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Anomalous Temperature-Dependent Charge Recombination in CH3NH3PbI3 Perovskite: Key Roles of Charge Localization and Thermal Effect Yutong Wang, and Run Long ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b12478 • Publication Date (Web): 19 Aug 2019 Downloaded from pubs.acs.org on August 23, 2019

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ACS Applied Materials & Interfaces

Anomalous Temperature-Dependent Charge Recombination in CH3NH3PbI3 Perovskite: Key Roles of Charge Localization and Thermal Effect

Yutong Wang,1 Run Long1

1College

of Chemistry, Key Laboratory of Theoretical & Computational

Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875, P. R. China

Abstract: Optimizing metal halide perovskite solar cells necessities understanding of nonradiative electron-hole recombination because it comprises a dominant route for charge and energy losses. In principle, electron-hole recombination rate increases as temperature grows due to enhanced electron-phonon coupling. Experiments defy this expectation in MAPbI3 (MA= CH3NH3). By performing nonadiabatic (NA) molecular dynamics combined with time-domain density functional theory simulations, we demonstrate that nonradiative electron-hole recombination in MAPbI3 at high temperature occurs slower than that at low temperature. First and the most important, increasing temperature enhances thermal disorder and leads to significant distortion of the inorganic Pb-I framework, giving rise to electron and hole wave functions locating



Corresponding author, E-mail: [email protected] 1

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spatial separation and reducing NA coupling by a factor of 28% in comparison with low temperature. Second, rising temperature enhances the thermal fluctuations of both the inorganic and organic components that accelerate decoherence process by a factor of 12%. Both factors particularly the small NA coupling contributes to suppress electron-hole recombination at high temperature. The simulations show excellent with experiments and emphasize how the charge localization driven by thermal effects affects electron-hole recombination in perovskites, as well as advances our understanding of the unusual charge dynamics.

Keywords: Hybrid Organic-Inorganic Perovskite, Temperature-Dependent ElectronHole Recombination, Nonadiabatic Molecular Dynamics, Time-Domain Density Functional Theory

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1. INTRODUCTION Hybrid organic-inorganic lead halide perovskite (HOIP) materials have drawn intense attention in recent years due to their prominent photoelectronic properties.1-3 Since the first report in 2009,4 the power conversion efficiency (PCE) of HOIP solar cells reaching 24.2% only took ten years.5 Besides applications in photovoltaic solar cells, HOIPs have extended their applications on light-emitting diodes,6,7 lasers8 and photodetector.9 Among all those devices, charge and energy losses due to nonradiative relaxation constitute the major issue for the performance further development.10 Borrowing the gradient energy band concept from semiconductor physics, Li and coauthors firstly reported an ordered gradient energy band structure to enhance charge transfer and suppress the charge recombination at the interface of perovskite and carrier transport layer. However, the relatively short charge carriers lifetime makes the PCE of HOIP solar cells still lag behind the Shockley–Queisser limit of an ideal single junction solar cell.11 As the traditional and classic HOIP, MAPbI3 (MA = CH3NH3+) holds a suitable bandgap and attains considerable efforts on optimizing the performance of the materials and devices. As a key parameter, charge carrier lifetime is directly related to the efficiency of photovoltaic solar cells. However, the reported carrier lifetimes show diversity and range from hundreds of picoseconds to tens of nanoseconds in different experiments,12-14 leaving that the charge recombination mechanism is under debate and remains active research. The influence factors include passivation of harmful defects,15 pressure-driven change of structure,16,17 formation of large polaron and ferroelectric domain,18,19 etc.20 Furthermore, the interplay between these two or more factors make 3



the charge dynamics become extremely complicated. Besides the above factors, spontaneous rotation of MA cations in the MAPbI3 largely inhibits electron-hole recombination and extends carrier lifetime,19 probably arising due to formation of large polarons.21 Increasing temperature enhances substantially the rotation and rearrangement of MA cations further, giving rise to notable distortion of I-Pb backbone22 that affects significantly electronic properties of MAPbI3,23-25 and leading to an unusual temperature-dependent charge carrier lifetime.26-28 Savenije et al.28 reported the charge recombination time scale in MAPbI3 increases with rising temperature. Milot et al.26 demonstrated a similar observation within the same kind of perovskite. Using temperature-dependent and time-resolved mid-infrared spectroscopy, Munson et al.27 recently showed the same phenomenon that increasing temperature suppresses charge recombination and prolongs charge carrier lifetime in MAPbI3. They attributed this interesting phenomenon to the enhanced disorder of the inorganic framework and charge localization under high temperature, disagreeing with previous theoretical prediction.29 Because the photovoltaic solar cells produce heating in work conditions, and performance relies on the carrier lifetime, a mechanistic understanding of the unusual and positive influence of temperature on the charge carrier dynamics is necessary to improve the efficiency further. Additionally, MAPbI3 exhibits an uncommon temperature-driven change of the bandgap. The bandgap broadens tens of meV with growing temperature.30 In contrast, the bandgap decreases along with the increased temperature in typically conventional semiconductors.31 Therefore, understanding of the photoexcitation electron-nuclei 4


