Intrinsic Point Defects in Inorganic Cesium Lead Iodide Perovskite

Article Cite This: J. Phys. Chem. C 2018, 122, 1345−1350

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Intrinsic Point Defects in Inorganic Cesium Lead Iodide Perovskite CsPbI3 Yang Huang,†,‡ Wan-Jian Yin,*,‡ and Yao He*,† †

School of Physics and Astronomy, Yunnan University, Kunming 650091, China 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

‡

S Supporting Information *

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 nonperovskite (δphase) 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-phases 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 a 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.

I

noteworthy is that a cubic perovskite (α- or black phase) CsPbI3 remains stable only at high temperature, and reverts to a photoinactive nonperovskite (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 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 projectoraugmented wave potentials14 as implemented in the Vienna ab initio simulation package (VASP) code.15 For the exchangecorrelation 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 was used for

n 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 © 2017 American Chemical Society

Received: October 10, 2017 Revised: December 18, 2017 Published: December 22, 2017 1345

DOI: 10.1021/acs.jpcc.7b10045 J. Phys. Chem. C 2018, 122, 1345−1350

Article

The Journal of Physical Chemistry C

Figure 1. 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, 0, −1.20) eV and (−2.95, −1.87, −0.31) eV for μCs, μPb, and μI, respectively. The corresponding values for δ-phase are (−2.22, 0, −1.20) eV and (−2.95, −1.94, −0.31) eV.

Table 1. Calculated Lattice Parameters, Band Gaps, Pb−I−Pb Angles, and Dissociation Energies for the Three Phases of CsPbI3 lattice constant (Å) phase

symmetry

exptl

α γ

Pm3m ̅ Pbnm

a = 6.187

δ

Pnma

a = 10.43,b = 4.79, c = 17.7619

band gap (eV) calcd

a = 6.40 a = 9.13, b = 8.66, c = 12.64 a = 10.79, b = 4.89,, c = 18.21

1.737

1.46 1.82

180 154.74

+0.04 −0.09

3.1720

2.54

95.09, 91.40

−0.16

structure and density of states for three phases are shown in Figures S1−S4. For both phases, the VBM consists of antibonding states, which is between Pb 6s and I 5p orbitals, while the conduction band minimum (CBM) is composed mainly of Pb 6p orbitals. Cs has no significant contribution around the band edge.22−24 The calculated band gaps for α-, γ-, and δ-phases are 1.46, 1.82, and 2.54 eV, respectively, which are smaller than the experimental ones. Our calculated band gaps for α and γ-phase are consistent with 1.49 and 1.82 eV from Grote and Berger.25 Note that the δ-phase in their paper actually is γ-phase in the present study. The underestimation of band gaps is the typical result 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 noncorner-sharing [PbI6] octahedra.24−27 In fact, the calculated dissociation energies from CsPbI3 to CsI and PbI2 are 0.04, −0.09, and −0.16 eV for α-, γ-, and δ-phases, respectively. The lower the dissociation energy, the more stable the structure. For α and δphases, our results are very close to 0.06 and −0.09 eV from ElMellouhi et al.,28 and also close to 0.07 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. However,

∑ ni[μi + E(i)]

+ q[E F + εVBM(host)]

dissociation energy (eV) CsPbI3 → CsI + PbI2

calcd

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 ΔHf (α , q) = E(α , q) − E(host) +

Pb−I−Pb angle calcd (deg)

exptl

(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 perfectcrystal 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 reservoir in forming the defect. As shown in eq 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 the Supporting Information (SI). As shown in Table 1, our calculated lattice parameters for both α- and δ-phases are larger than experimental 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 1346

DOI: 10.1021/acs.jpcc.7b10045 J. Phys. Chem. C 2018, 122, 1345−1350

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

Pb-rich condition.34 In MAPbI3, the n-type conductivity is due to the lower formation energy of interstitial MA. However, 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 transition energy level ε(q/q′) is defined as the Fermi level at which the formation energy ΔHf (α, q) = ΔHf (α, q′) for a α defect with two different charge states q and q′.17 In Figures 4, 5, and 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 Figures 4 and 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 MAPbI3.35 According to above discussion, the formation energies of ICs,

this paper emphasizes that the cubic phase is stable in nanosize.31 The electrical conductivity of a semiconductor is determined by the formation and compensation of charged defects. Figures 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 2a), 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 δphase CsSnI3 under Sn-rich condition.33 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 unipolar self-doping behavior (p-type conductivity), unlike MAPbI 3, whose conductivity can change from intrinsic good p-type to moderate to good n-type when chemical potential is at Pb-poor, moderate 1347

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(the tendency of a semiconductor to keep its properties despite the presence of defects36). As shown in Figure 3a, 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 3b). 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 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 factor 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 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 (CsPbI 3 , 95.09°, 91.40°; CsPbBr 3 , 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-phase (Table 1). For γ-phase, the Pb−I−Pb bond angle is more close to an

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.

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 are 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. A deep transition level will attract electron/hole and act as Shockley−Read−Hall nonradiative recombination centers. Therefore, these results indicate that γphase should have low nonradiative recombination rate, in other words, γ-phase CsPbI3 is a defect-tolerant semiconductor

Figure 6. Spatial distribution of the squared wave functions of the defect levels created by VI−, ICs0, VPb0, CsPb0, and PbCs0 in (a) γ- and (b) δ-CsPbI3. The blue−green, gray, and purple balls represent Cs, Pb, and I atoms, respectively. 1348

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The Journal of Physical Chemistry C 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 acceptors are generally shallower (Figure S6a). 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 S6b). For δ-phase, the Pb−I−Pb bond angle is almost twice smaller than that in αphase. 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 valence bandwidth 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 (Figures 4, 5, and S6). For VI, VPb, CsPb, and 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-phases of 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 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 valence bandwidth 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 four (γ-phase) to eight (δ-phase). Therefore, these results suggest that in order to make high performance perovskite solar cells, it is necessary to engineer the structure of perovskite with larger metal−halide− metal bond angle (smaller octahedral tilt).

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ACKNOWLEDGMENTS

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REFERENCES

W.-J.Y. acknowledges 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 and No. 11674237), and Natural Science Foundation of Jiangsu Province of China (under Grant No. BK20160299). Y.H. acknowledges National Natural Science Foundation of China (Grant No. 61366007), Program of high-end scientific and technological talents in Yunnan Province (Grant No. 2013HA019), and 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.

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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.jpcc.7b10045.

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Article

Numerical details used for obtaining Figure 1, electronic band structures, density of states, formation energies, and transition energy levels (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Yang Huang: 0000-0001-6813-904X Notes

The authors declare no competing financial interest. 1349

DOI: 10.1021/acs.jpcc.7b10045 J. Phys. Chem. C 2018, 122, 1345−1350

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The Journal of Physical Chemistry C

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DOI: 10.1021/acs.jpcc.7b10045 J. Phys. Chem. C 2018, 122, 1345−1350