Structural Evolution in Methylammonium Lead Iodide CH3NH3PbI3

Subscriber access provided by University of Otago Library

Article 3

3

3

Structural Evolution in Methylammonium Lead Iodide CHNHPbI Khuong Phuong Ong, Teck Wee Goh, Qiang Xu, and Alfred Huan

J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b09884 • Publication Date (Web): 13 Oct 2015 Downloaded from http://pubs.acs.org on October 15, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Structural Evolution in Methylammonium Lead Iodide CH3NH3PbI3 Khuong P. Ong,1 Teck Wee Goh,2 Qiang Xu,2 and Alfred Huan1 1

Institute of High Performance Computing, Agency of Science, Technology and Research (A*STAR), 1

Fusionopolis Way, 138632, Singapore 2

Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang

Technological University, 21 Nanyang Link, 637371 Singapore

AUTHOR INFORMATION Corresponding Author: Khuong P. Ong *Email: [email protected]

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 21

ABSTRACT The organic-inorganic hybrid perovskite, in particular methylammonium lead iodide (MAPbI3) is currently a subject of intense study due to its desirability in making efficient photovoltaic devices economically. It is known that MAPbI3 undergoes structural phase transitions from orthorhombic Pnma to tetragonal I4/mcm at ~170 K and then to cubic Pm3m at ~330 K. A tetragonal P4mm phase is also reported at 400 K considering total cation disorder is not appealing due to its hydrogen bonding capabilities. Resolving this ambiguity of phase transition necessitates study of the structural evolution across these phases in our work using abinitio methods. In this work, we show that the structural phase evolves from Pnma to I4/mcm to P4mm to Pm3m with increasing volume. The P4mm phase is a quasi-cubic one with slight distortion in one direction from cubic Pm3m due to the rotation of MA cations. Biaxial strain on MAPbI3 reveals that only the Pnma and P4mm phases are energetically stable at a < 9.14 Å and a > 9.14 Å, respectively. The Pnma, I4/mcm, P4mm and Pm3m phases can be stable at various uniaxial strain conditions. Our study provides a clear understanding of the structural phase transitions that occur in MAPbI3 and provides a guide for the epitaxial growth of specific phases under various strain conditions. TOC GRAPHICS

KEYWORDS Hybrid Perovskites, Solar cell, Density Functional Theory, Phase Transitions


2

Page 3 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The organic-inorganic hybrid perovskite (OIHP) has been a popular material of research for its potential in efficient and economical photovoltaic technology. Currently the most efficient laboratory solar cells fabricated from this material, having exceeded 19%1, is comparable to the performance of existing solar cell technologies. The pace of research to reach this stage is also impressive considering only five years have passed since first report2 on perovskite photovoltaic whose progress has surpassed those of other types solar cell in photovoltaic research. Even with the impressive application of OIHP in solar cells, fundamental research in understanding its physical properties is lacking, and only recently some of these properties have been illuminated despite the older papers on this material. These properties include the material’s long carrier diffusion length3,4,5,6, low exciton binding energy7,8, large dielectric constant9, large absorption coefficient10, and ferroelectricity11. Despite concerted efforts in the fundamental research of OIHP, much work remains to be done to understand the material from a theoretical viewpoint to illustrate the important chemical properties which make it desirable for its application. Perovskite is a general class of materials which has the chemical formula ABX3, where in this intensely studied OIHP A can represent the methylammonium (MA+), formamidinium (FA+) or guanidinium12 (GA+) cation, B the lead (Pb2+), tin (Sn2+) or germanium (Ge2+) cation and X the iodide (I-) cation which can be substituted with the other halide13 (Br-, Cl-) anions. Structurally, the MA cation resides within the network of corner sharing PbI6 cuboctahedral cage having different tilting characteristics at various structural phases of the material. It was found through powdered X-ray diffraction (XRD)14 that the methylammonium lead iodide (MAPbI3) perovskite exists in the cubic Pm3m phase at high temperature above 330 K, below which it undergoes a phase transition to the tetragonal I4/mcm phase and then to the orthorhombic Pnma phase below


