Effect of Bromine Substitution on the Ion Migration and Optical

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Effect of Bromine Substitution on the Ion Migration and Optical Absorption in MAPbI3 Perovskite Solar Cells: The First-Principles Study Chundan Lin, Siyuan Li, Wansong Zhang, Changjin Shao, and Zhenqing Yang ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.8b00026 • Publication Date (Web): 12 Feb 2018 Downloaded from http://pubs.acs.org on February 13, 2018

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ACS Applied Energy Materials

Effect of Bromine Substitution on the Ion Migration and Optical Absorption in MAPbI3 Perovskite Solar Cells: The First-Principles Study Chundan Lin§, Siyuan Li§, Wansong Zhang, Changjin Shao and Zhenqing Yang * State Key Laboratory of Heavy Oil Processing, Beijing Key Laboratory of Optical Detection Technology for Oil and Gas, College of Science, China University of Petroleum, Beijing 102249, P.R. China § These authors contributed equally

Corresponding Author:

[email protected]

Abstract In the latest few years, the remarkable energy conversion efficiency of lead halide-based perovskite solar cells (PSCs) has drawn extraordinary attention. However, some exposed problems in PSCs such as the low chemical stability et al. are tough to eliminate. Fundamental understanding of ionic transport at the nanoscale is essential for developing high-performance PSC based on the anomalous hysteresis current-voltage (I-V) curves and the poor stability. Our work is to understand the ionic transport mechanism by introducing suitable halogen substitution with insignificant impact on light absorption to hinder ion diffusion and thereby seeking the method to improve the stability. Herein, we used first-principles density functional theory (DFT) to calculate the band gaps and the optical absorption coefficients, the interstitial and the vacancy defects diffusion barriers of halide in the orthogonal phase MAPbX3 1

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(MA=CH3NH3, X = I, Br, I0.5Br0.5) perovskite, respectively. The research results show that a half bromine substitution not only prevents ion migration in perovskite, but also maintains a favorable light absorption capacity. It is maybe helpful to maintain the PSC’s property of light absorption with a similar atomic substitution. Furthermore, smaller atomic substitution for the halogen atoms may be essential for increasing the diffusion barrier. Key words: Perovskite Solar Cells; Ion Migration; Bromine Substitution; Optical Absorption; The First Principles

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1. Introduction In recent years, based on organic-inorganic hybrid perovskite solar cells, especially the methyl ammonium lead iodide (MAPbI3) and related mixed halides (such as MAPbI3-xBrx) have made explosive development. Up to now, the power conversion efficiency (PCE) of PSC has been promoted to more than 22 %.1-5 Long diffusion lengths of electrons and holes, excellent mobility of charge carriers and high optical absorption coefficients are all outstanding performance for lead halide perovskite solar cells, which contribute to this rapid growth.6-10 Currently, the problem of anomalous hysteresis in the PSC’s current-voltage (I−V) curves has caused a wider concern, despite the varieties of remarkable properties of perovskite.11-12 However, it is harder to evaluate the PCE on account of the dependence of I−V curves on the voltage scan direction and speed. There are still some knotty problems in this field, such as the origin of hysteresis, the understanding of the hysteretic behavior. Scientists had attempted to explain this behavior by structural changes13 and ferroelectricity14. Notably, Tress et al. suggested that ion migration is the main cause of exceptional retardation in the I-V curves, which has been widely recognized.15-19 Moreover, they put forward that it is the presence of mobile ions that results in aging of PSCs.20 Thus, it is very significant to suppress ion diffusions, for which not only improve the PCE but also enhance the stability of PSCs.21-23 Geng considered that the p orbital of the iodine atom the s orbital of the lead atom are mainly distributed for the valence band maximum (VBM), the p orbitals of the lead atom is mainly contributed to the conduction band minimum (CBM), 3



