Intrinsic Point Defects in Inorganic Cesium Lead Iodide Perovskite

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Intrinsic Point Defects in Inorganic Cesium Lead Iodide Perovskite CsPbI Yang Huang, Wan-Jian Yin, and Yao He J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10045 • Publication Date (Web): 22 Dec 2017 Downloaded from http://pubs.acs.org on December 23, 2017

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The Journal of Physical Chemistry

Intrinsic point defects in inorganic cesium lead iodide perovskite CsPbI3 Yang Huang1,2, Wan-Jian Yin2* and Yao He1*

1 School of Physics and Astronomy, Yunnan University, Kunming 650091, China 2 Soochow Institute for Energy and Materials InnovationS (SIEMIS), College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China

*Corresponding authors’ e-mails: [email protected]; [email protected]

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Abstract Cesium lead iodide (CsPbI3) has recently emerged as a promising solar photovoltaic absorber. However, the cubic perovskite (α phase) remains stable only at high temperature, and reverts to a photoinactive non-perovskite (δ phase) CsPbI3 at room temperature. In this work, the formation energies and transition energy levels of intrinsic point defects in γ (more stable than α phase) and δ phase have been studied systematically by first-principles calculations. It is found that CsPbI3 exhibits a unipolar self-doping behavior (p-type conductivity), which is in contrast to CH3NH3PbI3. Most of the intrinsic defects induce deeper transition energy levels in δ phase than in γ phase. This is due to the small Pb-I-Pb bond angles in δ phase that results in the weak antibonding character of valence band maximum (VBM). However, the strong antibonding character of VBM plays critical role in keeping defect tolerance in semiconductors. Therefore, these results indicate the importance of the large metal-halide-metal bond angle for the performance of perovskite solar cells.

Table of Contents Image

Keywords: Inorganic Perovskite, Point Defects, Transition Energy Levels, Formation Energies.


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In the past few years, hybrid organic-inorganic perovskites, for example methylammonium lead iodide (MAPbI3, MA = CH3NH3), have attracted significant research interests because of the inexpensive fabrication techniques, the rapid improvement in photovoltaic efficiency, and the superior material properties (such as long diffusion lengths, suitable band gap, small exciton binding energy, and high defect tolerance).1-4 However, perovskite solar cells have not been implemented on an industrial scale yet. For MAPbI3, this is due to the fact that it is very moisture-sensitive and can degrade to the hydrated phase and eventually decomposes to the yellow solid PbI2 with large band gap after long-term humidity exposure.2,5 Fortunately, the perovskites have the ability to tune their optoelectronic properties by ion substitution.1,6 Replacing the hygroscopic MA cation with robust inorganic cations can be considered as a promising approach to overcome the instability of MAPbI3. Recently, CsPbI3 has shown enhanced resistance to moisture and improved thermal stability,7-11 i.e., the loss ratio of the power conversion efficiency (PCE) of the MAPbIxCl3-x-based solar cells in air is 47%, which is higher than that of the CsPbI3-based solar cells (26%).8 In addition, it has been reported that improved PCE changes from 1.7% to 4.88%, based on solution-processing methods. In this method, hydroiodic acid (HI) is applied as an additive.7,8 Compared to solution-processing methods, however, all inorganic CsPbI3 perovskite solar cells with planar junction are fabricated by thermal coevaporation. And its PCE is close to 9.3 to 10.5%.9 Similar to CH(NH2)2PbI3, what is noteworthy is that a cubic perovskite (α or black phase) CsPbI3 remains stable only at high temperature, and reverts to a photoinactive non-perovskite (δ or yellow phase) CsPbI3 at room temperature. For example, the PCE of the CsPbI3-based solar cells is 4.88% at annealing temperature 100 °C (black phase), and is reduced to 2.71% at 80

°C (yellow phase).8 Since the defects in photovoltaic absorbers play critical roles in determining the nonradiative recombination, they influence the performance of solar cells made of these absorbers.12 Therefore, in this work, we are trying to understand the performance of the CsPbI3-based solar cells from the viewpoint of defects. It is found that the small Pb-I-Pb bond angles in δ phase can reduce the orbital overlap ACS Paragon Plus Environment