3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 21

170 K. However, in single crystal XRD it was reported that the phase transition from I4/mcm phase15 at high temperature tends to both the cubic16 Pm3m and tetragonal15,17 P4mm space groups. The P4mm space group was also proposed considering that total disorder of cation orientation is not ideal due to their hydrogen bonding capabilities with PbI6 cubo-octahedral cage. A slight ambiguity is present in the nature of crystal structure of this material at high temperatures. The physical origin leading to the existence of these MAPbI3 phases is not well understood, thus a careful re-examination of the crystallographic properties in this material is required. Despite initial theoretical work performed in recent years to elucidate properties of OIHP pertaining to doping and interfaces, the fundamental understanding is still premature to explore such more complex aspects of this material. Some of these fundamental understanding derived from theoretical calculations include characterization of defects18,19,20,21, the presence of dispersive forces22, optical properties23 and Rashba effect24. Other notable theoretical works in this area include charge screening by the cation25, interfacial phenomena26,27, hysteresis effect28, ion transport29, role of chlorine in mixed-halide perovskites30 and the role of MA cation orientation towards the perovskites’ band structure31. However, understanding of fundamental properties in OIHP is paramount before studying its more complex properties. Recently, the role of tetragonal lattice parameters (c/a) ratio towards the Pnma to I4/mcm phase transition has been elucidated32. This strain effect, facilitated by the hydrogen bonding interaction between the MA cation and the surrounding PbI6 cuboctahedral cage, could open up the possibility of inducing structural phase transitions through other means apart from a change in temperature. Experimental realization of this phenomenon could open up a new area of solar cell optimization by suitably inducing specific structural phases in devices.


4

Page 5 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


In this letter, we discuss the interplay between the various MA orientations in different phases of MAPbI3 and cubic cell volume to simulate how volume change reorients the MA cations and invoke structural phase transitions. The structural evolution of MAPbI3 under different epitaxial conditions, namely biaxial and uniaxial constraints, with the verified orientations of MA in structural phases of MAPbI3 is investigated to predict the conditions for the existence of various phases. The existence and phase transition of a distinct P4mm structure to Pm3m is confirmed. Throughout the paper, unless specified otherwise, the ratio of lattice constants c against a (c/a) for the cubic Pm3m and tetragonal P4mm structures will be referenced to the cubic/pseudo-cubic unit cell which is made up of one MAPbI3 formula unit, whereas those for the tetragonal I4/mcm and Pnma will be referenced to the tetragonal unit cell, which is the √2 × √2 × 2 transformation of the cubic/pseudo-cubic structure (see supporting information). MA cation orientations will always be referred with respect to the cubic/pseudo-cubic cells for easy comparison. Comparison of cell volume across all structural phases of MAPbI3 is done with respect with the cubic/pseudocubic cell volume. All energies in our calculation are normalized to the most stable Pnma structure, E = E - EPnma.


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 21

Figure 1. Analysis of chemical bonds between I atoms and H atoms within different structures P4mm a = b = 6.375 Å and c = 6.253 Å; Pm3m with a = b = c = 6.455Å; Pnma and I4/mcm at a = 8.98Å and c = 12.57Å (I4/mcm) and c = 12.30Å (Pnma). The change in cell volume by varying its lattice constants results in different structural phase transitions. The chemical bonding between MA cations and the PbI6 cuboctahedral cage dictates the orientation of MA cations in MAPbI3 and plays a key role in the structural phase transitions. Experimentally through nuclear magnetic resonance (NMR)33 it was found that the MA cations


6

Page 7 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


reorient themselves in the cubic phase in the order of ps, approaching that of a freely rotating motion which increasingly get arrested at low temperatures. The orientation and movement of MA cations in MAPbI3 were first predicted to be influenced by the c/a ratios and the H-I bonds32 in the I4/mcm and Pnma phase. This theoretical analysis reveals that the NH3 components of MA are strongly bonded to the I atoms compared to those of CH3, which results in the MA cations precessing about the NH3 component instead of a completely free rotation. This is an almost general feature of the OHIP class which is understood to be due to hydrogen bonding12,

