitable for different devices architectures.

materials (MACaI3, MASrI3, and MABaI3) show strong absorption at higher energies, 4.0−8.0 eV in the UV spectral region. Our calculated band gap for MASrI3 is consistent with the previous PBE calculations.46 However, we got a direct band gap at the Γ-point which is different from their indirect band gap (3.77 eV at R−Γ).46 For group 2, we can conclude that alkaline earth metals are promising alternatives to Pb with strong absorption in the UV spectral region. Group 12 consists of Zn, Hg, and Cd, in which we replace Pb only by Zn while we left Hg and Cd untouched due to their highly toxic nature. Our calculations show that MAZnI3 has a direct band gap of 3.77 eV through the HSE06 functional, while it has 2.72 eV by PBE, with a broad and strong absorption at high energies of 4.5−8.5 eV in the UV spectral region. The group 13 elements, MABI3, MAAlI3, and MAGaI3, are found to have indirect bandgaps, which are 0.40, 1.04, and 0.72 eV, respectively, at Γ−K. Metals In and Tl from the same group are unexplored due to their high toxicity. Group 14 consists of C, Si, Ge, Sn, and Pb, in which we did not study carbon (C) due to its smaller ionic radius. MASiI3 has the smallest band gap value (0.51 eV by HSE06) in all listed materials with a strongest absorption at low energy (0.5−1.0 eV). The present bandgap of MASnI3 is 1.23 eV (by HSE06), which is well consistent with the experimental value of 1.20 eV49 and better than the previous PBE-calculated band gap values of 0.78 eV,66 0.61 eV,67 and the HSE06 band gap value of 0.75.58 Figure 4b,c shows the dielectric function and device absorption efficiencies of MASnI3 and MAGeI3 in comparison to MAPbI3, respectively. MASnI3 has strong and broader absorption in the energy range of 1.5−4.0 eV, suitable for the absorption of visible and infrared spectral light, well consistent with previous results.28 Figure 4c shows a strong device (its schematic structure is shown in Figure 4a) absorption efficiency (better than MAPbI3) above 900 nm in the visible and infrared region of light. We here emphasize that the absorption efficiency is wavelength-dependent, which implies that the absorption varies with light of different colors. Therefore, we can only make a qualitative judgment on absorption. One character is the width of the absorption window. Compared with MAPbI3 the other two materials have wider absorption windows, which suggests that more light can be absorbed. Another character is the value of absorption efficiency. Within 300 to 600 nm, all the three materials are comparable. Thus, a qualitative conclusion may be made that MASnI3 and MAGeI3 have good absorption properties or are even better than MAPbI3. In the same group, germanium (Ge) is another best alternative in the single-replacement materials due to its stronger and broader optical absorption. The experimental band gap value of MAGeI3 is 1.90 eV,49 while our calculated value is 1.28 eV (HSE06), which underestimates the experimental value but is well consistent with the previous calculated PBE band gap values (1.17 eV and 1.33 eV)46,49 while smaller than the 2.16 eV (by HSE06).64 We can see that the optical absorption as well as device absorption efficiency of MAGeI3 is not better than that of MASnI3 but stronger and wider than that of MAPbI3 in the visible as well as infrared spectral region. Hence, MASnI3 and MAGeI3 would be a stronger solar absorber and promising candidate for PVapplications as compared to MAPbI3. Due to the stronger and broader optical and device absorption of MASnI3 and MAGeI3 we expect that mixing Sn/Ge or mixing them with any other suitable metal atom (like; Ca, Mg, Sr, Zn, etc.) could lead to 723


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Chemistry of Materials Due to the homovalency of Ca2+ and Zn2+ to Pb2+, we found wider band gaps for MACaI3 and MAZnI3, with strong optical absorption in the UV spectral region. On the contrary, MASiI3 is found to possess a narrow band gap (0.51 eV), giving rise to a strong reddish light absorption. Noting the fact that Si is from the same group of Pb, this motivates us to mix with Ca and Zn separately to replace Pb. It may render us to tune the band gaps by their relative ratios and obtain best materials for PV applications. Moreover, silicon, calcium and zinc are the 2nd, 5th, and 25th most abundant elements in the earth’s crust. They are easily available, commercially very cheap, and environmentally friendly as compared to Pb. Figure 5 shows the calculated band gaps of all mixed-replaced perovskite materials with a comparison to experimental

