Band Gap Engineering of Cs3Bi2I9 Perovskites with Trivalent Atoms

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Band Gap Engineering of CsBiI Perovskites with Trivalent Atoms Using a Dual Metal Cation Ki-Ha Hong, Jongseob Kim, Lamjed Debbichi, Hyungjun Kim, and Sang Hyuk Im J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12426 • Publication Date (Web): 16 Dec 2016 Downloaded from http://pubs.acs.org on December 19, 2016

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The Journal of Physical Chemistry

Band Gap Engineering of Cs3Bi2I9 Perovskites with Trivalent Atoms using a Dual Metal Cation Ki-Ha Hong,*,† Jongseob Kim,‡ Lamjed Debbichi,∥Hyungjun Kim,∥ and Sang Hyuk Im§

† Department of Materials Science and Engineering, Hanbat National University, 125 Dongseodaero, Yuseong-Gu, Daejeon, 305-719, Korea ‡ Samsung Advanced Institute of Technology, Samsung Electronics Co., Ltd. Yongin-Si, Gyeonggi-Do, 446-712, Korea

∥Graduate School of Energy, Environment, Water, and Sustainability (EEWS), Korea Advanced Institute of Science and Technology (KAIST), Yuseong-gu, Daejeon 305-701, Korea § Functional Crystallization Center (ERC), Department of Chemical Engineering, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do 446-701, Republic of Korea

KEYWORDS Perovskite Solar Cells, Lead-Free, Density Functional Theory, Double Perovskites, Band Gap Modulation.

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ABSTRACT

Ternary metal halides (A3X2I9) have attracted considerable interest because they have good stability and reduced toxicity compared with Pb based halide perovskites. The main issue with A3X2I9 is their band gap, which is relatively large for use in a single junction solar cell (1.9~2.2 eV for the Cs3Bi2I9). This theoretical study found that the band gap of Cs3Bi2I9 can be successfully modulated by using dual metal cations, i.e., by forming Cs3BiXI9 (X: tri-valent cation). Among the various tri-valent atoms investigated, In and Ga showed very promising band gap modulation behaviors. Additionally, the indirect band gap of Cs3Bi2I9 can be changed into a direct band gap.

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The stability and non-toxicity of the active absorbing materials in solar cells are the key factors affecting their commercialization. Perovskite solar cell materials have undergone unprecedented rapid development speed since the Miyasaka group first used organic-inorganic hybrid perovskites as a sensitizer for solar cells,1 and recently the Seok group reported a certified power conversion efficiency (PCE) of over 20 %.2 Additionally, there have been various attempts to develop highly efficient and robust perovskite solar cells.3-6 However it is still believed that further enhancement of stability, and lead-free alternatives are necessary before hybrid perovskites can be used in the human friendly environment such as potable power generators, building integrated photovoltaics, and vehicle integrated photovoltaics. Among the various efforts to develop Pb-free perovskite solar cells to date, Sn based materials have shown the best PCE.7,8 However, the stability of Sn-based perovskites are worse than Pbbased solar cells and the origin of their unstable performance is thought to be the multivalent features of Sn. Although Ge-based AGeI3 type perovskites have also been investigated, the PCE of Ge-based materials is still negligible and their stability is not very good. Recently, tri-valent metal halide perovskites (A3X2I9, A=CH3NH3+(MA)/Cs, X=Bi/Sb) have attracted significant attention because they have better stability and lower toxicity than Pb halide perovskites.9-11 While the PCE of the A3X2I9 has not been competitive with that of Pb/Sn based solar cells until now, the stability of the perovskites has been significantly improved. Lyu et al. showed that the MA3Bi2I9 solar cells can maintain their performance for 50 days under 50 % humidity and ambient air at room temperature.11 The fundamental bottle neck limiting the application of A3X2I9 perovskites in solar cells is their larger band gap which can be seldom manipulated to be less than 1.9 eV, by choosing different A