34

between the H atoms in NH3 components with their surrounding I atoms. Within our simulations the orientations of MA components in MAPbI3 are carefully studied in different directions35 depicted in Figure 1. This work reveals the existence of several metastable MA orientations in the cubic Pm3m and tetragonal P4mm structures where the MA cations do not preferentially rotate towards other directions even though that may not be the globally stable one. The origin relates to the strong and weak bonds between NH3 and CH3 components toward their surrounding I atoms, respectively. These metastable orientations are identified as following: 1) The MA cations orient along direction: atom H1 in NH3 component bonds to I6 or I5, H3 bonds to I9 and H2 bonds to I1, the MA cation will orient along [010] direction in Figure 1a; if H1 bonds to I9 or I10 and H2 bond to I12, H3 bonds to I10 then the MA cation will orient along [001] direction; if H1 bonds to I6 or I7 and H2 bond to I2, H3 bonds to I10 then the MA cation will orient along [100] direction. 2) The MA cations orient along [111], H atoms from NH3 component mainly bonds to I atoms at the corners such as H1 bonds to I9, H2 bonds to I5, H3 bond to I12 shown in Figure 1b.


7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 21

3) The MA cations orient along [110], [011], [101] which happens in two different ways: (1) H2 and H3 instead of bonding to I1 and I9 in case (i) will bond to I4 and I12 respectively, as shown in Figure 1c. (2) H2 and H3 instead of bonding to I1 and I9 in case (i) will bond to I5 and (I9, I10, I12), respectively shown in Figure 1d. These orientations strongly distort the rotations of PbI6 octahedra from no tilting in cubic Pm3m or in-phase tilting in tetragonal P4mm to anti-phase tilting in the orthorhombic Pnma and tetragonal I4/mcm structures.

Figure 2. Influence of cubic cell volume change to the phase transitions of MAPbI3. Inset: MAPbI3 structures for P4mm phase (left) and Pm3m phase (right) showing the orientation of MA cation in these phases. The data for I4/mcm and Pnma are reproduced from Ref [32]. To understand the interplay between MA cation orientations with phase transitions, we first need to determine the dependence of the respective phases with respect to volume change. The variation of energy with cubic/pseudo-cubic cell volume for the various phases is shown in Figure 2. Our results show that the transition from cubic Pm3m to tetragonal I4/mcm is not direct


8

Page 9 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


as originally believed. Instead, a tetragonal P4mm phase is established between I4/mcm and Pm3m. The P4mm phase is indeed a quasi-cubic phase with slight distortion in one direction having small energy difference between two phases. This tendency is vice versa with transitions in MAPbBr3 with cubic Pm3m (T>237K) to tetragonal I4/mcm (155 K < T < 237 K) then to tetragonal P4/mmm (149.5 K < T < 155 K) and to orthorhombic Pna21 at low temperature (T < 144.5 K)36. Our study on the P4mm phase shows that c/a is greater than 1 at small volumes with the MA cation oriented along [001] direction. This c/a ratio decreases with an increase in volume with the most stable P4mm phase achieved at c/a ~1. At larger volume the c/a ratio is less than 1 and the MA cation orients in either [010] or [100] direction while the orientation of MA cation in the Pm3m phase lies along [111] direction shown in the inset in Figure 2. Such reorientation of MA cation distorts the Pm3m structure along [001] direction, forming the P4mm structure but do not cause any octahedral tilt in both Pm3m and P4mm structures, which indicates that macroscopically the MA cations re-orient themselves in tandem while undergoing this phase transition. The phase diagram shows that the most stable P4mm structure occupies a volume of ~252 Å3, which is in agreement with 251.60 Å3 reported in experiment17 with a=b = 6.32 Å and c = 6.31 Å in comparison to experimental data a=b = 6.312 Å and c = 6.316 Å 17 (see table 1). With further decrease in volume, MAPbI3 undergoes a phase transition from P4mm to I4/mcm. It is interesting to see that this transition shown in Figure 2 takes place at the most stable P4mm structure where c/a ~1. At smaller volume, the P4mm structure with c/a (P4mm) > 1 is not stable in comparison to that of the I4/mcm (c/a

