Rashba Band Splitting in Organohalide Lead Perovskites: Bulk and

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Rashba Band Splitting in Organohalide Lead Perovskites: Bulk and Surface Effects Edoardo Mosconi, Thibaud Etienne, and Filippo De Angelis J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 03 May 2017 Downloaded from http://pubs.acs.org on May 4, 2017

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The Journal of Physical Chemistry Letters

Rashba Band Splitting in Organohalide Lead Perovskites: Bulk and Surface Effects

Edoardo Mosconi,a,b Thibaud Etienne, a,c Filippo De Angelis a,b *

a

Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, via Elce di

Sotto, I-06123, Perugia, Italy. b

CompuNet, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy.

c

Institut Charles Gerhardt - CNRS and Université de Montpellier, Place Eugène Bataillon - 34095

Montpellier, France.

E-mail: [email protected]

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Abstract A Rashba/Dresselhaus band splitting has been recently measured in organohalide perovskites and invoked in various experiments as a possible cause for the reduced electron-hole recombination rates observed in this class of materials. In this perspective we discuss the interplay of electronic and nuclear degrees of freedom in defining such an effect in realistic methylammonium lead iodide (MAPbI3) models. We distinguish between bulk and surface effects and find that while a spatially local (in time and space) effect may be at work in the bulk, a “static” band-splitting effect is found at surfaces due to structural distortion. The proposed surface effect is consistent with the low surface recombination reported for MAPbI3 single crystals and might contribute to the success of organohalide perovskites.


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Organohalide perovskites are dominating the landscape of emerging photovoltaic technologies.1-10 This class of materials exhibits a combination of physical properties which are hard to find even in well established inorganic semiconductors, including their optical11-14 and charge generation and transfer properties,9-10 the long carrier lifetimes15-17 and their sizable mobility.17-18 Having photovoltaic devices as a main applicative target, the most attractive property of organohalide lead perovskites is the low recombination rate of photogenerated carriers, which implies long diffusion length and allows efficient extraction of charge carriers even with modest mobility in polycrystalline films, thus high currents and voltages in optimized devices. On the one hand, it has been reported that methylammonium lead iodide (MAPbI3) and related compounds are generally defect-tolerant, thus scattering at defects or impurities does not severely limit the carrier lifetime and diffusion length, opposite to what found in typical semiconductors.

19-25,27-28

Keeping defect

tolerance in mind, it is then clear that the reasons behind the reduced carrier recombination rate in MAPbI326 are an inherent material property related to the combination of the constituent materials, i.e. lead, iodine (or different halide combinations) and the A-site cations. The presence of mobile dipolar organic cations has been related to the charge separation efficiency, by virtue of an exciton screening mechanism27 or by creating local screening domains,23, 28 although alloying of different cations, including the inorganic (spherical) caesium ion, has been shown to improve the solar cells efficiency.29 The presence of lead and to some extent of iodine imparts the material a giant spinorbit coupling (SOC),30 which dictates many materials properties, including band-gap variation in tin and lead perovskites,31 modulation of the band-gap with distortions from the cubic symmetry32 and the reduction of the carrier effective masses.33 SOC could be related to the observed spindependent charge recombination and spin-polarized carrier dynamics in MAPbI3,34-35 opening the way to spintronics based on organohalide perovskites.



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A property intimately connected to SOC is the so-called Rashba/Dresselhaus effect, which has received considerable attention from a theoretical point of view.31-36 This effect16, 37-39 is the consequence of the breaking of inversion symmetry in the crystal in a direction orthogonal to a k-point sampling plane, and it is described by the so-called Bychkov-Rashba Hamiltonian:

where we find the Rashba primary correlation factor ߙ’, the electrostatic potential V, the linear momentum ‫( ∥ܘ‬defining the momentum space sampling, which is orthogonal to the gradient vector), the Pauli spin matrices σ and the gradient operator (સୄ ). Re-writing the Hamiltonian as:

the electric field projection can be included into the general Rashba interaction coefficient, hereafter ߙ.

The eigenvalues difference (ߝ ஷ ) at a particular k-point (∆k) sets the ߙ value:

±∆k points the respective position of the two ߝ± wells vertices for energy curves crossing at the k origin, and ߝ ஷ is defining the difference between the two energy curves at the vertex positions, see Scheme 1 for a definition of relevant parameters.


