Poor Photovoltaic Performance of Cs3Bi2I9: An Insight through First

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Poor Photovoltaic Performance of CsBiI : An Insight through First Principles Calculations Biplab Ghosh, Sudip Chakraborty, Hao Wei, Claude Guet, Shuzhou Li, Subodh Mhaisalkar, and Nripan Mathews J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03501 • Publication Date (Web): 04 Jul 2017 Downloaded from http://pubs.acs.org on July 5, 2017

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The Journal of Physical Chemistry

Poor Photovoltaic Performance of Cs3Bi2I9: An Insight through First Principles Calculations

Biplab Ghosh1,2, Sudip Chakraborty3, Hao Wei4, Claude Guet2,4, Shuzhou Li4, Subodh Mhaisalkar2,4, Nripan Mathews2,4,* 1

2

Interdisciplinary Graduate School, Energy Research Institute at NTU, 639798 Singapore

Energy Research Institute at Nanyang Technological University (ERI@N), Research Techno Plaza, X-Frontier Block Level 5, 50 Nanyang Drive, Singapore 637553, Singapore 3

Materials Theory Division, Department of Physics and Astronomy, Uppsala University, Uppsala, SE- 75120, Sweden

4

School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798 Singapore

Keywords: Density functional theory, Bi-based perovskite, lead-free perovskite, defects calculations

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ABSTRACT

Bismuth-based halide perovskite derivatives have now attracted huge attention for photovoltaic (PV) applications after the unparalleled success of lead-based halide perovskites. However, the performances of PV devices based on these compounds are poor, despite theoretical predictions. In this article, we have investigated the electronic structure and defect formation energies of Cs3Bi2I9 using Density Functional Theory (DFT) calculations. The calculated electronic bandstructure indicates an indirect bandgap and high carrier effective masses. Our calculations reveal a large stability region for this compound, however deep level defects are quite prominent. Even, the varying the chemical potentials from stoichiometric region, do not eliminate the presence of deep defects, ultimately limiting photovoltaic efficiencies.

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INTRODUCTION Lead(Pb)-based organic-inorganic halide perovskites have revolutionized thin-film solar cell research due to their facile processability, bandgap tunability and power conversion efficiencies (PCE) exceeding 20%

1-3

. However, the toxicity and stability remain key issues in the

widespread application of Pb-based halide perovskite solar cells. Though homovalent substitution (Sn2+, Ge2+) could be a viable option to reduce the toxicity of Pb, it also reduces the stability of the perovskites in ambient atmosphere 4-8. As an alternative, heterovalent substitution by Bi3+ or Sb3+ has gained a lot of consideration recently

9-12

. Both elements have stable +3

oxidation state and are considered less toxic in comparison to Pb. In addition, Bi3+ and Pb2+ have similar electronic structure (presence of 6s2 electrons) and ionic radius, which may lead to similar optoelectronic properties. Cs3Bi2I9 was shown to be prominent among the Bi-based halides due to the higher efficiencies noted in photovoltaic devices by Park, et al.

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as well as

their higher chemical stability9. Brandt et. al. have pointed out that Cs3Bi2I9 could be a potential defect tolerant material due to similar halide chemistry as that of Pb-based halide perovskites 13. However, follow up reports have demonstrated poorer efficiency of Bi-based ternary halide perovskites 11, 14-15. Although the interest on Bi-based ternary halide perovskites for photovoltaic (PV) applications have remained, very few theoretical reports have assessed the suitability of Cs3Bi2I9. In this letter, we have investigated the role of the electronic bandstructure and defect characteristics in the optoelectronic properties of Cs3Bi2I9 using Density Functional Theory (DFT). Cs3Bi2I9 crystals exhibit a hexagonal structure at room temperature with space group P63/mmc and undergo a ferroelastic phase transition to monoclinic structure at 220K

16

. As the room

temperature phase is of primary interest in PV applications, we have only considered the


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hexagonal crystal structure of Cs3Bi2I9 in our study. The hexagonal structure can be considered as a distorted and defect modulated face-sharing perovskite structure (AMX3, A = +1 cation, M = +2 cation, X = Cl, Br, and I) in which every third layer of octahedra M sites are depleted for charge neutrality. Consequently, a pair of [BiI6]3- octahedra share faces to form a [Bi2I9]3bioctahedra, eventually forming a 0D structure, and the voids between these bioctahedra are filled with Cs+ cations (Figure 1. (a)). Consequently, the Bi-I bond lengths have been varied between 2.923 to 3.246 Å and I-Bi-I bond angle deviates from 90° as compared to conventional cubic perovskites.