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between lead and iodine atoms, and the δ phase exhibits deeper defect transition energy levels than γ phase. As a result, the VBM displays a weak antibonding character originating from the interaction of Pb 6s and I 5p. However, this character is difficult to push the VBM energy up. Our calculations are based on DFT13 and projector-augmented wave potentials14 as implemented in the Vienna ab initio simulation package (VASP) code.15 For the exchange-correlation functional, the Perdew-Burke-Ernzerhof functional (PBE)16 was employed. The electron wave function was expanded in plane waves up to a cutoff energy of 300 eV and Γ- Centered k-mesh with k-spacing of 0.3 Å-1 were used for geometry optimization and electronic structure calculations. Both the atomic positions and cell parameters were optimized until residual forces were below 0.01 eV/Å. A 2×4×1 (2×2×2) supercell containing 160 atoms is used for the calculations of defect formation energies and defect transition energy levels of δ phase (γ phase), and the Brillouin zone is sampled by the Γ point. The formation energy of a point defect is calculated as17,18 ∆Hf (α,q) = E(α,q) – E(host) + ∑ni[µi + E(i)] + q[EF + εVBM(host)]

(1)

where E(α,q) is the total energy of a supercell with defect α in charge state q and E(host) is the total energy of the perfect-crystal supercell. µi is the atomic chemical potential of constituent i referenced to the total energy E(i) of its pure elemental solid. εVBM(host) is the energy of the VBM and EF is the Fermi level measured from the VBM, varying in the range of the band gap Eg. ni is the number of atom i and q is the number of electrons exchanged between the supercell and the corresponding thermodynamic reservior in forming the defect. As shown in Eqs. (1), the calculated formation energies of charged defects depend sensitively on the selected values for µCs, µPb, and µI and the Fermi-level positions. Here, the calculated values at two representative chemical potential points are labeled as A point (Pb-rich) and C point (Pb-poor) in Figure 1. Calculation details are in Supporting Information (SI). As shown in Table 1, our calculated lattice parameters for both of α and δ phase


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Figure 1. The calculated stable chemical potential region (surrounded by A, B, C, and D points) for equilibrium growth condition of CsPbI3. The left is γ phase, and the right is δ phase. For γ phase, the exact values of chemical potentials at points A and C are (-2.15 eV, 0 eV, -1.20 eV) and (-2.95 eV, -1.87 eV, -0.31 eV) for µCs, µPb, and µI, respectively. The corresponding values for δ phase are (-2.22 eV, 0 eV, -1.20 eV) and ( -2.95 eV, -1.94 eV, -0.31 eV). Table 1. The calculated lattice parameters, band gaps, Pb-I-Pb angles, and dissociation energies for the three phases of CsPbI3. Phase

Symmetry

Lattice constant (Å)

Exp. α

Pm-3m

γ

Pbnm

Band gap (eV)

Cal. 7

a=6.18

Exp. 7

a=6.40 a=9.13,

1.73 b=8.66,

Pb-I-Pb

Dissociation

angle

energy (eV)

(degree)

CsPbI3 →

Cal.

Cal.

CsI + PbI2

1.46

180

+0.04

1.82

154.74

-0.09

2.54

95.09,

-0.16

c=12.64 δ

Pnma

a=10.43,b=4.79, 19

c=17.76

a=10.79, b=4.89,

3.1720

c=18.21

91.40

are larger than experimenl measurements, but the unit cell volumes (α phase: 262.14 Å3, δ phase: 960.82 Å3) are in good agreement with previous theoretical work (α phase: 260.42 Å3, δ phase: 963.44 Å3).21 The band structure and density of states for three phases are shown in Figure S1-S4. For both phases, the VBM consists of antibonding states which is between Pb 6s orbitals and I 5p orbitals, while the conduction band minimum (CBM) is composed mainly of Pb 6p orbitals. Cs has no any significant contribution around the band edge.22-24 The calculated band gaps for α,

γ and δ phases are 1.46 eV, 1.82 eV, 2.54 eV, respectively, which are smaller than the