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coupled dynamics in HOIPs from sole experimental measured methods exhibits largely challenging,

requiring

detailed

time-domain

simulations

of

electron-hole

recombination of MAPbI3 dependence of temperature. In this Letter, we provide an excellent explanation for the uncommon and beneficial temperature dependence of charge carrier lifetime in the MAbPI3. Stimulated by the recent experiments,26-28 we simulated nonradiative electron-hole recombination process of the tetragonal phase MAPbI3 at both 150 K and 300 K that directly mimic experimental temperature,27 using combination of time-dependent density functional (TDDFT)32-34 and nonadiabatic molecular dynamics (NAMD).35,36 Our simulations demonstrate that recombination in MAPbI3 at 300 K takes place slower than that at 150 K, occurring on several nanoseconds and showing agreement with the experiments and previous theoretical predicted values.13,37-39 We rationalize the observations by the different extent of charge localization caused by thermal disorder at different temperature. The bandgap changes little under thermal impact and whose influence on the recombination time becomes negligible. At low temperature 150 K, the inorganic Pb-I framework happens mild change in comparison with that at 0 K. As a result, the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbital charge densities retain largely unchanged and which are primarily supported by I and Pb atoms of the entire simulation cell. Increasing the temperature to 300 K gives rises to significant inorganic I-Pb lattice distortion, leading to that the HOMO and LUMO localized on I and Pb atoms of the spatially different positions. The situation minimizes the overlap between the HOMO and LUMO wave functions and decreases the NA 5



electron-phonon coupling by a factor of 28%. High temperature also enhances the atomic fluctuations and thus accelerates the phonon-induced loss of quantum coherence. Both the factors contribute to slow the electron-hole recombination and extend charge carrier lifetime. Our study establishes the key factors for the unusual temperaturedependent excited-state lifetime of MAPbI3 perovskite reported experimentally,26,27 providing a new route to improve the performance of perovskite materials though control of temperature.

2. RESULTS AND DISCUSSION A 96-atom

2 × 2 × 1 supercell based on tetragonal phase MAPbI340 has been

constructed to investigate the temperature-dependent nonradiative electron-hole recombination. Figure 1a shows the optimized MAPbI3 geometry at 0 K. The inorganic octahedrons remain uniform arrangements in the simulation cell. The calculated average I-Pb bond length of the optimized MAPbI3 is 3.19 Å, agreeing well with the previous reported value of 3.10-3.30 Å.41,42 Figure 1b shows the projected density of states (PDOS) of MAPbI3 calculated using the optimized structure. The PDOS is divided into contributions of the Pb, I, MA components. The HOMO LUMO molecular orbital are dominated by I 5p and Pb 6p orbitals, respectively. The organic MA cations do not contribute to the band edges and thus they have no direct influence on the electron-hole recombination across the bandgap. The calculated direct bandgap at Γpoint is 1.60 eV, agreeing well with the previous experimental and theoretical calculated values.43,44 6