respectively,24 which indicate that the lead and iodine atoms have great effect on the MAPbI3’s bandgap. As we all know, lead-based perovskites tend to release PbI2 as a degradation product, which is toxic. Human exposure to lead is harmful to the nervous and reproductive systems and to the hematopoietic and renal organs. Moreover, iodide ion is the main diffusing ion in PSCs. Compared to the lead, it seems that scarcely any alternative elements have been reported that makes the perovskite have better light absorption performance on the basis of current research.25-27 Thence, we focus on the replacement of iodine elements to understand the process and search a valid method for highly stable PSCs. In the past few years, numerous replacements of iodine by bromine and chlorine have been reported, but almost none of the PCE and light absorption capacity have been improved, even if not, their stability is unclear.28-31 A good light absorption capacity can directly reflect the solar cell’s maximum value of the incident monochromatic photon to current conversion efficiency (IPCE), which can directly reflect the level of PCE.32-33 Thus, we target on finding the optimum bromine substitution ratio, which can suppress ion diffusions and keep a good absorption capacity. In this work, we made a full replacement and a half substitution for iodine with bromine in bulk MAPbI3 (the low temperature phase with an orthorhombic structure). Then, we adopted density functional theory (DFT) to calculate diffusion barriers of vacancy/impurity migrations, for instance, Ii-/VI+ and Bri-/VBr+, which are the most dominant diffusing ions in MAPbX3(X = I, Br, I0.5Br0.5).34-37 All these calculations 4


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were carried on the ac plane, not including migrations on surfaces and at interfaces. The calculated diffusion barriers indicate that the bromide ions migrate sufficiently difficultly compared to iodide ions. Consequently, we demonstrate that the substitution with bromine is beneficial to prevent the transport of halogen ions in MAPb (I0.5Br0.5)3. This work is mainly to increase the barrier of ion migration in MAPbI3 perovskite, but it should be ensured that the light absorption performance of the substitutional perovskite is not greatly reduced as much as possible. In view of the above, we probed the electronic structure properties and optical absorption of MAPbX3. We suggest that partial bromine substitution is beneficial for the MAPbI3 perovskite to have a good light absorption property and high ion diffusion barrier values, although none of the substitutional has better optical absorption than lead iodine perovskite currently.

2. Computational Methods All DFT calculations were performed with the Vienna Ab-initio Simulation Package(VASP).38-39 The generalized gradient approximation (GGA) parametrized by Perdew-Burke-Ernzerhof (PBE) was used for the electron exchange-correction functional.40 The valence wave functions were expanded in a plane-wave basis with cut-off energy of 500eV, and the k-space integration was done with a 6 × 6 × 6 k-mesh in the Monkhorst-Park24, 41 scheme. The three perovskite structures (shown Figure 1) were relaxed with a conjugate-gradient algorithm until the energy on the atoms was less than 1.0 × 10 −4 eV. 24 The low-temperature phase of MAPbI3 with an orthorhombic structure and experimental lattice constants of a = 8.861 Å, b = 12.62 Å 5



and c = 8.581Å were used in the calculations.28 The three dimensions of the MAPbX3 structures have adopted periodic boundary conditions. The gamma-only k-point mesh and a 2×1×2 supercell were applied for the ion diffusion. The diffusion barriers were calculated on by climbing image nudged elastic band (cNEB) method. 42-44

Figure 1. Crystal structure of orthorhombic MAPbX3 (X = Br, I) perovskites. (a)The unit cell enclosed by the box consists of two stacked cells in the b direction due to the opposite dipoles of the CH3NH3+ cations. (b) Each CH3NH3+ cations located in the center of a distorted cuboctahedral pocket with twelve I−anions at the vertices, enclosed by eight corner-connected [PbI6] octahedra. Color key: purple, I; gray, Pb; blue, N; brown, C; pink, H.

