Effects of SpinâOrbit Coupling on Nonequilibrium Quantum Transport

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Effects of Spin-Orbit Coupling on Nonequilibrium Quantum Transport Properties of Hybrid Halide Perovskites Ya-Qing Liu, Hong-Liang Cui, and Dongshan Wei J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11407 • Publication Date (Web): 13 Feb 2018 Downloaded from http://pubs.acs.org on February 13, 2018

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The Journal of Physical Chemistry

Effects of Spin-Orbit Coupling on Nonequilibrium Quantum Transport Properties of Hybrid Halide Perovskites Ya-Qing Liu,† Hong-Liang Cui,*,†, ‡ and Dongshan Wei*,‡,§ †

College of Instrumentation & Electrical Engineering, Jilin University, Changchun, Jilin 130061, China ‡

Chongqing Key Laboratory of Multi-Scale Manufacturing Technology, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, 400714, China §

School of Electronic Engineering, Dongguan University of Technology, Dongguan, Guangdong, 523808, China

Corresponding Author Hong-Liang Cui, [email protected]. Dongshan Wei, [email protected].

ACS Paragon Plus Environment

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ABSTRACT: The ground-state properties of organic-inorganic hybrid halide perovskites (OHHP) are significantly affected by spin-orbit coupling (SOC). In this paper, we report on an investigation of the nonequilibrium quantum transport properties of MAPbI3 (MA = CH3 NH3 ), considering the cases of noncollinear spin polarization including SOC, noncollinear spin polarization excluding SOC, and no spin polarization, using Keldysh non-equilibrium Green’s function formalism combined with density functional theory calculations. Our results indicate that the enhancement of nonequilibrium quantum transport properties is largely determined by SOC. The calculated current density for noncollinear spin polarization including SOC is about one order of magnitude higher than that for no spin polarization, resulting from the increase of nonequilibrium transmission coefficient in the bias window and the increase of electron density in the conduction band contributed by the p-state of Pb . The results demonstrate that SOC is essential for understanding the nonequilibrium quantum transport properties of OHHP-based devices.


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■ INTRODUCTION Organic-inorganic hybrid halide perovskites (OHHP) with the chemical formula ABX3 ( A = NH3 + , CH3 NH3 + , HC(NH2 )+ ; B = Pb2+ , Sn2+ ; X = I− , Br − , Cl− ) have recently attracted enormous attention as photovoltaic materials due to their low fabrication cost and high solar-toelectrical power conversion efficiency (PCE).1-7 The PCE of OHHP-based solar cells has rapidly increased from 3.8% to a certified value of 22.1% in just a few short years,8-11 mainly attributable to the exceptionally long carrier diffusion length,3,

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which, together with additional unique

properties of OHHP, such as small effective masses for electrons and holes, tunable band gaps, and high optical absorption, has made this family of materials one of the most promising candidates for replacing the first- and the second-generation photovoltaics. Owing to these novel characteristics, they have also been used in other OHHP-based devices, such as light emitting diodes,13-16 photodetectors,13, 17 nanolasers,13-14, 18-19 and field-effect transistors.20-21 There have been a multitude of experimental and theoretical studies reported on OHHP.22-43 The theoretical works mostly focused on ground-state properties of OHHP, such as crystalline structure,33-36 electronic structure,33,

37-38

optical properties,33,

39

defects,33,

40-41

and ionic

transport,34, 42-43 using density functional theory (DFT). Most of these theoretical calculations produced reasonable results, consistent with experimental data.33, 35, 37, 39 In particular, it was predicted that spin-orbit coupling (SOC) related to heavy elements such as Pb has a remarkable impact on the ground-state electronic structure of OHHP, leading to a decrease in band gap by about 1 eV.33, 44-47 On the other hand, SOC was deemed insignificant in equilibrium transport properties, as discussed in the transmission spectrum without bias voltage.48 However, the mechanism through which SOC affects nonequilibrium quantum transport properties is still unclear, which may offer a more insightful understanding of the high performance of OHHP-based