cells and for a bottom cell in the tandem architecture. The band gap of MAZn0.5Si0.5I3 is 1.89 eV which is also an ideal value for the top cell in the tandem architecture. The PBE band gaps of the above four materials are also given in Figure 5. It is obvious that the PBE calculations underestimate the band gaps while HSE06 calculations are highly precise. Therefore, we can estimate the band gaps qualitatively based on the PBE data for other materials. Another feature is that the band gaps for MA(Ca/Si)I3 are narrowing with increasing Ca concentration (decreasing the Si concentration). This monotonically decreasing trend in the band gap is favorable for device architecture beyond p−i−n.43 For MA(Ca/Si)Br3 and MA(Ca/Si)Cl3, the calculated PBE band gap values are, 2.26, 1.25, 1.52, 1.73, 2.86, and 2.09 eV, while for MAZn0.5Si0.5Br3, and MAZn0.5Si0.5Cl3 the calculated PBE band gaps are 1.73 and 2.2 eV, respectively. It should be pointed out that MACa0.125Si0.875I3 has a band gap of 1.54 eV by HSE calculations, which is very close to the experimental value of MAPbI3 (1.55 eV). Hence, it could be an ideal replacement of MAPbI3 with high efficiency in PV cells. E. Optical Properties and Device Absorption Efficiencies for Mixed Ca/Si and Zn/Si Perovskites. Figure 6a

Figure 5. Bandgap values of our mixed study MA(Ca/Si)X3 and MA(Zn/Si)X3 (where X= I, Br, Cl). The red dotted line (1.3 eV) shows the ideal band gap for a single-junction solar cell according to the Shockley-Queisser theory. The blue dash-dot line (1.8 eV) shows the ideal band gap for the top-cell in tandem solar cells. Figure 6. (a) Imaginary part of dielectric function (ε2) and (b) Total device absorption efficiencies (single layer) for methylammonium Pbfree triiodides, MACa0.125Si0.875I3, MACa0.375Si0.625I3, MACa0.5Si0.5I3, and MAZn0.5Si0.5I3 in comparison to MAPbI3. The device architecture of solar cell is the same as in Figure 3a.

MAPbX3 (X= I, Br, Cl) data. The band structures of the mono-replaced materials are given in the Supporting Information (Figures S6 and S7). In the study of mixed replacements we also replaced I3 by Br3 (or Cl3) and found more tunability of the band gaps, which is a common phenomenon in these materials and has already been observed experimentally and computationally. Our calculated band gaps for MAPbBr3 and MAPbCl3 by PBE calculations are 2.1 and 2.6 eV, well consistent with the experimental values of 2.368 and 3.11 eV,72 respectively. For excellent solar absorber materials, an optimum band gap is a key factor. According to ShockleyQueisser theory,73 efficiency of ∼25% is achievable from the optimum band gap range of 0.9−1.6 eV. It is noted in Figure 5 that the red-dotted line and blue dashed-dotted line labeled the approximate values for ideal band gaps for single-junction and tandem solar cell. We perform PBE calculation for all materials studied in this work, but for accurate band gap values we perform HSE06 calculations for a few selected promising materials. In this way, we can reconcile the efficiency and precision of our search. From Figure 5, we see that the band gaps for MACa 0.125Si0.875I3, MACa0.375Si0.625I3, MACa0.5Si0.5I3, and MAZn0.5Si0.5I3 by HSE06 are 1.54, 1.47, 1.33, and 1.89 eV, respectively. Therefore, these materials are quite promising for single-junction solar cells, as well as in different architectures of tandem solar cells. For example, the band gap of MACa0.5Si0.5I3 is 1.33 eV which is in the ideal range of single-junction solar

shows the imaginary part of the dielectric function (ε2) for our mixed MA(Ca/Si)I3 and MA(Zn/Si)I3 perovskite materials in comparison to MAPbI3. These results are obtained by using the PBE functional first and applying a scissor operator to our mixed perovskite materials (MA(Ca/Si)I3 and MA(Zn/Si)I3). The scissor operator shifts the conduction bands up, reaching the band gap calculated by HSE06. The ε2 provides a direct measure of the optical absorption. All these mixed Pb-free perovskite materials have strong absorption with very sharp absorption edges, confirming the direct transition from the valence band (VB) to the conduction band (CB). It is clearly seen from Figure 6a that the strong optical absorption for all the mixed materials is below 3.0 eV. Furthermore, a second weaker absorption peak appears in the energy range of 3.0−4.0 eV, which may be induced by transitions from the VB to the CB at the K point in Figure 7a− c). According to the AM 1.5 solar spectrum, about 98% of the solar energy reaching the earth surface is composed of photons below 3.4 eV. Noteworthy is that almost all our mixed materials have strong absorption below 3.4 eV; hence, they might be strongly efficient candidates for solar energy applications. 724