We focus on the orthorhombic structure of MAPbI3, which is the best stable at low temperature.24 In a bulk orthorhombic MAPbI3 unit cell (Figure 1a), each Pb2+ is coordinated with six I-, and each I- is coordinated with two Pb2+. The lead center and 6


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the six directly coordinated iodine form a [PbI6] octahedron. The adjacent [PbI6] octahedra are corner-connected to form a three-dimensional Pb-I framework. Each CH3NH3+ is surrounded by eight [PbI6] octahedra, which is located at the center of the twisted cubic octahedral pocket with twelve I- anions at its apex (Fig. 1b).27, 30-31, 45

3. Results and Discussion 3.1 Diffusion Barriers of Defects Vacancy diffusion represents an ion migrating from one lattice site to its adjacent vacant lattice site (for example, the migration of VI+ as shown in Figure 2a).35, 46-48 Table 1 shows the diffusion barriers of VI+, Ii- in MAPbI3, VBr+, Bri- in MAPbBr3 and Ii-, Bri- in MAPb(I0.5Br0.5)3, respectively, which are the main diffusers in lead halide perovskite. However, the interstitials in MAPbI3 do not diffuse through hopping along different interstitial sites because the perovskite structure is a tightly packed structure and lacks sufficient space for an ion to move between two interstitial sites.34,

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Notably, we have some specific calculations to illustrate that this migration behavior is illogical. The diffusion barriers for migration in this way are generally increased by 0.5-1 eV, which is sufficient to prove that this approach is not desirable. Unlike the vacancy diffusion, the diffusion of an interstitial regards the ion on the regular lattice site as a bridge. Ii - and another iodine ion share a lattice site (forming a split-interstitial) in the ground state; one of the two iodine ions simply rotates around the same lead ion to move to the adjacent lattice site to form a new split-interstitial (see Figure 2b), and it is another ground state.34, 47, 50-53 Thus, we assume that the migration of Ii- is a process of chemical bond transfer, during which an old Pb-I bond 7



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breaks, and another new Pb-I bond forms.34-35 Table 1. Diffusion Barriers (eV) for ion migration on the ac plane in MAPbX3 (MA=CH3NH3). Sort

(eV)

Defects

MAPbI3

0.25/0.53

Ii-/VI+

MAPbBr3

1.14/1.41

Bri-/VBr+

MAPb(I0.5Br0.5)3

0.79/0.81

Ii-/Bri-

Figure 2. Transport mechanisms in the MAPbI3 perovskite structure. Schematic illustration of the two ionic transport mechanisms involving conventional vacancy hopping between neighboring positions: (a) VI+ migration on ac plane; (b) Iimigration on ac plane.

In MAPbI3, the migration of VI+ and Ii- is straightforward due to the simple rotation of the Pb-I bond. Therefore, the barrier values of VI+ and Ii- are 0.53eV and 0.25eV, respectively, exhibiting that these two defects are very easy to migrate at low temperature.15, 34, 47, 54 However, the diffusion barrier values of VBr+ and Bri- in MAPbBr3 are fairly high (1.41eV and 1.14eV, respectively), which indicates that the ion migration of halogen becomes more difficult when iodine is completely replaced 8


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by bromine. After a half substitution with bromine in MAPbI3, the diffusion barrier values of Ii- and Bri- are 0.79 eV and 0.81 eV, respectively, which are significantly reduced than that of the interstitials in MAPbBr3. In order to maintain a better lattice symmetry of the perovskite (substitution was carried out by ortho-substitution, this is, one iodine and another bromine atom), we give up the calculation of the diffusion barriers of vacancy migration in the half substitutional perovskite. So, the adjacent vacancy migration is not feasible here. The results exhibit that vacancies and interstitial ions have a similar diffusion barrier trend. Li and Duan suggested that the defect state is possibly attributed to iodine interstitials. Then they attributed the hysteresis to the migration of iodide ions/interstitials driven by an external electrical bias leading to shift in the effective work function at the respective electrodes.36-37 Therefore, we can simply characterize the total ion migration by the diffusion barriers of interstitial ions. Based on the above results, we believe that bromine substitution can indeed increase the diffusion barriers of iodine. It is too important to be ignored for inhibiting the main ion migration in perovskite, although the diffusion barrier itself is slightly reduced. Mainly due to other percent substitution methods as well as the half, we have no carry out other percentages of bromine substitution and we reduce the complexity of the system as much as possible to facilitate the study. Figure S1 shows the diffusion barrier curves for several ion migration, respectively. These curves also confirm that our analysis of the diffusion barriers for several defects is accurate and that bromine substitution can indeed alter the ease of ion transport to a large extent. In general, all these results demonstrate that bromine substitution has a 9