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solar cells. An OHHP photovoltaic device features a very thin active layer (a few tens nanometers), leading to a strong internal electric field even at moderate bias voltage. Such a device when operated under the condition of high carrier densities, and concurrently high current density, puts the system firmly in the realm of nonequilibrium, highly nonlinear, hot-carrier transport. Thus, to extract such important transport parameters as carrier lifetimes, diffusion constants, conductivity, etc., requires a correspondingly sophisticated theoretical model. To provide such a model and shed light on the issues raised above, we consider MAPbI3 (MA = CH3 NH3 ) which typifies this class of materials, constructing a two-probe transport model where two metallic electrodes sandwich the active MAPbI3 layer. Employing the Keldysh nonequilibrium Green’s function formalism (NEGF), combined with DFT (NEGF-DFT) calculations, we investigate the SOC effects on the nonequilibrium quantum transport properties of MAPbI3 based devices. As is known, MAPbI3 can function as a light absorber and a carrier transport layer in OHHP-based solar cells, so much so that the devices composed of MAPbI3 do not need any more additional transport layers.49 Here, we calculate the nonequilibrium quantum transport properties of MAPbI3 in three cases: noncollinear spin polarization including SOC (NCSP+SOC), noncollinear spin polarization excluding SOC (NCSP-SOC), and no spin polarization (NSP). We find that the calculated current density for NCSP+SOC is about one order of magnitude higher than that for NSP, while the current density for NCSP-SOC is equal to that for NSP. The calculated results indicate that the enhancement of nonequilibrium transport properties is caused by SOC, which results from the increase of the nonequilibrium transmission coefficient in the bias window, and the increase of electron population in the conduction band contributed by the p-state of Pb. Our results demonstrate that SOC must be included in studying nonequilibrium quantum transport properties of MAPbI3 -based devices to properly account for their behavior.


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■ COMPUTATIONAL DETAILS The model (Figure 1) consists of three sections: the central scattering region, the left and right electrodes. The device is periodic in the 𝑥 and 𝑦 directions, while electrons and holes transport along the 𝑧 direction. The two electrodes composed of silver atoms are semi-infinite structures and extend along the transport direction to 𝑧 = ±∞ where the bias voltage 𝑉𝑏 is applied and the current is collected. The central scattering region consists of six units of MAPbI3 and a few layers of electrodes that act as buffer layers to ensure that the Hartree potential and charge density automatically match at the interfaces between the central scattering region and the electrodes where MAPbI3 contacts with Ag (100). Moreover, since the grain boundaries are electrically benign in MAPbI3 , and dominant intrinsic defects are of the shallow-level variety which cannot become nonradiative recombination centers and trap carriers, the device is valid and can be used to explore the impact of SOC on the nonequilibrium quantum transport properties of MAPbI3 .50

Figure 1. Schematic quantum transport structure of the two-probe Ag-MAPbI3 -Ag device. The geometric structural parameters are initially optimized, including the unit of MAPbI3 , the distance between buffer layers and MAPbI3 , and the distance between adjacent layers of electrodes (Figure S1a-c), using DFT with VASP code.51 The Perdew-Burke-Ernzernhof (PBE) is applied to the exchange-correlation functional and the plane-wave cutoff energy is set to 500 eV.52 For optimization of the unit of MAPbI3 , a 6 × 6 × 6 k-point grid centered at the Γ point of the


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Brillouin zone is used. A 6 × 6 × 1 k-point mesh is used and the atoms of MAPbI3 are kept fixed while optimizing the distance of Ag-MAPbI3 . The van der Waals (vdW) dispersion interactions based on Grimme’s DFT-D2 method are considered during optimization.53 The calculated lattice constant of MAPbI3 is 6.310 Å, which is in good agreement with the experimental value of 6.313 Å (Figure S1a).54 In terms of the minimum of the total energy, the optimized distance of AgMAPbI3 is calculated to be 2.882 Å (Figure S1b), and the lattice-mismatch ratio is 7.236%. Owing to the extension of Ag in the 𝑥, 𝑦 directions, the distance between adjacent layers of Ag is found to be 1.826 Å (Figure S1c). Next, the nonequilibrium quantum transport properties are calculated using NEGF-DFT, as implemented in the Nanodcal package, using basis of linear combination of atomic orbitals (LCAO).55-56 The real-space NEGF-DFT method is used to calculate the nonequilibrium density matrix to diagonalize the Hamiltonian and determine the electronic structure of the system. In the NEGF-DFT self-consistent calculations, PBE is employed to describe the exchange-correlation potential and the electron orbitals adopt double-zeta-polarized (DZP) basis set for all atoms as wavefunction basis. The cutoff energy for the real-space grid is set to 100 Hartree and a 6 × 6 × 1 k-points mesh is used in the Brillouin zone. The convergence criteria for the Hamiltonian matrix, density matrix, total energy, and the band structure energy are set to 10−5 eV. Electron-electron interaction is the primary mechanism in the quantum transport model considered here, while electron-phonon interactions are ignored. Thus the present calculation should produce results that fully reflect the high-carrier density aspects of devices based on OHHP materials. ■ RESULTS AND DISCUSSION To make sure the device operates normally and to check whether the number of buffer layers is adequate, we calculate the potential drop in the central scattering region of MAPbI3 -based


