Influence of the Dimensionality and Organic Cation on Crystal and

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Influence of the Dimensionality and Organic Cation on Crystal and Electronic Structure of Organometalic Halide Perovskites Julian Gebhardt, Youngkuk Kim, and Andrew M. Rappe J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b00890 • Publication Date (Web): 02 Mar 2017 Downloaded from http://pubs.acs.org on March 5, 2017

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The Journal of Physical Chemistry

Influence of the Dimensionality and Organic Cation on Crystal and Electronic Structure of Organometalic Halide Perovskites Julian Gebhardt,∗ Youngkuk Kim, and Andrew M. Rappe Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, United States E-mail: [email protected]

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Abstract Layered perovskites open a plethora of possibilities for tuning organometallic halide perovskite (OMHPs) properties via the incorporation of larger organic cations. Promising applications of this increased structural freedom include enhanced chemical stability and tunable exciton binding. Due to the larger cation, crystal and electronic structure vary with layer stacking, having layered bulk and a monolayer as limiting cases. Using ab initio calculations, here we study the atomic and electronic structures of such a layered material, (C6 H5 C2 H4 NH3 )2 PbI4 , which has recently attracted attention as a promising solar cell material. The reduction of layer thickness between the bulk and a monolayer is investigated and compared to the benchmark OMHP, (CH3 NH3 )PbI3 , showing that the bulkier C6 H5 C2 H4 NH3 cations largely preserve the two-dimensional nature of the electronic structure in the layered bulk OMHP.

Introduction Organometallic (or hybrid) halide perovskites (OMHP) are intensively studied due to the drastic improvement of CH3 NH3 PbI3 (MAPbI3 )-based photocells from initialy 3.8 % 1 to the current record holder of 20.1 %. 2,3 However, current OMHPs are sensitive to humidity, oxygen, solvents and other chemicals, UV-light, and operating temperature. 4 The instability of OMHPs, in particular due to water degradation, can be suppressed by exchanging the small hydrophilic organic cations with cations that carry bulky, hydrophobic moieties. A plethora of molecules can be envisioned for this purpose, once one is no longer limited to small molecules. For example, it is possible to fabricate hydrophobic moieties with any desired size and hydrophobic character to shield hydrophilic end groups (like NH+ 3 ). One possible scenario is to use 2-phenylethane-1-aminium (or 1-phenethylaminium) (PEA) cations as a coating layer of MAPbI3 . Such a coating layer was reported recently to improve the stability towards water relative to pristine MAPbI3 . 5,6 Herein, we study the atomic and electronic structure of PEA2 PbI4 using first-principles 2


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calculations. First, we study 2D monolayer (ML) and quasi-2D PEA2 PbI4 bulk. Next, we compare the obtained atomic and electronic structures of the PEA systems with those of the benchmark OMHP systems, MAPbI3 , especially with regard to the effects of i) cation exchange accompanied by phase and stoichiometry change and ii) interlayer interaction change, i.e., bulk versus ML structures. This three-way comparison between 3D (MAPbI3 bulk), quasi-2D with weak interlayer interactions (PEA2 PbI4 bulk), and 2D systems (MA2 PbI4 and PEA2 PbI4 MLs) reveals that, unlike the MA case (band gap increase by 0.74 eV), the electronic structure of PEA2 PbI4 is largely preserved during the (structural) dimensionality change (band gap increase by only 0.07 eV). In the case of PEA, electronic states of the organic cation are located closer to the conduction band edge (CBE), which dominate the conduction band at corner points of the Brillouin zone (BZ). Furthermore, the large effects of spin-orbit coupling (SOC) on the electronic structure that were reported earlier for MAPbI3 are also found in the related layered perovskite.

Computational Details The electronic structure of PEA2 PbI4 is obtained from first-principles calculations based on non-collinear density-functional theory (DFT). We use the Perdew–Burke–Ernerhof (PBE) generalized gradient approximation 7 as implemented in the Quantum Espresso package 8 supplemented by the D2 method 9 in order to account for dispersive interactions. Core electrons are treated by norm–conserving, optimized, designed nonlocal, scalar-relativistic (SRL) pseudopotentials generated with Opium. 10,11 Thus, relativistic effects including SOC are treated for core orbitals, whereas the splitting due to SOC is averaged in the valence region. 12 Wave functions are expanded in a plane–wave basis with an energy cutoff of 680 eV. Total energies and atomic structures are fully relaxed to 3 × 10−9 eV/cell and until forces acting on ions are below 0.005 eV/˚ A. For the PEA2 PbI4 bulk, the BZ is sampled by a 4×4×4 Monkhorst-Pack k-point grid. 13 From the bulk, the 2D system is constructed by

