Organic Cation Substitution in Hybrid Perovskite CH3NH3PbI3 with

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Organic Cation Substitution in Hybrid Perovskite CHNHPbI with Hydroxylammonium (NHOH): A First Principles Study 3

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Markus Becker, and Michael Wark J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10359 • Publication Date (Web): 24 Jan 2018 Downloaded from http://pubs.acs.org on January 25, 2018

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The Journal of Physical Chemistry

Organic Cation Substitution in Hybrid Perovskite CH3NH3PbI3 with Hydroxylammonium (NH3OH+): A First Principles Study. Markus Becker and Michael Wark* Institute of Chemistry, Carl von Ossietzky University Oldenburg, Carl-von-Ossietzky Str. 9-11, 26129 Oldenburg, GER. AUTHOR INFORMATION Corresponding Author E-mail: [email protected]

Abstract: The exceptional success of hybrid perovskite materials in the next generation of photovoltaics has attracted the interest of scientists across many fields in photo-physics. Structural and optoelectronic properties are of main importance when searching for potential compounds beyond photovoltaics or as top-cell absorbers. In this article, we theoretically study the thermodynamic stability and electronic properties of organic cation substituted MAPbI3 with hydroxylammonium ions. Results from structural relaxations are compared to predictions from Goldschmidt tolerance factors. Our findings evidence that size effects and the initial orientation of the central cation result in strongly alternated octahedral distortions and markedly different

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optoelectronic properties. The latter becomes noticeable mainly due to band gap variations and significant frontier orbital splitting, which is observed in the case of relativistic calculations and seems to highly depend on the inorganic network deformation.

Introduction: Hybrid organic-inorganic perovskites have recently attracted great attention in optoelectronics due to their versatile chemical and structural tunability. Although the main interest is dedicated towards photovoltaic utilization, their attractive properties inspire applications beyond solar cells, revealing potential usage in for instance ferroelectrics, dielectrics or magnetism1-4. Intense research effort is devoted to find new perovskite compositions with unique electronic band structures and optical properties. The word “perovskite” represents a broad class of materials which exhibit the same crystal structure as the parental CaTiO35. The general formula is ABX3, in which the A-position is coordinated with 12 and the B-position with 6 anions (X), respectively. BX6 octahedrons constitute the basis and are corner-connected to form a 3D framework. Cations at the A-site are usually more bulky than the metal ions located at the B-site and occupy the cuboctahedral cavity formed from the inorganic framework, whereas the metal ion is octahedrally coordinated. Although CaTiO3 remains the name giving prototype for the formally cubic structure of perovskites, it crystallizes in the lower symmetric orthorhombic phase, due to the undersized Ca2+ ion which distorts the metal oxide network6-7. An own subgroup of ABX3 materials is established by hybrid organic-inorganic perovskites, in which the cation in the A-position is replaced by a small organic molecular cation. These have not been reported before 1978, when Weber replaced the large cesium cation (Cs+) in 3D CsPbI38 with a small organic group9. Today, the most common hybrid compounds in the emerging class of photovoltaics are composed of methylammonium (CH3NH3+, MA+) or formamidinium


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([NH2]2CH+, FA+) as organic components A+, Pb2+ or Sn2+ as the B2+metal ions and halides (Cl-, Br- or I-) as X- anions10-15. The spectacular rise of organic-inorganic perovskites in the photovoltaic community has attracted the attention of scientists in many other fields, which is boosted by the materials outstanding electronic, optical and structural properties. The combination of inorganic and organic semiconductor characteristics gives rise to high charge carrier mobility as well as large diffusion lengths16-17, while simultaneously providing chemical tunability18-19 accompanied by low temperature solution processability20-25. These features have stimulated research in fields other than solar cells, such as ferroelectrics, dielectrics and magnetism1, 26-27. The opulent combinatorial possibilities of metal salts and organic cations offer a huge number of potential hybrid perovskite compounds throughout the periodic table. However, the opportunities for ionic substitutions in 3D phases are restricted by the stability of the perovskite structure. V. M. Goldschmidt introduced the so called “tolerance factor” (TF) already in 1926, which is designed to assess the stability of 3D ABX3 structures28. This geometrical parameter sets the ionic radii of the constituents in correlation to each other (eqn. 1).