Figure 1. (a) Crystal structure of Cs3Bi2I9 (blue, green, and purple represent Bi, Cs, and I) and (b) GGA/PBE electronic bandstructure of Cs3Bi2I9 (P63/mmc) with and without Spin Orbit Coupling (SOC)

COMPUTATIONAL DETAILS The electronic structure calculations are performed using Vienna Ab-initio Simulation Package (VASP) within the framework of projected augmented-wave method (PAW) formalism. The energy cutoff has been taken as 400 eV as the converged energy cutoff17-22. The atomic


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coordinates are relaxed until the force acting on the individual atom are less than 0.05 eV/Å. All the structural relaxations are performed with Gaussian smearing of 0.01 eV. Cs, Bi, and I atoms are described by 5s25p66s1, 5d106s26p3, 5s25p5 valence electrons respectively. A 5x5x2 Monkhorst-Pack for unit cell was considered for the Brillouin zone integration. For defect studies, a 2x2x1 supercell was used with 3x3x2 Gamma K-point grid. The simulations of the band structures were carried out in two steps. The high symmetry path is assumed with respect to the Brillouin zone center Γ with the coordinates (0, 0, 0) to M (0.5, 0, 0), K (0.333, 0.333, 0), Γ (0, 0, 0), A (0, 0, 0.5), L (0.5, 0, 0.5), and H (0.333, 0.333, 0.5). The effect of nonlocal exchange has been considered using screened hybrid exchange correlation functional proposed by Heyd, Scuseria, and Ernzerhof (HSE06)23-25. 25% of Hartree−Fock (AEXX) and 75% of GGA-PBE (AGGAX) contributions sum up together for the exchange part in HSE06. The correlation part of the hybrid functional comes mainly from PBE type EC: =

1 , 3 , + + , + 4

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where is the HF exchange energy, and denote the exchange and correlation parts of PBE type exchange correlation functional respectively. Effective mass of the carriers was calculated assuming parabolic band diagram at CBM and VBM based on the following equation ∗ = ℏ [

() ]

Where ϵ(k) represents band eigenvalues and k is the crystal momentum vector. The defect formation energy has been calculated using the following equation26 ! [" # ] = $%$ [" # ] + & '( μ( − $%$ [+,-] + .(/01 + ) (


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Where, total energy Etot[Xq] is calculated for the supercell containing the defect X in charge state q, and Etot[bulk] for the perfect supercell. The integer ni is the number of atoms of species i (host atoms or impurity atoms). ni is positive when the it is removed from the supercell and negative when it is added to the supercell to create the defect, and the µi is the relative chemical potentials of i. The electrostatic energy correction value that carried out in this study is considered as less than 0.1. The transition level of the defects was calculated as Fermi level for which the formation energy of the charge states is equal: ! (" # ; = 0) − ! (" # ; = 0) .1 /2 4 = .2 .2 − .1 where Ef (Xq; EF=0) is the formation energy of the defect X in the charge state q when the Fermi level is at the VBM (EF = 0) 26.

RESULTS AND DISCUSSION A suitable value of the band gap is a minimal requirement for photovoltaics and optoelectronic applications. There are different published reports of the experimental value of the bandgap of Cs3Bi2I9. Machulin, et al.

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have reported a bandgap of ~2.8 eV for Cs3Bi2I9 single crystals.

However, recent works by Lehner, et al.

9

and Park, et al.

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have estimated an indirect optical

bandgap of 1.9 eV and 2.2 eV for Cs3Bi2I9 thin-films respectively. We have also synthesized Cs3Bi2I9 and the UV-Visible absorption spectrum of thin-films indicates the indirect optical and electronic bandgaps which is around 2.1 eV and 2.45 eV respectively (Figure S1). The presence of strong excitonic peak in the absorption spectrum often makes it difficult to extract exact electronic bandgap of low dimensional compounds such as Cs3Bi2I9. The reported bandgap values have also been provided in Table S1 along with our results. Figure 1. (b) illustrates the


