Rashba Effect and Carrier Mobility in Hybrid Organic–Inorganic

Jul 27, 2016 - Here we show that this giant RE can manifest itself in charge transport and is the key to understanding carrier mobility and its temper...
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Rashba Effect and Carrier Mobility in Hybrid Organic−Inorganic Perovskites Zhi-Gang Yu* ISP/Applied Sciences Laboratory, Washington State University, Spokane, Washington 99210, United States S Supporting Information *

ABSTRACT: The outstanding photovoltaic performance in hybrid organic−inorganic perovskites (HOIPs) relies on their desirable carrier transport properties. In the HOIPs, strong spin−orbit coupling (SOC) and structural inversion asymmetry give rise to a giant spin splitting in the conduction and valence bands, that is, the Rashba effect (RE), a subject intensively studied in spintronics. Here we show that this giant RE can manifest itself in charge transport and is the key to understanding carrier mobility and its temperature dependence in the HOIPs. The RE greatly enhances acoustic-phonon scattering (APS) and alters the temperature dependence of carrier mobility from T−3/2 to T−1. Meanwhile, it reduces polar-optical phonon scattering (POPS). In CH3NH3PbI3, the carrier mobility is limited by the APS for temperatures up to 100 K, above which the POPS becomes dominant. The effective polar coupling is moderate, α = 1.1, indicating that band conduction is still a valid description of charge transport. Our results account for the observed carrier transport behaviors over the entire temperature range and highlight the importance of SOC in charge transport in the HOIPs.

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device applications.23 It was also employed to explain the slow exciton recombination in the HOIPs.24 Here we show that the giant RE in the HOIPs can strongly influence charge transport: It modifies temperature dependence of carrier mobility from T−3/2 to T−1 for the APS, the limiting process for carrier mobility up to 100 K in CH3NH3PbI3, and reduces the POPS, the dominant process with an approximate temperature dependence of T−1.5 between 100 to 300 K. The crossover from T−1 to T−1.5 around 100 K naturally explains the observed temperature dependence of T−1.2 between 70 to 130 K. We also evaluate the polar coupling unambiguously from the dielectric response. The value for CH3NH3PbI3, α = 1.12, indicates that the system is in the weak (large) polaron regime, and the band conduction is still a reasonable description of charge transport. We consider the most studied HOIP CH3NH3PbI3, which has a tetragonal structure with C4v symmetry at room temperature.25,26 The tetragonal structure is also a good approximation for the low-temperature orthorhombic structure, which is almost axial.25 An 8-band effective-mass model for the tetragonal phase has been derived recently and can be simplified to 2 × 2 Hamiltonians for conduction and valence bands, both being a Γ6 representation of C4v.15 Because asgrown CH3NH3PbI3 tends to be of p type,2−4 we study transport of valence-band electrons, but the results are equally valid for the conduction band with suitable parameters. The

ybrid organic−inorganic perovskites (HOIPs) such as CH3NH3PbI3 represent a revolutionary breakthrough for low-cost solar cells.1 The extraordinary photovoltaic efficiency attained in the HOIPs is due largely to their favorable carrier transport properties.2−4 The underlying mechanism of carrier transport, however, is under intense debate.5−7 The observed temperature dependence of carrier mobility μ between 130 and 300 K approximately follows μ ∝ T−3/2,8−10 the hallmark of acoustic-phonon scattering (APS),11 which seems to suggest a dominant role of APS.5,7 On the contrary, theoretical calculations12,13 of the APS usually predict a mobility order of magnitude larger than the highest experimental values, ∼100 cm2/(V s) at room temperature.3 To account for the modest mobility, it was proposed that carriers are heavy (small) polarons7 rather than band electrons, which, however, seems inconsistent with the carrier effective masses estimated from cyclotron resonance.14,15 Very recently, polar-optical phonon scattering (POPS)16,17 has been invoked, but it does not explain a weaker temperature dependence of scattering time, τM ∝ T−1.2 between 70 and 130 K.10 Fundamentally, the polar coupling in the HOIPs, central to both polaron formation and POPS, is in itself unclear because the multitude optical phonon modes render the commonly used Fröhlich expression,18 derived for compounds with a single optical mode, inadequate. A unique feature of the HOIPs is their giant Rashba effect (RE),19,20 caused by strong spin−orbit coupling (SOC) associated with the heavy atoms21 and the lack of inversion symmetry in their crystal structures. The RE breaks spin degeneracy in the conduction and valence bands, and its significance in the HOIPs has been quantified from a variety of first-principles approaches22,23 and proposed for spintronic © XXXX American Chemical Society

Received: June 24, 2016 Accepted: July 27, 2016

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DOI: 10.1021/acs.jpclett.6b01404 J. Phys. Chem. Lett. 2016, 7, 3078−3083

Letter

The Journal of Physical Chemistry Letters Hamiltonian of the valence band at a given momentum k = (k⊥ cos ϕ, k⊥ sin ϕ, kz) reads H v = Ev0 −

ℏ2 2 (k⊥ + kz2) + γ(k yσx − kxσy) 2m

cyclotron resonance,14,27 m = 0.22m0, with m0 being the freeelectron mass. The Rashba strength, γ, estimated from the firstprinciples, ranges from 1.4 to 3.7 eV Å22,23 and is set to 2.5 eV Å in this study (effects of γ value are discussed in the Supporting Information). We treat the APS and POPS on an equal footing with the electron−phonon (e−p) coupling written in a general form

(1)

where m is the effective mass with its weak anisotropy ( θ0/4 ≡ ℏωl1/4kB = 48 K, with 3081

DOI: 10.1021/acs.jpclett.6b01404 J. Phys. Chem. Lett. 2016, 7, 3078−3083

Letter

The Journal of Physical Chemistry Letters mobility increasing with temperature,45 which is inconsistent with the observed temperature dependence in the HOIPs. In light of these results, many puzzling observations5,6 regarding charge transport in the HOIPs fall neatly into place. Because the RE alters the temperature dependence of the APS from T−3/2 to T−1, the observed T−3/2 dependence in carrier mobility actually suggests that the mobility be limited not by the APS but by the POPS1. Structural fluctuations, particularly those associated with organic ions and global motions of PbI6 cages in the HOIPs, do not give rise to polar coupling to the conduction and valence band electrons and therefore have little effect on charge transport. While the POPS1 is responsible for the low values of carrier mobility, the polar coupling is moderate with only a small enhancement of effective mass, which is consistent with the cyclotron resonance measurements. The higher mobility observed in other halide perovskites such as CsSnI3 and CsPbBr3 than in CH3NH3PbI3 is due to the lighter elements of Sn and Br (as compared with Pb and I), which result in higher stretching LO phonon frequencies and less effective POPS1. In summary, we have shown that the RE, a fascinating spindependent phenomenon due to SOC, can manifest itself in charge transport and is the key to understanding the carrier mobility in the HOIPs. The RE significantly enhances the APS and changes its temperature dependence from T−3/2 to T−1 and reduces POPS. With the RE properly included, the combination of APS and POPS consistently accounts for the observed carrier transport behavior over the entire temperature range. From the reliably estimated polar coupling, the polaron effect in the HOIPs is moderate and does not qualitatively modify the band conduction picture.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b01404. Methods, derivations, and additional results. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS This work was partly supported by the U.S. Army Research Office under Contract No. W911NF-15-1-0117. REFERENCES

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