Understanding the low-loss mechanism of general organic–inorganic perovskites from first-principles calculation

Accepted Manuscript Title: Understanding the low-loss mechanism of general organic-inorganic perovskites from first-principles calculation Author: Dan Li Jingjing Meng Yuan Niu Hongmin Zhao Chunjun Liang PII: DOI: Reference:

S0009-2614(15)00181-5 http://dx.doi.org/doi:10.1016/j.cplett.2015.03.028 CPLETT 32874

To appear in: Received date: Revised date: Accepted date:

10-2-2015 12-3-2015 17-3-2015

Please cite this article as: D. Li, J. Meng, Y. Niu, H. Zhao, C. Liang, Understanding the low-loss mechanism of general organic-inorganic perovskites from first-principles calculation, Chem. Phys. Lett. (2015), http://dx.doi.org/10.1016/j.cplett.2015.03.028 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Understanding the low-loss mechanism of general organic-inorganic perovskites from first-principles calculation

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Department of Physics, Beijing Jiaotong University, Beijing 100044, China

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Dan Lia,*, Jingjing Menga, Yuan Niua, Hongmin Zhaoa, Chunjun Liang b,*

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Key Laboratory of Luminescence and Optical Information, Ministry of Education, School of Science, Beijing Jiaotong University, Beijing 100044, China *

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Abstract

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Authors to whom correspondence should be addressed. Electronic addresses: [email protected] and [email protected]

To understand the low-loss mechanism of organic–inorganic perovskites, the electronic

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structures of nine halide perovskites were investigated by first principle methods. We provide evidence that spatial separation significantly influences the recombination rate of electrons and

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holes. For AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, and FAPbI3, the considerable remaining

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charge density localized at the organic cations in addition to a part of charge density of CBM localized at Pb atoms, leading to very few hopping with the surrounding inorganic matrix and

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further reducing the recombination rate of the carrier. Excellent optical absorption properties were found for all calculated APbI3 perovskites.

1. Introduction

Organometal halide hybrid perovskite solar cells based on solution-processed materials are

eliciting considerable attention in the field of photovoltaics. Since the first reports on solar cells based on organic–inorganic halide perovskites in 2009 [1], power conversion efficiencies have already exceeded 19.3% [2], thereby surpassing every other solution-processed solar cell technology. Methylammonium (MA) lead trihalide perovskite materials allow low-cost solution processing and broad absorption across the solar spectrum; thus, they are the exciting new materials for generating clean energy. A potential combination of various excellent properties, such as appropriate band gap, high absorption coefficient, high carrier mobility, low carrier recombination rate, and solution processability, make organic–inorganic perovskites very promising candidates for low-cost solar energy conversion [3–11].

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Understanding the origins of high carrier mobilities, low carrier recombination rates, and high absorption coefficient of solution-processed perovskites is urgent. This investigation could help in the design of more practical and promising light harvesters in solar cells. Two typical approaches result in low carrier recombination in impurity-free semiconductors. One approach

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entails separating the electrons and holes in momentum space using an indirect semiconductor. A perfect example is indirect semiconductor silicon, in which the recombination rate is very low,

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such that the carrier lifetime could reach several microseconds [12]. The other approach entails

separating the electron and hole in real space. An example is the extensively investigated

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polymer–fullerene blend system, in which ultrafast charge transfer from the polymer to the fullerene occurs after light excitation [13], leading to spatially separated electron and hole

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transport channels and very low carrier recombination rate (3 to 4 orders lower than the expected Langevin recombination rate) [14–16].

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In our study, the electronic structures of nine halide perovskites APbI3 (A = Cs, M (NH4), MA (CH3NH3), FM1 (NH2CHOH), FM2 (NH3CHO), DM (CH3NH2CH3), AM1 (CH3NH2COH), AM2

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(CH3NH3CO), and FA (NH2CHNH2)) were investigated by using first principle methods on the basis of density functional theory (DFT). We provide evidence that spatial separation significantly

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influences the recombination rate of electrons and holes in the materials. Finding the low-loss

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mechanism of this class of materials could inspire further studies to explore more enhanced solar energy materials with low carrier recombination rate and high carrier mobility.

