Moderate Humidity Delays Electron–Hole Recombination in Hybrid

Letter pubs.acs.org/JPCL

Moderate Humidity Delays Electron−Hole Recombination in Hybrid Organic−Inorganic Perovskites: Time-Domain Ab Initio Simulations Rationalize Experiments Run Long,*,†,‡ Weihai Fang,† and Oleg. V. Prezhdo*,§ †

College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China ‡ School of Physics, Complex & Adaptive Systems Lab, University College Dublin, Belfield, Dublin 4, Ireland § Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States ABSTRACT: Experiments show both positive and negative changes in performance of hybrid organic−inorganic perovskite solar cells upon exposure to moisture. Ab initio nonadiabatic molecular dynamics reveals the influence of humidity on nonradiative electron−hole recombination. In small amounts, water molecules perturb perovskite surface and localize photoexcited electron close to the surface. Importantly, deep electron traps are avoided. The electron−hole overlap decreases, and the excited state lifetime increases. In large amounts, water forms stable hydrogen-bonded networks, has a higher barrier to enter perovskite, and produces little impact on charge localization. At the same time, by contributing high frequency polar vibrations, water molecules increase nonadiabatic coupling and accelerate recombination. In general, short coherence between electron and hole benefits photovoltaic response of the perovskites. The calculated recombination time scales show excellent agreement with experiment. The time-domain atomistic simulations reveal the microscopic effects of humidity on perovskite excited-state lifetimes and rationalize the conflicting experimental observations.

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nitrogen.17 Similarly, the same group has demonstrated that MAPbI3 films fabricated in a humid environment have better optoelectronic properties than films fabricated under dry conditions.17 Zhou et al. have reported that exposure to a low level ( 2H2O > H2O > MAPbI3(001). This sequence correlates well with the pure-dephasing times, Table 1: The higher the peak intensity, the shorter the time. The optical pure-dephasing functions, computed using the second-order cumulant approximation, are shown in Figure 4b. The functions represent elastic electron−phonon scattering. The data were fit by Gaussians, exp[−0.5(t/τ)2], and the puredephasing times, τ, are summarized in Table 1. The puredephasing/decoherence times are very short, because the system contains a broad spectrum of vibrations, stemming from both inorganic and organic components, and because most of these vibrations couple to the electronic subsystem, either directly by wave function localization, or electrostatically. The 4 fs pure-dephasing times are much shorter than the 40− 300 ps electron−hole recombination times reported in experiments,29,32 necessitating incorporation of decoherence effects into NAMD simulation. The unnormalized autocorrelation functions (ACF), insert of Figure 4b, computed from the fluctuations of the HOMO− LUMO energy gaps provide additional insights into the origin of phonon-induced pure-dephasing within the electronic subsystem. The dephasing is fast if the electron−phonon coupling is strong, and if it arises from a wide range of phonon modes.61 The rate of ACF decay characterizes the range of participating modes. All ACFs decay on similar time scales, because similar modes participate in all cases, Figure 4a. Therefore, the differences in the pure-dephasing times arise from the electron−phonon coupling strength. The strength of coupling to individual modes is reflected in the FT peak amplitudes. The cumulative magnitude of the electron−phonon coupling determines the initial value of the unnormalized ACF, which equals the variance of the energy gap. Figure 5 shows evolution of the population of the first excited state in the four perovskite systems under consideration. The times summarized in Table 1 are obtained using the short-time, linear approximation to the exponential decay, f(t) = exp(−t/τ) ≈ 1 − (t/τ). The calculated electron−hole recombination times fall in the middle of the 40−300 ps experimental range.29,32 Such slow electron−hole recombination is beneficial for maintaining solar cell current, which leads to high photon-to-current conversion efficiency of perovskite solar cells.3,13,62 The calculated time scales demonstrate that

Figure 5. Electron−hole recombination across the MAPbI3(001) surface with and without water molecules. The MAPbI3(001) surface with one and two water molecules shows slower decay compared to the bare MAPbI3(001) surface, due to smaller NA coupling and faster decoherence, Table 1. The NA coupling is larger and the decay is faster when water maintains a continuous hydrogen-bonded network. The coupling decreases because the LUMO becomes localized, Figure 3b,c, reducing overlap with the hole wave function. The time scales summarized in Table 1 are in good agreement with experiment.29,32

small amounts of water notably reduce the electron−hole recombination and extend the excited-state lifetime. Increasing the number of water molecules accelerates the recombination. When the number of water molecules reaches a critical value, corresponding to formation of a continuous hydrogen bonded network, the recombination becomes faster than in bare MAPbI3. The observed changes in the electron−hole recombination rate with moderate and heavy humidity are rationalized by the trends in the values of the NA coupling and pure-dephasing time between the excited and ground states, Table 1. Note that the changes in the electronic energy gap are very small. Generally, quantum transitions are fast if coupling is strong and coherence is long-lived. Shorter coherence slows down the dynamics. The coherence time decreases slowly and continuously with increasing number of waters. The NA coupling shows a larger relative spread and is smallest with there are few water molecules. The NA coupling magnitude is the most important factor, and fully rationalizes the qualitative changes in the recombination time. The coherence time has a significant but smaller effect, cf. H2O vs 2H2O which exhibit similar recombination times, but different NA couplings and dephasing times. The effect of the energy gap on the changes in the 3219

