Charge Carrier Trapping at Surface Defects of Perovskite Solar Cell

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Charge Carrier Trapping at Surface Defects of Perovskite Solar Cell Absorbers: A First-Principles Study Hiroki Uratani, and Koichi Yamashita J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b00055 • Publication Date (Web): 27 Jan 2017 Downloaded from http://pubs.acs.org on January 28, 2017

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The Journal of Physical Chemistry Letters

Charge Carrier Trapping at Surface Defects of Perovskite Solar Cell Absorbers: A First-Principles Study Hiroki Uratani*,†,‡ and Koichi Yamashita*,†,‡

†Department of Chemical System Engineering, School of Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-8656 Tokyo, Japan ‡CREST-JST, 7 Gobancho, Chiyoda-ku, 102-0076 Tokyo, Japan

AUTHOR INFORMATION Corresponding Author *[email protected] *[email protected] Notes The authors declare no competing financial interests.

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ABSTRACT

The trapping of charge carriers at defects on surfaces or grain boundaries is detrimental for the performance of perovskite solar cells (PSCs). For example, it is the main limiting factor for carrier lifetime. Moreover, it causes hysteresis in the current-voltage curves, which is considered to be a serious issue for PSCs' operation. In this work, types of surface defects responsible for carrier trapping are clarified by a comprehensive first-principles investigation into surface defects of tetragonal CH3NH3PbI3 (MAPbI3). Considering defect formation energetics, it is proposed that a Pb-rich condition is preferred to an I-rich one, however, a moderate condition might possibly be the best choice. Our result paves the way for improving the performance of PSCs through rational strategy of suppressing carrier trapping at surface defects.

TOC GRAPHICS


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Organic-inorganic hybrid perovskites (OIHPs) such as CH3NH3PbI3 (MAPbI3) are attracting much interest for application as perovskite solar cells (PSCs). Since the report of the first PSC in 2009,1 their photoconversion efficiencies (PCEs) have increased from 3.8% to 22.1%2 to date. One of the detrimental factors in PSCs' performance is the trapping of charge carriers at defects on their surfaces or grain boundaries. First, the carrier trapping at surface defects causes nonradiative recombination loss and deteriorates the carrier lifetime. For example, Chen et al.3 passivated grain boundaries of MAPbI3 with PbI2, resulting in the improvement in the carrier lifetime and enhancement of PCE from 0.66% to 12.00%, because of the suppression of carrier trapping at defects on the grain boundaries. Noel et al.4 have prolonged carrier lifetime by almost seven times to achieve an improvement in PCE from 13.1% to 16.5% via surface passivation with Lewis bases, which donate electrons to fill midgap states that stem from surface defects, reducing carrier traps. Moreover, the carrier trapping on surfaces is one of main origins of the hysteresis in the current-voltage curves,5–7 which is a serious drawback of PSCs. Shao et al.6 eliminated the hysteresis by reducing electron traps using surface passivation by fullerene. Im et al.8 and Nie et al.9 also overcame the hysteresis through another approach: they fabricated grains with large size, which have reduced interfacial area associated with grain boundaries, i.e. reduced carrier trapping on surfaces. In conjunction with these successes, spectroscopic studies revealed that carrier trapping states actually exist on surfaces.10,11 However, to date, the types of surface defects that act as carrier traps are still not identified. Although theoretical works by Haruyama et al. revealed the absence of deep midgap states on surfaces without point defects,12,13 little is known about surfaces that have them. Defect physics of OIHPs has been substantially studied by first-principles,14–18 however, previous studies have focused on bulk point defects, not on surface defects.