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electronic bandstructure of Cs3Bi2I9 based on Density Functional Theory (DFT) with generalized gradient approximations (GGA) using PBE functional 21-22, 27-28. From our DFT calculations, the electronic bandgap is indirect in nature between Γ and M point. The calculated bandgap value of Cs3Bi2I9 is found to be 2.34 eV and 1.65 eV without and with Spin Orbit Coupling (SOC) respectively. Though DFT calculations within GGA approximation using PBE functional can approximately estimate the experimental bandgap for MAPbI3, similar calculations for other semiconductors generally do not provide an accurate bandgap estimation. To resolve the bottleneck of approximating bandgap based on ground state DFT calculations, we have further performed the DFT calculations using screened hybrid exchange correlation functional that is a mixture of 25% of Hartree−Fock exact exchange and 75% of GGA-PBE exchange correlational contribution (elaborated in experimental section)

29

. This leads to a more accurate band gap

estimation comparable to the experimental values due to this inclusion of HSE06 type hybrid exchange correlation functional. DFT calculations considering SOC, HSE06 as well as excitonic effect all together would not be viable as far the computational expense is concerned.

(a)

DOS (states/eV) 0

1

2

3

4

5

6

7

8

9

10

Total Bi(s) Bi(p) I(p)

With SOC

(b)

PBE - No SOC HSE06 - No SOC HSE06 - SOC

Absorption Coefficient (A.U)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Without SOC

-2

-1

0

1

2

3

4

Energy (eV)

Energy (eV)


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Figure 2. (a) Calculated optical spectra of Cs3Bi2I9 with different functional treatment, (b) Comparison of projected density of states (PDOS) of Cs3Bi2I9 calculated with and without pin Orbit Coupling (SOC) considerations To bypass the computational barriers, we have performed a comparative investigation to determine the optical absorption spectra in three different combinations: i. GGA-PBE without spin orbit coupling (SOC), ii. HSE06 without SOC and iii. HSE06 with SOC and illustrated in Figure 2. (a). The first prominent peak of the optical response shows a blue shift towards the higher photon energy range, when we consider the hybrid functional without spin orbit interaction. It is also interesting that the bandgap of Cs3Bi2I9 with PBE functional without SOC and HSE06 with SOC consideration nearly matches each other, similar to MAPbI330. Therefore, PBE without SOC consideration would give us the approximate electronic bandgap values for Cs3Bi2I9 due to the cancellations of errors created by standard DFT and that created by ignoring SOC, similar to what has been reported for MAPbI3 31. The mismatch in bandgap and optical absorption edge is most probably due to the lower energy excitonic peak which is common for this kind of low dimensional materials. Apart from having a proper bandgap value, “good” photovoltaic materials must exhibit excellent transport properties, enabling an efficient charge collection and low electron-hole recombination centers. The flat nature of the Conduction Band Minimum (CBM) and Valence Band Maximum (VBM) is also a stark contrast with CH3NH3PbI3 bandstructure in which large band dispersion provides smaller photocarrier effective mass

32

. The effective masses of holes

and electrons at CBM and VBM are given in SI (Table S2) and show values much higher than the Pb counterparts. In addition, carrier lifetime and minority carrier diffusion lengths are also important parameters to assess optoelectronic properties of a material- largely determined by the


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defect properties of the material. The role of defects is very critical for photovoltaics, as the formation of defects is inevitable in thin-film synthesis conditions necessary for device fabrication. They can create energy levels located within the bandgap, resulting in possible electron-hole recombination, thus degrading the photovoltaic performances. The “superior optoelectronic properties” of Pb-based halide perovskites are often attributed to its excellent defect tolerant properties which arise from unusual VBM and CBM characteristics33-34. Contrary to conventional semiconductor such as Si or GaAs; the CBM and VBM of [PbI6]4- cluster (the building block of Pb-based halide perovskites) are antibonding in nature, contributed by the partially oxidized Pb2+ cation and Pb-I antibonding orbital respectively33. For Bi-based ternary halide perovskite, a similar VBM nature is expected due to lone pair 6s2 electrons. The total density of states (DOS) and projected density of states (PDOS) of Cs3Bi2I9 are shown in Figure 2. (b). The contribution of Cs+ cation to VBM and CBM is negligible and have not been included for clarity. Analogous observations have also been proposed for conventional Pb-halide perovskites where the influence of protonated cation was predicted to be negligible on the VBM and CBM characteristics35. In addition, the valence band of Cs3Bi2I9 is mainly formed by contributions from the p orbital of I and the s orbital of Bi. The antibonding characteristics of VBM is expected to suppress the valence band derived states such as cation vacancies. The nature of the CBM on the other hand, is quite different when compared to MAPbI3. While the conduction band has mostly Pb(p) characteristics in Pb-based halide perovskites, a mixture of I(p) and Bi(p) orbitals dominates the CBM of Cs3Bi2I9- which would not support defect tolerance towards intrinsic donors. In order to further understand the defect characteristics in Cs3Bi2I9, we have followed the approach of Yin, et al. 36 who showed that point defects creating deep states in MAPbI3 have high formation energies, which would preclude the probability of non-radiative


