Charge Stripe Formation in Molecular Ferroelectric Organohalide ...

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have predicted that the valence and conduction band edges are localized in ... ACS Paragon Plus Environment. The Journal of Physical Chemistry. 1. 2. 3. 4. 5. 6 ... used in the calculations (Supplementary Fig. S7). We performed Born-Oppenheimer ..... The nature of excited species (excitons vs. free carriers) is shown to be ...
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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, United States S Supporting Information *

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 photoexcited 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 photoexcited electrons rotate in alignment with the deformation-induced electric fields. The latter triggers a 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 efficient charge separation and reduced charge recombination in the organohalide perovskites.

I. INTRODUCTION The past few years have witnessed a tremendous shift of momentum in photovoltaics research, galvanized by the emergence of organohalide perovskite based solar cells,1−12 whose power conversion efficiencies have now exceeded 20%.13 The impressive breakthrough is attributed to remarkable photophysical properties that the family of methylammonium (MA) lead halide materials possesses, including high optical absorption coefficient,1,14,15 ambipolar charge transport,2,16 long carrier diffusion length,6,14,17−21 and low charge recombination rate.21−24 Significant effort has been devoted to the elucidation of photophysics 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 photogenerated 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 explored.24 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 spatially separated regions owing to the dynamic © 2016 American Chemical Society

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 selforganize 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 25.6 × 25.2 × 25.2 Å, containing 768 atoms as shown in Figure 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 oriented randomly in the cage for the initial configuration and then the atomic structure was relaxed to reach a local minimum. A Received: August 2, 2016 Revised: October 11, 2016 Published: October 11, 2016 23969

DOI: 10.1021/acs.jpcc.6b07800 J. Phys. Chem. C 2016, 120, 23969−23975

Article

The Journal of Physical Chemistry C

Figure 1. Exciton charge density and the rotation of MA cations. Exciton charge density of MAPbI3 with (a) ferroelectric, (b) antiferroelectric, and (c) paraelectric order of MA cations, computed at 0 K. The blue (yellow) isosurface illustrates the electron (hole) charge density at 7 × 10−4 Å−3. (d) Definition of angles φ and θ. The arrow indicates the dipole direction of the MA cation. (e) Time evolution of φ (black) and θ (red) as well as their standard deviations during the MD simulation at 300 K for the ferroelectric (left), antiferroelectric (middle), and paraelectric (right) order.

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 materials.32−34 The DFT calculations were carried out using the projector-augmented wave method35 and Perdew−Burke−Ernzerhof general gradient approximation36 as implemented in the Vienna ab initio simulation package.37 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 (Figure 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 method.31 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 microcanonical 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 microcanonical 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 the Supporting 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 Figure 1a. Furthermore, it has been

shown that whether or not the SOC is included does not change the formation of an indirect gap.40

III. RESULTS AND DISCUSSION An important aspect of the organohalide perovskites is their structural diversity and flexibility, whose consequences have only begun to be appreciated.30,41 At low temperature, MAPbI3 adopts an orthorhombic (Pnma) structure, and as the temperature is increased, it assumes a cubic structure (Pm3̅m) by passing through a tetragonal (I4/mcm) phase.42 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 antiferroelectric (antiparallel),45 or paraelectric (random)46,47 orders, depending on the crystal structure, temperature, and time scale. 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 coexisting with paraelectric or antiferroelectric domains on a time scale 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, antiferroelectric, 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 Figure 1 (panels a−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 the 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 separation of the electron and hole at zero temperature despite the low exciton binding energy. In 23970

DOI: 10.1021/acs.jpcc.6b07800 J. Phys. Chem. C 2016, 120, 23969−23975

Article

The Journal of Physical Chemistry C

Figure 2. Cage deformation and charge stripe formation in MAPbI3 at 300 K. (a) Definition of cage deformation dt. Electric dipoles (p0) and net electric fields (E) are induced by the cage deformation. (b) Time evolution of dt during the MD simulation. Seven MD snapshots were selected to examine the exciton charge density. The red dashed line represents the critical value of dt beyond which the spontaneous charge separation occurs. (c) Charge density of the lowest energy exciton in MAPbI3 (upper panel) and NaPbI3 (lower panel) viewed along the z direction for the snapshot no. 2. The electron and hole density is colored in blue and yellow, respectively. The magenta spheres represent Na ions. (d) CB edge (upper) and VB edge (lower) of MAPbI3 for snapshot no. 2. The energy at Γ-point is taken to be zero.

