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First-Principles Modeling of Lead-Free Perovskites for Photovoltaic Applications Diwen Liu, Qiaohong Li, Huijuan Jing, and Kechen Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11695 • Publication Date (Web): 25 Jan 2019 Downloaded from http://pubs.acs.org on January 25, 2019

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The Journal of Physical Chemistry

First-Principles Modeling of Lead-Free Perovskites for Photovoltaic Applications Diwen Liu,a,c Qiaohong Li,*a Huijuan Jing a,c and Kechen Wu*a,b State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, P. R. China a

Center for Advanced Marine Materials and Smart Sensors, Minjiang University, Fuzhou 350116, P. R. China b

c

University of Chinese Academy of Sciences, Beijing 100049, P. R. China

ABSTRACT The material class of hybrid organicinorganic halide perovskites has been rapidly progressed in the field of photovoltaic applications. However, this class of materials has limitations associated with its poor stability and toxicity of the lead element. Therefore, there is a strong desire to search for environmentally friendly perovskite materials without affecting the conversion efficiency. First-principles calculations have been employed to study thermodynamic stability, electronic and optical properties of potential candidate lead-free perovskites. The results show that the ionization energy at A-site can provide an explaination for the stabilities of hybrid perovskites. The bond lengths and bond angles are likely responsible for the discrepancy in band gap.The results indicate that DAGeI3 has better stability and suitable band gap among Ge-based AGeI3 perovskites. It is observed that the Si-doped perovskites are energetically favorable. CsGe2/3Si1/3I3 can become the potential candidate for the light absorption layer due to the ideal band gap among the Si-doped perovskites. Our study offers insights on how composition variation affect thermodynamic stability and electronic properties in this family of Ge-based perovskites. This work is helpful to obtain further insights into developing lead-free perovskite solar cells. 1

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1. INTRODUCTION The material class of hybrid organicinorganic halide perovskites ABX3, where A is a monovalent organic cation, B is a bivalent metal cation, and X is a halide anion, have been attracted great attention in the past few years.1-4 With intense research efforts, the power conversion efficiency (PCE) of this class of materials has been rapidly developed from the original value of 3.8% in 20092 to a higher value of 22.1% in 2017.5 Furthermore, these perovskites contain earth-abundant essential elements and can be synthesied by low-temperature solution processing,6-9 making them highly promising for low-cost photovoltaic applications. However, the main issues of these materials are their stabilities along with the use of lead. The utilization of lead can cause serious pollution of the environment, so large-scale development of the Pb-based materials have been prohibited. Therefore, lead-free perovskites have been developed in order to obtain comparable or better photovoltaic performance than that of CH3NH3PbI3. Considering the high efficiency achieved by the Pb-based materials, so many attempts have been made to replace Pb with a similar element that is close to Pb in the periodic table with the hope that the photovoltaic performance of the Pb-based materials can be preserved.10-15 Sn is a suitable candidate of great interest. Pb and Sn have a similar radius of their ions. That might encourage Sn to replace Pb with no significant perturbation in the structure. However, the efficiency achieved by the pure Sn-based materials was much lower than that of the Pb-based materials.16-17 In addition, Sn2+ is relatively unstable and easily oxidized to Sn4+ leading to structure transformation and thus exhibiting poor performance.11 Another feasible alternative is the Ge element. Recently, a series of Ge-based perovskites with different organic cations were synthesized by Kanztzidis’s group.18 The results showed that the band gaps of CsGeI3 and MAGeI3 are 1.60 and 1.90 eV, respectively.18 However, the PCE of CsGeI3 and 2


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MAGeI3 were only 0.2% and 0.11%, respectively, which was ascribed to a relatively low VOC of 74 and 150 mV for CsGeI3 and MAGeI3, respectively.19 Ge is not easy oxidation compared with Sn,20 which is a drive for us to replace Pb with Ge in order to explore the photovoltaic properties of Pb-free perovskites. The photovoltaic properties of Pb-free perovskites have been reported by the replacements of Pb with Sn or Ge.2122