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solar cells act as free holes and electrons rather than as excitons and have high mobility.74 Hence, we consider the effective mass smaller than 1.5m0 as a suitable range for solar materials with high mobility, where m0 is the bare mass of electron. In almost all semiconducting materials, the CB dominated by cationic p states usually gives a small electron effective mass.58 In MAPbI3 type materials it is interesting that there exists a p−p transition from VB to CB, and this is the reason for their highly dispersive VB and CB which could lead to low hole effective mass (m*h ) or electron effective mass (m*e ).58 It has been shown that Sn doping at the B-site changes the shape of VBM by producing extra energy states above the VBM and is responsible for lowering the effective mass of holes.75 We also observed the same behavior of the p−p transition from VB to CB in all our mixed-replaced materials, as well as in MAPbI3. This could be confirmed through the projected density of states (PDOS) plot included in the Supporting Information (Figure S11). We calculated the effective masses for all the 27-listed mono- and mixed Pb-replaced materials. Effective masses for MA(Ca/Si)I3 and MAZn0.5Si0.5I3 are shown in Table 2 in comparison to

Figure 7. Band structures for MACa0.125Si0.875I3, MACa0.5Si0.5I3, and MAZn0.5Si0.5I3 are presented in a comparison to MAPbI3.

To further investigate the authenticity of the strong absorption we calculated the device absorption efficiencies (single layer) for our Pb-free mixed materials in Figure 6b. One can see that MAPbI3 has an abrupt decrease in the absorption efficiency above 600 nm, having a weak peak around 756 nm where the absorption efficiency is about 60%. At a wavelength longer than 800 nm, the absorption efficiency decreases abruptly to 20%. The position of the absorption spectra starting an abrupt decrease is called the absorption edge. The existence of the absorption edge means only partial solar photons can contribute to the absorption. The absorption edge basically depends upon the bandgap of a material. As we have different bandgaps for our mixed-replaced perovskites, we observe different absorption edges in Figure 6b. Smaller bandgap leads to stronger absorption of red, orange, and yellow light, which consists of about 95% sun radiations reaching the earth surface. Therefore, our mixed-replacementsbased solar cells exhibit high device absorption efficiency in a much wider solar spectra. The absorption edges are shifted to 850 nm for mixed Ca/Si materials and 750 nm for MAZn0.5Si0.5I3. It is noted that our mixed Ca/Si perovskites have strong and wider absorption efficiency above 900 nm while it is up to 800 nm for MAPbI3. This renders the mixed replacements promising candidates in application of Pb-free solar cells. F. Band Structure, Effective Mass, and Density of States. To get deeper insight, we explored the electronic properties such as band structures, effective masses (m*), and projected density of states (PDOS) for our single and mixedreplacement materials. We present the band structures of MACa0.125Si0.875I3, MACa0.375Si0.625I3, and MAZn0.5Si0.5I3 in comparison to that of MAPbI3, as shown in Figure 7. The band structures of other mixed and mono- (11−11 in total) replacement materials are shown in the Supporting Information (Figures S4−S8). In Figure 7, it is seen that the valence band (VB) as well as the conduction bands (CB) of all the mixedreplacement materials are more dispersive than those of MAPbI3. Moreover, it is noted that in all these mixed materials the band gaps at K points are also direct and highly dispersive, rendering the optical absorption at the K point feasible. These two direct valleys at the Γ and K points, which we cannot observe in MAPbI3, may be responsible for their high optical absorption. This behavior can also be observed in the remaining mixed-replacement materials except for a few cases, as given in the Supporting Information (Figures S6−S8). Effective mass is one of the most important factors responsible for the mobility of electron and hole carriers in solar cells. It has been observed that the charges in perovskite

Table 2. Calculated Effective Mass (m*, in units of m0) of Electrons and Holes for Our Highly Efficient Mixed Perovskite Materials, MACa0.125Si0.875I3, MACa0.375Si0.625I3, MACa0.5Si0.5I3, and MAZn0.5Si0.5I3a material

me* (this work)

mh* (this work)

Si MAPbI3 MACa0.125Si0.875I3 MACa0.375Si0.625I3 MACa0.5Si0.5I3 MAZn0.5Si0.5I3

0.25 0.37 0.21 0.24 0.18 0.28

0.13 0.28 0.21 0.18 0.12 0.17

m*e (prev)

mh* (prev)

0.19 0.19, 0.30

0.16 0.25, 0.25

a

Previous results (prev) are also given for comparison in the cases of MAPbI3 and Si.