2. Computational methods

The structural and electronic properties of nine kinds of pseudo-cubic halide perovskite were

calculated using the first principle methods based on DFT. The projector-augmented wave potentials [17] and Perdew–Burke–Ernzerhof [18] functions were implemented using the Vienna Ab Initio Simulation Package [19]. The orbitals Pb(5d, 6s, 6p), N(2s, 2p), C(2s, 2p), H(1s), I(5s,

5p), and O(2s, 2p) were treated as valences in the calculation. The wave functions were expanded in plane waves with a kinetic energy cut-off of 500 eV. A k-point set generated by the 21 × 21 × 21 Monkhorst–Pack mesh was used [20]. Gaussian smearing method was adopted for partial occupancies. The convergence criterion of the self-consistent calculations for ionic relaxations was 10-5 eV between two consecutive steps. With the conjugate gradient method, all atomic

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positions and the size of the unit cell were optimized until the atomic forces were lower than 0.005 eV/Å. As our tests show, the inclusion or exclusion of spin-orbit coupling does not affect the main results in the present work; thus, the effect of spin-orbit coupling can be neglected. Charge densities of the VBM states and CBM states on each atom were integrated using Bader analysis

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[21–23].

3. Results and discussions

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For MAPbI3, transitions from orthorhombic to tetragonal and from tetragonal to cubic

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occurred at ∼160 K and ~327 K, respectively. The tetragonal lattice contained a large unit cell

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because of the tilting of the octahedral. However, it could be considered as pseudo-cubic to some extent [24]. A pseudo-cubic basis was used in this paper, as shown in Figure 1, for the

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comparability of the calculated results for different organic cation-substituted halide perovskites. Given nine substitutional A cations for FM and AM molecules, the carbonyl (C=O) is a stronger dipole than the N–C dipole because of the greater electronegativity of oxygen atom. Thus, the

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oxygen atom can accept hydrogen bonds from water [25]. Although protonation occurs most often

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in the oxygen atom, two cases of protonation occurring in O atom and in N atom are calculated. Four cations formed by molecules FM and AM are defined as FM1 (NH2CHOH), FM2

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(NH3CHO), AM1 (CH3NH2COH), and AM2 (CH3NH3CO), as indicated in Figure 1, corresponding to FMPbI3-1, FMPbI3-2, AMPbI3-1, and AMPbI3-2 perovskite structures,

respectively. The total energy calculated results show that total energies of AMPbI3-1 and

FMPbI3-1 are reduced by 0.51 and 0.52 eV, respectively, compared with AMPbI3-2 and FMPbI3-2. This observation suggests that the protonation of FA and AM organic molecules are more likely to appear on the O atoms than on the N atoms. In addition, the structure of AMPbI3-1 is formed,

and FMPbI3-1 may be more stable than the formation of the structure of AMPbI3-2 and FMPbI3-2 in the experiment. The structures of all pseudo-cubic halide perovskite APbI3 were obtained upon relaxation of atomic coordinates and cell parameters, as shown in Table 1. For all halide perovskites, except perfect cubic CsPbI3 that maintained the same lattice constants, the lattice constants of the three directions were not equal because of the anisotropy of organic cations. The primitive cell volumes

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of all APbI3, except FAPbI3, increased with the increasing size of A cations from Cs to AM. The rotation of FA cations in inorganic scaffolds resulted in lattice large tilt (90°95°=90°), although the basic lattice constant was equal (a = 6.49 Å, b = 6.48 Å, c = 6.49 Å). The lattice constants of APbI3 also changed with the long axis lengths (L) of organic A cations. The anisotropy of lattice

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constants was obvious for AMPbI3-1, AMPbI3-2, FMPbI3-1, and DMPbI3, with a long L of organic

calculation, our results are in good agreement with these data [26, 27].

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cations. Comparing the obtained lattice constants with the available results of experiment and

Our previous study results show that chlorine substitution modifies the band structure of the

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halide perovskites, leading to significant changes in the effective masses of electrons and holes [28]. Different substitutional organic cations also significantly change the band structure of the

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halide perovskites. The band structures for all calculated halide perovskites are shown in Figure 2. Indirect band gaps existed in addition to AMPbI3-2 and DMPbI3, whose VBM and CBM of

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AMPbI3-2 and DMPbI3 appeared on points M and R of the first Brillouin zone, respectively. All of the remaining calculated materials showed direct band gaps at the vertex points R of the first

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Brillouin zone. The calculated band gaps at the R-point were 1.47 eV for CsPbI3 and 1.58 eV for MAPbI3, consistent with the experimental values [29, 30]. Different organic cations significantly

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changed the band gaps from CsPbI3 to AMPbI3-2. As the cell volumes enlarged, the energy band

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gaps increased. The three conduction bands derived mainly from px, p y, and pz states of Pb atoms at R-point were almost energy degeneracy for CsPbI3. Although three conduction bands showed different degrees of splitting for other calculated perovskites because of different degrees of anisotropy of lattice constants, an extremely localized band close to the bottom of the conduction band was observed in AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, and FAPbI3 halide perovskites,

as shown in Figure 2. For FAPbI3, this very small dispersion state was derived from unoccupied sp2 hybridization states of C-N bond. For AMPbI3-2 and FMPbI3-2, these very small dispersion states were derived mainly from anti-bonding states between the O atom 2p orbitals and C atom 2p orbitals in AM2 and FM2 cations. However, for AMPbI3-1 and FMPbI3-1, not only do the O and C atoms form covalent bonds, H atoms also form covalent bonds so that the energy differences between the bonding state and the anti-bonding states are further increased, resulting in bonding state and anti-bonding states that are further away from the Fermi level. This observation can be seen more clearly in the density of state (Figure 4).