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experimental ones. Our calculated band gaps for α and γ phase are consistent with 1.49 eV and 1.82 eV from Grote and Berger.25 Note that the δ phase in their paper actually is γ phase in present study. The underestimation of band gaps is the typical results of DFT calculations in the generalized gradient approximation (GGA). In all three phases, δ phase possesses the lowest energy, which consists of the double-chains of non-corner-sharing [PbI6] octahedra.24-27 In fact, the calculated dissociation energies from CsPbI3 to CsI and PbI2 are 0.04 eV, -0.09 eV and -0.16 eV for α, γ and δ phases, respectively. The lower the dissociation energy is, the more stable the structure is. For α and δ phases, our results are very close to 0.06 eV and -0.09 eV from El-Mellouhi et al.,28 and also close to 0.07 eV and -0.10 eV from Zhang et al..29 Moreover, the recent study of Zheng and Rubel shows that the ionization energy is the remaining contribution to the reaction enthalpy.

30

Combined

with the results of ionization energies (α phase: -5.29 eV, δ phase: -7.23 eV21), δ phase is also the most stable phase. According to the above discussion, it is not difficult to understand why the chemical potential range in Figure 1 is small. In addition, we will not consider the defect calculations of α phase in the next discussion because of its positive dissociation energy. It is worth noting that when our manuscript was under review, a paper about defects in α phase CsPbI3 was published. But this paper emphasizes that the cubic phase is stable in nanosize.31 The electrical conductivity of semiconductor is determined by the formation and compensation of charged defects. Figure 2 and 3 show the calculated formation energies of intrinsic point defects as a function of Fermi level at two chemical potential points. For γ-phase CsPbI3, at chemical potential point A, i.e., Pb-rich (Figure 2(a)), the Fermi level is pinned at 1.14 eV above the VBM by PbCs, VI and VPb. Therefore, CsPbI3 should be either intrinsic or slightly n-type. This conclusion is similar to α-phase MAPbBr3 under Pb-rich condition32 and δ-phase CsSnI3 under Sn-rich condition33. At chemical potential point C, i.e., Pb-poor (Figure S5), VPb has formation energy of 0.81 eV, which is lower compared with that of 2.68 eV under Pb-rich condition. In this case, the Fermi level is pinned at 0.20 eV above the VBM by VI and VPb, so CsPbI3 exhibits p-type conductivity. Therefore, CsPbI3 shows a ACS Paragon Plus Environment

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Figure 2. Calculated formation energies of intrinsic point defects in γ-CsPbI3 at chemical potentials (a) A and (b) C points, as shown in Figure 1.

Figure 3. Calculated formation energies of intrinsic point defects in δ-CsPbI3 at chemical potentials (a) A and (b) C points, as shown in Figure 1.

unipolar self-doping behavior (p-type conductivity), unlike MAPbI3, whose conductivity can change from intrinsic good p-type, moderate to good n-type when chemical potential is at Pb-poor, moderate, Pb-rich condition.34 In MAPbI3, the n-type conductivity is due to the lower formation energy of interstitial MA. But, under



Pb-rich condition, Csi has formation energy of 1.29 eV at CBM (Figure S5), which is too high to make CsPbI3 n-type. The higher formation energy of Csi in CsPbI3 is likely due to the larger octahedra tilting (Pb-I-Pb bond angle: 154.74°) compared with MAPbI3 (Pb-I-Pb bond angle: 180°). The conductivity of a semiconductor depends not only on the formation energies of defects, but also on their transition energy levels. The tansition energy level ε(q/q′) is defined as the Fermi level at which the formation energy ∆Hf (α,q) = ∆Hf (α, q′) for a α defect with two different charge state q and q′.17 In Figure 4, Figure 5, and Figure S6, the calculated transition energy levels of all possible intrinsic defects are plotted between different charge states relative to the VBM and CBM. As seen in Figure 4 and Figure S6, only four point defects can induce deep transition levelsICs, IPb, PbI, and Pbi. The reason for the deep transition level of ICs is the formation of an I trimer in the neutral state (Figure 6), as discussed for IMA in MAPbI335. According to above discussion, the formation energies of ICs, IPb, PbI, and Pbi are high, so their concentrations are low under all growth conditions. For example, the formation energies of acceptor ICs are 2.64 and 0.95 eV under Pb-rich and Pb-poor conditions at the VBM, which is higher than 1.63 eV of VCs (Pb-rich) and 0.61 eV of CsPb (Pb-poor), respectively. Similarly, the formation energies of donor PbI are 2.18 and 4.94 eV under Pb-rich and Pb-poor conditions at the CBM, which is also higher than 1.11 eV of PbCs (Pb-rich) and 2.01 eV of VI (Pb-poor), respectively. Because deep transition level will attract electron/hole and acts as Shockley-Read-Hall nonradiative recombination centers. Therefore, these results indicate that γ phase should have low nonradiative recombination rate, in a word, γ-phase CsPbI3 is a defect-tolerant semiconductor (the tendency of a semiconductor to keep its properties despite the presence of defetcs36). As shown in Figure 3(a), for the most stable δ phase at room temperature, the Fermi level is pinned to be at 1.45 eV by VCs and PbCs under Pb-rich condition, and the Fermi level is pinned to be at 0.48 eV by VI and CsPb under Pb-poor condition (Figure 3(b)). Therefore, the conclusion that δ-phase CsPbI3 also behaves as a p-type semiconductor is consistent with γ phase. From the transition energy levels of δ phase ACS Paragon Plus Environment