NH3 group in the MA cation and I− in the cage has been shown to drive the deformation of the cage.51 We subsequently examine the exciton charge density in the molecular ferroelectric MAPbI3 during the MD simulation. More specifically, we calculate the exciton charge density at seven different MD snapshots as labeled in Figure 2b. It is found that depending on dt, the exciton could self-organize into stripes of electron and hole. Specifically, if the cage deformation dt is greater than a critical value, indicated by the dashed line in Figure 2b, the stripes of electron and hole are formed. One such example corresponding to the MD snapshot no. 2 is shown in Figure 2c. For this snapshot, the electron and hole are separated in space, forming horizontal channels of net electron and hole density. The periodicity of the stripes is 2a0, where a0 is the lattice constant of MAPbI3. These stripes could provide separated transport channels for electron and hole, thereby reducing the probability of charge recombination. The similar stripe formation is also observed for the MD snapshot nos. 2, 3, and 4 but absent for the snapshot nos. 1, 5, 6, and 7, as shown in Figure S2. This is the most important result of the paper, providing direct evidence of charge separation in MAPbI3 upon photoexcitation. The Fourier analysis of exciton−phonon coupling suggests that the exciton dynamics are assisted by the phonon modes primarily associated with the inorganic cage (see Figure S1). Interestingly, if we replace the MA cations by Na cations while maintaining the same cage distortion, the stripes persist as shown in Figure 2c. This indicates that the stripe formation is not induced by the permanent dipole of the MA cation but rather the deformation of the inorganic lattice. In other words, the stripe formation is not directly tied with the MA cations. Interestingly, we observe that whenever the stripes are formed, the excited electron would occupy Pb 6px orbital as shown in Figure 2c. While in the absence of the stripes, the electron would occupy 6pz orbital as displayed in Figure 1a. This is the second important result which correlates the stripe formation with the orbital orientation of the photoexcited electron. This correlation is particularly revealing in comparing the snapshot nos. 4 and 5: a minute increase of dt from nos. 5 to 4 triggers the stripe formation, accompanied by an electronic

this case, excitons may appear as the dominating species of photoexcitations. Next, we perform first-principles Molecular Dynamics (MD) simulations at 300 K to examine the dynamic disorder of MA cations. As shown in Figure 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 Figure 1e, we display the time evolution of the angles at 300 K when their initial orientations are of ferroelectric, antiferroelectric, and paraelectric order, respectively. For the ferroelectric order, we find that although the MA cations can rotate easily inside the cage,49 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 (∼1 ps). The thermally stable ferroelectric order is consistent with the finding from other ab initio MD simulations.44 In contrast, the antiferroelectric 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 Figure 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 lattice.50 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 Figure 2a. For the ideal lattice, dt = 0, and a larger dt indicates a stronger distortion to the PbI6 cage. As shown in Figure 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− ions.28 This observation is supported by the lowfrequency ( Ed[C] (see Supporting Information). Therefore, the competition between the Stark effect and the Coulomb repulsion would result in a striped charge distribution. Recent experiments have shown that mixed halide perovskite with a small addition of chloride to MAPbI3 resulted in 1 order of magnitude increase in the electron−hole diffusion 23972

DOI: 10.1021/acs.jpcc.6b07800 J. Phys. Chem. C 2016, 120, 23969−23975

Article

The Journal of Physical Chemistry C length.17,18 Two possible mechanisms have been proposed to explain this dramatic increase. First, it was speculated that nonradiative recombination in MAPbI3−xClx was suppressed due to the presence of Cl,17,22,52 the precise underlying mechanism, however, is unknown. Second, some experiments suggested that Cl ions could reduce morphological and energetic disorder of the perovskite crystal, thus enhancing carrier diffusion length.53,54 Here, we focus on the first mechanism and examine whether the incorporation of Cl in MAPbI3 could inhibit the nonradiative recombination. Since only a low percentage (