TF =

rA + rX √ 2 r B + r X

(1)

with rA, rB and rX representing the effective ionic radii of the ions A, B and X respectively. This semi-empirical relationship is based on the idea of dense ionic packing and has been initially developed to estimate the formability of oxide based perovskites29. However, today it is in equal measure applied for the prediction of potential halide phases and can guide a rational design for the synthesis of new hybrid perovskites with desirable functionalities30-32.


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Empirical results indicate that hybrid perovskites with unsliced 3D crystal structures, which are the main goal for photovoltaic applications due to their smaller band gaps (Egap’s), form when TF is in the range of 0.76 – 1.1333. Compounds with smaller values usually show covalent bonds between the A-cation and the halides resulting in a different kind of structure. If the TF is too large, the 3D framework is broken, whereby layered phases with face-sharing octahedrons are formed. These low-dimensional structures reveal larger Egap’s as well as stronger exciton binding energies and show potential use in ferroelectric or ion conducting applications as well as in tandem solar cells as top absorber materials. Recently they have attracted attention in single junction solar cells due to their promising humidity and heat stability. However, sufficient performance is only achieved with highly crystalline and vertically oriented thin films34-35. The classes of 2D, 1D and 0D perovskites have been extensively reviewed by Mitzi2, 4. Another geometrical concept, which similarly seems important to consider, is the ability of halides to coordinate with a metal cation. Since the commonly utilized Shannon radii for metals are determined from hard oxides and fluorides only36-37, caution is necessary to account for the greater covalency of the higher halide homologues (Cl-, Br- and I-) and modified ionic radii should instead be used31. The B-site cation must have the appropriate size to fit into the octahedral cavity formed by the six anions. Evaluation of the latter is provided by the octahedral factor:

µ=

rB rX

(2)


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When the hard sphere model is combined with non-overlapping anions, the minimum radius of the metal ion in the octahedron is 0.414rx30. Both geometrical concepts (TF and µ) allow the 2D mapping of stability criteria for the formation of 3D perovskite compounds. Our previous study elucidates the possible formation of 3D perovskite structures with various small monovalent organic cations, whose effective ionic radii are guessed by gas phase structural relaxations. It has been found that the predicted stability criteria agree very well with particularly high temperature phases reported in literature, due to the thermally enabled rotation of the molecules, which resembles the unhampered movement in vacuum33. Consequently, there still remains exciting synthesis work to be done in the development of new hybrid perovskite compounds for applications beyond the field of single junction solar cells. In the present work, we systematically investigate the hypothetical substitution of the methylammonium cation (MA+) in MAPbI3 with hydroxylammonium (HA+) by first principle calculations. The resulting compound HAPbI3 has recently been found to potentially exist as a perovskite phase, due to its promising TF of 0.976 and µ of 0.486, both of which are reliably positioned in the stable range of 3D perovskite structures33. Additionally, mixed halide HAPbI3-xClx compounds have successfully been prepared, which adopt the perovskite structure. A tetragonal unit cell can be confirmed for x = 2, whereas Egap is slightly reduced when moving to higher iodine contents (where the minimum accessible value for x is 1)38. HA+ is a slightly stronger polar molecular cation than MA+, but is not expected to form severe hydrogen bonds to the inorganic network with its OH-group at ambient temperatures due to its smaller effective size. However, at low temperatures, HAPbI3 may exhibit preferred orientations of the organic cation and reveal alternated octahedral rotations and/or distortions.