Silicon is the leading player in the photovoltaic field. Silicon also possesses many

excellent properties, such as non-toxicity, environment-friendly, and stability. However, silicon as absorbing layer material in solar cells is an indirect bandgap semiconductor.23 We expect that the band gaps of Ge-based perovskites can be tuned by the Si replacement to obtain the ideal value. The main goal of this work is to search for potential candidates of lead-free perovskite materials that preserve the optoelectronic properties of the Pb-based perovskites. In the former, we consider the replacements of the A-site cations by the suitable size of the cations. In the latter, we systematically study replacements of Ge by Si with different ratios. We expect that this work can provide a deep insight for exploring new lead-free perovskites in photovoltaic applications. 2. COMPUTATIONAL DETAIL All the first-principles calculations were carried out by means of the Vienna Ab initio Simulation Package (VASP) based on density functional theory (DFT).24 The projectoraugmented wave function (PAW) method25 was used to denote the electron–ion interactions and the Perdew–Burke–Ernzerhof (PBE) type of the generalized gradient approximation (GGA)26 was chosen to describe the exchangecorrelation effect of electrons. The 4 × 4 × 4 k-meshes were adopted to optimize atomic structure and calculate electronic property. The cut-off energy for the plane wavefunctions was set to 500 eV. The atom coordinates were fully optimized until the residual forces were 3



smaller than 0.01 eV Å1. The total energy was converged to 105 eV. Van der Waals interactions play an important role in the hybrid organicinorganic halide perovskite materials.27-28 The optB86b-vdW functional29 was chosen for the structural optimization. Besides, to account for the underestimation of the band gap in GGA-PBE calculations, HeydScuseriaErnzerhof (HSE06) hybrid functional calculations were performed to obtain accurate electronic structures.30-31 The exact Hartree-Fock exchange contribution for hybrid functional was set to 50% and 60% for MAGeI3 and CsGeI3 perovskites to reproduce their expermential values, respectively. Based on the calculated electronic structures from the HSE06 method, we employed much denser 6 × 6 × 6 k-meshes to obtain the optical absorption. In addition, the spin-orbit coupling (SOC) effect had a weak influence on the electronic properties of Ge-based perovskites,32 thus the band structures were calculated without considering the SOC effect. 3. RESULTS AND DISCUSSION 3.1 Structure Properties Figure 1(a) demonstates the geometric structure of hybrid perovskite MAGeI3 is a distorted octahedron with the space group R3m at room temperature. Compared with the centric PbI6 framework in tetragonal MAPbI3 perovskite, the octahedral GeI6 is highly distorted due to the significant discrepancy of GeI bonds.33 The orientation of all CN dipole distributes the same direction, as shown in Figure 1(b).

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Figure 1. Optimized structure of MAGeI3. The left panel shows the structure in polyhedron graphs. The right panel is a top view in atomic structure.

In total eight inorganic/organic cations are considered on the A-site of Ge-based perovskites. The molecular structures of A-site cations are depicted in Figure 2. The chosen monovalent cations have comparable ionic sizes, including Cs+, ammonium NH4+ (M), hydroxylamine NH3OH+ (HA), diamine NH2NH3+ (DA), methylammonium CH3NH3+ (MA), formamidinium CH(NH2)2+ (FA), cyclopropenium C3H3+ (Cy), and aziridinium (CH2)2NH2+ (Az). To our knowledge, among these candidate materials only three were synthesized experimentally (including CsGeI3, MAGeI3, and FAGeI3).18 The calculated lattice constants and volumes of AGeI3 (A = Cs, MA, and FA) perovskites are in good agreement with the exprimental results (see Table 1),18 which justifies the reliability of our method.

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Figure 2. The molecular structures of the A-site cations in hybrid perovskites. Table 1. Calculated lattice parameters for AGeI3 (A = Cs, MA, FA) perovskites at the optB86bvdW level.

CsGeI3 CsGeI3 (exp.)a MAGeI3 MAGeI3 (exp.)a FAGeI3 FAGeI3 (exp.)a a From Reference 18.

a/Å 8.33 8.36 8.27 8.55 8.29 8.47

b/Å 8.33 8.36 8.27 8.55 8.16 8.47

c/Å 10.41 10.61 11.18 11.16 11.90 11.73

V/Å3 625.82 641.89 661.19 707.20 700.36 728.20

To evaluate thermodynamic stabilities of Ge-based perovskites, we calculated the formation energies with respect to the possible pathways. According to the previous report, MAPbI3 decomposes into the corresponding binary materials (MAI + PbI2).34 In a similar way, we calculated the formation energies of AGeI3 perovskites through the following approach:

H  E ( AGe 3 )  E ( A)  E (Ge 2 )

(1)

For the Si-doped CsGeI3 and MAGeI3 perovskites, we adopted the special approach to calculate the formation energies of the mixed perovskites:35

H  E (AGe1 nSi n I 3 )  [ E (AI)  (1  n) E (GeI 2 )  nE (I 2 )  nE (Si)] (2) where n represents the ratios of 1/3, 2/3, and 1. According to eq 1 and 2, the negative value of H means that the material is stable. The larger magnitude of the negative H indicates the higher stability of the material and vice versa. The formation energies of AGeI3 are shown in Figure 3(a). Our calculated value for MAGeI3 is well consistent with the previous values and these values are quite close to zero.35 The CsGeI3 is more stable than MAGeI3 and FAGeI3 based on their formation energies, which is in good agreement with the experimental results.19 DAGeI3 is the most stable structure among AGeI3 perovskites. However, MGeI3, HAGeI3, and CyGeI3 are little stable. Using Si5I10 as reference, the results indicated that CsSiI3 was found to be intrinsically unstable.36 6


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Our results reveal that the stabilities of the mixed perovskites are apparently improved by the introduction of Si, as shown in Figure 3(b).

Figure 3. Calculated formation energies of (a) AGeI3 and (b) Si-doped CsGeI3 and MAGeI3 perovskite systems. A represents a series of organic cations.

According to the previous study, the ionization energy at A-site has an important effect on the stabilities of hybrid perovskites.37 The lower ionization energy, the more stable is the structure. The ionization energies of Cs and MA are in good agreement with the theoretical and experimental results.37-38 Results in Table 2 demonstates Cs and Az have lower ionization energies than those of the other molecules, which explain the better stabilities of CsGeI3 and AzGeI3. M, HA, and Cy have larger ionization energies than Cs. This result suggests that MGeI3, HAGeI3, and CyGeI3 should be less stable than CsGeI3, which matches well with the above results. Although DA has a larger ionization energy than Cs, the result indicates that DAGeI3 is the most stable structure among Ge-based perovskites. Therefore, the ionization energy of DA can not provide an explanation for the stability of DAGeI3. Table 2. Ionization energies of atoms and molecules calculated with DFT. 7



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H (eV) 4.67 3.89 4.21 4.41 4.63 5.63 3.87 4.23

Ions M+ Cs+ MA+ DA+ HA+ Cy+ Az+ FA+

The tolerance factor is usually employed to estimate the formation of a stable perovskite crystal-phase by using the following formula:1 t

RA  RX 2 ( R  RX )

(3)

where RA, RB, and RX are the effective ionic radii for the A, B and X position, respectively. The results suggest that the value of the tolerance factor ought to fall between 0.81 and 1.11.39 As a matter of fact, in order to get a stable perovskite, the ideal t should be close to 1. The tolerance factors of the Si-doped perovskites are presented in Table 3. The tolerance factor of CsGe2/3Si1/3I3 is 0.97, which is consistent with the relevant conclusions.39 Table 3. Calculated the tolerance factors (t) of the Si-doped perovskites. CsGeI3 CsGe2/3Si1/3I3 CsGe1/3Si2/3I3 CsSiI3

t 0.93 0.97 1.01 1.05

MAGeI3 MAGe2/3Si1/3I3 MAGe1/3Si2/3I3 MASiI3

t 0.95 1.00 1.04 1.09

3.2 Electronic Properties As the light absorption layer in solar cells, the band gap is an important factor for the efficient spectral absorption. The band structures of all the perovskite systems are given in the Supporting Information (Figure S1-S3). The band structures of all the perovskite systems are similar to each other, in which the conduction band minimum (CBM) and 8


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valence band maximum (VBM) are located at the same Z (0, 0, 0.5) position in the Brillouin zone. This indicates that all the perovskite systems are direct-bandgap materials. The calculated band gaps of CsGeI3, MAGeI3, and FAGeI3 with the different methods are presented in Table 4. The band gaps of CsGeI3, MAGeI3, and FAGeI3 with the PBE method are 0.68, 1.05, and 1.36 eV, respectively, which are in good agreement with the previous theoretical results except for FAGeI3.35,