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introducing 15 ˚ A of vacuum in order to detach periodic images along z and reducing the k-point grid to 4×4×1. An analogous procedure was followed for MAPbI3 bulk and ML systems. Alternative phases were computed with similar k-point density. For the evaluation of the projected density of states (PDOS), an increased k-point mesh of 12×12×4 was used. For the computation of band structures, we also show results including the effect of SOC on the valence levels explicitly, using full-relativistic (FRL) pseudo-potentials in noncolinear calculations. Charge-density differences (CDDs) are computed by subtracting the charge of either neutral or charged isolated systems A and B from a combined system, ̺CDD = ̺A+B − ̺A − ̺B .

Results and Discussion Crystal structure Phase stability The structural phase of layered perovskites 14–17 can be related to the 3D parent material. Due to the large organic cation, horizontal, 2D BX2 perovskite-like layers are separated by a double layer of the A-site cation as shown in Fig. 1. This means the stacking sequence changes from · · · BX2 −AX · · · in the perovskite crystal to · · · AX −BX2 −AX · · ·. The coordination number of A-site cations is reduced from twelve to nine in the layered material. In addition, the stoichiometry changes from ABX3 to A2 BX4 , joining the class of Ruddlesden-Popper phases. 18 The latter can be envisioned as members of the family of structures with formula unit An−1 A′2 Bn X3n+1 , where n is a positive integer. This structural change is accompanied by a change of the vertical bonding motifs. The ionic bonds of the backbone connecting B and X atoms are decoupled along the stacking direction, with the 2D sheets being connected by the interactions of the A′ X double layer. We first identify the thermodynamically most stable phase of PEA OMHPs. Diverse

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crystal structures have been experimentally reported for a variety of bulk phases of layered perovskites, including those with PEA cations for X=Cl, 19 Br, 20 and I. 14 They all have a similar structure in triclinic P1 space group (# 2), which are our primary concern in the present study. We tested other crystal structures in diverse space groups known from similar compounds including orthorhombic, monoclinic, and other triclinic phases. They all were found to be energetically unfavorable compared to the triclinic P1 phase (the energetic and geometric details of the alternative phases are discussed in detail in the supporting information (SI)). Ion arrangement Table 1: Lattice parameters, averaged volumes of the PbI6 octahedra (VPbI6 ), and averaged Pb–I bond lengths (dPbI (x)) oriented along each crystal direction for bulk and ML structures of MAPbI3 and PEA2 PbI4 , respectively. Lattice dimensions and angles are obtained from a (2×2×2) supercell whereas the cell volume Ω is given per formula unit.

a/˚ A b/˚ A ˚ c/A α β γ 3 Ω/˚ A 3 VPbI6 /˚ A dPbI (a)/˚ A dPbI (b)/˚ A dPbI (c)/˚ A

MAPbI3 bulk 12.20 12.20 12.79 89.35 89.34 90.47 237.81 42.77 3.18 3.18 3.20

MA2 PbI4 ML 12.37 12.05 — 88.80 89.61 90.39 — 44.53 3.22 3.21 3.26

PEA2 PbI4 bulk ML 11.88 11.94 11.75 11.91 16.48 — 100.25 100.36 106.32 106.76 89.97 89.97 542.62 — 41.70 43.46 3.13 3.15 3.10 3.14 3.28 3.36

The ground-state triclinic structure is shown in Fig. 1. The observed symmetry is low, preserving only an inversion symmetry, due to the distortion of the PbI6 cages. We observe a buckling of the PbI2 layers, caused by an off-center movement of Pb ions in the PbI6 octahedra (Fig. 1 (a)). This leads to a bond length alternation in each octahedron along the vertical (polar) axis (which is defined to be the stacking direction hereafter), with a long 5