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The effective masses of electrons and holes for all calculated halide perovskites are derived by parabolic band fitting along the seven high-symmetry directions (Figure 2) around the R-points of the Brillouin zone, as listed in Table 2. Organic cations are large, and the lattice constants of the three directions are not equivalent, hence the obvious anisotropic effective masses. The average

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effective masses of the electrons and holes in AMPbI3-1, FMPbI3-1, FMPbI3-2, MAPbI3, MPbI3,

and CsPbI3 are all less than m0. These values are similar to that of a typical semiconductor silicon

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[12]. The average effective masses of the electrons and holes in AMPbI3-2, FAPbI3, and DMPbI3

are greater than or close to m0, as indicated in Table II. The carrier mobility  is inversely

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proportional to the effective mass m* expressed as m= qτs/m* [31], where q is the elementary charge and τs is the average scattering time. The effective masses of the halide perovskites that

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validate the high mobilities and the long-range ambipolar charge transport the properties of the materials. In particular, the small effective mass of perovskite is beneficial for high mobility. For

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pseudo-cubic AMPbI3-2 and DMPbI3, three lattice constants are more obviously different (i.e., a = 7.64, b = 6.48, c = 6.24 for AMPbI3-2; a = 7.43, b = 6.42, c = 6.39 for DMPbI3) because of the

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molecular long axis along the direction of the basis vectors of a. When the lattice constants of the direction of the basis vector a are larger, the reciprocal lattice vector length along the M1-R (Kx)

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direction is shorter than those in other directions of the Brillouin zone. The conduction and

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valence bands show considerably smaller dispersion along the M1-R (Kx) direction (Figure 2). The result is an enlarged effective mass (i.e., me* = 3.47 m0 and mh* = 4.01 m0 for AMPbI3-2, me* = 3.77 m0 and mh* = 17.03 m0 for DMPbI3). Therefore, the calculation predicts anisotropic carrier

transport because of the significantly anisotropic effective mass in these two kinds of halide perovskites.

Electrons transport at the bottom of the conduction bands and holes transport at the top of the

valence bands, so the electronic structure of VBM and CBM should be examined. For all calculated halide perovskites, the charge densities of three conduction bands and one valence band in the vicinity of the R-point of the first Brillouin zone were calculated. Given that AMPbI3-2 and

DMPbI3 are indirect band gaps, the charge densities of one valence band in the vicinity of M-points were also calculated. In addition, given that the first Brillouin zone of pseudo-cubic deviates from a cubic symmetry, all seven high-symmetry directions near the vertex point R should be considered to eliminate the influence of symmetry reduction. The charge densities of the

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same number of K points along the seven high-symmetry directions were added to obtain the charge densities of the highest VBM and the lowest CBM (CBM-1) because the influence of carrier recombination rate should be the transition probability of CBM1 state to VBM state. In addition, given the degeneracy of the three conduction bands in the R-point in APbI3 perovskite

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(e.g., CsPbI3, MPbI3, MAPbI3, and DMPbI3), the charge densities of three or four CBM (CBM-3/4) states were added. That is, four CBM states for AMPbI3-2 and FMPbI3-2 and three CBM states for

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the remaining materials were calculated because those bands are very close and difficult to distinguish from the energy in the vicinity of the R-point of the first Brillouin zone.

