Organic Lead Iodide

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Rashba-Dresselhaus Effect in Inorganic/ Organic Lead Iodide Perovskite Interfaces Chang Woo Myung, Saqib Javaid, Kwang S. Kim, and Geunsik Lee ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.8b00638 • Publication Date (Web): 07 May 2018 Downloaded from http://pubs.acs.org on May 8, 2018

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ACS Energy Letters

Rashba-Dresselhaus Effect in Inorganic/Organic Lead Iodide Perovskite Interfaces Chang Woo Myung,1 Saqib Javaid,1 Kwang S. Kim1*, Geunsik Lee2* 1

Center for Superfunctional Materials, Department of Chemistry, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Korea. 2 Department of Chemistry, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Korea. Corresponding Author *

Correspondence and requests should be addressed to G.L. (email: [email protected]) or K.S.K. (email: [email protected]). ABSTRACT Despite the imperative importance in solar-cell efficiency, the intriguing phenomena at the interface between perovskite solar-cell and adjacent carrier transfer layers are hardly uncovered. Here we show that PbI2/AI-terminated lead-iodide-perovskite (APbI3; A=Cs+/ methylammonium(MA)) interfaced with the charge transport medium of graphene or TiO2 exhibits the sizable/robust Rashba-Dresselhaus (RD) effect using density-functional-theory and ab initio molecular dynamics (AIMD) simulations above cubic-phase temperature. At the PbI2terminated graphene/CsPbI3(001) interface, ferroelectric distortion towards graphene facilitates an inversion breaking field. At the MAI-terminated TiO2/MAPbI3(001) interface, the enrooted alignment of MA+ towards TiO2 by short-strong hydrogen-bonding and the concomitant PbI3 distortion preserve the RD interactions even above 330K. The robust RD effect at the interface even at high temperatures, unlike in bulk, changes the direct-type band to the indirect-type to suppress recombination of electron and hole, thereby letting these accumulated carriers overcome the potential barrier between perovskite and charge transfer materials, which promotes the solar-cell efficiency. TOC GRAPHICS

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Solar energy is a highly efficient and eco-friendly energy source for future energy harvesting. In recent years, inorganic/organic hybrid halide perovskite solar cells (PSC) based on ABX3 (A = Cs+, CH3NH3+ (MA+), CHN2H4+ (FA+); B = Pb2+; X = Cl-, Br- or I-) have shown rapid progress achieving over 22 % 1 solar cell efficiency which is considered to be most promising large-scale solar energy materials.2 PSC owns many interesting physical properties including giant dielectric screening, 3,4 bottleneck of hot phonon relaxation process,5 excitonic states,6,7 and polaron state.8,9,10,11. Nevertheless, despite explosive discoveries in experiments, theoretical understandings underneath ongoing experiments are hardly made yet particularly regarding the Rashba-Dresselhaus (RD) effect at the interface between PSC and adjacent carrier transfer layers. The spin-orbit coupling (SOC) field, which is odd-in-k (momentum) and time reversal symmetric, in non-centrosymmetric crystals or at the interface of heterostrucures, gives rise to intriguing Rashba-Dresselhaus (RD) splitting. The effective low order perturbation terms of RD interactions are derived according to a given symmetry of the model. The lowest order Hamiltonian12 in k·p is

= + + − , = ,

(1)

where k is momentum, σi = x, y, z is the spin Pauli matrices and the strength of RD interactions is defined by coupling constant αRD (eV·Å). The RD interactions are universal so that many systems such as noncentrosymmetric crystals, heterojunction,13 metal surface,14 and graphene15 show a sizable energy splitting. αRD varies depending on systems ranging from 0.067 eV·Å (InAlAs/InGaAs)16 to 4.0 eV·Å (Bi2Se3).17 Recently, it is realized that PSC materials containing heavy elements like Pb or I show large RD coupling constants: αRD ~ 1.6 eV·Å in 2D PSC