(I4/mcm)

> 1). The result shows that during the phase

transition from P4mm to I4/mcm the MA cations rotate from in-plane [010] direction towards the out-of-plane c-direction. Such rotations of the MA cations cause an anti-phase tilt in the PbI6 octahedra which is stabilized by I4/mcm symmetry. The √2 × √2 × 2 cell of the I4/mcm


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 21

structure is derived from either Pm3m or P4mm structure by rotating the cubic or pseudo-cubic cell of Pm3m or P4mm structure respectively by 45° and doubling the unit cell along c-direction, therefore the [010] direction in the P4mm structure corresponds to [110] direction in I4/mcm structure. The orientations of MA cations along the [111] direction for I4/mcm structure are equivalent to the rotations of MA components in [010] direction out of plane to the c-direction in P4mm structure. The transition between the tetragonal I4/mcm and orthorhombic Pnma phases was well studied32. Figure 2 shows that the real stable I4/mcm structure (at B, see Fig.2) is not with the most stable I4/mcm structure (at A, see Fig.2). The calculation shows that the I4/mcm lattice parameters at B are in better agreement with experimental reports (see table 1). Table 1. Lattice constants of I4/mcm and P4mm structure. a (Å) I4/mcm

Exp

b (Å )

V(Å3)

c (Å )

Cubic

Tetra

Cubic

Tetra

Cubic

Tetra

Cubic

Tetra

6.194

8.76

6.194

8.76

6.255

12.51

240.2

960.8

6.222

8.8

6.222

8.8

6.34

12.68

245.48

981.9415

6.258

8.85

6.258

8.85

6.22

12.44

243.58

974.3314

Cubic/Tetra = cubic/tetra representation: aT/ bT = aC / bC x √2; cT = cC x 2; VT = VC x 4 P4mm

Exp

6.320

6.320

6.310

252

6.312

6.312

6.316

251.60 17


10

Page 11 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. Influence of biaxial constraint on the (001) MAPbI3 thin film. To make a reasonable comparison with I4/mcm and Pnma structures the in-plane lattice constant a of P4mm and Pm3m is multiplied by √2. Experimental reports14,15 show that at low temperatures MAPbI3 perovskite has the Pnma orthorhombic phase and undergoes a phase transition to the I4/mcm tetragonal phase at higher temperatures from 161.4 K. At T > 330K the MAPbI3 is stabilized with cubic Pm3m phase. A different tetragonal P4mm space group, which can be considered as pseudo-cubic having lattice difference of 0.005Å between its in-plane and out-of-plane lattice constants, was also reported17 at 400K in single crystals. However, the transition from tetragonal to cubic is widely believed to be from the I4/mcm phase to the Pm3m phase. The physical origin of the P4mm phase and how it comes into the picture of phase transition is not well understood. Strain engineering of materials through epitaxial growth has been a particularly effective approach for realizing novel properties.


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 21

We therefore study the existence of these possible phases in MAPbI3 by strain engineering with different biaxial and uniaxial constraints. The influence of biaxial constraint on the (001) MAPbI3 thin films is shown in Figure 3. The results show that under biaxial constraint the Pnma phase is stabilized up to aI4/mcm = bI4/mcm ~9.14 Å. At higher tensile constraint aI4/mcm > 9.14 Å, the tetragonal P4mm is stabilized (aP4mm = / /√2, following the stated convention) instead. The cubic Pm3m and tetragonal I4/mcm phases are not stable under biaxial constraint on the (001) MAPbI3 thin films. At larger in-plane lattice constant a, the out-of-plane lattice constant c, is less than √2 (cI4/mcm < √2 / ). The structural transition from orthorhombic Pnma to tetragonal P4mm is simply the rotation of MA cations from [110] direction to [100] or [010] direction and the tilt of PbI6 octahedral changes from anti-phase tilt a-b-c+ to in-phase tilt in P4mm. As reported, the Pnma phase is stable at high (c/a)I4/mcm ratio (c/a >1.45). When the in-plane lattice constants increase, (c/a)I4/mcm decrease thus Pnma phase becomes unstable. On the other hand, the P4mm is stabilized at low (c/a)I4/mcm ratio. As a result, when the lattice constant aI4/mcm increases, the MA cations are forced to rotate from [110] direction to the [100] or [010] directions, i.e., transform from Pnma structure to P4mm structure. Therefore, the P4mm structure is stabilized at aI4/mcm > 9.14 Å while the Pnma phase is stabilized at aI4/mcm < 9.14 Å under biaxial strain.