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The charge densities at the VBM, CBM-1, and CBM-3/4 with isosurface value of 0.0003 e/Å3, 0.0003 e/Å3, and 0.0009/0.0012 e/Å3 are shown in Figure 3. The results show that for

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AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, DMPbI3, and FAPbI3, the charge densities are localized mainly on I atoms at the VBM states, whereas the CBM-3/4 states are derived mainly

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from the Pb atom 6p orbitals, a part of the organic cation sp orbitals, and a very small part of the I atom 5p orbitals. The charge densities in the VBM and CBM-3/4 states are distinctly separated in

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space. If only the lowest energy CBM-1 states were analyzed rather than CBM-3/4 states, I atom 5p orbitals give almost no contribution to CBM-1 states in AMPbI3-1, AMPbI3-2, FMPbI3-1,

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FMPbI3-2, and FAPbI3. Completely separated charge densities in the VBM and CBM-1 states are

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observed. Evidently, a poor overlap of the charge density in the CBM and VBM states will lead to a low recombination transition rate. Therefore, spatial separation of the charge densities in the CBM and VBM states, which indicates reduced overlap of the wave functions of electron and hole, will lead to a significantly reduced charge recombination rate in the material. The extreme case of non-overlap (completely separated charges) will slow down the recombination to zero. However, considerable overlaps of the charge densities of the VBM states and CBM-1 states,

as well as VBM states and CBM-3 states, were found in MPbI3 and CsPbI3. For MPbI3, 6s orbitals

of Pb are also the major contributor to the VBM states, in addition to the 5p orbitals of I atoms. However, the CBM-1 and CBM-3 states are also derived mainly from the Pb atom 6p orbitals, similar to other perovskites (Figure 3). For CsPbI, in addition to the 5p orbitals of I atoms as the major contributor to the VBM states, 6s orbitals of Pb are the minor contributor to the VBM states. Although CBM-1 and CBM-3 states are also derived mainly from the Pb atom 6p orbitals, I atoms 5p orbitals also have a small contribution to CBM-1 and CBM-3 states. Therefore, considerable

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overlaps of the charge densities of VBM and CBM-1 states, as well as VBM and CBM-3 states, which occur in Pb atoms and I atoms were observed in CsPbI3. MAPbI3 is between these extremes; only very small amounts of overlap of the charge densities of the VBM and CBM-1 states, as well as CBM-3 occurring in I atoms rather than Pb atom, was observed (Figure 3). The analytical

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results coincide with the view of Herz et al. who discovered that the bimolecular recombination rate in lead trihalide perovskite is more than four orders of magnitude lower than the one predicted

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from Langevin theory, which expresses that a preferential localization of electrons and holes in different regions of the perovskite unit cell causes the reduced recombination rate [14].

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The transition probability of CBM state to the VBM state that affects carrier recombination to a final state |  v , is

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rate, which is the rate of spontaneous transition from an initial state | c proportional to the square of the transition dipole moment [32].

(1)

P   c | ( qr) |  v  q   c* (r)r v (r)d 3r  q   c* (r) v (r)rd 3r    c* (r) v (r) d 3r    c ( r )  v ( r )d 3r

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where q is the charge of the particle, r is its position, and the integral is over all space.

  (r ) (r )d r 3

v

in the equation represents the overlap integral of the electron densities of the initial

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c

and final states. For quantitative comparisons, we calculate the overlap integral charge density

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percentage of the lowest CBM and VBM states, that is,

  (r )  (r )d r / (   (r )d r   (r )d r) , and 3

c

v

3

c

3

v

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the integral is over a unit cell. In addition, the integrated charge densities on each atom at the lowest CBM and VBM are obtained using Bader analysis. Table 3 lists the percentage of the integral charge density of each atom at the lowest CBM (CBM) and VBM (VBM) and the overlap integral charge density percentage of the lowest CBM and VBM states (OIP). For all APbI3, the

charge density of CBM is mainly localized around Pb atoms and/or organic cations, whereas the charge density of VBM is more localized around I atoms. Except for MPbI3 and CsPbI3, overlap

integrals of charge density percentage of other APbI3 materials are very small and account for less

than 10%. In particular, the overlap integrals of charge density percentage of the lowest CBM and VBM states of AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, and FAPbI3 were less than that of MAPbI3, which implies a low carrier recombination rate in the experiment [33,34]. However, considerable overlap integrals of about 26.5% and 24.8% of the charge densities of the VBM states and CBM states were found in MPbI3 and CsPbI3, respectively. For AMPbI3-1, AMPbI3-2,

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FMPbI3-1, FMPbI3-2, and FAPbI3, in addition to a part of charge density of CBM localized around Pb atoms, the considerable remaining charge density localized around the organic cations. Those small dispersion anti-bonding states of organic cations are very close to the CBM states (Figure 2)

inorganic matrix and further reducing the recombination rate of the carrier.