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The aim of this work is to clarify the types of surface defects responsible for carrier trapping, and to understand the relationship between surface defects formation and chemical conditions, in order to propose design rules for high-performance PSCs. We investigate the energy levels of defect states and the formation energy of various types of surface defects comprehensively, by first-principles calculations based on density-functional theory (DFT) for MAPbI3 systems containing surface defects, using slab models. We discuss the possible types of carrier-trapping surface defects for different conditions: I-rich, Pb-rich, and moderate. Finally, we show that the Pb-rich condition is more suitable than the I-rich condition and propose that the moderate condition might be the most appropriate. We focused on (001) surface, which is determined as one of the major types of MAPbI3 facet by first-principles calculations12,13 and powder X-ray diffraction measurements.19 2 × 2 surface models containing 384-552 atoms were constructed from the tetragonal MAPbI3 crystal structure. Three types of surface termination, that have been typically studied,12,13,20–22 were considered: "MAI", "flat", and "vacant" termination (Figure 1).

Figure 1. "MAI", "flat", and "vacant" type of termination. H, Pb, C, I, and N atoms are shown as pink, gray, brown, purple, and blue, respectively. The simulation cell is shown by dotted lines.


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The outermost layers of "MAI" and "flat" termination are composed of MAI and PbI2, respectively. "Vacant" termination is constructed by eliminating eight PbI2 units from the "flat" termination. The cell parameters were fixed to the twice of experimental value (a = b = 17.602 Å)23 during calculations. A vacuum region of 15 Å or more was added to each model. Following the conventional approach,12,13,24 the directions of MA cations were alternated so that slabs had almost no net electric dipole moment. For each calculation of defect-containing systems, one side of the slab contained a defect. The types of surface defects considered are shown in Table 1. Here, VX (where X is an atom or a group of atoms) means that X is removed from the outermost layer, Xi means that excessive X is placed on the surface, and XY (where Y is an atom or a group of atoms) means that Y site of the outermost layer is substituted by X.


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Table 1. Considered types of surface defects and their formation energy (in eV) under different conditions. termination

defect

I-rich

moderate

Pb-rich

MAI

VI

2.38

1.77

1.15

MAI

VMA

0.32

0.91

1.54

MAI

Pbi

4.69

3.45

2.24

MAI

PbMA

2.35

1.70

1.13

MAI

PbI

5.97

4.14

2.31

flat

Ii

-0.03

0.57

1.19

flat

VI

4.55

3.94

3.32

flat

Pbi

2.94

1.71

0.50

flat

VPb

-0.13

1.10

2.31

vacant

Ii

-0.12

0.48

1.10

vacant

VI

1.76

1.15

0.54

vacant

Pbi

2.71

1.48

0.26

vacant

VPb

-1.40

-0.17

1.04

The calculations were performed with Vienna Ab-initio Simulation Package25–28 using a planewave basis set with the projector augmented-wave (PAW) method.29 For H, Pb, C, I, and N atoms, 1, 14, 4, 7, and 5 valence electrons were explicitly treated, respectively. Structural relaxations were performed and then defect formation energy calculations were conducted at the relaxed structure, with 500 eV of a plane-wave cutoff. In structural relaxations, positions of all atoms were relaxed until the Hellman-Feynman forces became below 0.02 eV⁄Å. The Brillouin zone (BZ) was sampled at the Γ-point in the structural relaxations, and the 2 × 2 × 1 Γ-centered k-point mesh was adopted in the defect formation energy calculations. For structural relaxations and defect formation energy calculations, Perdew-Burke-Ernzerhof formalism of generalized


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gradient approximation (GGA-PBE)30 was adopted without the inclusion of spin-orbit coupling (SOC), as it is widely used for DFT studies of OIHPs including MAPbI3 and has provided reliable results for structure and thermodynamic properties.12–15,17,21,22,24,31–33 However, for defect level calculations, GGA-PBE without SOC fails because of valence band maxima (VBM)/conduction band minima (CBM) levels overestimation as a result of self-interaction error inherent in GGA and the neglect of SOC.16,18 For this reason, to calculate defect levels, we adopted Heyd-Scuseria-Ernzerhof (HSE) hybrid functional34 with 43% of Hartree-Fock exchange (denoted as = 0.43) and the inclusion of SOC following the approach of Du,16,18 which provides reasonable positioning of VBM, CBM and defect levels for MAPbI3. In defect level calculations, we used the structure relaxed in the above-mentioned manner. Because the computational cost of the hybrid functional is much larger than that of GGA-PBE, the calculations were conducted using 400 eV of a plane-wave cutoff and BZ was sampled at the Γpoint. Note that VBM and CBM of MAPbI3 are located at the Γ-point.35 The energy levels of defect states were determined as the corresponding Kohn-Sham orbital levels. It should be noted that we did not determine the defect levels by the difference in total energy between the charged and the neutral system, which is the usual strategy for bulk defects,14,16–18 because, for slab models, the total energy of a charged system is meaningless because of the electrostatic repulsion between slabs. For visualization, VESTA software36 was used. The energy levels of defect states compared with the VBM and CBM of each system are shown in Figure 2.