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It is well known that the optoelectronic properties of perovskites strongly depend on deformations of the inorganic framework39-41. As a consequence, this study is focused on possible crystal structures and their associated electronic band energetics. We utilize density functional theory (DFT) calculations to find the geometrical ground states of both, MAPbI3 and HAPbI3 and extract the electronic features for comparison. Calculations of total energies for the product formation are additionally performed for both materials. The combination of the Goldschmidt TF and detailed ab initio investigations provides an encouraging pathway for the exploration of new hybrid perovskite compounds as well as general insight into their unknown photo-physical properties. Results: We investigate the organic cation substitution in hybrid halide perovskite MAPbI3 with HA+ ions via periodic DFT calculations. Different initial orientations of the HA+ cations have been adopted and the electronic properties are examined after structural relaxation. To find suitable computational parameters, first prototypic MAPbI3 is investigated and the results are compared to published work. Calculations are performed without any symmetry constraints as well as with alternating cutoff energies and k-point mesh densities for the Brillouin zone integration (see Density Functional Theory Calculations). Two variants of MAPbI3 are investigated, which differ in the initial alignment of the MA+ cations. Both models exhibit the typical a0a0c- tilting of the octahedral framework according to Glazer notation42. In the first structure the C-N bonds of all MA+ cations are oriented along the c-axis in a parallel fashion (cMAPbI3), as it is proposed by Stoumpos et al. from XRD results43. The second model (oMAPbI3) exhibits alternating head-to-head orientations of the carbon atom when viewed along the c-axis, with an angle of approximately 90° between two subsequent MA+ cations and an additional rotation of 90° when moving from one cuboctahedral cavity to the next one along the


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b-axis (adapted from ref44). A summary of the total energies after structural relaxation and the crystallographic parameters of the initial and optimized geometries for the two tetragonal models of MAPbI3 can be found in the ESI, Table S 1. The used cutoff energies and k-point mesh densities are also depicted. After computational relaxation, both structures reveal a different kind of inorganic framework deformation (Figure 1). Whereas the characteristic octahedral tilting around the c-axis is largely maintained in o-MAPbI3, no significant rotation is further observed for c-MAPbI3. Energetically, o-MAPbI3 is favored over c-MAPbI3 by ~ 0.1 eV. Both observations are nicely in accordance with results from recent reports which emphasize the critical impact of the orientation of the organic cation on the perovskite network distortions39, 45. The applied initial models of MAPbI3 can be found in the ESI, Fig. S 1. a) c-MAPbI3

b) o-MAPbI3

Figure 1 Optimized structures of a) c-MAPbI3 and b) o-MAPbI3 (see text for details). The conventional tetragonal unit cell is depicted in black. The crystal axes are shown in the top right.


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For each structure, views along the (001) and (010) directions are provided. Pb = dark grey; I = purple; C = brown; N = blue, H = white. It has to be noted at this point that pure DFT geometry optimizations are ground state energy calculations (at T = 0 K)46 neglecting thermal movements of the central cation. This gives rise to computational results which demonstrate stronger distortions and/or rotations of the inorganic framework, since hydrogen bonds get more impacted. These findings are in agreement with a recent DFT study, which demonstrates that the cell parameters, as expected, decrease due to attracting van-der-Waals forces39. Moving towards higher temperatures causes the organic cations to rotate and/or vibrate in the cuboctahedron, which is already intense at room temperature for the tetragonal phase of MAPbI347-50. Consequently, we expect that van-derWaals interactions become less important, as it is confirmed by the nice agreement between initial (exp.) and optimized cell parameters when dispersion is omitted. In addition, preliminary calculations including van-der-Waals forces by dispersion corrected functionals reveal differences in the interaction energies of at most 0.05 eV which is well within the uncertainty of our computational approach. HA+ possesses a smaller effective ionic radius compared to MA+ and is expected to be able to freely rotate in the inorganic network at elevated temperatures, as a result of the lower overall steric effect33. The thermodynamic stability of MAPbI3 is estimated by calculating the energy differences per formula unit (4 formula per unit cell) between the simulation cells for the product and the educts44. The total energies for PbI2, MAI, c-MAPbI3 and o-MAPbI3 after structural relaxations can be found in the ESI, Table S 2. The resulting decomposition reaction energies (∆Etot) are found to be 0.100 and -0.003 eV for c-MAPbI3 and o-MAPbI3, respectively. Consequently, oMAPbI3 reveals a slightly improved thermodynamic stability over c-MAPbI3. However, the