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ACS Energy Letters

(C6H5C2H4NH3)2PbI418 and αRD ~ 2.75-3.75 eV·Å (in the original paper αR is 7-11 with different definition of αRD = 2∆E/∆k) in MAPbBr319 and 3D CsPbBr3 nanocrystal.20 Previous studies on RD splitting in PSCs have focused on an inversion symmetry breaking in bulk phases with an artificial condition such as uniaxial pressure to trigger ferroelectricity in PSC.21 Recent work clarified the importance of the RD effect on 1s exciton state of PSC.22 Meanwhile, an interesting aspect has been realized that dynamical Rashba splitting occurs in both centrosymmetric I4/mcm and non-centrosymmetric I4cm tetragonal phases simulated by Car-Parrinello molecular dynamics.23,24 It has been proposed that on a large scale (> 8 nm3) where the entropy of MA+’s orientations is high, the RD effect might be quenched.24 An application to the spin filter device that makes the spin precess during the propagation in PSC has been proposed using RD interaction. 25 A technological impact is that the RD interaction changes the direct-type band structure to the indirect one to suppress the recombination of carriers and to promote carrier accumulation on the barrier between PSC and charge transfer materials. Although the understanding of interface phenomena in solar cell device is crucial, until now there is no work related to RD interaction at the interface of PSC and other material layers including electron and hole transport materials and the impact of RD interaction on solar cell performance. Graphene is a fascinating material for various applications such as transistors, optoelectronics, nanoelectronics, medical application etc.26 Particularly multi-layer graphene has been proposed as an effective hole transfer material.27 TiO2 is widely used for electron transport layer materials (ETM) because of its transparency, ideal band alignment and synergetic effect with PSC.28,29,30


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In this work, for the first time, we clarify an elusive aspect of PSC heterostructures using the first principles calculations and AIMD simulations accounting for the RD effect. We have carried out the calculations for graphene/cubic-CsPbI3(001) as a prospect interface for improving carrier transport and for TiO2/cubic-MAPbI3(001) as a well-known ETM for PSCs device. Although we observed RD interactions at both interfaces, their mechanisms are different in intriguing ways. At PbI2-terminated Gr/CsPbI3(001), the ferroelectric Pb-I distortion promotes significant Rashba interactions both at 0 K and above 600 K. On the other hand, at MAIterminated TiO2/MAPbI3(001), the direction of organic MA+ is nearly fixed due to strong-short hydrogen bonding (SSHB) 31 , 32 even above 330 K and the concomitant distortion of PbI3 sublattice promote the RD interactions. Here, we show that unlike bulk where high entropic disorder of MA would quench the RD effect, the interfacial RD effect is robust in thermal effects and is beneficial for solar cell efficiency. We constructed an interface of graphene/CsPbI3(001)/graphene modeled by a slab of 10(9) layers of (√2 × √2 × 1) PbI2-(CsI-)terminated cubic CsPbI3 with the lattice mismatch ~ 1.93 % between two systems (Fig. 1a, 1b and 1c). We confirmed that the surface dipole does not affect both the relaxed geometry and the corresponding electronic structure because any pair of a cation and an anion or anions (Pb2+I‒2 or Cs+I‒) either on surface at the termination or along surface-normal direction is oriented anti-parallel to either the surface or the surface-normal direction with respect to neighboring pairs. Furthermore, we adopted a symmetric slab sandwiched by graphene at each end to avoid any unphysical artifact. As reported from a previous LDA+D2 calculation of Gr/tetragonal-MAPbI3,33 we observe a ferroelectric distortion driven by an attraction between graphene and cation Pb2+ in the PbI2-termination. A measured distance between PbI2 layer and graphene (Fig. 1a) is dPBE-D3 ~ 3.21 Å at the PBE+D3 level and


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ACS Energy Letters

dPBE-TS ~ 3.28 Å at the PBE+ Tkatchemko-Scheffler(TS) level of theory (which is smaller than LDA+D2 dLDA-D2 ~ 3.45 Å). As for CsI-termination, a distance between CsI layer and graphene (Fig. 1b) is dPBE-TS ~ 3.4 Å slightly larger than PbI2-terminated surface. Despite the ferroelectric distortion,34 C4v point symmetry of cubic structure is conserved which is manifested as pure Rashba type splitting in contrast to TiO2/MAPbI3 interface that will be discussed later. The displacement directions (Fig. 1d) of both cases are opposite to each other. For PbI2-termination, the displacements are δ(Pb) ~ +0.4 Å and δ(I) ~ -0.6 Å, while for MAI-termination, the displacements are δ(Pb) ~ -0.5 Å and δ(I) ~ +0.6 Å (Fig. 1d). The binding energy (BE) of graphene in PbI2-termination is 20.5 meV/atom, 3.3 times larger than that in CsI-termination (Table 1). The electronic band structure of PbI2-(CsI-)terminated Gr/CsPbI3(001)/Gr with PBE+TS+SOC (Fig. 2) reveal intriguing features. Due to sizable Rashba interactions, in both conduction band (CB) and valence band (VB), surface bands split by momentum ∆k and energy