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Scheme 1. Schematic representation of Rashba splitting for parabolic bands, along with relevant interaction parameters, see text for definitions. The valence and conduction bands (VB and CB) in the presence (absence) of Rashba splitting are the solid red and blue (dashed) lines, respectively. The shifted absorption and radiative recombination processes are also illustrated.

A single (parabolic) band will split into two bands by virtue of the Rashba effect, which are separated in k-space by ∆k and in energy by ε≠. The Rashba effect is intimately connected to the presence of heavy nuclei and to the presence of internal electric fields such as those due to the presence of polar (ferroelectric) structures. In MAPbI3 the valence (conduction) bands (VB and CB in Scheme 1) are mainly contributed by iodine (lead) and thus they undergo a different band 5 Environment ACS Paragon Plus


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splitting, by virtue of the different SOC characterizing lead and iodine. This introduces a different splitting for the VB and CB, Scheme 1. The connection to recombination in a perovskite solar cell is then clear: as the photogenerated carriers thermalize at the band extrema which are located at different points in k-space, radiative recombination, which preserves k, will be quenched as in an indirect band-gap semiconductor. In MAPbI3 and in organohalide perovskites in general the VB and CB usually have different curvature, thus a different density of states, and spin helicity, which would further slow down recombination.16 While this band-splitting mechanism is an elegant framework that has gained considerable attention in the literature, it requires in principle a non-centrosymmetric crystal or a local-site symmetry breaking.40 Considering the I4/mcm space group of MAPbI3 it is likely that the material does not exhibit a macroscopic polarization at room temperature,41 though it could show an observable ferroelectric behaviour at lower temperature, i.e. just above the transition to the orthorhombic phase.42,43 This would in principle prevent the Rashba mechanism to be operative at room temperature, unless polar inclusions in polycrystalline samples are considered.44 Rappe and co-workers have however put forward the hypothesis that structural fluctuations, possibly accessible at room temperature, may give rise to local electric fields extending beyond the characteristic Rashba length scale (1-2 nm),16 thus not requiring the presence of macroscopic lack of inversion symmetry for this effect to be operative. We previously reported on the temporal and spatial scale of this “dynamical Rashba effect” in bulk MAPbI3,45 by means of Car-Parrinello Molecular Dynamics (CPMD),46-47 finding that even in a globally centrosymmetric structure, Figure 1a-b, the coupled inorganic/organic degrees of freedom evolution gives rise to a Rashba splitting which fluctuates on sub-ps time scale, Figure 1c-d. A similar effect was reported by Azarhoosh et al.48 The time average of this local Rashba effect is non zero on the investigated ∼2 ps time scale, longer than the expected time scale of electronic transitions, Figure 1c-d. This effect is however progressively quenched in globally centrosymmetric structures on increasing the probed


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spatial scale from 1 to 4 formula units both in polar and apolar structures,45 compare the magnitude of the effect in Figure 1c and 1d. For the entire (initially apolar) 2x2x2 system a single band structure calculation carried out an a randomly selected structure from the dynamics delivers α values of ∼ 2 and ∼1 for the CB and VB, suggesting the persistence of the local Rashba effect up to this spatial scale.45 Notice that the data for the smaller sub-systems are purely indicative and are reasonably exaggerated since periodicity was enforced a posteriori for these sub-systems.

Figure 1. a-b) Structural models of MAPbI3viewed along the [001], a), and [110], b), directions. The native 2x2x2 supercell is enclosed by blue lines, while the reduced systems employed to sample different space scales are enclosed by green (4 formula units) and red (1 formula unit) lines. The notation 1-apolar/polar and 4-apolar/polar in c) and d) refers to globally polar and apolar



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structures, respectively, made by 1 and 4 MAPbI3 units, in relation to the starting orientation of the methylammonium cations, whose dipoles are schematically represented by the arrows in panel b). The dashed lines in c) and d) represent the α time average, with values of 6.2-9.6 eV Å (c) and 2.72.4 eV Å (d), blue and red dashed lines, respectively. The φ dihedral angle discussed in Figure 2 is illustrated schematically.