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and a short Pb–I bond length dPbI (c) differing by 0.4 ˚ A. The off-center movements along c are arranged in a way that Pb atoms are displaced into the same direction along two lattice directions (b and c) and in an alternating pattern along the third lattice direction (a), resulting in an antiferroelectric ordered structure analogous to an a-type ferromagnet. Besides this distortion of the PbI6 cage, the main structural variety is introduced via the organic cation. On one hand, the NH+ 3 group can form different H–X bonding motifs: i) bonds to iodines bridging two Pb ions and ii) terminal iodines that are only attached to one Pb ion 21 (see Fig. 1 (a)). We find that bonding to two terminal and one bridging iodines is energetically favorable (Fig. 1 (b)), in agreement with experimental results. 19,20 On the other hand, different orientations of the phenyl units are also plausible, with competing effects of maximizing the phenyl–phenyl interactions (via π-π stacking) and reducing the steric demands of being incorporated into the PbI4 backbone. The phenyl units are intertwined, forming horizontal layers along one direction (b) that resemble parallel-displaced benzene dimers (Fig. 1 (d)). 22 Along the other horizontal direction (a), these layers are arranged in an alternating pattern, without apparent interactions. Along the stacking direction, phenyl arrangements that are closest to the displaced T-shape (TT structure) 22 benzene dimer structure are observed between PEA layers, i.e., perpendicular phenyl moieties, one pointing towards the plane of the other. We also investigate the lateral packing of the PEA units and find that the PEA units would prefer a closer proximity and a more upright orientation towards each other than it is allowed by the PbI4 backbone (Fig. S2). This demonstrates the flexibility of the organic cation double layer, which adjusts to the rigid PbI4 backbone. Influence of dimensionality and organic cation We also compare our results for the novel PEA2 PbI4 phase with results for MAPbI3 using the same computational setup. We consider the most stable “crossed” structure, 23 in which MA units alternate their tilt angles along two different crystal axes (Fig. 1 (g)). With our setup

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this structure is 0.16 eV more stable than a bulk structure where all MA units are oriented into the same direction. The structure agrees well with experimental results, 24 validating our computational setup. In this bulk MAPbI3 structure, the bonding motif of the NH3 units differs from the layered structure. Here, one hydrogen atom interacts equally with three iodine neighbors with almost identical bonding distances (Fig. 1 (e)). We also discuss the atomic structures of MLs of PEA2 PbI4 and MA2 PbI4 , which can be considered as the extreme thin film limit of these materials. A PEA2 PbI4 ML is directly obtained from the layered perovskite bulk structure by introducing vacuum between two units. For a ML from the MAPbI3 bulk it can be expected to be energetically favorable that the tilt direction is alternating for both sides of the PbI2 plane, so that the NH3 groups are pointing towards the PbI2 plane on both sides. There are two different possibilities to fulfill this. One introduces a mirror symmetry between the MA units in the PbI2 plane, whereas in the other structure, MA units are related to each other by inversion. We find that the latter structure (Fig. 1 (h)) is energetically favorable by 0.25 eV per MA unit. In this geometry, the NH3 bonding motif changes compared to MAPbI3 bulk and is identical to the arrangement found in layered perovskites, i.e., bonding of hydrogen atoms to two terminal and one bridging iodine atom, with a single closest iodine neighbor for each H–I bond (see Fig. 1 (f)). This arrangement is also slightly more stable (by 0.03 eV per MA unit) than a “crossed” structure, i.e., MA units that are rotated alternating along one axis by 90◦ , which is observed in the MAPbI3 bulk (or analogously for PEA units in PEA2 PbI4 ). For the most stable structures, we can compare structural changes between ML and bulk structures, as well as changes due to a reduction of dimensionality from 3D over quasi2D towards 2D. Comparing first the bulk systems with the MLs, the latter have expanded lattice parameters in the PbI2 plane, leading to an overall increase of the PbI6 octahedra by 4.11 % for MA2 PbI4 and 4.23 % for PEA2 PbI4 (Table 1). The Pb–I bond length changes are comparable for both OMHPs, with dPbI increasing on average by 0.06 (0.08), 0.03 (0.04), and 0.04 (0.02) ˚ A along c, b, and a, respectively, for the MA2 PbI4 (PEA2 PbI4 ) ML compared

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to the bulk structure. This means, despite the observed phase change between MAPbI3 and MA2 PbI4 , which leads to a decrease of one in-plane lattice vector (b), the averaged Pb–I bond lengths expand similarly along a and b. When changing the organic cation from MA to PEA, both bulk and ML are compressed within the PbI2 plane, with Pb–I bonds shortened by 0.05-0.07 ˚ A (Table 1). Overall, this leads to a volume reduction of PbI6 octahedra by ≈ 2.5 %. Along the stacking direction c, however, the Pb–I bonds are increased on average, due to the more pronounced buckling of the PbI2 plane for PEA. In MAPbI3 the buckling along z is weaker, with a maximal bond length difference an order of magnitude smaller (0.05 ˚ A) compared to the PEA case. Consequently, we hypothesize that a larger polarizability should be observed in the layered perovskite.