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relative stabilities of both structures lie within a quite narrow energy range of approximately 0.103 eV per f. u.. The thermal energy kBT represents the heat required to increase the thermodynamic entropy of the molecule and amounts to ~ 0.03 eV at room temperature. Therefore, the molecular cation is expected to easily rearrange between different crystallographic directions at elevated temperatures. This behavior reflects the soft character of hybrid perovskite materials and demonstrates that structural distortions of the inorganic framework are associated with rather low energetic costs. We next investigate the electronic properties of c-MAPbI3 and o-MAPbI3 through their band structures as shown in the ESI, Figure S 2 (SR-DFT) and S 3 (SOC-DFT). Egap’s calculated with the PBE exchange correlation functional are found to be 1.73 and 1.49 eV for c-MAPbI3 and oMAPbI3, respectively, and are direct at Γ. The significant difference in the values of Egap between the two structural models indicates the strong influence of the orientation of the molecular cation on the inorganic framework deformation and, in turn, on its electronic properties. Whereas the direct Egap of o-MAPbI3 agrees quite well with the value found experimentally (~ 1.55 eV), c-MAPbI3 demonstrates a marginally alternated CB structure associated with an enlarged Egap of 1.73 eV. The higher formation energy of c-MAPbI3 indicates that the preferential alignment of the cations along the c-axis is rather unlikely. Both findings are confirmed by a study from Quarti et al., who reports a strong destabilization of MAPbI3 associated with an increased Egap when the MA+ cations are oriented along the c-axis (Egap = 1.62 eV) and that the tilted orientation (Egap = 1.48 eV) with respect to the ab-plane is energetically preferred by 0.39 eV39. As is reported by previous DFT studies on solid-state semiconductors, SR-DFT calculations only incidentally deliver values of Egap that agree with experimental results. This is mainly due to an error cancellation between many-body electron correlation and spin-


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orbit coupling effects when pure (non-hybrid) functionals are applied40, 51-53. Typically, an underestimation of < 30 % can be observed, which is attributed to the energy costs associated with electron-hole-pair excitation. SOC is also included in the calculations and the resulting band structures can be found in the ESI, Fig. S 3. As has previously been reported, SOC-DFT yield a strong Egap underestimation54-56, revealing decreased values of about 1.17 and 0.90 eV for cMAPbI3 and o-MAPbI3, respectively. Different shapes of frontier band separations can be observed and are in agreement with results from Ref39, where a strong orbital splitting is reported for parallel orientations of the MA+ cation, which is absent in the case of isotropic alignments. This phenomenon is called Rashba/Dresselhaus effect39-40, 57-59, and we can confirm the influence of the cation orientation on the latter. It has to be noted at this point that accurate results for hybrid perovskites can be obtained more reliably by the so-called GW-method including SOC effects, which is based on many-body perturbation theory. This is reported to allow for a better simulation-balance in band structure calculations60. However, it is known that SOC-DFT Egap’s qualitatively follow the results from SOC-GW calculations40. The following section considers the cation substitution of MAPbI3 with HA+. For that purpose, we first concentrate on the thermodynamic stabilities when different initial orientations of the HA+ ions are applied inside the cuboctahedral cavities. The inorganic [PbI3]- framework exhibits the same established starting geometry as applied to MAPbI3 (equivalent lattice parameters and a0a0c- tilting of the octahedral network). Three categories of initial orientations of the HA+ cations are adopted. In the first case, the N-O bonds are either arranged along the [100], [010] or [001] direction in a parallel fashion, which corresponds to the molecules lying exclusively on one of the three crystallographic axes. Second, based on the afore-mentioned categories, the pointing directions of the N-O bonds are changed for every second molecule in a staggered way


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by about 180°. We denote these orientations as [1 00], [01 0] and [001 ]. In the third case, all N-O bonds exhibit angles of 45° with respect to each of the three crystal axes, (denoted as [111] and [111] for the reverse direction), and additionally every second molecule is turned by about 180° in a staggered way, denoted as [1 1 1 ]. All of these nine guess structures are fully optimized without any symmetry constraint. After computational relaxation all starting structures are found to roughly preserve the initial orientation of the central cations without undergoing a transition between different categories. These arrangements present minima on the potential energy surface (PES). However, variations of the angles between the N-O bonds and their initial alignments with respect to the crystal axes are observed. Furthermore, the distortions of the octahedral framework vary substantially between the different conformations. The optimized geometries are presented in Figure 2. Table 1 summarizes the relative energies, crystallographic parameters and decomposition reaction energies. All relative energies (Etot,rel) are related to the lowest Etot value (-5201.093 eV per f. u.), which is observed for the initial [001] orientation of the HA+ cations. [100]