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Figure 4. Calculated transition energy levels for intrinsic point defects in γ-CsPbI3.

Figure 5. Calculated transition energy levels for intrinsic point defects in δ-CsPbI3.

shown in Figure 5, it is seen that ICs, IPb, PbI, and Pbi can introduce deep levels, and Ii, VI, CsI, and Csi also introduce deep levels. For example, the ε(0/+1) of VI is located at 0.03 eV below the CBM in γ phase, but it becomes 0.37 eV in δ phase. One of factors that determines the electron trapping energy in the halogen vacancy is the short-range potential resulting from the cation orbital hybridization at the vacancy.37 As shown in Figure 6, in VI-, the two Pb ions adjacent to the iodine vacancy form a covalent bond. This explains why the transition energy level of VI is deeper in δ phase. On the contrary, the squared wave function of the defect state is spatially distributed away ACS Paragon Plus Environment


Figure 6. Spatial distribution of the squared wave functions of the defect levels created by VI-, ICs0, VPb0, CsPb0, PbCs0 in (a) γ- and (b) δ-CsPbI3. The blue-green, gray, purple balls represent Cs, Pb, I atoms, respectively. from VI- in γ phase (Figure 6), suggesting that VI- introduces a delocalized state. These conclusions are consistent with the previous transition energy levels calculations. Although the formation energy of VI (1.69 eV) is lower under Pb-rich condition than that of 2.21 eV under Pb-poor condition at the CBM, the difference between VI (1.69 eV) and PbCs (1.32 eV) is not obvious. Therefore, it is essential to limit the effect that changes the chemical potential of synthesizing δ phase to reduce the influence of deep donor VI. Above discussion about deep levels of defects in δ phase partially explains the measured low open circuit voltage (VOC) in CsPbI3-based solar cells.8 In contrast to δ-phase CsPbI3, although CsPbBr3 also has Pnma symmetry, it can maintain its good electronic quality despite the presence of defects.38 In fact, the difference of tolerance factor between CsPbI3 and CsPbBr3 is small (CsPbI3: 0.970,22 0.896;26 CsPbBr3: 0.993,

22

0.89826), but the difference of Pb-X(I, Br)-Pb bond angles is

obvious (CsPbI3: 95.09°, 91.40°; CsPbBr3: 166.42°,39 157.31°39). The change in Pb-X(I, Br)-Pb bond angles should be responsible for the situation that the defect transition levels in CsPbI3 are deeper than that in CsPbBr3. The properties of defects are bonded together with the structural properties. Based on the following discussion, we note that the properties of defects in CsPbI3 depend on the Pb-I-Pb bond angles. In fact, the corner-sharing octahedra of PbI6 in γ phase becomes edge-sharing in δ phase, and the tilting of octahedra significantly changes the Pb-I-Pb bond angle from 154.74° in γ phase to 95.09° and 91.40° in δ


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phase (Table 1). For γ phase, the Pb-I-Pb bond angle is more close to an ideal 180° in