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and B atoms. The optimum band gap for the single junction solar cells should be near 1.3 eV12 and the band gap of MAPbI3 is 1.55 eV. Consequently, band gap engineering is essential if A3X2I9 perovskites are to be strong alternative candidate materials for Pb-free perovskite solar cells. The unique properties of organic-inorganic hybrid perovskites have been successfully explained by the theoretical studies including density functional theory.13-16 Computational materials screening can be an efficient tool for finding appropriate materials, and has recently been applied to search for robust Pb-free hybrid perovskites compositions.17-19 Volonakis et al. showed that the proper band gap Pb-free perovskites can be made by forming double perovskites via heterovalent substitution of metals17 and Sun et al. suggested that the potential candidates can be obtained by anion splitting approaches.18 Tri-valent halide perovskites have multiple numbers of metal anions within a unit lattice, i.e., 4 Bi in a P63/mmc lattice and 2 Bi in a P3തm1 lattice. Based on these results, it can be expected that alloying with different tri-valent atoms can be an effective way to manipulate the band gap of A3X2I9. This study presents a computational search for Pb-free hybrid perovskites using density functional theory to investigate the alloying of different tri-valent atoms into Cs3Bi2I9. Cs is an appropriate choice for materials screening due to its isotropic ion feature, compared with molecular cations such as MA. Recent reports have also shown that stability can be greatly enhanced by inserting Cs instead of molecular cations.20-22 Lattice distortion produce severe band gap changes23, which can also make the numerical convergence worse. Bi was chosen due to the previous successful synthesis of Bi-based tri-valent perovskites.10,11


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First, the band gap transitions of Cs3BiXI9 (X= Al, As, B, Bi, Co, Ga, In, Ir, La, P, Sb, Sc, Y) were evaluated within a P63/mmc lattice structure (shown in Figure 1a) which is the crystal structure of Cs3Bi2I9 (shown in Figure 1b) reported by previous studies.10,11 Secondly, the study investigated how the band gap changed when the lattice structures were changed into a P3തm1 lattice structure, which is the polymorph lattice structure of Cs3Sb2I9.24

Band structures and electronic properties were calculated by DFT calculations using the Vienna ab initio simulation package (VASP).25,26 Electronic wave functions were expanded with an energy cutoff of 500 eV. The core-valence interaction was described by the projector augmented wave (PAW) method.27 We used the PBEsol exchange correlation because the PBEsol exchange correlation can predicts the experimental lattice constants well, and they are important factors for determining the band gap of hybrid perovskites.23,28 To compare various compositions for hybrid perovskites, it is necessary to consider spin-orbit coupling (SOC),28 and consequently the band structures presented in this study were calculated by considering SOC. The Heyd-Scuseria-Ernzerhof (HSE06)29 hybrid density functional was used to compensate the underestimated band gap produced by the SOC calculations. Screening parameters of 0.2 and mixing parameters of 0.25 were used. As the computation using HSE06 is too expensive, the lattice structures were frozen from the optimized lattice structure using a conventional GGA calculation and the eigenvalues of the band edges were calculated by adding the reciprocal lattice points, which were predicted to be band edge points by the SOC band structure calculation. A previous study showed that the band edge points are seldom changed even though the size of the band gap can be changed by the band gap correction.30


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Optimized lattice structures were obtained by fully relaxing atomic positions until residual forces were less than 0.01 eV/Å keeping the initial symmetry. Monkhorst-Pack sampling with 3 × 3 × 1 and 3 × 3 × 2 k-point grids were used for the P63/mmc and the P3തm1 lattice structures respectively. The calculated lattice parameters and band gaps are summarized in the Table S1-S2.

Figure 1. Crystal structures of (a) P63/mmc Cs3BiXI9 (X= Al, As, B, Bi, Co, Ga, In, Ir, La, P, Sb, Sc, Y) (b) P63/mmc Cs3Bi2I9 (c) P 3ത m1 Cs3BiXI9 and (d) P 3ത m1 Cs3Bi2I9. Cyan/Red/Green/Purple balls represent Cs/Bi/X/I respectively.

Previously reported lattice structures and the electronic band data obtained by experiments and computations were compared with those of this study for the Cs3Bi2I9 (P63/mmc) and the Cs3Sb2I9 (P63/mmc) in Table 1. Our results based on the PBEsol exchange correlation, show good agreement with the experimental lattice structures, and the resulting computational band


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gaps using the HFSO method were similar to the experimental values. Since the calculated band gap of the Cs3Bi2I9 (P63/mmc) is 2.12 eV, our purpose was to find a composition with a narrower band gap than 2.12 eV.

Table 1. Lattice structures and band gap data for the Cs3Bi2I9 (P63/mmc) and the Cs3Sb2I9 (P63/mmc).