[010]

[001]


11


[1 00]

[01 0]

[001 ]

[111]

[111]

[1 1 1 ]

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Figure 2 Crystal structures of HAPbI3 after SR-DFT computational optimization. The compounds differ in the initial orientations [xyz] of the organic cations (see text for details). For each structure, views along the (001) and (010) directions are provided. Pb = dark grey; I = purple; O = red; N = blue, H = white. Table 1. Relative energies (Etot,rel), decomposition reaction energies (∆Etot) and relaxed cell parameters (a, b and c) for the nine optimized guess structures of HAPbI3. The orientations of the HA+ cations along the three crystallographic axes are denoted on the left (see text for details). Ecut [Ry] wfc. = 30; Ecut [Ry] charge density = 240; k-points = 2 x 2 x 2 Initial orientation of HA+

Etot,rel [meV/f. u.]

∆Etot [meV/f. u.] = Etot (HAPbI3) - Etot (PbI2) - Etot (HAI)

optimized cell parameter [Å] a, b, c

[100]

82

-154

8.94, 8.29, 12.58

[010]

10

-227

8.55, 8.77, 12.43

[001]

00

-236

8.76, 8.45, 12.50

[1 00]

16

-220

8.86, 8.40, 12.50

[01 0]

46

-191

8.42, 8.88, 12.53

[001 ]

44

-192

8.78, 8.47, 12.44

[111]

14

-223

8.69, 8.64, 12.29

[111]

82

-155

8.79, 8.47, 12.51

[1 1 1 ]

19

-218

8.93, 8.41, 12.42

As reported in Table 1, the optimized structure with an initial parallel alignment of the HA+ cations along the [001] direction is the most stable one among the investigated series. Furthermore, the arrangements denoted as [010], [111], [1 00] and [1 1 1 ] are nearly isoenergetic, presenting deviations of + 10, + 14, + 16 and + 19 meV respectively. Since these values are all smaller than kBT at room temperature (~ 30 meV) the structures are expected to undergo conformational transitions at ambient thermal conditions. All other structures are found within a


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quite narrow energetic range of up to 82 meV per f. u. and may rearrange at elevated temperatures. The decomposition reaction energies for HAPbI3 are given in Table 1. Here, more negative values indicate a better stability of the perovskite structure. All optimized geometries investigated demonstrate clearly negative energies in the range of -154 to -236 meV, suggesting strongly exothermic formation reactions from (partially) hypothetical precursor materials. Consequently, HAPbI3 can be rendered as a stable compound (even more stable than MAPbI3) which features cationic reorientation associated with low energetic costs. The different orientations of the central cation induce significantly alternated cell parameters for the inorganic framework (Table 1). Though, these findings should be regarded with care since the computational approach may tend to relax the non-zero temperature structures towards 0 K ones. The consequence would be an exaggeration of the inorganic framework distortion. In general, the c-axis is shortened from the experimental value of MAPbI3 (12.64 Å)43 by about 0.5 – 2.7 %, depending on the direction of cation alignment. The lattice parameters for the a- and baxes differ in both directions compared to the starting value (a = b = 8.85 Å). Minimum lengths are found to be 8.42 Å (a-axis) for the [01 0] and 8.29 Å (b-axis) for the [100] orientation, respectively. The longest observed lattice parameters are found to be 8.94 Å (a-axis) for the [100] and 8.88 Å (b-axis) for the [01 0] orientations, respectively (vice versa compared to the aaxis). The largest c/a ratio of 1.49 is demonstrated by the [01 0] geometry and is higher than the value found experimentally for MAPbI3 (~ 1.43), whereas the smallest relationship of 1.39 (smaller than experiment) is demonstrated by the [1 1 1 ] arrangement. These findings can be related to different tilting and/or rotations of the octahedrons in the optimized structures. Remarkably, the difference of total energies between the two structures with the largest deviation in the c/a ratio ([01 0] vs. [1 1 1 ]) are found to be as small as 27 meV.