40

However, these values

seriously underestimates the corresponding experimental values. It is well known that GGA-PBE underestimates the band gaps of hybrid perovskites. In order to get more accurate band gaps, we performed HSE06 calculations. The band gaps of CsGeI3, MAGeI3, and FAGeI3 with HSE06 functional are 1.56, 1.89, and 2.33 eV, respectively, which matches well with the experimental values.18-19 It indicates that HSE06 functional can give accurate band gaps for other perovskite systems. The HSE06 approach with the default parameters still underestimates the band gap of MAGeI3 according to previous theoretical results.35, 41 The calculated band gaps of Ge-based AGeI3 perovskites are displayed in Figure 4(a). Although the A position does not significantly influence the band structures, the alternation on A can still tune the band structure to a certain extent. With the increase in the size of A, from Cs to MA and FA, the value of the band gap gradually increases. A similar trend is also shown in the other perovskite systems. However, on further increasing the size of A to CH3C(NH2)2, the perovskite CH3C(NH2)2GeI3 structure will turn into the monoclinic phase, with a larger band gap of 2.5 eV.18 Among the eight Ge-based perovskites, CsGeI3 and DAGeI3 possess proper band gaps. Although MGeI3 and HAGeI3 also have suitable band gaps, their structures are little stable. Meanwhile, MAGeI3, FAGeI3, and AzGeI3 are not suitable for photovoltaics due to their larger band gaps.

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Table 4. Calculated band gaps of CsGeI3, MAGeI3, and FAGeI3 at different levels of theory along with previous theoretical and experimental values. PBE HSE06 PBE HSE06 Exp. (this) (this) (prev.) (prev.) CsGeI3 0.68 1.56 0.73,a 1.07b 1.55b 1.60,e 1.63f a c d c d MAGeI3 1.05 1.89 1.20, 0.87 , 0.96 1.28, 1.41 1.90,e 2.00f FAGeI3 1.36 2.33 1.91a 2.20,e 2.35f  The unit of band gap is eV. “this” indicates this work, “prev.” means previous result, and “Exp.” represents experimental work. aReference 40. bReference 32. cReference 35. dReference 41. eReference 18. fReference 19.

The band structure of the perovskite is primarily dependent on the inorganic components. This indicates that the lattice parameters are highly related to the electronic structures of perovskites. The bond lengths of GeI and bond angles of GeIGe of Ge-based perovskites are listed in Table 5. The results show that FAGeI3 exhibits more significant discrepancy between short and long bond lengths. Furthermore, the calculated GeIGe bond angle in perovskite FAGeI3 is about 162.6, which demonstrate that the GeI6 octahedra is highly distorted. These results give rise to a larger band gap of FAGeI3 (2.33 eV), compared with a band gap of 1.56 eV for CsGeI3. A similar phenomenon is observed in the other perovskite systems. Previous reports have indicated that the SnISn bond angle as a main factor in the controlling electronic properties of Sn-based layered perovskites.42-43 In fact, analysis of the bond lengths and bond angles provides an explanation for the variation in band gap among Ge-based perovskites.

Table 5. Calculated bond lengths of GeI and bond angles of GeIGe of Ge-based perovskites.

MGeI3 CsGeI3 DAGeI3 HAGeI3 MAGeI3 CyGeI3

GeI bond length (Å) Short Long 2.80 3.11 2.80 3.15 2.77 3.28 2.81 3.29 2.78 3.32 2.76 3.38

GeIGe bond angle (deg)

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171.0 170.3 166.9 170.3 166.2 164.6

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AzGeI3 FAGeI3

2.77 2.74

3.38 3.69

171.4 162.6

According to the ShockleyQueisser theory, single junction solar cells with an ideal band gap of 1.34 eV may have the maximum theoretical efficiency.44 In other words, when the band gap is smaller than 1.34 eV, the efficiency increases as the increase of band gap. However, when the band gap is larger than 1.34 eV, the efficiency decreases as the increase of band gap.45 For the Si-doped perovskites, with an increase of the Si proportion, the band gaps of the mixed perovskites gradually decrease until keep almost unchanged, as shown in Figure 4(b). The Si-doped MAGeI3 perovskite materials have still larger band gaps, making them undesirable for solar cells. Therefore, CsGe2/3Si1/3I3 can become the potential candidate for the light absorption layer due to the optimum band gap among the mixed perovskites.