∆E. For the bulk cubic Pm3m (centrosymmetric) CsPbI3 crystal, strong SOC splits the conduction band into one j = 1/2 doublet and one j = 3/2 quartet. Because the valence band is slike, there is no effective splitting in the highest valence band. 35 However, at the Gr/CsPbI3 interface, we note that s-like valence band at M experiences an asymmetric field with respect to the xy plane and its eigenstate is not s = 1/2 but j = 1/2 being mixed with pz state and other states of adjacent layers. This is manifested in the calculated band structure with non-vanishing Rashba splitting of the surface valence band. In CB, the energy splitting [∆E(PbI2-termination) ~ 280 meV] between = −1/2 and = 1/2 is significant; this large barrier would hinder electrons to overcome the barrier from the CB extremum in order to directly recombine with the VB extremum.36 Effective Hamiltonian (eq. (1)) should preserve | = 1/2 so that the eigenstate of


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Rashba split bands for both CB and VB are spanned by | = 1/2, = ±1/2 . Diagonalization of the Hamiltonian gives an entangled spin-orbital texture which resembles the surface state of topological insulator Bi2Se3 (Fig. S1), “spin-momentum locking”.37 Indeed, a recent experiment confirmed an emergence of spin-orbital chiral nature by observing circularly polarized light.38 An explicit calculation of direct transition amplitude from | = 1/2 conduction band to all valence band states |"| = ∑$%, ,|"$ | (Fig. S2a) shows that a direct band-to-band transition is largely suppressed due to spin-orbit entanglement and 2D confinement of wavefunction with the ferroelectric distortion. We also find that Rashba split band promotes the density of states (Fig. 2c). In Gr/CsPbI3(001)/Gr, a surface or gap state shows a rather peculiar structure than usual semi-conductors in which gap states are mainly composed of surface states. For PbI2termination, while the lowest unoccupied surface state is at the CBM, the highest occupied surface state sits at 1 eV below the VBM. Interestingly, the maximum of VB is composed of bulk state without Rashba splitting due to its centrosymmetry. The surface state shows the opposite trend in CsI-termination. The highest occupied surface state is the VBM, but the lowest unoccupied surface state is 0.5 eV above the CBM. The origin of peculiar energy levels of Gr/CsPbI3(001) can be explained by observing the ferroelectric displacement on CsPbI3 surface. It is found that both CsI- and PbI2-terminated CsPbI3(001) experience an intrinsic ferroelectric displacement resembling the relaxed hetero-interface with graphene (Fig. S3). Compared with unrelaxed and relaxed CsPbI3 slabs, significant energy shifts of surface states are observed (Fig. S4). This natural ferroelectric surface distortion would hint the origin of recent observations of Rashba splitting in CsPbBr3 nanocrystal.20 However, the role of graphene differs at each termination. At PbI2 termination, graphene further promotes the ferroelectric distortion and the