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Our calculations show that in HAPbI3 the apical Pb-I-Pb bond angles vary to a large extent between the different cation alignments, with values from 144.4° for the [111] to 164.8° for the [100] optimized structure. The octahedral tilting around the c-axis reveals a minimum of 15.1° for the [001 ] and a maximum of 40.1° for the [100] structure (a full list of bond and dihedral angles of the octahedral network can be found in the ESI, Table S 3). Although these geometrical deviations seem considerable, we do not identify a clear trend between energetic stability (Etot) and associated systematic deformation of the inorganic metal-halide framework. Merely a coarse trend can be recognized for the lowest and highest relative energies. Typically, lower distortions of apical bond angles accompanied by strong tilting around the c-axis yield rather unstable structures. On the other hand, stronger apical bending associated with low dihedral distortions result in more stable compounds (see Table 1 and ESI, Table S 3). In line with recent results on prototypic MAPbI339, it is suggested that the orientation of the HA+ cations in the HAPbI3 structure significantly influences the inorganic network. Summarizing the results presented above, we find that many stable geometrical arrangements for HAPbI3 might exist, differing mainly in the orientation of the HA+ cations and in the octahedral tilting. Various structures lie within an energy range accessible at room temperature and it is expected that there may be coexistence of different crystalline domains in a macroscopic crystal. In the next step, we discuss the influence of the octahedral deformations on the electronic band structures of HAPbI3. For all investigated compounds, the SOC-DFT Egap’s are found to lie within a range of 0.37 eV and a typical Egap underestimation of 0.89 – 1.02 eV can be observed (Table 2). SR-DFT Egap’s are observed to spread by about 0.49 eV. The orientation of the HA+ cations obviously induces the deformation of the inorganic network with consequences on the electronic structures. The SOC band structures can be found in Figure 3 (for SR-DFT bands see


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the ESI, Fig. S 4). Since we allowed for unconstraint geometrical relaxation, which results in significant alternations of cell parameters and inorganic network distortions, these results demonstrate the large variability of Egap by the deformation of the metal-halide network. Although not strictly following a quantitative line, it is suggested that the highest values for Egap (for both methods, SOC- and SR-DFT) result from conformations exhibiting strong metal halide apical bending, but weak dihedral tilting. By contrast, more linear Pb-I-Pb bond angles yield lower Egap’s. Notably, the structure with the lowest Etot after optimization ([001]) shows the largest Egap of 1.21 eV in SOC-DFT (2.23 eV in SR-DFT) and is the only arrangement which demonstrates a band splitting of the CB edge in SR-DFT (see ESI, Fig. S 4). Generally, the trend between Egap’s and associated geometrical structures in SOC-DFT is well preserved compared to results from SR-DFT. Furthermore, VB and CB splitting at the Γ-point (Rashba/Dresselhaus effect) demonstrates different intensities in SOC-DFT calculations and is observed in the cases of [010], [001], [001 ], [111] and [111]. Therefore, we present this effect for HAPbI3 (accompanied by an indirect transition) and confirm the influence of the cation orientation on the latter. However, due to the possibility of the exaggeration of inorganic framework deformations, the true intensities of Rashba-splitting may somewhat be mitigated. Typically, Rashba-splitting is connected to inversion-symmetry breaking and to spin-orbit coupling effects due to the presence of heavy nuclei, both of which are found in polar hybrid perovskite structures. Thus, it has been reported in various experiments to be the possible cause of suppressed carrier recombination and can be explained as follows61: the frontier orbitals of the VB and CB are mainly composed of I and Pb orbitals, respectively. Therefore, due to diverse SOC strengths, different splitting intensities can be observed. Consequently, photogenerated carriers thermalize to the band extrema located at different k-points and radiative recombination is quenched as for