12

Page 13 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Influence of uniaxial constraint along [001] direction on the phase transitions of MAPbI3 thin film. The lattice constants c of P4mm and Pm3m structures are doubled to make a reasonable comparison to I4/mcm and Pnma structures. In contrast to introducing biaxial strain, the influence of uniaxial constraint along [001] direction on the phase transitions of MAPbI3 reveals the possibility of obtaining multiple structural phases. The Pnma phase is stable at low strain with a phase transition to the I4/mcm tetragonal phase32 at cI4/mcm ~12.42 Å. The MA cations re-orient themselves from [110] in Pnma structure to [011] in I4/mcm structure as shown in Figure 1. At larger c, the I4/mcm is unstable and transforms to tetragonal P4mm at cI4/mcm = 12.74 Å - 12.78 Å (cP4mm = c/2 = 6.37 Å - 6.39 Å) as shown in Figure 4, as the MA cations rotate from [011] direction in I4/mcm to [001] direction in P4mm structure. At c from 12.78 Å to 12.95 Å (c 3̅ ,

P4mm

= 6.39 Å -6.495 Å) the Pm3m

structure is more stable than the P4mm structure but the energy difference between these two structures is very small shown in Figure 4 inset, implying the co-existence of these two phases. At c larger than 12.95 Å (cP4mm = 6.495 Å) the P4mm is stabilized with a discontinuity at c =


13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 21

12.95 Å (cP4mm = 6.495 Å). This discontinuity is due to the change in chemical bonding between I atoms and H atoms from CH3 components. For P4mm structure, increasing lattice constant c results in decrease of lattice constant a. This brings the I atoms I5, I6, I7, I8 closer to CH3 component making bonds H5-I7, H5-I8, H6-I6, H4-I5 being comparable to chemical bonds H5I3, H4-I4, H6-I2 shown in Figure 1. These additional bonds between CH3 components to I5, I6, I7, I8 further stabilize the P4mm structure at high tensile strain along the [001] direction. The lattice constants at which the various phase transitions occur is summarized in Table 1 below. In conclusion, we have studied the evolution of structural phases in MAPbI3 and obtaining them under biaxial and uniaxial strain conditions. We show the existence of P4mm structure which is distorted along one direction from the Pm3m by rotations of MA cations. Towards larger crystal volume, MAPbI3 transforms from tetragonal I4/mcm to tetragonal P4mm and not directly to the cubic Pm3m as commonly believed. The cubic Pm3m phase is also more stable at larger volume when MAPbI3 transforms from P4mm to Pm3m. The increase in crystal volume causes the MA cations to rotate from [110] direction (Pnma phase) → [011] direction (I4/mcm phase) → [001] direction (P4mm phase) → [111] direction (Pm3m phase). The influence of strain on the epitaxial growth of MAPbI3 reveals that the biaxial constraint helps to stabilize the P4mm structure at a > 9.14 Å (a P4mm > 6.46 Å) while the Pnma phase is stable at a < 9.14 Å. The uniaxial constraint along the c-direction reveals that all structural phases could be obtained, and shows an ambiguity in the phase transition from I4/mcm to P4mm and Pm3m with c from 12.74 Å to 12.95 Å. We show the actual origin for the structural evolution of MAPbI3 from orthorhombic Pnma → tetragonal I4/mcm → tetragonal P4mm and to cubic Pm3m of large single crystals which can now be grown by methods such as antisolvent vapor-assisted crystallization6 and top-seeded solution growth5, or solution-based hot-casting technique37 in the