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Heating system to 150 K, the obtained average Pb-I bond length of the MD trajectories becomes 3.18 Å and remains almost unchanged in comparison with the bond length at 0 K, indicating that the system exhibits high stability under mild thermal impact, Figure 2a. Increasing temperature to 300 K, thermal fluctuations induce significant distortion in I-Pb octahedron and increase the average Pb-I bond length to 3.54 Å. It shows a growing factor of 11% compared to the system at 0 K. As a result, higher temperature gives rise to significant geometry change. This observation is further confirmed by the numbers labelled in Figure 2a and 2c-2d. The data show that the difference of both Pb-I bond length and Pb-I-Pb angle between 300 K and 0 K is larger than those between 150 K and 0 K. According to the formula presented in the ref.,30 we obtained the bandgap of 1.54 and 1.55 eV at 150 K and 300 K, respectively. The 10 meV bandgap difference has little influence on the electron-hole recombination time scales. To further clarify the temperature-dependent nuclear dynamics for MAPbI3, we calculated the root mean square deviations (RMSDs) of nuclear velocity of each type of atom in the two systems at both 150 K and 300 K. The data shown in Table 1 are split into contributions from Pb, I, and MA atoms. Since the I and Pb atoms constitute the inorganic sublattice and dominate the HOMO and LUMO, their fluctuations reflect primarily the strength of electron-vibrational interactions. Despite the MA cations do not contribute to the band edges directly, they affect the electron-phonon coupling in an indirect manner via perturbing the I-Pb octahedron and the electric field they created. The data show that atomic fluctuations at 300 K are notable larger than those at 150 K. 7



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The observation is further confirmed by the time-evolution orbital energy of the HOMO and LUMO at both 150 and 300 K, Figure S1 in the Supporting Information. Figure S1 shows the fluctuations of both HOMO and LUMO at high temperature exhibit significantly stronger than those at low temperature. Strong electron-vibrational interactions lead to the simultaneously shortened decoherence time and enhanced NA coupling, Table 2. The two factors have an opposite influence on the quantum dynamics. Short decoherence time favors suppressing electron-hole recombination, while strong NA coupling accelerates the recombination. However, NA coupling depends not only on the nuclear velocity, dR/dt, but also on the overlap of initial and final state wave functions, ― iħ⟨ϕj│∇𝐑│ϕk⟩, which enters the NA coupling matrix element. Here, the nonradiative electron-hole recombination takes place across the LUMO-HOMO energy gap since they constitute the initial and final state, respectively.

Table 1. Root Mean Square Deviations (RMSDs) of Nuclear Velocity (Å/fs) for Pb, I and MA Atoms in the Tetragonal MAPbI3 at 150 K and 300 K, Respectively. Pb

I

MA

150 K

0.0016

0.0109

0.0540

300 K

0.0021

0.0142

0.0835

8


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Figure 1. (a) Optimized MAPbI3 geometry (b) PDOS for MAPbI3 at 0 K. A representative snapshot of the MD trajectories at (c) 150 K and (d) 300 K. The PDOS is split into contributions to the MA, I, and Pb orbitals. The HOMO and LUMO are supported by iodine and lead orbitals. The zero energy is set to the Fermi level. A comparison between (a) and (c), (d) shows that high temperature induces significant distortion of the inorganic Pb-I framework, and has strong influence on electronic structure.

Figure 2 shows that the HOMO and LUMO charge densities of MAPbI3 at 0 K, 150 K, and 300 K, calculated using the optimized geometry at 0K and a representative snapshot of the MD trajectories at both 150 K and 300 K. At 0 K, Figure 2a demonstrates that the HOMO and LUMO are primarily supported by I and Pb atoms in 9



the entire simulation cell. Increasing temperature to 150 K, the HOMO and LUMO remain delocalized on the almost of all I and Pb atoms because thermal effect only brings mild distortion on inorganic I-Pb sublattice (Figure 2b) compared to that at 0 K. The situation facilitates mixing of two wave functions and achieving large NA coupling. Keeping increase temperature to 300 K, the HOMO and LUMO get localized on I and Pb atoms in different positions caused by the significant distortion of I-Pb framework, leading to formation of a charge separated state and thus reducing the NA coupling, 0.69 meV at 300 K vs 0.96 meV at 150 K (Table 2). Decreased NA coupling helps to prolong the nonradiative electron-hole recombination time.

Figure 2. HOMO and LUMO charge densities of pristine MAPbI3 in tetragonal phase at (a) 0 K, (b) 150 K and (c) 300 K. The temperature-dependent charge densities are 10


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obtained using the representative snapshot of the MD trajectories. Charge localization increases as the temperature increases.