Lattice Constants (Å) Cs3Bi2I9 (P63/mmc) Cs3Sb2I9 (P63/mmc)

a = 8.335, c = 21.326

*

a = 8.300, c = 21.088* a = 8.555, c = 21.817c)

Band gap (eV)

Lattice Constants (Exp)

Band gap (Exp)

a = 8.4163, c = 21.200b)

2.2a) 1.9b)

a = 8.420, c = 21.200b)

2.05c)

*

2.12 2.32b) 1.98* 2.40c)

* Calculated values in this study a) Ref[9], b) Ref[10], c) Ref[24] The band gaps calculated with the conventional GGA (GGA), considering SOC (SOC), and the HSE06 combined with SOC (HFSO) are represented in the Figure 2a and 2b for the P63/mmc and the P3തm1 structure of the Cs3BiXI9. The band structures calculated with SOC can be found in Figure S1 and S2. Compared with the band gap of Cs3Bi2I9, Ga and In shows very promising behavior for both symmetry structures. The calculated band gap of P63/mmc/P3തm1 Cs3BiGaI9 is 1.60/1.20 eV which is lower than that of Cs3Bi2I9 by 0.65/0.54 eV. Although the band gap reduction of Cs3BiInI9 is smaller than that of Cs3BiGaI9 by ~0.3 eV, In can also act as an efficient doping element to modulate the band gap. The smaller lattice constant and volume can be considered the origin of this band gap narrowing.23


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While B also shows a considerable band gap decrease, the lattice structure is distorted from the initial symmetry condition due to the smaller ionic radius of B. In the case of Co, although the band gap at the Γ-point with SOC is 1.27 eV, the band structures are changed into an indirect band gap feature.

Figure 2. Calculated band gaps for (a) the space group P63/mmc and (b) the space group P3തm1of Cs3BiXI9. The band structures of (c) Cs3BiGaI9 (P63/mmc), (d) Cs3Bi2I9 (P63/mmc), (e) Cs3BiGaI9 (P3തm1), and (f) Cs3Bi2I9 (P3തm1). The calculated band structures of Cs3BiGaI9 and Cs3Bi2I9 with P63/mmc symmetry were obtained through SOC calculation and are presented in Figure 2c and 2d, respectively. In addition to the reduction in band gap, the incorporation of Ga or In shifts the valence band maximum (VBM) point near the Γ-point so that the band structure of Cs3BiGaI9 exhibits a direct-band-gap-like feature. The band structures of Cs3BiGaI9 and Cs3Bi2I9 when their


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symmetry was P3തm1 are shown in Figure 2e and 2f, respectively. The band gap can be further reduced by 0.5 eV when the symmetry is changed from P63/mmc to P3തm1 for Cs3Bi2I9.

Figure 3. Density of states of (a) Cs3Bi2I9 (P63/mmc), (b) Cs3BiGaI9 (P63/mmc), (c) Cs3BiInI9 (P63/mmc), (d) Cs3Bi2I9 (P3തm1), (e) Cs3BiGaI9 (P3തm1), and (f) Cs3BiInI9 (P3തm1). DOS figures are drawn based on the SO calculation results without HSE06 correction.

The density of states of Cs3Bi2I9 (P63/mmc), Cs3BiGaI9 (P63/mmc), Cs3BiInI9 (P63/mmc), Cs3Bi2I9 (P3തm1), Cs3BiGaI9 (P3തm1), and Cs3BiInI9 (P3തm1) are represented in Figure 3. Due to the enormous computation burden, in order to produce a clear DOS figure, we used 147 k-points, so that only the spin orbit interaction was considered, without considering HSE06. The DOS


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figures considering both the SOC and HSE06 with coarse grids are represented in Figure S3, which shows that the orbital configuration can be successfully understood with just the SOC calculation, except for the band gap underestimation. The valence band minimum (VBM) and the conduction band minimum (CBM) consist of (I p + Bi s) and (I sp + Bi p) orbitals for the Cs3Bi2I9 type perovskites. For the valence band formation, the energy levels of Ga p and In p are lower than VBM by ~ 2 eV. Conduction bands are formed with the hybridization of I sp, Bi p, and In/Ga s orbitals. The partial charge densities (PARCHDs) at the CBM are found in Figure 4. Comparing the DOS figures in Figure 3 with PARCHDs, we can suggest that In and P3തm1 are more appropriate than Ga and P63/mmc for fabricating efficient solar cells. In Figure 3b, the DOS of CBM consists mainly of Ga and there is splitting between Bi p + I p and Ga s + I p hybridization for the P63/mmc. This feature can also be found in Figure 4b, which shows that the PARCHD of CBM is localized between Ga s + I p and cannot extended into the Bi ions. For In, the DOS (Figure 3c) and the PARCHD at the CBM (Figure 4c) show that the CBM can be extended through the Bi-I and In-I bonds even for the P63/mmc symmetry. This kind of charge localization can be overcome because the crystal structure is changed into P3തm1. Even Cs3BiGaI9 (P3തm1) shows the extended states formation of the CBM (Figure 4e). Moreover, the calculated band gaps of the P3തm1 structures are always lower than those of the P63/mmc structures except Cs3BiLaI9 (Figure 1a and 1b, Table S1, and S2).