From an experimental standpoint we are aware of a few studies which have directly or indirectly probed or invoked a Rashba effect to explain the observed phenomenology. Niesner et al. have directly observed a “giant Rashba splitting” in MAPbBr3 using angle-resolved photoelectron spectroscopy.49 They found a ring-shaped valence band and circular dichroism due to SOC in the low-temperature orthorhombic phase, which was maintained also in the high temperature cubic phase. A high α value of ∼10 eVÅ was reported for both phases, comparable to the highest values we found in our simulated dynamical Rashba effect for MAPbI3, see Figure 1c-d. Notably, these measurements are likely surface sensitive and probe a large fraction of the sample. Hutter et al. have reported time-resolved photo-conductance measurements showing that generation of free mobile charges is maximized for excitation energies just above what appears as an indirect band-gap, possibly related to the Rashba band splitting, Scheme 1.50 The employed microwave conductivity technique should probe photogenerated charge carriers in fairly small volumes, depending on the carrier mobility, though the signal is obtained from the entire sample. Wang et al. also suggested the presence of an indirect band-gap in MAPbI3 which they attributed to Rashba band splitting.51 Under hydrostatic pressure the Rashba splitting would be reduced due to a pressure-induced reduction in local electric field around the lead atom. Associated to this change, an increased carrier recombination and radiative efficiency was measured, consistent with the removal of the indirect band-gap. In this case, the optical measurements supposedly probe


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the entire material volume, with some possible surface sensitivity due to the strong perovskite absorption coefficient limiting the light penetration depth. At the current stage of research, a question likely arises: Assuming a perfectly crystalline environment with no defects or other imperfections, are the experiments above probing an inhomogeneity in the sample due to local (time-dependent) distortions, or are they probing the sample surface, or a combination of the two? In other words, is the proposed Rashba effect an intrinsic bulk (but local) material property that can be measured or are the sample surfaces “interfering” with the possible observation of a bulk effect? Since the effect of surfaces on the Rashba effect in organohalide perovskites has not to our knowledge been reported, here we simulate two prototypical MAPbI3 (001) surfaces characterized by MAI- and PbI2-terminations, see Figure 2a and 2d, respectively, likely representing MAPbI3 surfaces when the material is grown in MAI-rich or PbI2-rich conditions.52 Our models are based on a 2x2x2 slab of the tetragonal unit cell with four layers of MA cations,53 with a starting apolar arrangement of the organic cations originated from the bulk structures of Figure 1. To simulate the investigated systems under thermal conditions we performed CPMD simulations on both slabs, setting the temperature at 330 ± 20 K.



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Figure 2. a) - d). Optimized structures of the MAI-terminated and PbI2-terminated model slabs. b) e). Distribution of the angles formed between the methylammonium C-N axis and the perovskite ab plane during the CPMD simulation, see Figure 1 for the definition of the angle, for the bare MAIand PbI2-terminated MAPbI3 slabs. e) - f) SOC-DFT band structures calculated on the optimized structures of the MAI-terminated and PbI2-terminated slabs. The inset on the left side of panel c) represents the tetragonal Brillouin zone with labels of the high symmetry points. The inset on the right side of panel c) shows the calculated VB structure for the PbI2-terminated slab after cutting the capping PbI2 layers, i.e. for the system enclosed by the dashed lines in panel d) without further geometrical optimization.


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An interesting parameter describing the impact of surfaces and of surface termination on the systems’ structure is the average arrangement of the organic cations, Figures 2b and 2e. As it can be noticed the organic cations in the outermost layers show a different orientation than those in the inner layers (bulk-like) in both MAI- and PbI2-terminated surfaces. This surface effect only marginally affects the inorganic sub-lattice in MAI-terminated slab, with almost perfectly preserved PbI6 octahedra, Figure 2a, while a pyramidalization of the outermost lead atoms is observed in the PbI2-terminated surface, Figure 2d. The band structure for the two slabs calculated by SOC-DFT on the optimized geometry obtained by the average dynamical structure reflects this geometrical difference, showing a larger Rashba splitting for the PbI2- than for the MAI-terminated slab, Figures 2f and 2c, respectively, despite the latter shows a stronger preferential orientation of the outermost MA cations. Notice the typical underestimate of the band-gap typical of SOC-DFT in both cases, with the PbI2-terminated slab showing a band-gap comparable to that of the bulk at the same level of theory.31 As in bulk MAPbI3, the largest Rashba splitting is observed along the Γ→X and Γ→M directions, see inset of Figure 2c for a representation of the tetragonal Brillouin zone. As expected, the bands are flat (and not split) along the Γ→Z direction, corresponding to the direction of surface truncation. A notable difference between the investigated slabs and the bulk is the comparable Rashba effect on the VB and CB in the former, while in the bulk the CB exhibits ca. a factor 2 larger splitting than the VB, due to the dominant lead contribution to the CB.45 This fairly large Rashba effect on the VB (∼2 eVÅ) calculated for the PbI2-terminated slab is smaller albeit of the same magnitude to that observed for MAPbBr349 and it clearly indicates that structural distortion due to surface termination may be responsible of a sizable fraction of the observed effect, especially when surface-sensitive techniques are employed. We cannot exclude that even higher effects could be observed for less ideal surfaces than the ones considered here, such as those predicted by Haruyama et al. characterized by partial loss of PbI2 units.54 We also investigated the effect of