DOI: 10.1021/acs.jpclett.6b01412 J. Phys. Chem. Lett. 2016, 7, 3215−3222

Letter

The Journal of Physical Chemistry Letters

short-lived coherence is beneficial for the photovoltaic response, because it prevents charge recombination. The study highlights the importance of relative humidity in electron−hole recombination and advances our understanding of excited-state dynamics in perovskite solar cells. The shortrange chemical and long-range electrostatic mechanisms of perovskite-water interaction, seen in the present work, provide means of control over charge localization and recombination. These general principles should apply in other situations, including chemical doping45,46,67,68 and ordered electric phases69 observed in hybrid perovskites.

electron−hole recombination time is insignificant in the present systems. The calculated electron−hole recombination times show that relative humidity plays an important role in determining the excited-state lifetime. The simulations provide a straightforward rationalization of the variable experimental data on the effect of humidity on the performance of hybrid organic−inorganic perovskites and advance our understanding of the fundamental principles underlying design of highly efficient solar cells. To recapitulate, using NAMD combined with ab initio realtime TDDFT, we investigated the nonradiative electron−hole recombination in methylammonium lead halide perovskites with different amounts of adsorbed water. The electron−hole recombination constitutes a major pathway of charge and energy losses in these materials, limiting the photon-to-electron conversion efficiency. Experimental data show that humidity can both increase and decrease the efficiency. Thus, the effects of humidity on the excited-state lifetime of hybrid organic/ inorganic perovskites remain a matter of debate. Our simulations show that moderate humidity extends the excitedstate lifetime, while heavy humidity reduces the lifetime, in agreement with experiments. Small amounts of water localize the electron on the surface, while avoiding deep trap states, and decouple the electron from the hole. In addition, quantum coherence time decreases. Both effects reduce the nonradiative charge recombination. Other solvent molecules could have a similar effect on wave function localization, provided they can enter the perovskite surface. Under heavy humidity, water aggregates on the perovskite surface forming a continuous hydrogen bonded network, as evidenced by both binding energies and finite temperature sampling. The perovskite− water interaction is weaker than water−water interaction, and therefore, a continuous water layer creates a smaller perturbation to the perovskite surface than isolated water molecules. The delocalization of the electron into the bulk and the electron−hole overlap are restored with increasing amounts of water, the nonadiabatic coupling increases above the value for the bare surface, and the recombination accelerates. The previous simulations of electron−hole recombination in bulk perovskites24,45 report time scales that are similar to those obtained here for the perovskite surface, around 100 ps. Perovskite grain boundaries24 can accelerate the recombination by an order of magnitude, to 10 ps, while electron−hole separation at perovskite/TiO2 interfaces46 slows down the recombination to about 1 ns. The investigation also shows that the quantum coherence time of the interacting electron and hole is very short due to participation of a broad spectrum of phonon modes in the decoherence process. The electronic subsystem couples not only to the modes of the inorganic Pb−I framework, but also to those of the organic MA and water. The coupling to the Pb−I vibrations is direct because electrons and holes localize on Pb and I atoms. MA and water do not contribute to the electron and hole wave functions. However, they carry charges and large dipole moments, and couple to the photogenerated electron and hole electrostatically. The very short coherence time favors long excited state lifetime and slow electron−hole recombination, ultimately contributing to high photovoltaic efficiencies of hybrid organic−inorganic perovskites. Typically, long-lived coherence is associated with more efficient charge separation and solar energy harvesting in biological and nanoscale materials.63−66 Here, we demonstrate the opposite effect:

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.L. is grateful to the National Science Foundation of China, grant no. 21573022, the Recruitment Program of Global Youth Experts and the Science Foundation Ireland SIRG Program under grant no. 11/SIRG/E2172. W.H.F. thanks the National Science Foundation of China, grant no. 21520102005 and Science Fund for Creative Research Groups of the National Natural Science Foundation of China, grant no. 21421003. O.V.P. acknowledges support of the U.S. National Science Foundation, grant no. CHE-1565704.

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