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and remain well localized in the space, leading to very few hopping with the surrounding

The total density of states (TDOS) and the projected density of states (PDOS) of all

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calculated APbI3 perovskites were analyzed to further understand the electronic structure and the interaction of organic cations and adjacent I anions. The procedure is shown in Figure 4. The

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PDOSs show p orbitals of three I atoms, s and p orbitals of Pb atoms, and sp orbitals of organic cations. PDOS structures of the p orbitals of three I atoms were significantly different. Given the

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different orientations of organic cations, which have different interactions with three I atoms, their status are not equivalent. The protonation occurs in the O-H bonds (e.g., for AMPbI3-1 and

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FMPbI3-1) or N-H bonds (e.g., for AMPbI3-2, FMPbI3-2, DMPbI3, MAPbI3, and MPbI3). One I atom close to the H atom of O-H or N-H bond has strong interactions with organic cations.

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Therefore, the sp orbitals of organic cations hybridized with the p orbitals of one I atom in unit cell whose valence states were relatively but largely corrected, thus causing the valence states to

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shift to lower energy and away from the top of the valence band, as shown in Figure 4. Therefore,

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the major contributors to VBM states are the 5p orbitals of the remaining I atoms in the unit cell, which have weak interaction with the organic cations and instead form ionic bonds with Pb atoms. Meanwhile, the Pb atom p orbital dominates the conduction-band states in a wide energy range in all calculated APbI3 perovskites. For AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, and FAPbI3, in

addition to p orbitals of Pb atoms, localized sp anti-bonding orbitals of organic cation are also major contributors to CBM states, confirming that charge carriers are further separated and localized in space, leading to a further decrease in the recombination rate of the carrier. The simulated optical absorption spectra for all APbI3 are reported in Figure 5. Significantly anisotropic optical absorption exists because long axis lengths of organic cations lead to the anisotropy of lattice constants in AMPbI3-1, AMPbI3-2, and DMPbI3. The lattice constant is larger,

and the light absorption of the direction is more blue shifted. For the direction along the larger lattice constants, optical absorption energy ranges are blue shifted, corresponding to the lesser light absorption in the 400–800 nm wavelength range. However, in the plane perpendicular to the

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larger lattice constant, large absorption coefficients in the 400–800 nm wavelength range are observed in AMPbI3-1, AMPbI3-2, and DMPbI3, as shown in Figure 5. Given the isotropy of lattice constants in FAPbI3 and CsPbI3, all diagonal components of absorption coefficients are identical (xx=yy=zz). However, the anisotropy of the optical absorption of FMPbI3-1, FMPbI3-2,

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MAPbI3, and MPbI3 is between the above two extremes. For the highest absorption coefficient up

to 0.05–0.06 nm-1 for all calculated APbI3 perovskites, even in the 600–700 nm wavelength range,

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the optical absorption coefficients reached 0.01 nm-1, which corresponding to 300-nm-thick

perovskites that absorb 90% of incident light. The 300-nm thickness is an optimized value in

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several highly efficient planar heterojunction devices [35, 36]. In order to quantitative comparison with the experiments term, the absorbance for MAPbI3 over a film thickness of L=150 nm

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reported in Ref. [32] were calculate using the formula A  l o g I 0 I   L 2.303 where L is the film thickness, and the factor 2.303 converts from natural to common logarithm. The calculated

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average absorbance of Axx, Ayy, and Azz for MAPbI3 are A = 2.02 at 500nm, which is in good agreement with the measured value A = 1.8 at 500nm [34]. Results show that FAPbI3, FMPbI3-1,

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and FMPbI3-2 perovskites exhibit excellent optical absorption properties in the solar light

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irradiation range. FMPbI3-1 is predicted to exhibit the best photovoltaic performance in all calculated APbI3 perovskites, along with light effective masses of the electrons and holes, reduced

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band gap, and large optical absorption.

4. Conclusions

The electronic structures of nine kinds of APbI3 perovskites were investigated using first

principle methods on the basis of DFT. We found that (i) different organic cations significantly change the band gap from CsPbI3 to AMPbI3-2, and the three lowest conduction bands show different degrees of splitting for calculated APbI3 (except CsPbI3) because of the anisotropy of

lattice constants. (ii) The average effective masses of the electrons and holes in AMPbI3-1, FMPbI3-1, FMPbI3-2, MAPbI3, MPbI3, and CsPbI3 are all less than the electron rest mass and similar to that of a typical semiconductor silicon; small effective mass of the perovskite is beneficial for high mobility. (iii) The charge densities of electrons and holes were localized in different atoms of the unit cell, suggesting spatially separated charge carriers in all calculated materials. The spatial separation significantly influenced the recombination rate of electrons and

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holes in the materials. (iv) The overlap integral of charge density of the lowest CBM and VBM states of AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, and FAPbI3 was found to be less than that of MAPbI3, which implies a very low carrier recombination rate. For AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, and FAPbI3, in addition to a part of charge density of CBM localized around

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Pb atoms, the considerable remaining charge density localized around the organic cations, leading to very few hopping with the surrounding inorganic matrix and further reducing the recombination

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rate of the carrier. (v) Excellent optical absorption properties with the highest absorption

coefficient up to 0.05–0.06 nm-1 of all calculated APbI3 perovskite in the solar light irradiation

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range were found. Along with the light effective masses of the electrons and holes, reduced band gap, and large optical absorption, FMPbI3-1 is predicted to be a promising candidate to replace

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prototypical MAPbI3 for even higher photovoltaic performances.