Electronic Structure Figure 2 (a) shows the CDD of the bulk between neutral species of PEA and PbI4 backbone, respectively. It shows charge redistribution from the organic molecules to the PbI4 backbone, in line with the expected charge transfer and the nominal charge of +1 for each PEA cation. Interestingly, charge is mainly depleted from pz orbitals of the phenyl units. We also confirm the charge transfer by a Bader analysis, 25 which attributes ≈ 0.7 electrons of each PEA cation to the PbI4 backbone. Figure 2 (c) shows a similar CDD with respect to charged isolated species PEA+ and PbI2− 4 . It shows that charge is accumulated on the H–I bonds to terminal iodides (indicated by green, dashed lines for one NH+ 3 group), whereas no such charge accumulation is found between the third hydrogen atom and the nearest bridging iodides, indicating a stronger interaction of hydrogen atoms with terminal iodides. Charge is depleted from the terminal iodides along the stacking direction, which is, in addition to the H–I bonds, also accumulated on the phenyl moieties. Figure 2 (b) and (d) show the electron-localization function (ELF) 26 for the same struc8


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ture. As expected, a high degree of electron localization is observed on covalent bonds between carbon atoms in the phenyl units and on C–H and N–H bonds. In contrast, such features are absent in the PbI4 backbone, showing typical features of metal organic bonds with strong ionic bonding character for Pb–I bonds. Despite the charge rearrangements on the H–I bonds for terminal iodides, no ELF is observed between PbI and PEA, exhibiting weak covalent character. The discussed non-covalent interactions (NCI) between the fragments can also be visualized by NCI-plots (see Fig. S3). In order to quantify the bonding strength between PbI2 layers along the stacking direction in PEA2 PbI4 , we calculate the cleavage energy of a layer from the PEA2 PbI4 bulk as Ecl = 2

[E0 (ML) − E0 (bulk)] /2 = 0.91 meV/˚ A from the energies of the isolated ML (E0 (ML)) and the bulk system (E0 (bulk)), respectively. For reference, this is roughly 19 times less then the cleavage energy in graphite for the same computational method (estimated from the 2

PBE-D2 cleavage energy of 17.01 meV/˚ A that agrees well with experimental values). 27 We now investigate the PDOS of the PEA2 PbI4 bulk and ML, respectively (Fig. 3 (e,f)). The states around the Fermi level mainly comprise p orbitals originating from the PbI4 backbone. The valence band edge (VBE) states are of mainly iodine p character mixed with some Pbs contributions. The CBE states, on the other hand, contain Pbp orbitals. The latter are split into two separate contributions of p orbitals parallel to the PbI2 plane (Pbpx,y ) and pz orbitals perpendicular to this plane. Thus, the band gap is dominated by the PbI2 layers. The differences between quasi-2D bulk and 2D ML are small, yielding almost the same gap as well as VB and CB regions. The PDOS of the PEA cations is narrower for the ML, which is due to the missing interactions to the next PEA sheet. In order to further analyze the changes in the PDOS, we compare the band structures of PEA2 PbI4 bulk and ML in Fig. 3 (a,b). We first neglect the explicit effects of SOC on the valence levels, discussing SRL calculations (see computational details in SI). Our DFT calculations predict that bulk PEA2 PbI4 is a semiconductor with a direct band gap of 1.40 eV at the Γ point. The strong band dispersion is due to bands with mainly Pb and I character,

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whereas bands with PEA character appear flat (Fig. 3 (e,f)), indicating the weak interaction between PEA units among each other and with the PbI4 backbone. Comparing bulk and ML, the band structure is mostly retained, with a small band gap increase of 0.07 eV in the ML. This justifies the classification of layered hybrid perovskites as quasi-2D systems, since the multilayer systems are, to a large extent, electronically identical to a single ML. The related MAPbI3 system is known to show a very strong influence of SOC in the electronic structure. Predicted band gap energies (Eg ) of SRL DFT calculations are in very good agreement with experiments and high level many-body calculations, whereas FRL DFT and SRL many-body calculations lead to under- and overestimated band gaps, respectively. 28 Thus, we also investigate the effect of SOC in our system (Fig. S4). Comparison of band structures and PDOS including SOC reveals that both VBE and CBE are considerably broadened. The broadening is mainly observed around the Γ point, affecting both Pbp and Ip bands. Overall, SOC reduces the band gap by ≈ 0.8 eV for the studied layered hybrid perovskite as well as the traditional OMHP, independent of organic cation or dimensionality (Table 2). Table 2: Scalar- and full-relativistic band gaps (Eg ) for quasi- and truly 2D PEA2 PbI4 compared to band gaps for MAPbI3 bulk and MAPbI4 ML, respectively. Structure MAPbI3 (bulk) MA2 PbI4 (ML) PEA2 PbI4 (bulk) PEA2 PbI4 (ML)