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quantum transport device for NCSP+SOC, NCSP-SOC, and NSP at the bias voltage 𝑉𝑏 = 0.4 V (Figure 2). Along the 𝑧 direction, from 0 to 0.730 nm and from 5.093 to 6.189 nm represent the regions of the buffer layers on the left and right, respectively, and in-between them lies the central scattering region. We find that the potential drop of the buffer layers in all cases is almost unchanged, which means that the screening effect of the buffer layers is active and the applied bias voltages from 0.2 to 1.0 V do not significantly affect the performance of the device (Figure S2a, b). Moreover, the potential drop for NCSP-SOC is coincident with that for NSP, which indicates that the effects for NCSP-SOC on the potential drop is negligible. It is interesting to note that the main distinction between NCSP+SOC and NSP is in the central scattering region. The slope of the potential drop for NCSP-SOC and NSP is nearly constant while it decreases continually for NCSP+SOC along the 𝑧 direction. It means that SOC changes the potential distribution of the central scattering region.

Figure 2. Potential drop across the central scattering region of MAPbI3 -based quantum transport device for NCSP+SOC, NCSP-SOC, and NSP at bias voltage 𝑉𝑏 = 0.4 V. To analyze the significant impact of SOC on nonequilibrium transport properties of MAPbI3 systematically, the effects of SOC on the equilibrium properties of MAPbI3 are first investigated. We calculate the band structures of MAPbI3 for NCSP+SOC and NSP (Figure 3a). We note that


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MAPbI3 has a direct band gap of 1.621 eV at the R-point of the Brillouin zone without SOC interaction, while the electronic population at energies close to the Fermi level changes and the band gap becomes 0.469 eV when the SOC effect is included, which results from the energy splitting of the conduction band minimum (CBM) and valence band maximum (VBM) caused by SOC interaction. The CBM for NCSP+SOC is closer to the Fermi energy resulting in more conduction electrons at the CBM. The results are in accord with previous reports,33, 44-47 indicating that the contribution of SOC interaction to electronic properties of MAPbI3 is significant and should not be consciously neglected.

Figure 3. Band structures (a) for NCSP+SOC (blue line) and NSP (red line). Projected density of states of MAPbI3 for NCSP+SOC (b) and NSP (c). Moreover, we present the projected density of states (PDOS) for the p-states of Pb atoms, I atoms and the total MAPbI3 in the central scattering region for NCSP+SOC (Figure 3b) and NSP (Figure 3c). The contributions of Pb and I atoms at s- and d- states to PDOS are shown in Figure S3. The PDOS shows that the VBM is contributed predominantly from the p-state of I, whereas the CBM is contributed from the p-state of Pb and p-state of I. Associated with the calculated band structure, the electrons in the CBM mainly come from the p-state of Pb.


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Figure 4. Average differential distribution of real-space electron density between NCSP+SOC and NSP along the 𝑥 and 𝑧 directions at 𝑉𝑏 = 0 V (a), and the average differential distribution of realspace electron density between NCSP+SOC and NSP at 𝑉𝑏 = 0.4 V relative to the 𝑉𝑏 = 0 V case (b). In addition, we calculate the average differential distribution of real-space electron density between NCSP+SOC and NSP along the 𝑥 and 𝑧 directions without bias voltage (Figure 4a). Obviously, the electron density for NCSP+SOC is richer in composition from the s-state of Pb than that for NSP, while it is lower in p-state of I, indicating that the VBM for NCSP+SOC has more electrons and the CBM has fewer compared to those for NSP in the equilibrium state. Figure 4b shows the differential distribution of real-space electron density between the following two cases. One case is the average differential distribution of real-space electron density between 𝑉𝑏 = 0.4 V and 𝑉𝑏 = 0 V for NCSP+SOC, and the other is the average differential distribution of realspace electron density between 𝑉𝑏 = 0.4 V and 𝑉𝑏 = 0 V for NSP. The electron density in the first case is comparable to that in the second case in p-state of I, nevertheless, it is more in p-state of Pb. Combined with the calculated band structure and PDOS, the higher electron density of p-state of Pb might result from the lower conduction band edge at the R-point caused by the inclusion of


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SOC. Our results imply that SOC leads to the increase of electrons in the conduction band of the nonequilibrium state and it is the origin of the enhancement of nonequilibrium quantum transport properties of MAPbI3 .