considerable impact on increasing the diffusion barriers of halogen interstitials and hindering the rapid migration of ions in MAPbI3. In order to explore the mechanism of the effect of bromine substitution on the ion diffusion barriers in the MAPb (I0.5Br0.5)3 perovskite, we calculated the Pb-X bond lengths and Pb-X-Pb (X = I, Br) bond angles of the three perovskites (as shown in Table 2). Among the three perovskites, MAPbI3 has the longest Pb-I bond length, which is about 3.25 Å. The corresponding Pb-I-Pb dihedral angle is about 152° on the ac plane and about 162° along the b-axis direction.24, 28 When the structure changes from MAPbI3 to MAPbBr3, the radius of the halogen ions decreases and the electronegativity increases, leading to an enhancement in the attraction between lead and halogen ions. The Pb-Br bond length of MAPbBr3 is about 3.05 Å, which is the shortest among that of the three structures. The corresponding Pb-Br-Pb dihedral angle is about 158° on the ac plane and about 164° along the b-axis direction. For MA (I0.5Br0.5)3, whether Pb-X bond lengths, or the corresponding Pb-Br-Pb bond angles, are between that of the above two perovskites. It is worth noting that the Pb-I-Pb bond angles in the substitutional perovskite are smaller than that in MAPbI3, indicating that bromine substitution causes the iodide ions between the two lead ions to be squeezed and deviate its previous position. It is well known that the longer the bond length is, the smaller its chemical bond energy is. That is, the binding force between the atoms will decrease as the bond length grows longer. As a result, the Pb-I bond is more easily broken, meaning that iodide ion are easier to migrate than bromide ion, which explains that the diffusion barrier for bromine atom is much higher than iodine atom 10


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for the same kind of defects. If the iodine atom is partially substituted with bromine atom, the Pb-X bond length of the new perovskite will be shortened inevitably, which will enhance the binding force of lead and halogen ions, thereby increasing the diffusion barrier and hinder the migration of halogen ions. Michael et al. also suggest that in MAPbI3, Pb-I bond is easily broken and tends to form lead dimer and iodide trimer, and the strong covalent effect within the respective multimers makes MAPbI3 more stable than before.55 Therefore, a long Pb-I bond indicates that the binding force between the two ions is not strong enough, which lead to the formation of defects and low stability of perovskite.

Table 2. Bond Lengths of Pb-X, Bond Angles of Pb-X-Pb, in MAPbX3. Sort

Pb-X bond length (Å)

Pb-X-Pb bond angle (deg)

ac plane

b axis

ac plane

b axis

MAPbI3

3.249/3.245

3.249

152.028

161.619

MAPbBr3

3.047/3.054

3.031

158.024

163.688

Pb-Br/I

Pb-Br/I

Pb-Br/I-Pb

Pb-Br/I-Pb

3.139/3.176

3.122/3.162

155.380/151.245

162.884/159.080

MAPb(I0.5Br0.5)3

Table 3 shows the optimized lattice constant of MAPbX3 structures by PBE methods. MAPbI3 has a lattice constant of a = 8.87 Å, b = 13.13 Å, c = 8.64 Å, the maximum of the three perovskites, and the lattice constant of MAPbBr3 is the smallest. 11



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All of them are in a good agreement with the experimental values. Interestingly, the lattice constant of MAPb (I0.5Br0.5)3 is once again between the two above perovskites. It should be noted that for the three perovskites, the relationship between the size of the lattice constant and the bond length is consistent. Notably, the outermost electron arrangement of bromine atom is 4s24p6, and the outermost layer of iodine atom is 5s25p5, which has one more layer than bromine atom. Obviously, Pb-I bond is longer than Pb-Br bond.