In summary, the study on the electronic structure of more APbI3 perovskites materials sought

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to find the low-loss mechanism of this class of materials. This investigation could inspire further research to explore more enhanced solar energy materials with low carrier recombination rate, high carrier mobility, and large optical absorption.

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Acknowledgements The authors acknowledge the financial support from the National Natural Science Foundation of China (Nos. 61106056 and 21174016) and the Fundamental Research Funds for the Central Universities (Nos. 2011JBZ013, 2013JBM102, and 2009JBM105). [1] A. Kojima, K. Teshima, Y. Shirai and T. Miyasaka, J. Am. Chem. Soc. 131 (2009) 6050. [2] H. P. Zhou, Q. Chen, G. Li, S. Luo, T. –B. Song, H. –S. Duan, Z. R. Hong, J. B. You, Y. S. Liu, Y. Yang, Science 542 (2014) 345.

[3] D. Liu and T. L. Kelly, Nat. Photon. 8 (2014) 133. [4] P. Docampo, F. Hanusch, S. D. Stranks, M. Döblinger, J. M. Feckl, M. Ehrensperger, N. K. Minar, M. B. Johnston, H. J. Snaith and T. Bein, Adv. Energy Mater. 4 (2014) 1400355. [5] M. Liu, M. B. Johnston and H. J. Snaith, Nature 501 (2013) 395. [6] J. Burschka, N. Pellet, S. -J. Moon, R. Humphry-Baker, P. Gao, M. K. Nazeeruddin and M. Gratzel, Nature 499 (2013) 316. [7] C. Wehrenfennig, G. E. Eperon, M. B. Johnston, H. J. Snaith and L. M. Herz, Adv. Mater. 26 (2014) 1584.

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[8] B. Suarez, V. Gonzalez-Pedro, T. S. Ripolles, R. S. Sanchez, L. Otero and I. Mora-Sero, The J. Phy. Chem. Lett. 5 (2014) 1628. [9] S. D. Stranks, G. E. Eperon, G. Grancini, C. Menelaou, M. J. Alcocer, T. Leijtens, L. M. Herz, A. Petrozza and H. J. Snaith, Science 342 (2013) 341.

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[10] L. Dou, Y. Yang, J. You, Z. Hong, W.-H. Chang, G. Li, Y. Yang, Nat Commun, 5 (2014) 5404.

[11] J. You, Z. Hong, Y. Yang, Q. Chen, M. Cai, T.-B. Song, C.-C. Chen, S. Lu, Y. Liu, H. Zhou, Y.

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Yang, Acs Nano, 8 (2014) 1674.

[12] S. M. Sze, Physics of Semiconductor Devices, 2nd Ed., John Wiley & Sons, 1981.

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[13] S. Singh and Z. Vardeny, Materials 6 (2013) 897. [14] C. Liang, Y. Wang, D. Li, X. Ji, F. Zhang and Z. He, Sol. Energ. Mat. Sol. C 127 (2014) 67. [15] A. Pivrikas, G. Juška, A. Mozer, M. Scharber, K. Arlauskas, N. Sariciftci, H. Stubb and R. Österbacka, Phys. Rev. Lett. 94 (2005) 176806. [16] G. Juška, K. Arlauskas, J. Stuchlik and R. Österbacka, J Non-Cryst. Solids 352 (2006) 1167. [17] P. E. Blöchl, Phys. Rev. B 50 (1994) 17953. [18] J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett 77 (1996) 3865. [19] G. Kresse and D. Joubert, Phys. Rev. B 59 (1999) 1758. [20] H. J. Monkhorst, J. D. Pack, Phys. Rev. B 13 (1976) 5188. [21] W. Tang, E. Sanville, and G. Henkelman, J. Phys.: Condens. Matter. 21 (2009) 084204. [22] E. Sanville, S. D. Kenny, R. Smith, and G. Henkelman, J. Comp. Chem. 28 (2007) 899. [23] G. Henkelman, A. Arnaldsson, and H. Jónsson, Comput. Mater. Sci. 36 (2006) 254. [24] S. A. Bretschneider, J. Weickert, J. A. Dorman and L. Schmidt-Mende, APL Materials, 2 (2014) 040701. [25] C. R. Kemnitz, M. J. Loewen, J. Am. Chem. Soc. 129 (2007) 2521. [26] L. Lang, J. –H. Yang, H. –R. Liu, H. J. Xiang, X. G. Gong. Phys. Lett. A 378 (2014) 290. [27] K. Yamada, Y. Kuranaga, K. Ueda, S. Goto, T. Okuda, Y. Furukawa, Bull. Chem. Soc. Jpn. 71 (1998) 127.