α phase. Therefore, the orbital overlap between lead and iodine is relatively large, and gives rise to the result that the VBM appears with strong antibonding character originating from the interaction of Pb 6s and I 5p.23,27,40 This strong antibonding character pushes the VBM energy up,38,41 higher than the p orbital of I atom, so most of acceptors are generally shallower (Figure S6(a)). The CBM mainly consists of empty Pb 6p orbitals, and these orbitals couple to each other. As a result, the CBM is lower than the p orbital of Pb atom,38,41 so most of donors are generally shallower (Figure S6(b)). For δ phase, the Pb-I-Pb bond angles are almost twice smaller than it in α phase. The small bond angle reduces the orbital overlap between lead and iodine atoms, and the Kohn-Sham energies of the Pb 6s-I 5p antibonding character decrease. In consequence, this antibonding interaction becomes weak, hence the valance band width will be narrower and the band gap will be increased.23,42,43 Therefore, the properties of defects in δ phase are worse than that in γ phase (Figure 4, Figure 5, Figure S6). For VI, VPb, CsPb, PbCs, the comparison of the squared wave function of the defect state are shown in Figure 6. In addition, besides the defect properties and band gap, the exciton binding energy and effective mass also show similar dependence character on the Pb-I-Pb bond angles.44,45 In conclusion, the formation energies and transition energy levels of all possible intrinsic point defects in γ- and δ-phase CsPbI3 are investigated by using first-principles calculations. Defect calculations show that the formation energies of VCs, VPb, and CsPb are low under Pb-poor condition, and the Fermi level is pinned at near the VBM. Thus CsPbI3 is a p-type semiconductor. Because the Pb-I-Pb bond angles in δ phase (95.09° and 91.40°) are smaller than that of γ phase (154.74°), the orbital overlap between lead and iodine atoms in δ phase decreases. And the antibonding character originating from the interaction of Pb 6s and I 5p becomes weak. Consequently, besides narrowing the valance band width and increasing the band gap, this character worsens the transition energy levels of defects in δ phase. It is seen that the number of the deep transition levels of defects increases from 4 (γ phase) to 8 (δ phase). Therefore, these results suggest that in order to make high performance ACS Paragon Plus Environment


perovskite solar cells, it is necessary to engineer the structure of perovskite with larger metal-halide-metal bond angle (smaller octahedral tilt).

Acknowledgment Wan-Jian Yin acknowledge the funding support from National Key Research and Development Program of China under grant No. 2016YFB0700700, National Natural Science Foundation of China (under Grant No. 51602211, No. 11674237), Natural Science Foundation of Jiangsu Province of China (under Grant No. BK20160299). Yao He acknowledge National Natiral Science Foundation of China (Grant No. 61366007), Program of high-end scientific and technological talents in Yunnan Province (Grant No. 2013HA019), Program for Excellent Young Talents in Yunnan University. The work was carried out at National Supercomputer Center in Tianjin, Lvliang and Guangzhou, China and the calculations were performed on TianHe-1(A) and TianHe-II. Supporting Information Numerical details used for obtaining Figure 1, electronic band structures, density of states, formation energies, and transition energy levels. Notes The authors declare no competing financial interest. References (1) Correa-Baena, J.-P.; Abate, A.; Saliba, M.; Tress, W.; Jacobsson, T. J.; Gratzel, M.; Hagfeldt, A. The Rapid Evolution of Highly Efficient Perovskite Solar Cells. Energy Environ. Sci. 2017, 10, 710-727. (2) Leijtens, T.; Hoke, E. T.; Grancini, G.; Slotcavage, D. J.; Eperon, G. E.; Ball, J. M.; Bastiani, M. D.; Bowring, A. R.; Martino, N.; Wojciechowski, K.; McGehee, M. D.; Snaith, H. J.; Petrozza, A. Mapping Electric Field-Induced Switchable Poling and Structural Degradation in Hybrid Lead Halide Perovskite Thin Films. Adv. Energy Mater. 2015, 5, 1500962. (3) Yin, W.-J.; Yang, J.-H.; Kang, J.; Yan, Y.; Wei, S.-H. Halide Perovskite Materials for Solar Cells: a Theoretical Review. J. Mater. Chem. A 2015, 3, 8926-8942. ACS Paragon Plus Environment

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Intrinsic Point Defects in Inorganic Cesium Lead Iodide Perovskite

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