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Figure 2. Defect levels compared with VBM and CBM calculated by HSE ( = 0.43) with SOC. Energy levels are referenced to the VBM of each system. Defect levels are shown by red horizontal lines. VBM and CBM are shown by black horizontal lines. Note that defect states are described if and only if they are located between the VBM and CBM. These energy levels are referenced to the VBM of each system. The Kohn-Sham states corresponding to the VBM, CBM, and defect states were determined by their absolute energy levels, occupation numbers, and orbital shapes (for details, see the Supporting Information). The slight fluctuations in the VBM-CBM gap depending on the types of defects are presumably attributed to the finite-size error and the doping effect of defects. The defect formation energy was calculated taking into account the chemical potential of I, Pb, and MA denoted as , , and , respectively, following the approach introduced by Yin et al.14 (for details, see the


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Supporting Information). Assuming equilibrium among MAPbI3, MAI, and PbI2, the defect formation energy under the I-rich condition ( = 0 eV, = −2.44 eV, and = −3.15 eV), moderate condition ( = −0.61 eV, = −1.21 eV, and = −2.57 eV), and Pb-rich condition ( = −1.22 eV, = 0 eV, and = −1.93 eV) is shown in Table 1. On the "MAI" surface, only VMA has low formation energy, however, it has no deep midgap defect states (Figure 2). This means that no or very few carrier traps can form on the "MAI" surface regardless of the conditions, therefore "MAI" is the most suitable surface termination from the viewpoint of avoiding carrier trapping on surfaces. Remarkably, the Br counterpart of the “MAI” termination, i.e. “MABr” termination, was experimentally observed by Ohmann et al.37 on mechanically cleaved MAPbBr3 crystals. However, it should be noted that Lindblad et al. reported an understoichiometry in I and/or N at the annealed MAPbI3/TiO2 interfaces,38 suggesting that "MAI" is not the dominant surface termination in annealed samples. This observation can be supported by the fact that PbI2 species remains in grain boundaries after thermal annealing,3 because MAI has higher volatility than PbI2. From Table 1, it is suggested that different types of defects are dominant depending on the condition (I-rich, moderate, and Pbrich). Under the I-rich condition, MA vacancies (VMA) on “MAI” surface, excessive I atoms (Ii) on “flat” and “vacant” surfaces, and Pb vacancies (VPb) on “flat” and “vacant” surfaces are dominant. Among these, only Ii has a deep carrier-trapping state (Figure 2). Hence, only Ii can be the origin of carrier trapping on surfaces under the I-rich condition. Note that Ii have remarkably low formation energy (-0.03 eV on “flat” surface and -0.12 eV on “vacant” surface) under the I-rich condition (Table 1). The charge density distribution derived from the KohnSham orbitals corresponding to the defect states of Ii on "flat" and "vacant" surfaces are shown in


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Figure 3a and b, respectively, revealing that these defect states are mainly composed of p orbitals of excessive I atoms, and Pb s orbital also contributes in the case of "vacant" surface.