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recombination. Defects with low formation energies are found to have transition energies less than 0.05 eV above (below) the VBM (CBM) in CH3NH3PbI3. This “unusual defect physics” was claimed to explain the exceptional optoelectronic properties of Pb-halide perovskites. To further understand the role of defects in Cs3Bi2I9, we characterized the possible point defects in Cs3Bi2I9 and their transition energies in the bandgap. The following methodology is used to define the range of the chemical potentials The chemical potential of the respective elements (Cs, Bi, I) should be lower than that of the bulk counterparts in equilibrium, otherwise, it would precipitate in the elemental phase: 789 ≤ 789[;] = ?, 7@A ≤ 7@A[;] = ? BCD 7E ≤ 7E[;] = ? … … … … … … . (H) The conditions for the formation of secondary phases (CsI, BiI3) can be expressed as 789 + 7E ≤ ∆J(89E) = −H. HK LM … … … … … … … … … … … … … … … … … … … … . . (N) 7@A + O7E ≤ ∆J(@AEO ) = −H. PK LM … … … … … … … … … … … … … … … … … … … … (O) In thermodynamic equilibrium, the formation enthalpy of Cs3Bi2I9, which is stable in solid phase and the chemical potentials of the constituent atoms need to be equal. O789 + N7@A + Q7E = ∆J(89O @AN EQ ) = −HO. P LM … … … … … … … … . . … … … … (K) The chemical potentials corresponding to Bi and I that satisfy Equations (1) - (4) have been shown as grey region in Figure 3 and the chemical range is the boundary of the equilibrium growth conditions for Cs3Bi2I9. Any point, which is out of this region, will lead to the formation of secondary phases during the synthesis of Cs3Bi2I9. The dissociation energy of Cs3Bi2I9 defined as 3*E(CsI) + 2*E(BiI3) – E(Cs3Bi2I9), is about 6.8 eV which suggests the high stability of this compound. The large stability range for Cs3Bi2I9 as well as the high calculated dissociation energy indicates little influence of the growth conditions on the phase, unlike CH3NH3PbI3 for which the stability region is quite narrow36.


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µBi (eV) -6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0 0

BiI3

A (-3.13, 0)

-0.2 -0.4

B (-1.565, -0.57)

-0.6

µI (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-0.8

CsI

-1

C (0, -1.14)

-1.2 -1.4 -1.6 -1.8

Figure 3. Thermodynamically stable range for equilibrium growth of Cs3Bi2I9 We have considered all the possible point defects in Cs3Bi2I9 keeping the chemical potential within the stability range (Figure 3). The chemical potential points are taken at the center of the stability range which could give three different stoichiometric conditions such as Bi-rich/I-poor conditions (point C), moderate conditions (point B), and I-rich/Bi-poor conditions (point A). Table S3 illustrates the formation energies of three vacancies (VI, VCs, VBi), three interstitials (iCs, iBi, iI), two cation substitutions (CsBi, BiCs) and four antisites (CsI, BiI, IBi, ICs) type of defects in Cs3Bi2I9 compound. In the Bi-rich/I-poor region (point C) and moderate region (point B), the dominant types of defects are iodine vacancies with the lowest formation energies. On the other hand, at I-rich/Bi-poor condition (point A), CsBi cation substitution defect has the lowest formation energy. Apart from CsBi substitution, all Bi-type of defects are difficult to form, possibly due to the strong covalent bonding during the Bi-I dimer formation.