Eg (SRL)/eV Eg (FRL)/eV Eg (exp.)/eV 1.52 0.73 1.3 - 1.8 24,29–31 2.26 1.52 2.17 1.40 2.4 - 3.14 32–34 2.24 1.43

Despite the spread in the reported experimental band gaps (see Table 2), the SRL DFT gap for PEA2 PbI4 is similar to the lowest reported value of optical band gaps. This indicates that similar error cancellation as for MAPbI3 occurs and that SRL DFT underestimates the true band gap only by a small margin. In any case, this shows that any future highlevel many-body calculations for these systems must be carried out fully relativistic or are otherwise likely to systematically underestimate Eg . 10


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We now investigate the influence of dimensionality on the band gaps. First we compare MAPbI3 bulk and MA2 PbI4 ML at the SRL DFT level. The band gap of MAPbI3 is 1.52 eV, in agreement with literature. 28,35 It increases by roughly 0.7 eV in MAPbI3 . To analyze the band gap increase, we compare the PDOSs and band structures of both systems in Fig. 3 (g,h). The PDOS has many common features. On closer inspection, however, the CBE changes in agreement with structural differences between bulk and ML. Due to the lack of long-range bond delocalization along z in the ML, the Pbpz bands are more confined and shifted away from the Fermi edge. Pbpx and Pbpy remain mostly unchanged, despite the small difference between both species that is only noticeable in the bulk (see phase transition in Fig. 1). Similar changes are also observed in the Ip contributions to the VBE. Ipx and Ipy show again small differences in the ML structure while being identical in the bulk. Bands with Ipz contribution are destabilized in the ML due to the broken Pb–I bonds along z. Overall, these changes lead to the observed band gap increase in the 2D system. Since this effect is caused by the lack of long-range bond delocalization along z, it is also observed in the PEA2 PbI4 bulk, due to the structural changes induced by the larger PEA cation. Since some of the vertical Pb–I bonds are already broken along the stacking direction, the band structure and gap are similar to the 2D cases (MA2 PbI4 and PEA2 PbI4 MLs), with only small modifications between PEA2 PbI4 bulk and ML due to the weak interlayer PEA interactions. The band gap opening of PEA2 PbI4 compared to MAPbI3 bulk by ≈ 0.7 eV opens the possibility of adjusting the band gap in this range by controlling the number of MAPbI3 layers in the family of MAn−1 PEA2 Pbn I3n+1 Ruddlesden-Popper phases, which might be interesting for light harvesting or sensors. Comparing PEA2 PbI4 and MAPbI3 band structures, we also observe that the flat bands of the organic cation are even further away from the band edges in the case of MA cations. For PEA2 PbI4 , the CBE is located at the organic cation around the BZ corners S. This opens possibilities for band gap engineering by shifting these bands via chemical modification of

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the PEA cations. These states could also be related to the electron-phonon coupling that is observed in this material with phonons that are located at the PEA units. 36

Conclusion We investigated the effects of exchanging small MA with PEA cations in the OMHP benchmark case MAPbI3 . We identify and discuss the resulting most stable Ruddlesden-Popper phase, which is in agreement with experiments and shows off-center displacement of Pb cations leading to antiparallel Pb–I distortions. By analyzing the bonding of the organic cation with the PbI4 backbone and the interactions within the hydrophobic moieties, we show that the vertical interaction along the stacking direction is weak. This is also consistent with the electronic structure of the layered bulk phase, which is rather unaffected by reducing the dimensionality to a ML. In contrast, the electronic structure changes significantly when comparing 3D bulk with 2D ML for MAPbI3 . Thus, interlayer bonding in layered perovskites is weaker compared to 3D OMHPs, opening the possibility towards thin film growth down to MLs for the layered material. There, the empty bands of the organic cation are significantly lowered in energy and contribute to the conduction band edge, which opens the possibility of band gap engineering. Besides these changes, the electronic structure of layered and traditional OMHPs are similar, including the previously reported huge influence of SOC on the electronic structure.

Acknowledgement This work was supported by the U.S. Office of Naval Research, under Grant N00014-14-1-07. J. G. thanks the German Research Foundation for support from Research Fellowship GE 2827/1-1. Y. K. acknowledges support from NSF grant No. DMR-1120901. Computational support is provided by the HPCMO of the U.S. DOD.

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Supporting Information Available The following files are available free of charge.

Details on structural variants and further

discussion of the thermodynamical minimum of PEA2 PbI4 . Analysis of the non-covalent interactions in PEA2 PbI4 . Influence of FRL treatment on electronic structure.

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Influence of the Dimensionality and Organic Cation on Crystal and

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