14

Page 15 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


case of practical solar cell applications. Our study guides the solar cell community to explore conditions for the existence of these different structural phases in MAPbI3 to utilize beneficial properties in each of them to optimize better devices. For the electronic structures of MAPbI3 calculations, we use the all-electron-like projector augmented wave (PAW) method38 with the Perdew-Burke-Ernzerhof (PBE)39 and PBE revised for solids (PBEsol)40 exchange correlation potential as implemented in the VASP code41. The cut-off energy for the plane wave expansion of the wave functions is 500 eV, and all atoms in the unit cell are fully relaxed till the Hellman-Feynman forces are less than 0.01 eV/Å. The 3x2x3 Monkhorst-Pack grid of k-points42 for Brillouin zone integration was used in calculations. The semicores of Pb atoms are treated as valence electrons; i.e., 14 valence electrons for Pb (5d106s2 6p2). The I-5s25p5, C-2s22p2, N-2s22p3 and H-1s were considered as valence electrons. To study the effect of epitaxial biaxial strain on MAPbI3, we employ a 48-atom unit cell (Pnma and I4/mcm) / 12-atom unit cell (P4mm and Pm3m) with lattice vectors a1=aIPx, a2=aIPy and a3=cz, here aIP is the in-plane lattice constant (for Pnma and I4/mcm we make an approximation with a=b=aIP) while c is fully relaxed. For uniaxial strain engineering along the c-direction the lattice vectors of new unit cell are a1=ax, a2=by and a3=cz, here we make approximation with a=b and they are fully relaxed at specified c. To unique in studying the structural evolution between Pnma, I4/mcm, P4mm and Pm3m the biaxial constraint on the (001) substrate and uniaxial constraint along the [001] direction have been selected.

ASSOCIATED CONTENT AUTHOR INFORMATION


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 21

Corresponding Author: Khuong P. Ong *Email: [email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was supported by Institute of High Performance Computing, Agency of Science, Technology, And Research (A*STAR). Work at Nanyang Technological University (NTU) was supported by NTU Research Student Scholarship (NTU-RSS).

REFERENCES 1.

Zhou, H.; Chen, Q.; Li, G.; Luo, S.; Song, T.-b.; Duan, H.-S.; Hong, Z.; You, J.; Liu, Y.;

Yang, Y., Interface Engineering of Highly Efficient Perovskite Solar Cells. Science 2014, 345, 542-546. 2.

Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T., Organometal Halide Perovskites as

Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050-6051. 3.

Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Gratzel, M.; Mhaisalkar, S.;

Sum, T. C., Long-Range Balanced Electron- and Hole-Transport Lengths in Organic-Inorganic CH3NH3PbI3. Science 2013, 342, 344-347. 4.

Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J. P.; Leijtens, T.;

Herz, L. M.; Petrozza, A.; Snaith, H. J., Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber. Science 2013, 342, 341-344.


16

Page 17 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5.

Dong, Q.; Fang, Y.; Shao, Y.; Mulligan, P.; Qiu, J.; Cao, L.; Huang, J., Electron-Hole

Diffusion Lengths > 175 m in Solution-Grown CH3NH3PbI3 Single Crystals. Science 2015, 347, 967-970. 6.

Shi, D.; Adinolfi, V.; Comin, R.; Yuan, M.; Alarousu, E.; Buin, A.; Chen, Y.; Hoogland,

S.; Rothenberger, A.; Katsiev, K.; others, Low Trap-State Density and Long Carrier Diffusion in Organolead Trihalide Perovskite Single Crystals. Science 2015, 347, 519-522. 7.

