Charge Stripe Formation in Molecular Ferroelectric Organohalide

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Charge Stripe Formation in Molecular Ferroelectric Organohalide Perovskites for Efficient Charge Separation Xu Zhang, Mingliang Zhang, and Gang Lu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07800 • Publication Date (Web): 11 Oct 2016 Downloaded from http://pubs.acs.org on October 13, 2016

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The Journal of Physical Chemistry

Charge Stripe Formation in Molecular Ferroelectric Organohalide Perovskites for Efficient Charge Separation Xu Zhang, Mingliang Zhang, and Gang Lu∗

Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330-8268, USA *

Email: [email protected]; Tel: 1-818-677-2021

ABSTRACT: Despite rapid progress in the efficiency of organohalide perovskite based solar cells, physical mechanisms underlying their efficient charge separation and slow charge recombination still elude us. Here we provide direct evidence of spontaneous charge separation via first-principles simulations. The excitons are predicted to self-organize into stripes of photo-excited electrons and holes, spatially separated as effective channels for charge transport. The rotation of organic cations deforms the inorganic framework, and as the deformation reaches a critical value, a direct band gap transforms to an indirect one, and the photo-excited electrons rotate in alignment with the deformation-induced electric fields. The latter triggers Stark effect which in turn leads to the formation of charge stripes. The interplay between dynamic disorder, ionic bonding and polarization is responsible for the formation of the charge stripes and the indirect band gap, both of which could lead to

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efficient charge separation and reduced charge recombination in the organohalide perovskites. I. INTRODUCTION Past few years have witnessed a tremendous shift of momentum in photovoltaics research, galvanized by the emergence of organohalide perovskite based solar cells1-12, whose power conversion efficiencies have now exceeded 20%13. The impressive breakthrough is attributed to remarkable photo-physical properties that the family of methylammonium (MA) lead halide materials possesses, including high optical absorption coefficient1,14,15, ambipolar charge transport2,16, long carrier diffusion length6,14,17-21, and low charge recombination rate21-24. Significant effort has been devoted to the elucidation of photo-physics underlying efficient charge separation. Central to this effort is the experimental revelations that exciton binding energy in CH3NH3PbI3 (MAPbI3) is very small (only a few meV at room temperature)25-27, implying a spontaneous free carrier generation following light absorption. However, how these photo-generated carriers are separated in the perovskite remains largely unknown. Unlike traditional solar cells where charge carriers are separated across p-n junctions, MAPbI3 is ambipolar and has no apparent p-n junction for charge separation. To unravel the mystery behind efficient charge separation in MAPbI3 in the absence of p-n junctions, two theoretical models have recently been put forward. On the one hand, Frost et al.28 hypothesized that the antiphase boundaries between ferroelectric domains may act as “ferroelectric highways” for charge separation. As pointed out by the same authors, these antiphase boundaries may be influenced by the applied voltage, giving rise to hysteresis. Hence, whether such “ferroelectric highways” are robust enough for charge separation needs to be further explored24. On the other hand, Ma et al.29 and Quarti et al.30 have predicted that the valence and conduction band edges are localized in


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spatially separated regions owing to the dynamic disorder in MAPbI3, which could reduce charge recombination. However, since the carriers are localized in random regions, they could encounter and recombine. In this paper, we make an important step forward and provide the first direct computational evidence of spontaneous charge separation in MAPbI3 upon light adsorption. We predict that excitons can self-organize themselves into stripes of delocalized electrons and holes within a ferroelectric domain, i.e., our prediction does not require the existence of antiphase boundaries. Since the electrons and holes are separated into different stripes, the probability of their encounter and recombination is diminished. More importantly, we find that concomitant with charge separation in real space, the band structure of MAPbI3 undergoes a transition from a direct band gap to an indirect band gap. We reveal that the physical origin of the charge separation in both real space and momentum space is the distortion of the inorganic lattice, deformed by the rotation of MA molecules. II. COMPUTATIONAL DETAILS The cubic MAPbI3 was modeled by a 4×4×4 supercell with the dimensions of 25.6Å×25.2Å×25.2Å, containing 768 atoms as shown in Fig. 1. To model the mixed halide MAPbI3-xClx with 4% (or 0.5%) concentration of Cl, eight (or one) I ions were substituted by Cl ions in the supercell, i.e., there was one Cl ion per 2×2×2 (or 4×4×4) unit cell. To model molecular paraelectric MAPbI3, 64 MA cations were orientated randomly in the cage for the initial configuration and then the atomic structure was relaxed to reach a local minimum. A recently developed TDDFT method31 was employed to compute the exciton charge density. The method has been applied with success to study exciton charge density in organic and inorganic materials32-34. The DFT calculations were carried out using the projector-augmented wave method35 and Perdew-Burke-Ernzerhof general gradient approximation36 as implemented in the