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removing the PbI2-capping layers from the PbI2-terminated slab, see right inset of Figure 2c, finding a splitting which is ca. a factor 2 larger than in the MAI-terminated case, having the same composition but different structure. This suggests that the PbI2-surface termination introduces structural distortions which are propagated to the inner layers. In summary, we have shown how surfaces will likely play a role in defining a bandsplitting effect in organohalide perovskites, possibly related to a Rashba/Dresselhaus effect. The bulk effect is likely a local (in space and time) effect which could play a role in diminishing electron-hole recombination and thus boost the solar cell efficiency. We believe, however, that this effect will be difficult to probe with conventional techniques, while it could be explored by microwave-conductivity experiments, which could locally probe the photogenerated charge carriers. On the other hand, the reported surface band-splitting is consistent with the low surface recombination reported MAPbI3 single crystals,55 ∼2–3 orders of magnitude lower than that in conventional (unpassivated) semiconductors employed in solar cells,55 and might be a key contribution to the success of organohalide perovskites.


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Methods. For all calculations the experimental cell parameters reported by Poglitsch and Weber56 have been used. Geometry optimization and CPMD simulations have been carried out with the Quantum Espresso package57 along with the GGA-PBE58 functional. Electron-ion interactions were described by scalar relativistic ultrasoft pseudopotentials with electrons from N and C 2s, 2p; H 1s; I 5s, 5p; Pb 6s, 6p, 5d shells explicitly included in the calculations. Plane-wave basis set cutoffs for the smooth part of the wave functions and the augmented density were 25 and 200 Ry, respectively. CPMD simulations of the bulk have been performed with an integration time step of 5 au, for a total simulation time of ca. 12 ps after a few ps of thermal equilibration. The fictitious mass used for the electronic degrees of freedom is 500 au, and we set the atomic masses to their real values except for hydrogen atoms, for which the deuterium mass is used. CPMD simulations on perovskite slabs were performed with an integration time step of 10 au, fictitious mass for the electronic degrees of freedom 1000 au and atomic masses set to an identical values of 5 amu to enhance the dynamical sampling. Initial ion position randomization has been used to reach a temperature of ∼350 K, without further applying any thermostat. The electronic structure analysis has been carried out on the optimized geometries using the PWscf code with Plane-wave basis set cutoffs for the smooth part of the wave functions and the augmented density were 25 and 200 Ry. Spin-orbit coupling has been included using ultrasoft PBE-GGA pseudo potentials. References (1) 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. (2) Im, J.-H.; Lee, C.-R.; Lee, J.-W.; Park, S.-W.; Park, N.-G. 6.5% efficient perovskite quantum-dot-sensitized solar cell. Nanoscale 2011, 3, 4088-4093. (3) Etgar, L.; Gao, P.; Xue, Z.; Peng, Q.; Chandiran, A. K.; Liu, B.; Nazeeruddin, M. K.; Grätzel, M. Mesoscopic CH3NH3PbI3/TiO2 Heterojunction Solar Cells. J. Am. Chem. Soc. 2012, 134, 17396-17399. (4) Burschka, J.; Pellet, N.; Moon, S.-J.; Humphry-Baker, R.; Gao, P.; Nazeeruddin, M. K.; Gratzel, M. Sequential deposition as a route to high-performance perovskitesensitized solar cells. Nature 2013, 499, 316-319. (5) Heo, J. H.; Im, S. H.; Noh, J. H.; Mandal, T. N.; Lim, C.-S.; Chang, J. A.; Lee, Y. H.; Kim, H.-j.; Sarkar, A.; NazeeruddinMd, K., et al. Efficient inorganic-organic



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Rashba Band Splitting in Organohalide Lead Perovskites: Bulk and

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