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Figure 4. Formation energy of twelve point defects (see text) as a function of Fermi energy level, at three different chemical potentials A, B, and C (see Figure 3 and text). Defects with high formation energies are displayed as dotted lines. Figure 4 depicts the formation energy of the possible point defects as a function of Fermi energy level. Unlike MAPbI3 which shows a transition from p-type to n-type conductivities, Cs3Bi2I9 exhibits p-type conductivities in all the stoichiometric regions36. The transition level of the defects indicates whether the defect can accept or donate electrons. Defects with deep transition levels usually act as Shockley-Read-Hall non-radiative recombination centers and the defects with shallow levels usually control the mobility of the charge carriers. As illustrated in Figure 5, among the three possible vacancies, VBi and VI exhibit deep transition level in the bandgap region. However, the formation energy associated with the VBi is quite high as compared to VI which would deteriorate the photovoltaic performance of the Cs3Bi2I9. On the other hand, VCs can act as an acceptor as the transition level lies near the vicinity of the VBM, however its contribution would be minimum as the formation energy of the defect is quite high. The cation substitution CsBi has low formation energy as well it creates two transition level: ϵ(0/1-) which is shallow acceptor and ϵ(1-/2-) which is deep acceptor. The other cation substitution, BiCs has a high formation energy which would prohibit it from forming any deep midgap states. Although, most of the antisite and interstitial defects also form deep bandgap


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states, the probability of antisite defect formation is less due to high formation energy. It is interesting to note that although Cs+ cations are not directly involved in optoelectronic properties, they can create deep states inside the bandgap, in contrast to CH3NH3PbI3 in which methylammonium ions do not create additional gap states. The tendency for Cs to contribute to sub-band gap states have been borne out by calculations in CsPbBr337 and CsAgBiBr638. Based on these considerations, organic-inorganic (CH3NH3)3Bi2I9 may be expected to exhibit better defect tolerance properties compared to inorganic Cs3Bi2I9. The tendency for Cs related defects to form would also have implications for ionic transport within these semiconductors. 3.5 3.2

(a)

3.0

(b)

(0/1+)

2.4 2.0

(0/1+)

1.6

(1+/2+)

1.2

(2+/3+)

(0/1+)

(0/1+)

(0/1+)

0.8

(0/1+) (1+/2+)

0.4

(1+/2+)

0.0

(3+/4+)

-0.4

Transition energy level (eV)

2.8

Transition energy level (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.5

(3-/4-)

2.0 (0/1-)

1.5 (2-/3-) 1.0

(0/1-) (0/1-) (1-/2-)

0.5 0.0

(0/1-)

(0/1-)

VCs

VBi

(1-/2-) (0/1-)

-0.5

-0.8

VI

-1.0

Csi

Bii

BiCs

CsI

BiI

V

Ii

CsBi

ICs

IBi

V

Figure 5. Transition energy levels of (a) intrinsic donors and (b) intrinsic acceptors CONCLUSION In conclusion, our study reveals the important differences between conventional Pb-based perovskites and Bi-based ternary halide perovskites from an electronic structure point of view. We have studied the most important factors for good PV devices based on the first principle calculations. The electronic bandstructure of Cs3Bi2I9 indicates the high carrier effective masses along with large indirect bandgap which would exclude its use in single junction solar cell. However, primary concerns arise from the defect characteristics of this material. Most of the


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defects that have low formation energies, form deep level states in the bandgap which would act as recombination centers in PV applications. Although the compound was initially thought to be partially defect tolerant

13

, our calculations suggest otherwise. The chemical potentials

considered in our calculations do not result in elimination of the undesirable deep defects. Overall, based on our first principle calculations, we suggest that the presence of deep level defects is a major issue for the performance of the Bi-based ternary halide perovskites in the PV applications. It is worth to mention that our study is limited to the intrinsic point defects present in Cs3Bi2I9, which does not include the possibility of defect passivation by external doping or non-equilibrium synthesis that may lead to better performance of the same.

ASSOCIATED CONTENT Supporting Information Tauc plot of experimental absorption spectrum, effective mass of carriers, and defect formation energy values can be found in supporting information.


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AUTHOR INFORMATION Corresponding Author *(N.M) E-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources This work was funded by the National Research Foundation Singapore (NRF) Program, the National Research Foundation, Prime Minister’s Office, Singapore under its Competitive Research Program (CRP Award No. NRF-CRP14-2014-03) and through the Singapore–Berkeley Research Initiative for Sustainable Energy (SinBeRISE) CREATE Program. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The authors would like to thank High Performance Computing Center, Nanyang Technological University, Singapore for allowing the computing resources. Dr. Xu Qiang is acknowledged for valuable discussions.

REFERENCES


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Table of Contents Graphic


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Poor Photovoltaic Performance of Cs3Bi2I9: An Insight through First

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