Sun, S.; Salim, T.; Mathews, N.; Duchamp, M.; Boothroyd, C.; Xing, G.; Sum, T. C.;

Lam, Y. M., The Origin of High Efficiency in Low-Temperature Solution-Processable Bilayer Organometal Halide Hybrid Solar Cells. Energy Environ. Sci. 2014, 7, 399. 8.

D'Innocenzo, V.; Grancini, G.; Alcocer, M. J. P.; Kandada, A. R. S.; Stranks, S. D.; Lee,

M. M.; Lanzani, G.; Snaith, H. J.; Petrozza, A., Excitons Versus Free Charges in Organo-Lead Tri-Halide Perovskites. Nat. Commun. 2014, 5. 9.

Juarez-Perez, E. J.; Sanchez, R. S.; Badia, L.; Garcia-Belmonte, G.; Kang, Y. S.; Mora-

Sero, I.; Bisquert, J., Photoinduced Giant Dielectric Constant in Lead Halide Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, 2390-2394. 10. Singh, S. P.; Nagarjuna, P., Organometal Halide Perovskites as Useful Materials in Sensitized Solar Cells. Dalton Trans. 2014, 43, 5247. 11. Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A., Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells. Nano Lett. 2014, 14, 2584-2590.


17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 21

12. Giorgi, G.; Fujisawa, J.-I.; Segawa, H.; Yamashita, K., Organic-Inorganic Hybrid Lead Iodide Perovskite Featuring Zero Dipole Moment Guanidinium Cations: A Theoretical Analysis. J. Phys. Chem. C 2015, 9, 4694-4701.13.

Mosconi, E.; Amat, A.; Nazeeruddin, M. K.;

Gratzel, M.; De Angelis, F., First-Principles Modeling of Mixed Halide Organometal Perovskites for Photovoltaic Applications. J. Phys. Chem. C 2013, 27, 13902-13913. 14. Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J., Synthesis and Crystal Chemistry of the Hybrid Perovskite (CH3NH3)PbI3 for Solid-State Sensitised Solar Cell Applications. J. Mater. Chem. A 2013, 1, 5628. 15. Kawamura, Y.; Mashiyama, H.; Hasebe, K., Structural Study on Cubic-Tetragonal Transition of CH3NH3PbI3. J. Phys. Soc. Jpn 2002, 71, 1694-1697. 16. Mashiyama, H.; Kurihara, Y.; Azetsu, T., Disordered Cubic Perovskite Structure of CH3NH3PbX3 (X= Cl, Br, I). J. Korean Phys. Soc. 1998, 32, S156-S158. 17. Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G., Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties. Inorg. Chem. 2013, 52, 9019-9038. 18. Yin, W.; Shi, T.; Yan, Y., Unusual Defect Physics in CH3NH3PbI3 Perovskite Solar Cell Absorber. Appl. Phys. Lett. 2014, 104, 063903. 19. Agiorgousis, M. L.; Sun, Y.-Y.; Zeng, H.; Zhang, S., Strong Covalency-Induced Recombination Centers in Perovskite Solar Cell Material CH3NH3PbI3. J. Am. Chem. Soc. 2014, 136, 14570-14575.