Figure 4. Calculated band gaps of (a) AGeI3 and (b) Si-doped CsGeI3 and MAGeI3 perovskite systems. A represents a series of organic cations.

To further understand the electronic structures of hybrid perovskites, the density of states (DOS) are analyzed. The DOS and partial DOS of AGeI3 perovskites exhibit similar curves, as depicted in the Supporting Information (Figure S4-S6). The organic 11



cations do not contribute to the band edge states because the states of organic cations are far from the Fermi level. The VBM of AGeI3 is mainly contributed by the I 5p and Ge 4s orbitals, whereas the CBM is mainly composed of Ge 4p orbitals. The electronic states in the edge of the band gap are in good agreement with previous theoretical investigations.40 All the Si-doped perovskites give a similar component of orbital contribution. With an increase of the Si proportion, the orbital contribution of Ge drops sharply, and the contribution of Si increases apparently. 3.3 Optical Properties Strong optical absorption is particularly crucial for the light absorption layer. In order to investigate the optical performance of Ge-based perovskites, we further calculated the optical absorption coefficients in the visible spectrum. The absorption coefficient I() was calculated from the dielectric function as below:46 I ( )  2

  ()   () 2

1

2

2

  1 ( )



1/ 2

(4)

where 1() and 2() represent the real and imaginary parts of the dielectric function depending on the light frequency , respectively. For comparison, the optical absorption of MAPbI3 was also calculated. The calculated optical absorption spectra are displayed in Figure 5. Considering the stability and suitable band gap of material, the optical absorption of CsGeI3, DAGeI3, and CsGe2/3Si1/3I3 are analyzed. The optical absorption of MAPbI3 in this work agrees well with previous results.47 In the whole visible region, Ge-based perovskites show slightly weak absorption abilities compared with that of MAPbI3. In the range of 200300 nm, the absorption abilities are stronger in the Ge-based systems compared with that of MAPbI3. All the Ge-based perovskites exhibit a comparable absorption ability to each other. Taking the stability, band gap,

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and optical property into consideration, CsGe2/3Si1/3I3 can become the potential candidate in perovskite solar cells.

Figure 5. The optical absorption spectra of DAGeI3, CsGeI3, and CsGe2/3Si1/3I3 in comparsion to MAPbI3.

4. CONCLUSIONS First-principles calculations were employed to investigate the structures, electronic and optical properties of Ge-based AGeI3 and Si-doped AGeI3 perovskites. In AGeI3 perovskite systems, the stabilities of MGeI3, HAGeI3, and CyGeI3 are poor based on their formation energies. The thermodynamic stabilities of the mixed perovskites are apparently improved by the introduction of Si. Our results exhibit that the value of the band gap gradually increases as the increase in the size of A. DAGeI3 has the better stability and suitable band gap, which can be chosen as a competitive potential candidate of efficient light absorption layer. The Si-doped CsGeI3 and MAGeI3 perovskites show relatively lower band gaps compared with the pure Ge-based perovskites. The results indicate that CsGe2/3Si1/3I3 with the ideal band gap of 1.34 eV can become the potential candidate for lead-free perovskite material in the future. Our results not only highlight the effects of A and Si-doping on the stabilities and electronic properties of Ge-based perovskites, but also it provides a deep insight for the

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development of environmentally friendly perovskite materials in photovoltaic applications. Supporting Information The band structures and density of states for perovskite materials with HSE06 functional. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (Q. Li), [email protected] (K. Wu) Fax: +86 591 63173138 ORCID Diwen Liu: 0000-0001-8119-7666 Qiaohong Li: 0000-0001-9286-3580 Huijuan Jing: 0000-0003-1627-9803 Kechen Wu: 0000-0002-9531-2239 Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS This work was supported by the National Science Foundation of China (No. 21673240) and the Foreign Cooperation Project of Fujian Province (No. 2017I0019). REFERENCES (1) Snaith, H. J., Perovskites: The Emergence of a New Era for Low-Cost, HighEfficiency 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, 60506051. (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, 506-514. 14


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First-Principles Modeling of Lead-Free Perovskites ... - ACS Publications

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