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an indirect transition (due to the preservation of k-momentum). Since the Egap of HAPbI3 depends on the octahedral deformations, an average which lies between the minimum and maximum computed values may be observed at ambient conditions. This is due to the thermally enabled interchange of different octahedral conformations. Table 2. SOC and SR Egap’s for the nine investigated structures of HAPbI3. The initial orientation of the HA+ cations is reported for each geometry (see text for details). Initial orientation of HA+

Egap (SOC-DFT) [eV]

Egap (SR-DFT) [eV]

[100]

0.85

1.74

[010]

0.98

1.99

[001]

1.21

2.23

[1 00]

0.87

1.78

[01 0]

0.84

1.80

[001 ]

1.03

1.99

[111]

1.13

2.15

[111]

0.99

1.95

[1 1 1 ]

0.88

1.87

[100]

[010]

[001]

[1 00]

[01 0]

[001 ]


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[111]

[111]

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[1 1 1 ]

Figure 3 SOC-DFT calculated band structures of the nine optimized HAPbI3 compounds in the first Brillouin zone. Significant Rashba-splitting can be observed in part of the structures and depends on the inorganic framework deformations. The VB maximum is arbitrarily set to zero eV. The corresponding Egap’s are reported in Table 2. PDOS calculations are performed on two HAPbI3 structures in order to check for variations in atomic orbital contributions to the VBM and CBM. The [100] and [001] conformations are chosen since they differ more significantly in the energetic stability, octahedral deformation and Egap. The corresponding total DOS as well as PDOS spectra are shown in Figure 4. [100]

[001]


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Figure 4 Total density of states (total DOS) and partial density of states (PDOS) of atoms; a) and c) represent the [100] and b) and d) the [001] conformation of HAPbI3, calculated by SR-DFT calculations using the PBE functional. The VBM is mainly composed of I 5p electrons with a slight overlap from Pb 6s states. On the other hand, the CBM comprises mainly of Pb 6p orbitals with a negligible contribution of I 5p states. As a consequence, the PDOS indicates that I 5p electrons can be photoexcited into empty Pb 6p states with I atoms becoming photo-hole sites. Since in [100] HAPbI3 the PDOS of I at the VB region is shifted towards lower energies, a stronger hybridization with Pb atoms can be expected compared to [001] HAPbI362. The organic NH3OH+ cation does not contribute to the


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relevant DOS due to its deep location of at least - 2.5 eV. It demonstrates little overlap with Pb or I states and is therefore not expected to form covalent bonds with the inorganic framework. PDOS calculations of the MAPbI3 references confirm these observations and imply that an organic cation with the appropriate effective steric size can be substituted without significantly altering the atomic orbital contributions to the band edge states (VBM, CBM). The DOS and PDOS of c- and o-MAPbI3 can be found in the ESI, Fig. S 5. Conclusions: We present the results of first-principles calculations on the hypothetical cation substitution in prototypic MAPbI3 with hydroxylammonium (HA+). Overall, nine guess structures which differ in the initial alignments of the HA+ cations, are investigated. Appropriate computational parameters for the treatment of hybrid compounds are deduced from trial optimizations on MAPbI3 and compared to reported data. All structures of HAPbI3 are found to be stable due to strongly exothermic formation energies, whereby the differences in octahedral tilting and final cell parameters are partially significant. All arrangements lie within a narrow energy range of roughly ~ 80 meV and it is expected that conformational transitions may occur close to room temperature and that a macroscopic crystal may contain domains with different octahedral tilting. Band structure calculations reveal that the inorganic network deformation strongly influences Egap as well as the shape of relevant frontier orbitals. The latter partially gives rise to transitions from direct to indirect due to the shift of band extrema in k-space. The variation in Egap’s when including SOC in the calculations is ~ 0.37 eV, however, the inclusion of SOC effects results in the typical Egap underestimation. SR-DFT calculations, on the other hand, fortuitously yield values in better agreement with experimental data due to the compensative effects of two errors. Significant Rashba-splitting of the bulk phase material, associated with symmetry breaking and spin-orbit coupling effects due to the presence of heavy