MAPbI3 and silicon (Si). The effective masses for the remaining mono- and mixed-replacement materials are given in the Supporting Information (Table S2). It is clear from Table 2 that the electron effective masses m*e as well as the hole effective masses m*h for our mixed-replacement materials are lower than those of MAPbI3 and Si (today’s PV leading champion). Our calculated effective masses for MAPbI3, m*e = 0.37, m*h = 0.28, are in good agreement with the previous results, i.e., m*e = 0.19, m*h = 0.2567 and m*e = 0.30, m*h = 0.25.46 Similarly, our calculated effective mass for Si is m*e = 0.25, m*h = 0.13 is also consistent with the previous results (m*e = 0.19, m*h = 0.16).46 Such low effective masses m*, as calculated for our mixed-replacement materials, are beneficial to ambipolar conductivity favored by PV applications. These entrusting explorations reveal that our work could present better transport properties in the PV industry. We observed that as we replace I3 by Br3 or Cl3, the effective mass starts to increase, but is still favorable (below 1.5m0), as clearly seen from Table S2. Effective masses for Sn, Ge, Si, and Sr (single replacements) are a little bit smaller than those of the previous calculations. For other single-replacement materials, the effective masses are calculated for the first time and also in a favorable range of high mobility. 725


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IV. CONCLUSIONS We present here a systematic ab initio study demonstrating the replacement of Pb in MAPbI3 perovskite by nontoxic single elements and binary elements. We explored, for the first time, the mixing of Ca/Si and Zn/Si with different ratios leads to the Pb-free perovskite materials with excellent absorption efficiencies. A narrow band gap of 1.33 eV for MACa0.5Si0.5I3 is in the ideal range for a single-junction solar cell, which can also be used as a bottom cell in the tandem architecture. MACa0.125Si0.875I3 with excellent absorption efficiency and suitable band gap value (1.54 eV) may be the best alternative to MAPbI3 (Eg = 1.55 eV). The band gap of 1.89 eV for MAZn0.5Si0.5I3 is also an ideal value for the top cell in the tandem architecture. The ratio adjustment of Ca/Si and Zn/Si open a way to tailor the materials properties, such as photovoltaic performance and electronic transport properties. We presented good effective mass values for our mixedreplacement materials, which are smaller than that of MAPbI3 but comparable with that of Si. We performed the ab initio molecular dynamic simulation confirming the stability of the mixed replacements. Our mixed-replacement study shows a high device absorption efficiency in a much wider range of solar spectra compared to MAPb3, which makes them excellent candidates for applications in Pb-free solar cells. This new family of materials could establish an unexplored area and may offer more members in materials library for PV technology. It is expected that more Pb-free alternatives such as MA(Mg/Si)I3 will be discovered, which allows us to tune the material properties while preserving their excellent optoelectronic properties. We expect that this work will inspire researchers to experimentally investigate these new lead-free perovskites species for solar cell applications.

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programme for Ph.D. study. This work is supported by Hundred Talents Program of the Chinese Academy of Sciences (CAS) and NSFC (Grant No. 11674317). G.S. is supported in part by the MOST (Grant No. 2013CB933401), NSFC (Grant No. 11474279), and CAS (Grant No. XDB07010100). This work is also supported in part by the Key Research Program of the CAS (Grant No. XDPB08).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b04036. Graphs for tolerance factor, ab initio molecular dynamics simulations, crystal parameters, dielectric functions for materials, band structures for some mono-replaced materials with PBE functional, calculated effective masses, band structures for some mono-replaced materials with HSE functional, and band structures and density of states for some bi-replaced materials (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*(Z.-G.Z.) E-mail: [email protected]. *(G.S.) E-mail: [email protected]. ORCID

Zhen-Gang Zhu: 0000-0002-2837-6072 Qing-Bo Yan: 0000-0002-1001-1390 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are thankful to Naeem Ullah, M. Sajjad, Majid Khan, Li-Chuan Zhang, Faisal Munir, Saadi Ishaq, and Prof. Hui Huang for useful discussions and suggestions. R.A. is financially supported by the CAS-TWAS president’s fellowship 726


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