Figure 5. Transmission coefficient (unnormalized) for MAPbI3 -based quantum transport device as a function of electron energy for NCSP+SOC and NSP at different bias voltages 𝑉𝑏 = 0 V (a), 𝑉𝑏 = 0.4 V (b), and 𝑉𝑏 = 1.0 V (c), and current density for NCSP+SOC, NSP, and experimental values from Ref. 58 (d). The bias window in each panel is between the two green vertical dasheddotted lines, and the Fermi level is at the energy zero. Blue solid circles and red solid squares are data for NCSP+SOC and NSP, respectively. We then analyze the transmission coefficient for NCSP+SOC and NSP as a function of electron energy at bias voltages 𝑉𝑏 = 0, 0.4, and 1.0 V (Figure 5a-c). To ensure the accuracy of the calculated transmission coefficient while managing a reasonable computational time, we use a 100 × 100 × 1 k-points mesh for the electron energy range from -1 to 1 eV, and a 60 × 60 × 1 kpoints mesh for the remaining ranges of electron energy. The zero bias transmission coefficients for NCSP+SOC and NSP are also consistent with the assertion that the band gap decreases with the inclusion of the SOC interaction, even though the magnitude of the reduction cannot be easily


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quantified with the transmission data alone, which is in accord with the previous reports and our calculated band structure.33,

44-47

In addition, the zero bias transmissions coefficient for

NCSP+SOC and NSP are comparable for the given electron energies, while the nonequilibrium transmission coefficient for NCSP+SOC and NSP decreases and shifts left as the bias voltage increases. Moreover, the nonequilibrium transmission coefficient for NCSP+SOC is larger than that for NSP in the bias window at all two bias voltages (see insets of Figure 5b, c), which is crucial for determining the nonequilibrium quantum transport properties. Our results imply that SOC can enhance the probability of the electrons transferring from the left electrode to the right one under an applied bias voltage. The nonequilibrium quantum transport properties are closely related to the bias window [− 𝑉𝑏 ⁄2, 𝑉𝑏 ⁄2], where the current can be obtained by integrating the transmission coefficient over the bias window.57 Here, we calculate the current density for NCSP+SOC and NSP versus the bias voltage from 0.2 to 1.0 V (Figure 5d). The current density goes up with increasing voltages for both NCSP+SOC and NSP. Note however, the current density for NCSP+SOC is nearly one order of magnitude higher than that for NSP at the same bias voltage. In addition, we also calculate the current density for NCSP-SOC at bias voltage 𝑉𝑏 = 0.4 V to evaluate the effect for NCSP. We find that the current density for NCSP-SOC is identical to that for NSP, indicating that the increase of current density is contributed by SOC. Experimental data for the Au-MAPbI3 -Au system from 0.2 to 1.0 V are also presented for comparison in Figure 5d,58 where we note that the current density values for NCSP+SOC are much closer to the experimental data, implying that it is essential to consider the effect of SOC when calculating the nonequilibrium quantum transport properties of devices composed of heavy atoms. The small discrepance between the present calculation for


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NCSP+SOC and experimental measurement may come from the differences in device geometry, and the neglect of electron-phonon interactions in our calculations. We consider that electron-electron interactions contribute to the elastic transport properties in our calculation. However, thermal effect is one of the important factors to affect the electronic structures, which is closely related to the inelastic transport properties of devices, and electronphonon interactions should be considered in the calculation. To date there have been few reports on thermal effects, on this class of devices, particularly ones including spin polarization concurrently. Li et al.59 combined non-equilibrium Green's function and density functional theory to investigate the inelastic transport properties of graphene nanoribbons with collinear spin polarization. Their results showed that phonons with lower vibration energy may have more possibilities to contribute thermally-driven inelastic currents, and the inelastic processes may contribute approximately twice the elastic current. In addition, Markussen et al.60 combined Green's function based transport calculations and molecular dynamics (MD) to obtain a temperature dependent transmission and evaluated the mobility of a bulk system and onedimensional systems without spin polarization. The results were in good agreement with the values obtain by Boltzmann transport equation and experimental data. The thermal effects on SOC in the calculation of nonequilibrium quantum transport properties will be an interesting topic in future research along these lines. ■ CONCLUSIONS We construct a two-probe transport model device where two sliver electrodes sandwich an active MAPbI3 layer to investigate the impact of SOC on nonequilibrium quantum transport properties of MAPbI3 using the NEGF-DFT approach. To carefully analyze the impact of SOC, we consider the scenarios of NCSP+SOC, NCSP-SOC, and NSP individually. We find that the effect of NCSP-


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SOC is negligible compared to the case without spin polarization, which indicates that the enhancement of nonequilibrium quantum transport properties is only determined by SOC. The calculated current density for NCSP+SOC is about one order of magnitude higher than that for NSP, resulting from the increase of nonequilibrium transmission coefficient in the bias window, and the increase of electron density in the conduction band contributed by the p-state of Pb. Our results demonstrate that SOC is a key factor in a theoretical understanding of the nonequilibrium transport properties of MAPbI3 -based devices, and as such, it should be included in future device design considerations based on this and similar families of materials.