Table 3. The optimized lattice constant of MAPbX3 structures by PBE methods. Sort/Å

a

b

c

MAPbI3

8.87

13.13

8.64

MAPbBr3

8.51

12.00

8.43

MAPb(Br0.5I0.5)3

8.78

12.43

8.60

Haruyama et al. believe that, compared to ABO3-type perovskite, MAPbI3 consists of low-valent ions. Consequently, the weak ion bonds in MAPbI3 cause fierce ion diffusion.35, 56 Combined with our results, we suggest that only by trying to reduce the concentration of easily diffused ions (such as I-) can effectively suppress the ion transport in MAPbI3 and reduce the aging of PSCs. When the diffusion material is assumed to be at a low concentration, the dilution diffusion theory is valid and the diffusion coefficient can be written as:

12


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where

and

are the Boltzmann constant and a temperature, respectively, and

is the concentration of the diffusion mediating defect.57 In accordance with the expression, reducing the concentration of easily diffused ions is a quite effective way to inhibit ion transport. Meanwhile, Nie implied that a relationship between defect concentrations and hysteresis.58 Based on the above theory, bromine substitution can make the perovskite crystal distortion and contraction, resulting in the reduction of iodine defect concentration. Therefore, the bromine substitution method can inhibit the migration of iodide ions in MAPbI3 perovskite. 3.2 Electronic and Optical Properties of MAPbX3 (X = I, Br, I0.5Br0.5) In accordance with our above strategies, we believe that bromine substitution may suppress the migration of ions in MAPbI3 perovskite, and reduce the aging of PSCs. Nevertheless, in the past few years, many researchers have replaced iodine with bromine and chlorine, but both the PCE and light absorption capacity have been reduced to varying degrees. For the purpose of further exploring how well-behaved the proportion of bromine, which not only effectively reduce the ion diffusion, but maintain good light absorption performance, we investigated thoroughly the electronic and optical properties of MAPbX3 (X = I, Br, I0.5Br0.5) with PBE method. The band structures of the three configurations are shown in Figure S2, and we find that the difference between them is negligible.27, 31 On the basis of the band dispersion of MAPbX3 (X = I, Br, I0.5Br0.5) compounds, we can clearly see the direct bandgaps of the three perovskites in the Brillouin zone. Compared to the values between the calculated bandgap and the corresponding experimental values,28-31 it exhibits that the 13



calculated value(1.73eV) is slightly larger than the experimental value(1.55eV) of MAPbI3, because of PBE method overestimated the bandgap value.40, 59 Further, the previous theoretical result is about 1.63 eV, with which our calculated result is in a good agreement.60 Calculated lead-bromine perovskite has a band gap value of 2.01 eV, and the value deceased 1.86 eV after half substitution. Clearly, partial bromine substitution can effectively reduce the band gap than full replacement. We target on analyzing whether the bromine substitution has a greater effect on the bandgap of the lead iodine perovskite itself or not, thus, our demand is merely to obtain the general trend of band gap change. It is gratifying that the results demonstrate that the half substitutional perovskite band gap is between that of the lead iodine perovskite and the lead bromine perovskite, which is consistent with the existing research results.28-30, 61

It is recognized that the band gap of lead-iodine perovskite is the most suitable

light-absorbing materials. Above all, replacing iodine with bromine completely will increase the band gap, which is not expected. Therefore, we tend to select partial bromine substitution rather than complete replacement, although the total substitution will greatly reduce the ion diffusion. Overall, we expect partial bromine substitution because it allows both the band gap and ion transport of MAPbI3 perovskite to remain at satisfactory values. In addition, the electronic structure and the light absorption capacity of the bromine-substitutional perovskite in the visible region should also be included. We compare the optical absorption coefficients of the three structures,28-30, 62 with the PBE method, as shown in Figure 3. The shapes of the three curves are very close, where 14


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the light absorption coefficient will appear redshift as the structure of perovskite changes from MAPbBr3 to MAPbI3. When the structure of perovskite changes from MAPbI3 to MA (I0.5Br0.5)3 and then changes to MAPbBr3, the absorption coefficient curves are blue shifted by about 30 nm, respectively. Although full substitution with bromine can greatly increase the ion diffusion barriers, it also significantly impairs the light absorption capacity of perovskites. However, the partial replacement with bromine can reduce this weakened effect to a certain extent, therefore, we believe that partial substitution is necessary to maintain a good light absorption. Such result is in line with the trend of the band gap as discussed above. This once again demonstrates that partial bromine substitution is superior to total replacement in maintaining good absorbance of the MAPbI3 perovskite.