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ACS Energy Letters

resulting αRD is enhanced to 0.42(VB) and 1.17(CB) compared with 0.18(VB) and 1.00(CB) of the pristine slab. At CsI termination, graphene suppresses the ferroelectric distortion (Fig. 1b and Fig. S3b) and the RD effect is comparable or even less (Table 1). The Rashba effect has been shown to exist in bulk MAPbI3: the organic cation MA+ breaks the inversion symmetry and distorts the PbI3 sublattice.24,25 However, this effect could be local due to orientational disorder of MA+ cations which significantly reduces the Rashba interaction parameter (αRD) at the length scale of ~ 3 nm.23,24 Previous work for pristine tetragonal MAPbI3 slab has shown that surface reconstruction could lead to a large RD effect and the effect is more pronounced at PbI2-termination.39 We calculated the band structure of rutile TiO2/MAPbI3 (001) interface for PbI2-(MAI-) termination (Fig. 3a and 3b) and also the pristine cubic MAPbI3 slab for comparison (Fig. S5). Despite that the bare rutile (001) is not stable, this facet is favored in device configuration.40 As reported for tetragonal MAPbI3 slab, αRD of CB and VB in the cubic MAPbI3 slab scales by a factor of 330 K) with small variance. Because of large SOC nature and geometrical complexity of PSCs, its interface with other layers poses rich phenomena. A clever manipulation of such interfaces using this study could accelerate further improvement of the PSC efficiency. Computational Methods We used Vienna Ab initio Simulation Package (VASP) 49 for non-collinear DFT calculations using PBE functional plus Tkatchenko-Scheffler (TS)50 / Grimme DFT-D351 van der Waals correction with inclusion of spin-orbit coupling by switching off any presumed symmetry. Our previous work has shown that GGA+SOC results are consistent with that of higher level but computationally expensive HSE06 52 +SOC calculations. For Gr/CsPbI3(001) system, we used (4 × 4 × 1) kmesh for sampling the BZ and 500 eV for the energy cutoff. As we checked the convergence of band gap with respect to the thickness of CsPbI3 slab, the convergence has been met from 6 cubic CsPbI3 layers. For the TiO2/MAPbI3(001) system, we used (6 × 6 × 1) kmesh with 520 eV energy cutoff. A supercell consists of 11 rutile TiO2 layers and 3 cubic MAPbI3 layers with (001) orientation for both, where the lattice mismatch using TiO2(001)-√2 × √2 is as small as ~ 3 %. A vacuum size of ~ 30 Å is included. We also used Quantum ESPRESSO package v.6.153 with fully relativistic PAW PBE pseudopotential for Pb 6p6s5d, I 5p5s and Cs 6s5p5s at the energy cutoff of 40 Ry. Ab initio MD simulations with time step ∆t = 0.5 fs using Nosé thermostat were performed with total duration of 12 ps and 30 ps at 600 K and 330 K for Gr/CsPbI3 and TiO2/MAPbI3, respectively. We discarded 3 ps for the initialization. ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXX. Spin-orbital texture of graphene/CsPbI3 system, dipole transition amplitudes of graphene/CsPbI3 and TiO2/MAPbI3, relaxed structures of pristine PbI2- and CsIterminated CsPbI3 slabs, band structure of CsPbI3 slab without graphene, relaxed structure of pristine PbI2- and MAI-terminated MAPbI3 slabs. AUTHOR INFORMATION Corresponding Authors * E-mail: [email protected] (G.L.).


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ACS Energy Letters

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E-mail: [email protected] (K.S.K.). Notes Competing financial interests: The authors declare no competing financial interests. ACKNOWLEDGEMENTS C.W.M. conceived the idea, performed DFT and AIMD simulations and analyzed the data. S.J. helped in DFT calculation. All discussed and C.W.M., K.S.K. and G.L. wrote the manuscript. This work was supported by National Honor Scientist Program (2010-0020414) and Basic Science Research Program (2015R1C1A1A01055922) of NRF. Computation was supported by KISTI (KSC-2017-S1-0025, KSC-2017-C3-0081).


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(48) Weller, M. T.; Weber, O. J.; Henry, P. F.; Di Pumpo, A. M.; Hansen, T. C. Complete Structure and Cation Orientation in the Perovskite Photovoltaic Methylammonium Lead Iodide between 100 and 352 K. Chem. Commun. 2015, 51, 4180-4183. (49) Kresse, G.; Furthmuller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors using a Plane-Wave Basis Set. Comput. Mater. Sci., 1996, 6, 15–50. (50) Tkatchenko, A. & Scheffler, M. Accurate Molecular van der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data. Phys. Rev. Lett. 2009, 102, 073005. (51 ) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A. Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (52) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2006, 124, 219906. (53) Giannozzi, P. et al. QUANTUM ESPRESSO: a Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys.: Condens. Matter 2009, 21, 395502.