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■ ASSOCIATED CONTENT Supporting Information 

Optimized structures and results of the 𝐂𝐇𝟑 𝐍𝐇𝟑 𝐏𝐛𝐈𝟑 , 𝐂𝐇𝟑 𝐍𝐇𝟑 𝐏𝐛𝐈𝟑 -Ag, and 𝐀𝐠-Ag.



Potential drop for NCSP+SOC and NSP at different applied bias voltage.



Projected density of states for Pb and I atoms of s- and d- states in the central scattering region for NCSP+SOC and NSP.

■ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. *E-mail: [email protected]. Notes The authors declare no competing financial interest. ■ ACKNOWLEDGMENTS This work was financially supported by the National Key Research and Development Program of China (2017YFF0106303, 2016YFC0101300, 2016YFC0101002), and Dongguan Industry University Research Cooperation Project (2015509102211). ■ REFERENCES 1.

Zhang, W.; Saliba, M.; Moore, D. T.; Pathak, S. K.; Hörantner, M. T.; Stergiopoulos, T.;

Stranks, S. D.; Eperon, G. E.; Alexander-Webber, J. A.; Abate, A., Ultrasmooth Organic-Inorganic


14

Page 15 of 27 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


Perovskite Thin-Film Formation and Crystallization for Efficient Planar Heterojunction Solar Cells. Nat. Commun. 2015, 6, 6142. 2.

Li, X.; Dar, M. I.; Yi, C.; Luo, J.; Tschumi, M.; Zakeeruddin, S. M.; Nazeeruddin, M. K.;

Han, H.; Grätzel, M., Improved Performance and Stability of Perovskite Solar Cells by Crystal Crosslinking with Alkylphosphonic Acid Ω-Ammonium Chlorides. Nat. Chem. 2015, 7, 703-711. 3.

Yang, W. S.; Noh, J. H.; Jeon, N. J.; Kim, Y. C.; Ryu, S.; Seo, J.; Seok, S. I., High-

Performance Photovoltaic Perovskite Layers Fabricated through Intramolecular Exchange. Science 2015, 348, 1234-1237. 4.

Chiang, C.-H.; Wu, C.-G., Bulk Heterojunction Perovskite-PCBM Solar Cells with High

Fill Factor. Nat. Photonics 2016, 10, 196-200. 5.

Brenner, T. M.; Egger, D. A.; Kronik, L.; Hodes, G.; Cahen, D., Hybrid Organic-Inorganic

Perovskites: Low-Cost Semiconductors with Intriguing Charge-Transport Properties. Nat. Rev. Mater. 2016, 1, 15007. 6.

Tan, H.; Jain, A.; Voznyy, O.; Lan, X.; de Arquer, F. P. G.; Fan, J. Z.; Quintero-Bermudez,

R.; Yuan, M.; Zhang, B.; Zhao, Y., Efficient and Stable Solution-Processed Planar Perovskite Solar Cells Via Contact Passivation. Science 2017, 355, 722-726. 7.

Matsui, T.; Seo, J. Y.; Saliba, M.; Zakeeruddin, S. M.; Grätzel, M., Room-Temperature

Formation of Highly Crystalline Multication Perovskites for Efficient, Low-Cost Solar Cells. Adv. Mater. 2017, 29, 1606258. 8.

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.


15


9.

Page 16 of 27

Shao, Y.; Yuan, Y.; Huang, J., Correlation of Energy Disorder and Open-Circuit Voltage

in Hybrid Perovskite Solar Cells. Nature Energy 2016, 1, 15001. 10. Bi, D.; Yi, C.; Luo, J.; Décoppet, J.-D.; Zhang, F.; Zakeeruddin, S. M.; Li, X.; Hagfeldt, A.; Grätzel, M., Polymer-Templated Nucleation and Crystal Growth of Perovskite Films for Solar Cells with Efficiency Greater Than 21%. Nature Energy 2016, 1, 16142. 11. Research

Cell

Efficiency

Records,

National

Renewable

Energy

Laboratory.