Figure 3. Calculated absorption coefficients of MAPbI3, MAPbBr3, and MAPb (I0.5Br0.5)3 with PBE method, respectively.

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Figure 4. Progression of relative absorption (the red curve) and relative barrier (the black curve) of CH3NH3PbI1-xBrx as a function of x. The relative absorption represents the ratio of the maximum absorption intensity at different x, which is relative to the maximum value of them. The relative barrier represents the ratio of diffusion barrier at different x, which is also relative to the maximum value of them.

3.3 How to find a suitable range of bromine substitution? As we all know, stability and energy conversion efficiency are as well as important for a good-performance perovskite solar cell. We hope to provide a way to find a suitable range of bromine replacement ratios. It is well known that the photon absorption ratio at the maximum absorption peak is about 100%. In this case, the amount of photon absorption depends only on the energy density of sunlight at that wavelength, so we referred to the solar spectrum and extracted the corresponding solar energy densities at each maximum absorption peak. Then, the relative value of each photon absorption amount was determined by taking the maximum photon absorption amount as ONE. Similarly, we set the maximum value of the diffusion 16


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barriers to ONE and then calculated the relative value of each barrier. Based on the calculation of the diffusion barriers and the optical absorption coefficients, we employ the ratio of bromine as x, the relative diffusion barrier and the relative light absorption as a function of x, respectively.63 As shown in Figure 4, the relative diffusion barrier is monotonically increasing, while the relative light absorption coefficient is continuously declining with the increase of bromine substitution ratio, respectively. Thus, partial bromine substitution should have both good light absorption and a high diffusion barrier. Based on the above discussion, if we can accurately characterize the relationship between perovskite’s PCE and bromine replacement ratio, we can roughly determine a suitable range for bromine substitution. Similarly, if we take into account the time, temperature, and other factors that may affect the stability of the perovskite and then find out the relationship between the stability and the ratio of bromine replacement, we can also determine the appropriate range of bromine substitution. In fact, it is hard to consider all kinds of complicated factors in our calculations, but we can accomplish some work through experiments. Therefore, it is possible to determine the approximate range of bromine substitution ratios.

4. Conclusion We have performed first-principles calculations to study the dominant diffusing ions (I-) in lead iodine perovskite, and the results indicate that bromine substitution has great influence on increasing ion diffusion barriers and hindering the migration of halogen ions. The reason for the ease of iodide ions’ migration is the unstable Pb-I bond and larger iodine ionic radius, which cause a smaller binding force with the lead 17



ion and the formation of iodine defects. Partial substitution of bromine(such as half bromine substitution) exhibits not only high ion diffusion barriers and low band gap, but also good light absorption performance by carrying out the calculation of the electronic structure and optical properties of the orthorhombic phase of MAPbI3, MAPbBr3 and MAPb (I0.5Br0.5)3 perovskite, respectively. We suggest that the selection of anions may be have similar properties if the migration of ions is reduced by adopting substitution, while ensuring the light absorption properties PSC. If we take into account the time, temperature, and other factors that may affect the stability and the PCE of the perovskite by combining experiments, and then find out their relationships, it is possible to determine the approximate range of bromine substitution ratios.

ASSOCIATED CONTENT Supporting Information available: Diffusion barriers curves for interstitial and vacancy ion migration, band structures of MAPbX3 (MA=CH3NH3, X = I, Br, I0.5Br0.5) perovskites, and a description of the method for calculating the band structures

ACKNOWLEDGMENTS

This work is supported by the China Scholarship Council Fund (201506445024) and by the Higher Education Young Elite Teacher Project (2462015YQ0603) from CUP (China University of Petroleum-Beijing). 18


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Effect of Bromine Substitution on the Ion Migration and Optical

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