18

Page 19 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


20. Kim, J.; Lee, S.-H.; Lee, J. H.; Hong, K.-H., The Role of Intrinsic Defects in Methylammonium Lead Iodide Perovskite. J. Phys. Chem. Lett. 2014, 5, 1312-1317. 21. Walsh, A.; Scanlon, D. O.; Chen, S.; Gong, X.; Wei, S.-H., Self-Regulation Mechanism for Charged Point Defects in Hybrid Halide Perovskites. Angew. Chem. Int. Ed. 2015, 6, 18111814. 22. Egger, D. A.; Kronik, L., Role of Dispersive Interactions in Determining Structural Properties of Organic-Inorganic Halide Perovskites: Insights from First Principles Calculations. J. Phys. Chem. Lett. 2014, 5, 2728-2733. 23. Filippetti, A.; Mattoni, A., Hybrid Perovskites for Photovoltaics: Insights from First Principles. Phys. Rev. B. 2014, 89, 125203. 24. Kim, M.; Im, J.; Freeman, A. J.; Ihm, J.; Jin, H., Switchable S= 1/2 and J= 1/2 Rashba Bands in Ferroelectric Halide Perovskites. Proc. Natl. Acad. Sci. U.S.A. 2014, 111, 6900-6904. 25. Even, J.; Pedesseau, L.; Katan, C., Analysis of multi-valley and multi-bandgap absorption and enhancement of free carriers related to exciton screening in hybrid perovskites. J. Phys. Chem. C, 2014, 118, 11566 - 11572. 26. Roiati, V.; Mosconi, E.; Listorti, A.; Colella, S.; Gigli, G.; De Angelis, F., Stark effect in perovskite/TiO2 solar cells: Evidence of local interfacial order. Nano Lett. 2014, 14, 2168-2174. 27. Butler, K. T.; Frost, J. M.; Walsh, A., Band Alignment of the Hybrid Halide Perovskites CH3NH3PbCl3, CH3NH3PbBr3 and CH3NH3PbI3. Mater. Horiz. 2015, 2, 228-231. 28. Frost, J. M.; Butler, K. T.; Walsh, A., Molecular Ferroelectric Contributions to Anomalous Hysteresis in Hybrid Perovskite Solar Cells. APL Mat. 2014, 2, 081506.


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 21

29. Eames, C.; Frost, J. M.; Barnes, P. R.; O’Regan, B. C.; Walsh, A.; Islam, M. S., Ionic Transport in Hybrid Lead Iodide Perovskite Solar Cells. Nat. Commun. 2015, 6. 30. Mosconi, E.; Ronca, E.; De Angelis, F., First Principles Investigation of the TiO2/Organohalide Perovskites Interface: The Role of Interfacial Chlorine. J. Phys. Chem. Lett. 2014, 5, 2619 - 2625. 31. Motta, C.; El-Mellouhi, F.; Kais, S.; Tabet, N.; Alharbi, F.; Sanvito, S., Revealing the role of organic cations in hybrid halide perovskite CH3NH3PbI3. Nat. Commun. 2015, 6. 32. Ong, K. P.; Goh, T. W.; Xu, Q.; Huan, A., Mechanical Origin of the Structural Phase Transition in Methylammonium Lead Iodide CH3NH3PbI3. J. Phys. Chem. Lett. 2015, 6, 681685. 33. Wasylishen, R.; Knop, O.; Macdonald, J., Cation Rotation in Methylammonium Lead Halides. Solid State Commun. 1985, 56, 581-582. 34. Amat, A.; Mosconi, E.; Ronca, E.; Quarti, C.; Umari, P.; Nazeeruddin, M. K.; Gratzel, M; De Angelis, F., Cation-Induced Band-Gap Tuning in Organohalide Perovskites: Interplay of Spin-Orbit Coupling and Octahedra Tilting. Nano Lett. 2014, 14, 3608 - 3616. 35. Fan, Z.; Xiao, J.; Sun, K.; Chen, L.; Hu, Y.; Ouyang, J.; Ong, K. P.; Zeng, K.; Wang, J., Ferroelectricity of CH3NH3PbI3 Perovskite. J. Phys. Chem. Lett. 2015, 6, 1155-1161. 36. Poglitsch, A.; Weber, D., Dynamic Disorder in Methylammoniumtrihalogenoplumbates (II) Observed by Millimeter-Wave Spectroscopy. J. Chem. Phys 1987, 87, 6373-6378.


20

Page 21 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


37. Nie, W.; Tsai, H.; Asadpour, R.; Blancon, J.-C.; Neukirch, A. J.; Gupta, G.; Crochet, J. J.; Chhowalla, M.; Tretiak, S.; Alam, M. A.; others, High-Efficiency Solution-Processed Perovskite Solar Cells with Millimeter-Scale Grains. Science 2015, 347, 522-525. 38. Blochl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953. 39. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. 40. Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406. 41. Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169. 42. Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188.


21

Structural Evolution in Methylammonium Lead Iodide CH3NH3PbI3

Recommend Documents