https://www.nrel.gov/pv/assets/images/efficiency-chart.png (accessed Accessed: 30 Aug, 2017.). 12. Chen, Y.; Yi, H.; Wu, X.; Haroldson, R.; Gartstein, Y.; Rodionov, Y.; Tikhonov, K.; Zakhidov, A.; Zhu, X.-Y.; Podzorov, V., Extended Carrier Lifetimes and Diffusion in Hybrid Perovskites Revealed by Hall Effect and Photoconductivity Measurements. Nat. Commun. 2016, 7, 12253. 13. Zhao, Y.; Zhu, K., Organic-Inorganic Hybrid Lead Halide Perovskites for Optoelectronic and Electronic Applications. Chem. Soc. Rev. 2016, 45, 655-689. 14. Sutherland, B. R.; Sargent, E. H., Perovskite Photonic Sources. Nat. Photonics 2016, 10, 295-302. 15. Yuan, M.; Quan, L. N.; Comin, R.; Walters, G.; Sabatini, R.; Voznyy, O.; Hoogland, S.; Zhao, Y.; Beauregard, E. M.; Kanjanaboos, P., Perovskite Energy Funnels for Efficient LightEmitting Diodes. Nat. Nanotechnol. 2016, 11, 872-877. 16. Xiao, Z.; Kerner, R. A.; Zhao, L.; Tran, N. L.; Lee, K. M.; Koh, T.-W.; Scholes, G. D.; Rand, B. P., Efficient Perovskite Light-Emitting Diodes Featuring Nanometre-Sized Crystallites. Nat. Photonics 2017, 11, 108-115.


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Page 17 of 27 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


17. Wei, H.; Fang, Y.; Mulligan, P.; Chuirazzi, W.; Fang, H.-H.; Wang, C.; Ecker, B. R.; Gao, Y.; Loi, M. A.; Cao, L., Sensitive X-Ray Detectors Made of Methylammonium Lead Tribromide Perovskite Single Crystals. Nat. Photonics 2016, 10, 333-339. 18. Jia, Y.; Kerner, R. A.; Grede, A. J.; Brigeman, A. N.; Rand, B. P.; Giebink, N. C., DiodePumped Organo-Lead Halide Perovskite Lasing in a Metal-Clad Distributed Feedback Resonator. Nano Lett. 2016, 16, 4624-4629. 19. Huang, C.; Wang, K.; Yang, Z.; Jiang, L.; Liu, R.; Su, R.; Zhou, Z.-K.; Wang, X., UpConversion Perovskite Nanolaser with Single Mode and Low Threshold. J. Phys. Chem. C 2017, 121, 10071-10077. 20. Senanayak, S. P.; Yang, B.; Thomas, T. H.; Giesbrecht, N.; Huang, W.; Gann, E.; Nair, B.; Goedel, K.; Guha, S.; Moya, X., Understanding Charge Transport in Lead Iodide Perovskite ThinFilm Field-Effect Transistors. Sci. Adv. 2017, 3, e1601935. 21. Zhang, C.; Sun, D.; Liu, X.; Sheng, C.-X.; Vardeny, Z. V., Temperature-Dependent Electric Field Poling Effects in CH3NH3PbI3 Optoelectronic Devices. J. Phys. Chem. Lett. 2017, 8, 1429-1435. 22. Li, Z.; Yang, M.; Park, J.-S.; Wei, S.-H.; Berry, J. J.; Zhu, K., Stabilizing Perovskite Structures by Tuning Tolerance Factor: Formation of Formamidinium and Cesium Lead Iodide Solid-State Alloys. Chem. Mater. 2016, 28, 284-292. 23. Berhe, T. A.; Su, W.-N.; Chen, C.-H.; Pan, C.-J.; Cheng, J.-H.; Chen, H.-M.; Tsai, M.-C.; Chen, L.-Y.; Dubale, A. A.; Hwang, B.-J., Organometal Halide Perovskite Solar Cells: Degradation and Stability. Energy Environ. Sci. 2016, 9, 323-356.