Figure 3. Charge density distribution corresponding to defect states (left) and atomic structure of defects (right) of (a): Ii on "flat" surface, (b): Ii on "vacant" surface, (c): Pbi on "flat" surface, (d): Pbi on "vacant" surface, and (e): VI on "vacant" surface. Atoms in the outermost two layers are drawn. The charge density is illustrated by yellow isosurfaces. Blue isosurfaces indicate negative charge density in the core region, which is a common artifact of the PAW method. On the other hand, under the Pb-rich condition, excessive Pb atoms (Pbi) are dominant for "flat" and "vacant" surfaces, and I atom vacancies (VI) are also dominant for "vacant" surfaces. From


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Figure 2, it is revealed that Pbi generates deep carrier trapping states near the middle point between VBM and CBM on both "flat" and "vacant" surfaces. Also, on "vacant" surfaces, VI creates carrier trapping states. However, it is important to point out that the formation energy of Pbi (on “flat” and “vacant” surfaces) and VI (on “vacant” surface) under the Pb-rich condition (+0.26 eV or more) is higher than that of Ii under the I-rich condition (-0.03 eV or less). The charge density distribution of the defect states of Pbi on "flat" and "vacant" surfaces, and VI on "vacant" surfaces are shown in Figure 3c, d, and e, respectively. For Pbi, charge localization in the bonding region between the excessive Pb and a Pb atom in the outermost layer can be observed, indicating that the carrier trapping states come from Pb-Pb bonding orbitals. Also, the defect state of VI on "vacant" surface is found to be mainly composed of p orbital of the undercoordinated Pb atom. From the above discussion, I-rich and Pb-rich conditions entail carriertrapping surface defects that have different origins: excessive I atoms under I-rich conditions, and excessive Pb atoms and I atom vacancies under Pb-rich conditions. Since the formation energy of carrier-trapping surface defects under the Pb-rich condition is higher than that under the I-rich condition, the Pb-rich condition is better than the I-rich condition. This can account for the fact that higher photovoltaic performance is realized by the two-step method39 than the onestep method1,40 because of the use of high PbI2 concentration (namely, excess Pb relative to I, for growth of MAPbI3) in the two-step method; in the two-step method, PbI2 is first introduced into mesoporous TiO2 by spin-coating and then the PbI2/TiO2 composite film is dipped into MAI solution, whereas in the one-step method, stoichiometric mixed solution of MAI and PbI2 is dropped onto TiO2. Under the moderate condition, only VPb on "vacant" surfaces, which does not act as carrier traps, has low formation energy, suggesting that no or very few carrier-trapping surface defects can form under the moderate condition. Hence, from the aspect of minimizing


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carrier trapping at surface defects, the moderate condition might be the best choice. Notably, Hsu et al. reported that moderate concentration of excess PbI2 maximizes carrier lifetime in MAPbI3,41 suggesting that the moderate condition actually minimizes the charge carrier trapping at surface defects. In summary, we studied various types of surface defects on three types of terminations: "MAI", "flat", and "vacant", by first-principles calculations. Combining the calculated defect levels and the defect formation energy, our results can be summarized in three points as follows. (i) Under the I-rich condition, excessive I atoms on “flat” and “vacant” surfaces are responsible for the carrier trapping. On the other hand, under the Pb-rich condition, I atom vacancies on "vacant" surface and excessive Pb atoms on both "flat" and "vacant" surfaces act as carrier traps. (ii) The formation of carrier-trapping surface defects under the Pb-rich condition is thermodynamically more unfavorable than under the I-rich condition. (iii) Under the moderate condition, any surface defects that act as carrier traps have high formation energy, i.e. cannot easily form. From the above, to reduce carrier trapping on surfaces or grain boundaries so as to improve carrier lifetime and avoid hysteresis, the Pb-rich condition is better than the I-rich condition, consistent with the superiority of the two-step method39 over the one-step method1,40 in terms of photovoltaic performance. Also, the moderate condition can be potentially the most desirable. ACKNOWLEDGMENT Computational resources were provided by Reserch Center for Computational Science, National Institutes of Natural Sciences, Okazaki, Japan. ASSOCIATED CONTENT


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Supporting Information Available: Details of the determination of relevant Kohn-Sham states to obtain Figure 2, and details of the defect formation energy calculations (PDF)

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Charge Carrier Trapping at Surface Defects of Perovskite Solar Cell

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