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ACS Energy Letters

Table 1. Binding energy (BE) and Rashba-Dresselhaus parameter αRD for graphene-, TiO2interfaced cubic perovskite solar cell materials along BZ depending on the terminations, PbI2 and AI where A refers to the A-site cation, Cs+ or MA+. Substrate

Graphene

TiO2

a

Termination

ΒΕ (meV/atom)

Gr/CsPbI3/Gr (PbI2-terminated)

αRD (eV·Å) VB

CB

20.54

0.42 (M-X)

1.17 (Γ Γ-M)

Pristine CsPbI3 (PbI2-terminated)

-

0.18 (Γ Γ-M)

1.00 (Γ Γ-M)

Gr/CsPbI3/Gr (CsI-terminated)

6.23

0.59 (Γ Γ-X)

0.50 (Γ Γ-M)

Pristine CsPbI3 (CsI-terminated)

-

0.53 (Γ Γ-M)

0.54 (Γ Γ-M)

TiO2/MAPbI3 (PbI2-terminated)

15.64

0.08 (M-X)

0.17 (M-X)a

Pristine MAPbI3 (PbI2-terminated)

-

0.78 (M-X)

0.81 (M-X)

TiO2/MAPbI3 (MAI-terminated)

10.33

0.29 (M-X)

0.58 (M-X)

Pristine MAPbI3 (MAI-terminated)

-

0.18 (M-X)

0.30 (M-X)

It is not the conduction band minimum.


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Figure 1. 10 layers of (√2 × √2 × 1) (a) PbI2-terminated and (b) CsI-terminated cubic CsPbI3 for (001) surface sandwiched by graphene (yellow) viewed from [100] after structural relaxation. The number denotes the layer number. Each PbI2 layer undergoes a ferroelectric distortion of Pb (red arrow) and I (green arrow) along [001] direction with its magnitude gradually increasing towards graphene. For the correct description of the system, the bulk region (dashed red box) retained to have the inversion symmetry by surrounding it with 5-6 layers. (c) A unit cell of Gr/CsPbI3(001)-√2 × √2 viewed from [001]. (d) Schematic displacements of Pb and I atoms near surface along [001] direction, denoted as δ(Pb) and δ(I), respectively. Atomic displacements near surface are only significant along [001]. The ferroelectric displacement gradually increases when approaching the interface with its maximum at the very interface. Bulk-like (or inversion symmetric) layers, 5 th and 6 th layers, are crucial for illustrating a reasonable band structure, unless the band gap closes because of ferroelectricity over the whole structure.


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ACS Energy Letters

Figure 2. (a) Electronic band structure of 10(9) layers of PbI2-terminated (CsI-terminated) Gr/CsPbI3(001)/Gr-(1×1) symmetric slab with the contributions from the topmost Pb (red), I (blue) and graphene (green). (b) Magnified 2D band of conduction band | = 1/2, = ±1/2 around Kramer point M of BZ with the energy difference (∆E) between the minimum and the upper band and the momentum change (∆k) between the minimum and M. (c) Density of states in the vicinity of conduction band extremum for Pb p of bulk CsPbI3 (blue) and topmost Pb p (red) of Gr/CsPbI3(001)/Gr.


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Figure 3. The schematics of optimized (a) PbI2-terminated and (b) MAI-terminated TiO2/cubic MAPbI3(001) interface. Presence of PbO and TiI bonding in PbI2 termination and SSHB in MAItermination are highlighted by connecting lines of Pb(light red)-O(red) atoms (~ 2.44 Å), Ti(light blue)-I(purple) atoms (~ 2.90 Å) and H(light blue)-O(red) atoms (~ 1.47 Å). (c) Band structure for optimized TiO2/MAPbI3(001) interface calculated with PBE+TS+SOC. The blue(red) circles indicate the contribution of the surface I(Pb) interfaced to TiO2 layer.


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ACS Energy Letters

Figure 4. Schematic of electron transfer process with and without Rashba-Dresselhaus Effect at the interface between perovskite solar cell and ETM. (a) Without the RD effect, the large potential barrier between PSC and ETM cannot be overcome by a rapid electron(red dot)hole(white dot) pair recombination process. (b) With the RD effect, long lifetime of the electronhole pair contributes to the accumulation of electrons to overcome the barrier.


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Organic Lead Iodide

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