[28] D. Li, C. Liang, H. Zhang, C. Zhang, F. You, Z. He, J. Appl. Phys. 117 (2015) 074901. [29] M. M. Lee, J. Teuscher, T. Miyasaka, T. N. Murakami, and H. J. Snaith, Science 338 (2012) 643. [30] P. E. Schulz, E. Edri, S. Kirmayer, G. Hodes, D. Cahen, A. Kahn, Energy Environ. Sci. 7 (2014) 1377. [31] P. YU and M. Cardona, Fundamentals of Semiconductors: Physics and Materials Properties, Springer, 2010. [32] D. J. Griffiths, Introduction to Quantum Mechanics, Prentice Hall, 1995. [33] P. K. Nayak, J. Bisquert and D. Cahen, Adv. Mater. 23 (2011) 2870. [34] M. M. Lee, J. Teuscher, T. Miyasaka, T. N. Murakami, and H. J. Snaith, Science 338 (2012) 643. [35] D. Liu and T. L. Kelly, Nat Photon 8 (2014) 133. [36] Z. Xiao, C. Bi, Y. Shao, Q. Dong, Q. Wang, Y. Yuan, C. Wang, Y. Gao and J. Huang, Energ.

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Environ. Sci. 7 (2014) 2619.

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Table 1. Calculated lattice constants (a, b, and c), angles between the vectors, primitive cell volumes (V), organic cation long axis lengths (L), total energy, and band gaps (Eg) of AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, DMPbI3, FAPbI3, MAPbI3, MPbI3, and CsPbI3. L(Å)

(eV)

a, b, c(Å)

°

3

ip t

(eV)

V(Å )

AMPbI3-1

1.81

-66.526

4.03

7.01, 6.48, 6.62

91, 88, 91

AMPbI3-2

1.89

-66.020

4.23

7.64, 6.48, 6.24

90, 89, 91

309.3

FMPbI3-1

1.60

-49.663

3.89

6.37, 6.64, 6.50

90, 90, 91

275.0

FMPbI3-2

1.66

-49.142

2.89

6.54, 6.44, 6.37

90, 90, 91

268.3

DMPbI3

1.84

-67.034

4.23

7.43, 6.42, 6.39

90, 86, 92

303.9

FAPbI3

1.58

-55.634

4.06

6.49, 6.48, 6.49

us

Species

90, 95, 90

272.0

90, 90, 90

268.8

6.34, 6.42, 6.47

89, 90, 90

263.0

6.38, 6.38, 6.38

90, 90, 90

259.7

an

cr

300.4

24

(6.47 )

MAPbI3

1.58

-50.858

2.44

6.44, 6.48, 6.44

MPbI3 CsPbI

1.55

-34.410

1.71

1.47

-14.065

---

M

(6.4624, 6.3325)

Ac ce p

te

d

(6.3924)

Page 13 of 22

Table 2. Effective masses (relative to the electron rest mass m0) of electrons (me) and holes (mh) of MAPbI3-<100> and MAPbI2Cl1-<100>-2 along the three M-R directions, three R-X directions,

Kx(M1-R)

Kzx(R-X1)

Kz(M2-R)

Kyz(R-X2)

Ky(M3-R)

Kxy(R-X3)

Kxyz(-R)