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Vienna ab initio simulation package37. The energy cutoff for the planewave basis set was 400 eV. All atoms were allowed to fully relax until the force on each atom was less than 0.04 eV/Å. The Γ-point was sampled which provides sufficiently reliable results in light of the large supercell used in the calculations (Supplementary Fig. S7). We performed Born-Oppenheimer Molecular Dynamics (BOMD) simulations for MAPbI3 at room temperature. In the BOMD simulations, the ionic forces were calculated in the excited states made possible by the developed TDDFT method31. The equilibrium structure at 0 K was brought to 300 K by using a repeated velocity scaling with a heating rate of 3 K/fs, and the system is then kept at 300 K for 500 fs with a 1 fs time step to reach the thermal equilibrium. Finally, a micro-canonical production run was carried out for 1000 time-steps with the time-step of 1 fs. The temperature fluctuation is within 20 K in the micro-canonical MD simulations indicating that the system has reached the thermal equilibrium. We have performed calculations with the dispersion correction in TDDFT and the stripe formation remains the same, indicating that the BOMD simulations at 300 K could yield sufficient cage deformation for the stripe formation. In the TDDFT calculations, 96 occupied orbitals were included, which was shown to yield converged results for both energy and ionic force of the excited states. More details of TDDFT method can be found in Supplementary Information. The spin-orbital coupling (SOC) is generally important for band splitting and dispersion in MAPbI3.20,38 However, since the charge density of the lowest exciton is determined primarily by the CBM and VBM, and is insensitive to the band dispersion, SOC was not included in the present TDDFT calculations. Moreover, the charge density of VBM and CBM with the SOC correction39 was very similar to that of the hole and electron, respectively, from our TDDFT calculations as shown in Fig. 1a. Furthermore, it has been shown that whether or not the SOC is included does not change the formation of an indirect gap40.


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III. RESULTS AND DISCUSSION An important aspect of the organohalide perovskites is their structural diversity and flexibility, whose consequences have only begun to be appreciated30,41. At low temperature, MAPbI3 adopts an orthorhombic (Pnma) structure, and as the temperature is increased, it assumes a cubic structure (Pm-3m) by passing through a tetragonal (I4/mcm) phase42. In addition to the crystal structure variation, the MA cation could rotate in the inorganic cage with low energy barriers of ~10 meV12. As a result, the MA cations could arrange themselves to form molecular

ferroelectric

(parallel)43,44,

anti-ferroelectric

(anti-parallel)45

or

paraelectric

(random)46,47 orders, depending on the crystal structure, temperature and timescale. Although there is ongoing debate in the literature on the orientation order of the MA cations, it is plausible that upon thermal fluctuations, nanoscale or larger domains of molecular ferroelectric phase could be present in MAPbI3, perhaps co-existing with paraelectric or anti-ferroelectric domains on a timescale of picoseconds12,48 during which charge separation in completed. In the following, we carry out time-dependent density functional theory (TDDFT) calculations31 to examine optical excitation in the cubic phase of MAPbI3 with the ferroelectric, anti-ferroelectric and paraelectric order of MA cations, respectively. First, we study the lowest exciton state of MAPbI3 at zero temperature in which the static relaxation of the inorganic lattice is small. In Fig. 1a~c, we display the charge density of the exciton in the ferroelectric, antiferroelectric and paraelectric phase, respectively. The exciton charge density is defined as the differential charge density between the excited state and the ground state with the positive (negative) charge density corresponding to hole (electron). Although the wave-functions of the electron and hole are delocalized, they are entangled in space. In other words, there is no spatial


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separation of the electron and hole at zero temperature despite the low exciton binding energy. In this case, excitons may appear as the dominating species of photo-excitations. Next, we perform first-principles Molecular Dynamics (MD) simulations at 300 K to examine the dynamic disorder of MA cations. As shown in Fig. 1d, the dipole direction of the MA cation is represented by two angles φ and θ whose time evolution is determined as a function of their initial orientation. In Fig. 1e, we display the time evolution of the angles at 300 K when their initial orientations are of ferroelectric, anti-ferroelectric and paraelectric order, respectively. For the ferroelectric order, we find that although the MA cations can rotate easily inside the cage49, they do so to preserve the ferroelectric order at 300 K. This fact is illustrated in the figure inset where the standard deviation of both angles remains zero during the course of the MD simulation (~ 1ps). The thermally stable ferroelectric order is consistent with the finding from other ab initio MD simulations44. In contrast, the anti-ferroelectric order is thermally unstable at 300 K and it transforms to the paraelectric order in ~ 0.6 ps, manifested by the nonzero standard deviation shown in Fig. 1e. The polarization in the molecular ferroelectric MAPbI3 consists of two contributions: the permanent dipole of the MA cations and the polarization due to the deformation of the inorganic lattice50. In the following, we denote dt as the displacement of an I- ion from the bond-center of its two nearest neighbor Pb2+ ions in the primitive unit cell as shown in Fig. 2a. For the ideal lattice, dt =0, and a larger dt indicates a stronger distortion to the PbI6 cage. As shown in Fig. 2b, dt varies considerably during the MD simulation with its maximum value reaching 0.9 Å. The highly deformable cage caused by the rotation of the MA cation is a unique feature of the organohalide perovskites, thanks to the soft bonds between Pb2+ and I- ions28. This observation is supported by the low-frequency (

Charge Stripe Formation in Molecular Ferroelectric Organohalide

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