17


Page 18 of 27

24. Endres, J.; Egger, D. A.; Kulbak, M.; Kerner, R. A.; Zhao, L.; Silver, S. H.; Hodes, G.; Rand, B. P.; Cahen, D.; Kronik, L., Valence and Conduction Band Densities of States of Metal Halide Perovskites: A Combined Experimental-Theoretical Study. J. Phys. Chem. Lett. 2016, 7, 2722-2729. 25. Wang, L.; Wang, K.; Xiao, G.; Zeng, Q.; Zou, B., Pressure-Induced Structural Evolution and Band Gap Shifts of Organometal Halide Perovskite-Based Methylammonium Lead Chloride. J. Phys. Chem. Lett 2016, 7, 5273-5279. 26. Parrott, E. S.; Milot, R. L.; Stergiopoulos, T.; Snaith, H. J.; Johnston, M. B.; Herz, L. M., Effect of Structural Phase Transition on Charge-Carrier Lifetimes and Defects in CH3NH3PbI3 Perovskite. J. Phys. Chem. Lett. 2016, 7, 1321-1326. 27. Kerner, R. A.; Rand, B. P., Linking Chemistry at the TiO2/ CH3NH3PbI3 Interface to Current-Voltage Hysteresis. J. Phys. Chem. Lett. 2017, 8, 2298-2303. 28. Li, D.; Cheng, H.-C.; Wu, H.; Wang, Y.; Guo, J.; Wang, G.; Huang, Y.; Duan, X., GateInduced Insulator to Band-Like Transport Transition in Organolead Halide Perovskite. J. Phys. Chem. Lett. 2017, 8, 429-434. 29. Bae, S.; Park, J.-S.; Han, I. K.; Shin, T. J.; Jo, W. H., CH3NH3PbI3 Crystal Orientation and Photovoltaic Performance of Planar Heterojunction Perovskite Solar Cells. Sol. Energy Mater. Sol. Cells 2017, 160, 77-84. 30. Yuan, Y.; Li, T.; Wang, Q.; Xing, J.; Gruverman, A.; Huang, J., Anomalous Photovoltaic Effect in Organic-Inorganic Hybrid Perovskite Solar Cells. Sci. Adv. 2017, 3, e1602164.


18

Page 19 of 27 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


31. Murali, B.; Yengel, E.; Peng, W.; Chen, Z.; Alias, M. S.; Alarousu, E.; Ooi, B. S.; Burlakov, V.; Goriely, A.; Eddaoudi, M., Temperature-Induced Lattice Relaxation of Perovskite Crystal Enhances Optoelectronic Properties and Solar Cell Performance. J. Phys. Chem. Lett. 2016, 8, 137-143. 32. Guo, Z.; Wan, Y.; Yang, M.; Snaider, J.; Zhu, K.; Huang, L., Long-Range Hot-Carrier Transport in Hybrid Perovskites Visualized by Ultrafast Microscopy. Science 2017, 356, 59-62. 33. Yin, W.-J.; Yang, J.-H.; Kang, J.; Yan, Y.; Wei, S.-H., Halide Perovskite Materials for Solar Cells: A Theoretical Review. J. Mater. Chem. A 2015, 3, 8926-8942. 34. 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, 7497. 35. Neukirch, A. J.; Nie, W.; Blancon, J.-C.; Appavoo, K.; Tsai, H.; Sfeir, M. Y.; Katan, C.; Pedesseau, L.; Even, J.; Crochet, J. J., Polaron Stabilization by Cooperative Lattice Distortion and Cation Rotations in Hybrid Perovskite Materials. Nano Lett. 2016, 16, 3809-3816. 36. Lee, J.-H.; Bristowe, N. C.; Lee, J. H.; Lee, S.-H.; Bristowe, P. D.; Cheetham, A. K.; Jang, H. M., Resolving the Physical Origin of Octahedral Tilting in Halide Perovskites. Chem. Mater. 2016, 28, 4259-4266. 37. Wright, A. D.; Verdi, C.; Milot, R. L.; Eperon, G. E.; Pérez-Osorio, M. A.; Snaith, H. J.; Giustino, F.; Johnston, M. B.; Herz, L. M., Electron-Phonon Coupling in Hybrid Lead Halide Perovskites. Nat. Commun. 2016, 7, 11755.


19


Page 20 of 27

38. Saidi, W. A.; Poncé, S.; Monserrat, B., Temperature Dependence of the Energy Levels of Methylammonium Lead Iodide Perovskite from First-Principles. J. Phys. Chem. Lett 2016, 7, 5247-5252. 39. Shirayama, M.; Kadowaki, H.; Miyadera, T.; Sugita, T.; Tamakoshi, M.; Kato, M.; Fujiseki, T.; Murata, D.; Hara, S.; Murakami, T. N., Optical Transitions in Hybrid Perovskite Solar Cells: Ellipsometry, Density Functional Theory, and Quantum Efficiency Analyses for CH3NH3PbI3. Phys. Rev. Appl. 2016, 5, 014012. 40. Yang, D.; Ming, W.; Shi, H.; Zhang, L.; Du, M.-H., Fast Diffusion of Native Defects and Impurities in Perovskite Solar Cell Material CH3NH3PbI3. Chem. Mater. 2016, 28, 4349-4357. 41. Li, W.; Liu, J.; Bai, F.-Q.; Zhang, H.-X.; Prezhdo, O. V., Hole Trapping by Iodine Interstitial Defects Decreases Free Carrier Losses in Perovskite Solar Cells: A Time-Domain Ab Initio Study. ACS Energy Letters 2017, 2, 1270-1278. 42. Frost, J. M.; Walsh, A., What Is Moving in Hybrid Halide Perovskite Solar Cells? Acc. Chem. Res. 2016, 49, 528-535. 43. Zhao, T.; Shi, W.; Xi, J.; Wang, D.; Shuai, Z., Intrinsic and Extrinsic Charge Transport in CH3NH3PbI3 Perovskites Predicted from First-Principles. Sci. Rep. 2016, 7, 19968. 44. Jong, U.-G.; Yu, C.-J.; Jang, Y.-M.; Ri, G.-C.; Hong, S.-N.; Pae, Y.-H., Revealing the Stability and Efficiency Enhancement in Mixed Halide Perovskites MAPb(I1–XClX)3 with Ab Initio Calculations. J. Power Sources 2017, 350, 65-72.