Average

me

me

me mh

me

me

me mh

me

me

0.29 0.44

0.68 0.70

--- 0.44

1.01 1.00

0.31 0.33

0.54 0.41

us

mh

mh

mh

mh

1.80 1.50

0.22 0.95

0.21 1.02

0.26 0.41

0.92 0.23

1.09 0.33

AMPbI-2

3.47 4.01

0.69 0.70

0.51 0.46

---

0.32

0.13 0.34

0.25 0.75

FMPbI-1

0.79 0.25

0.35 0.32

0.21 0.59

0.27 0.54

0.98 0.53

0.88 0.30

FMPbI-2

0.26 0.69

0.63 0.49

0.89 0.43

0.82 0.31

0.83 0.34

DMPbI

3.77 17.03

1.17 0.24

1.05 0.36

0.74 0.28

0.39 0.31

FAPbI

1.82 1.34

1.95 1.02

1.88 1.66

1.34 0.45

0.34 0.28

MAPbI

0.81 0.33

0.87 0.25

0.75 0.21

0.27 0.26

MPbI

0.81 0.21

0.66 0.31

0.37 0.50

0.22 0.27

CsPbI

0.75 0.20

0.76 0.20

0.75 0.20

0.76 0.20

mh

0.23 0.44

0.36 0.36

0.57 0.44

0.76 0.56

0.29 0.26

1.17 2.72

0.20 0.44

0.37 0.47

1.13 0.81

an

AMPbI-1

mh

cr

Species

ip t

and one -R direction.

1.11 0.38

0.33 0.26

0.65 0.31

0.57 0.29

0.72 0.23

0.25 0.24

0.51 0.29

0.75 0.20

0.76 0.20

0.22 0.20

0.68 0.20

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M

0.43 0.49

Page 14 of 22

Table 3. Percentage of the integral charge density of each atom at the lowest CBM (CBM) and VBM (VBM) and the overlap integral charge density percentage of the lowest CBM and VBM states (OIP). Pb (%)

I (%)

I (%)

I (%)

Cation (%)

ip t

Species

OIP (%)

VBM

CBM

VBM

CBM

VBM

CBM

VBM

CBM

VBM

CBM

AMPbI3-1

2.1

29.1

62.8

2.3

34.1

3.5

0.7

1.0

0.4

64.0

5.1

2.6

9.3

6.9

2.0

73.0

1.1

16.7

0.8

0.8

86.9

3.2

3.0

12.1

55.5

1.9

40.8

2.8

0.6

0.5

0.2

83.0

3.8

FMPbI3-2

3.0

0.0

17.8

1.5

75.1

1.8

3.7

0.0

0.5

96.7

2.6

72.2

5.7

1.3

2.0

9.3

36.4

2.4

0.7

52.0

7.7

9.7

4.5

0.5

28.1

8.3

35.5

0.2

0.0

0.1

26.5

12.5

3.9

0.3

19.3

24.8

70.4

1.4

16.7

22.8

5.2

3.2

39.0

48.5

3.7

11.3

2.9

MAPbI3

1.5

54.2

81.3

4.4

7.1

8.9

MPbI3

22.4

92.9

13.7

6.9

28.5

0.1

CsPbI3

6.1

63.1

41.6

5.6

39.6

us

2.4

an

DMPbI3 FAPbI3

Ac ce p

te

d

M

8.2

cr

AMPbI3-2 FMPbI3-1

Page 15 of 22

ip t cr us

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Figure 1. Crystal structures of pseudo-cubic halide perovskite APbI3 and structures of A cations (A=Cs, M, MA, FA, DM, FM1, FM2, AM1, AM2).

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ip t cr us an M d te Ac ce p Figure 2. Energy band structures of AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, DMPbI3, FAPbI3, MAPbI3, MPbI3, and CsPbI3. Inset in the lower right corner indicates the high-symmetry directions in the first Brillouin zone.

Page 17 of 22

ip t cr us an M d te Ac ce p Figure 3. Charge densities at one VBM, one CBM (CBM-1), and three or four CBM (CBM-3) states of AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, DMPbI3, FAPbI3, MAPbI3, MPbI3, and CsPbI3. One VBM and one CBM exhibit an isosurface value of 0.0003 e/A, three CBM exhibit an isosurface value of 0.0009 e/A, and four CBM exhibit an isosurface value of 0.0012 e/A.

Page 18 of 22

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Figure 4. TDOS and PDOS of (a) AMPbI3-1, (b) AMPbI3-2, (c) FMPbI3-1, (d) FMPbI3-2, (e) DMPbI3, (f) FAPbI3, (g) MAPbI3, and (h) MPbI3. Density of state is broadened by Gaussian smearing with 0.05 eV. PDOSs of I (p), Pb (s), Pb (p), and organic cation (sp) are enlarged three times for clarity.

Page 19 of 22

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Figure 5. Absorption coefficients of AMPbI3-1, AMPbI3-2, FMPbI3-1, FMPbI3-2, DMPbI3, FAPbI3, MAPbI3, MPbI3, and CsPbI3.

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Highlights The low-loss mechanism of organic–inorganic perovskites was understand.



The electronic structures of nine halide perovskites were investigated.



The spatial separation influenced the recombination rate of electrons and holes.



Excellent optical absorption was found for all calculated APbI3 perovskites.

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

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Graphical Abstract (pictogram) (for review)

Page 22 of 22