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elements, may lead to reduced carrier recombination. Finally, the significant influence of the cation orientation on the strength of frontier orbital splitting can be confirmed for HAPbI3. Though, these results should be viewed with care due to the possible exaggeration of octahedral deformations by the standard DFT approach with high temperature structures. PDOS calculations confirm the negligible influence of the HA+ cation on relevant states near the Egap and reveal that the atomic orbital contribution of I and Pb states does not change in a considerable manner. Density Functional Theory Calculations: All reported DFT calculations are carried out under periodic boundary conditions without symmetry constraints by using the PWSCF code as included in the Quantum Espresso package63. A Generalized Gradient Approximation (GGA) via the Perdew−Burke−Ernzerhof (PBE) exchange correlation functional64 is used along with scalar relativistic (SR), ultrasoft pseudopotentials (US-PP’s) for all elements65. The description of electron-ion interactions is performed with electrons from Pb 5d10, 6s2, 6p2; I 5s2, 5p5; N 2s2, 2p3, C 2s2, 2p2 and H 1s1 shells explicitly included in the calculations. During the structural optimizations, both the cell parameters and atomic positions are allowed to relax freely. The simulation cells for all investigated educts as well as products consist of four formula units (f. u.) each. Although SR-DFT calculations have shown to nicely reproduce the structural properties, SOC is additionally included, since it was found to be compulsory for a correct description of the electronic structure of perovskite compounds55, 66. For SOC calculations of band structures the PBE exchange correlation functional is used along with fully relativistic PP’s for the heavy Pb and I atoms. For the lighter elements (H, C, N and O) we do not expect significant contribution of relativistic effects. Cutoff energies for the plane wave functions and charge densities are investigated in the range of 20 – 30 and 160 – 240 Rydberg, respectively. Two sets of Monkhorst Pack Grids (MPG), a 2 x 2 x 2 and a 4 x 4 x 4 k-point mesh, are tested for sampling of the


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Brillouin zone67. The tetragonal I4cm unit cell, which has been reported for MAPbI3 at room temperature43, is adopted as a starting point for the geometry optimizations, while for HAPbI3 the MA+ cations are completely substituted by HA+ with different initial orientations. Stabilities of MAPbI3 and HAPbI3 are estimated by calculating the differences in formation energies of educts and products. Standard structures of PbI2 (hexagonal, space group P3m1, No. 164)68 and MAI (α’-phase, tetragonal, space group P4/nmm, No. 129)69 at room temperature are adopted in these calculations, whereas in the case of HAI, due to the lack of experimental data, the cell parameters and atomic positions of HABr are assumed (monoclinic, space group P21/c, No. 14) 70. Accordingly, the Br atoms are exchanged by I’s associated with the corresponding SR-PP. Structural optimizations for the educts are performed with equivalent cutoff energies and k-point mesh densities as for the products. The stability of HAPbI3 is compared by considering different initial orientations of the HA+ cations in the cuboctahedral cavity. For the PDOS analysis, the k-point mesh density during the SCF cycle is increased to 6 x 6 x 6 and the energy grid step width is set to 0.02 eV. ASSOCIATED CONTENT Supporting Information. Additional data on crystal geometries and electronic band structures of MAPbI3 and HAPbI3 as well as geometrical bond and dihedral angles relevant for the discussion presented in the main article are provided. The PDOS of MAPbI3 is additionally contained. AUTHOR INFORMATION Corresponding Author *Phone (+49) 441 798 3675; e-mail: [email protected]


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69. Ishida, H.; Maeda, H.; Hirano, A.; Fujimoto, T.; Kubozono, Y.; Kashino, S.; Emura, S., Exafs Study on the Phase-Transition (Phase-Alpha' Phase-Delta) in Ch3nh3i. Z Naturforsch A 1995, 50, 876-880. 70. Jerslev, B., The Structure of Hydroxylammonium Chloride, Nh3ohcl, and Hydroxylammonium Bromide, Nh3ohbr. Acta Crystallogr 1948, 1, 21-27. TOC GRAPHICS


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Organic Cation Substitution in Hybrid Perovskite CH3NH3PbI3 with

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