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Page 21 of 27 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


45. Even, J.; Pedesseau, L.; Jancu, J.-M.; Katan, C., Importance of Spin-Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications. J. Phys. Chem. Lett. 2013, 4, 2999-3005. 46. Giorgi, G.; Fujisawa, J.-I.; Segawa, H.; Yamashita, K., Small Photocarrier Effective Masses Featuring Ambipolar Transport in Methylammonium Lead Iodide Perovskite: A Density Functional Analysis. J. Phys. Chem. Lett. 2013, 4, 4213-4216. 47. Amat, A.; Mosconi, E.; Ronca, E.; Quarti, C.; Umari, P.; Nazeeruddin, M. K.; Grätzel, M.; De Angelis, F., Cation-Induced Band-Gap Tuning in Organohalide Perovskites: Interplay of SpinOrbit Coupling and Octahedra Tilting. Nano Lett. 2014, 14, 3608-3616. 48. Berdiyorov, G.; Madjet, M.; El-Mellouhi, F.; Peeters, F., Effect of Crystal Structure on the Electronic Transport Properties of the Organometallic Perovskite CH3NH3PbI3. Sol. Energy Mater. Sol. Cells 2016, 148, 60-66. 49. Park, N.-G., Organometal Perovskite Light Absorbers toward a 20% Efficiency Low-Cost Solid-State Mesoscopic Solar Cell. J. Phys. Chem. Lett. 2013, 4, 2423-2429. 50. Yin, W. J.; Shi, T.; Yan, Y., Unique Properties of Halide Perovskites as Possible Origins of the Superior Solar Cell Performance. Adv. Mater. 2014, 26, 4653-4658. 51. Kresse, G.; Furthmüller, J., Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169-11186. 52. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868.


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Page 22 of 27

53. Grimme, S., Semiempirical GGA-Type Density Functional Constructed with a LongRange Dispersion Correction. J. Comput. Chem. 2006, 27, 1787-1799. 54. 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. 55. Taylor, J.; Guo, H.; Wang, J., Ab Initio Modeling of Quantum Transport Properties of Molecular Electronic Devices. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 63, 245407. 56. Waldron, D.; Haney, P.; Larade, B.; MacDonald, A.; Guo, H., Nonlinear Spin Current and Magnetoresistance of Molecular Tunnel Junctions. Phys. Rev. Lett. 2006, 96, 166804. 57. Büttiker, M.; Imry, Y.; Landauer, R.; Pinhas, S., Generalized Many-Channel Conductance Formula with Application to Small Rings. Physical Review B 1985, 31, 6207. 58. Saidaminov, M. I.; Abdelhady, A. L.; Murali, B.; Alarousu, E.; Burlakov, V. M.; Peng, W.; Dursun, I.; Wang, L.; He, Y.; Maculan, G.; Goriely, A.; Wu, T.; Mohammed, O. F.; Bakr, O. M., High-Quality Bulk Hybrid Perovskite Single Crystals within Minutes by Inverse Temperature Crystallization. Nat. Commun. 2015, 6. 59. Li, B.-L.; Chen, K.-Q., Effects of Electron-Phonon Interactions on the Spin-Dependent Seebeck Effect in Graphene Nanoribbons. Carbon 2017, 119, 548-554. 60. Markussen, T.; Palsgaard, M.; Stradi, D.; Gunst, T.; Brandbyge, M.; Stokbro, K., ElectronPhonon Scattering from Green's Function Transport Combined with Molecular Dynamics: Applications to Mobility Predictions. Physical Review B 2017, 95, 245210.


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Effects of SpinâOrbit Coupling on Nonequilibrium Quantum Transport

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