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Figure 4. Charge Density Profiles at the conduction band minimum of Cs3Bi2I9 (P63/mmc) (b) Cs3BiGaI9 (P63/mmc), (c) Cs3BiInI9 (P63/mmc) (d) Cs3Bi2I9 (P3തm1) (e) Cs3BiGaI9 (P3തm1), and (f) Cs3BiInI9 (P3തm1). Absorption spectra of Cs3Bi2I9, Cs3BiGaIn9, and Cs3BiInI9 are presented in the Figure 5 which were obtained by the SOC calculation. Band gap narrowing induced by Ga and In incorporation can be clearly found in the absorption spectra and it can be expected that the photon conversion current can be enhanced by In or Ga incorporation considering larger absorption coefficients of Cs3BiGaIn9, and Cs3BiInI9 near band edges. The effective masses of Cs3Bi2I9, Cs3BiGaIn9, and Cs3BiInI9 are presented in Table S3 which can be regarded as the important parameters to determine the carrier transport characteristics. It is hard to conclude if the transport characteristics by Ga and In insertion because there are significant asymmetries in effective masses but resulted values shows that we can expect the carrier transport can be comparable with that of Cs3Bi2I9. Finally, the formation energies (Ef) of Cs3BiGaIn9, and Cs3BiInI9 are calculated by following equations.


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Ef= E(Cs3BiXI9) - E(Cs3Bi2I9) + µ(BI3) -µ(XI3) µ is chemical potential which are considered as the energy of metal iodides in this study. The resulting formation energies of Cs3BiGaIn9, and Cs3BiInI9 are -5.7 meV/atom and 10 meV/atom respectively. Therefore, the synthesis of In based dual metal perovskites may be more easier to realize than that Ga based dual metal perovskites although the band gap modulation effect is weaker.

Figure 5. Absorption spectra of Cs3Bi2I9 (P63/mmc), Cs3BiGaI9 (P63/mmc), and Cs3BiInI9 (P63/mmc) obtained by PBEsol+SOC calculation.

In summary, this study suggests that the dual metal cation engineering can be an efficient way to reduce the band gap of Cs3BiXI9 (X: tri-valent atom) type perovskites. The relatively higher band gaps of the Cs3BiXI9 type perovskites are considered to be an obstacle to fabricate highly efficient Pb-free perovskites even though they showed very good stability.


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Our density functional study indicates that the band gap of Cs3Bi2I9 can be successfully reduced by applying dual tri-valent metal cations such as Cs3BiXI9. Our study explored 13 kinds of trivalent cations, Al, As, B, Bi, Co, Ga, In, Ir, La, P, Sb, Sc, Y and two types of lattice symmetries are considered, i.e. P63/mmc and P3തm1. The theoretical investigation determined that In and Ga have the potential to be an efficient band gap reduction elements for Cs3Bi2I9 and that the P3തm1 symmetry is more appropriate for realizing lower band gap tri-valent metal based perovskites. Considering the solar device performance, In may be better choice than Ga. The conduction band minimum of Cs3BiInI9 (P63/mmc) exhibits well developed extended states between Bi-I and In-I bonds while that of Cs3BiGaI9 (P63/mmc) tends to be confined around the Ga ions. Given that the symmetry of Cs3BiGaI9 is P3തm1, this charge localization is not found and moreover the calculated band gaps shows much lower values. The polymorph control of A3X2I9 type perovskites to create P3തm1 symmetry will be the key to making highly efficient Pb-free perovskites with A3X2I9 stoichiometric materials, and will be our next research subject.

ASSOCIATED CONTENT Supporting Information. Lattice structures, calculated band gaps, and band structures for P63/mmc Cs3BiXI9, P3തm1 Cs3BiXI9 can be found in Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Funding Sources The author(s) declare no competing financial interests

ACKNOWLEDGMENT This

research

was

supported

by

Basic

Science

Research

Program

(NRF-

2015R1A1A1A05001241) and the Technology Development Program to Solve Climate Changes (NRF-2015M1A2A2055836) through the National Research Foundation of Korea (NRF). Supercomputing resources including technical support were supported by the Supercomputing Center/Korea Institute of Science and Technology Information (KSC-2016-C2-0003).

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Band Gap Engineering of Cs3Bi2I9 Perovskites with Trivalent Atoms

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