In order to further quantify the localization of the key electronic states depending on temperature, we computed the time-evolution of inverse participation ratio (IPR)45,46 for HOMO and LUMO at both 150 K and 300 K along the 1.2 ps MD trajectories, Figure 3. The following equation gives the definition of the IPR of a particular KohnSham orbital.

k IPR  N  ( k )

4 i 2 2

i

IPR  (0,1] where N represents the number of grids of a given Kohn-Sham state and ki denotes the charge density within the volume of a unit grid. According to the formula, the IPR is large for highly localized states and small for delocalized states. Ideally, IPR = 1 means a totally localized state. Shown in Figure 3a and 3b, the time-dependent IPRs of the HOMO and LUMO at 300 K exhibit larger than those at 150 K, agreeing with the charge densities shown in Figure 2c and 2d. In particular, the calculated average values of IPR for HOMO and LUMO are 8.22×10-5 and 9.12×10-5 at 150 K, while which increase to 1.04×10-4 and 1.08×10-4 at 300 K, respectively. The data lead to the conclusion that higher temperature results in stronger charge localization for both electrons and holes, minimizing the overlap of their wave functions along the MD trajectory and resulting in a smaller NA coupling (Table 2).

11



Figure 3. Time-evolution inverse participation ratio (IPR) of (a) HOMO and (b) LUMO for tetragonal MAPbI3 at 150 K and 300 K. Higher temperature induces larger atomic fluctuations and stronger charge localization.

In order to characterize the phonon modes that take part into the nonradiative electron-hole recombination, we computed the spectral density by performing Fourier transforms (FTs) of the autocorrelation functions for the fluctuations of the HOMOLUMO energy gap and IPR difference at both 150 K and 300 K. Figure 4 shows that only low-frequency modes contribute to create NA electron-phonon coupling and accommodate the excess energy dissipation during electron-hole recombination of MAPbI3 under two temperatures. The peak intensities grow as the temperature increases for both the FTs of energy and IPR. The stronger electron-vibrational coupling reflected in the peak intensity leads to shorter decoherence time, Table 2. Both FTs show several modes in the 30-300 cm-1 frequency range at 150 K and 300 K. Shown in Figure 4a, the major peak of energy FT at low temperature can be attributed to the Pb-I bond stretching at 94 cm-1.47 The side peak can be designed as the Pb-I bond bending at 62 cm-1.47 Both the modes create the majority of NA coupling, 12


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induce decoherence, and lead to electron-hole recombination. The small peaks in the range of 150-300 cm-1 can be associated with the librations and torsional modes of the organic cations.48,49 These modes contribute little to NA coupling because neither HOMO nor LUMO localize on the organic components. Increasing temperature broadens the major peak, enhances its intensity, and actives more phonon modes. The FTs of IPR exhibit similar major modes and the main conclusions derived from the energy FTs retain, Figure 4b. Higher peak intensities and a broader range of frequencies favor shorter dephasing time.

Figure 4. Spectral density obtained from Fourier transforms (FTs) of autocorrelation functions of the HOMO and LUMO for the (a) energy gap and (b) IPR difference in MAPbI3 at 150 K and 300 K.

Quantum decoherence, known as the pure-dephasing in the optical response theory,50,51 is another important factor affecting the nonradiative electron-hole recombination. Figure 5 demonstrates the pure-dephasing functions calculated using 13



the second-order cumulant approximation.50 Fitting the functions to a Gaussian, exp[0.5(t/τ)2], gives the pure-dephasing times τ of 10.4 fs at 150 K and 9.13 fs at 300 K, presented in Table 2. A short pure-dephasing time favors suppressing charge recombination, as manifested by quantum Zeno effect.52-54 In addition to the stronger atomic fluctuations shown in Table 1, the unnormalized autocorrelation functions (unACF) of the fluctuations of the HOMO-LUMO energy gap provide another mechanistic understanding for the variation in dephasing times at different temperature. Generally, a larger initial value of un-ACF leads to a faster pure-dephasing process. The inset of Figure 5 shows the un-ACF of the two systems at 150 K and 300 K, in which the initial value of the un-ACF at higher temperature is larger than that at lower temperature, accelerating the decoherence.

Figure 5. Pure-dephasing functions for the HOMO−LUMO transition in tetragonal 14


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MAPbI3 at 150 K and 300 K. Inset shows the unnormalized autocorrelation function (un-ACF). The larger initial value of the un-ACF and the faster dephasing.

Figure 6 displays the time-evolution of the LUMO population for the MAPbI3 at 150 K and 300 K. The bandgap was set to 1.54 eV at 150 K and 1.55 eV at 300 K30 for the NAMD simulations in order to reveal experimental temperature effect directly. Fitting the data to a short-linear approximation to exponential decay, f(t) = exp (−t/τ) ≈ 1 – (t/τ), obtains the electron-hole recombination time scales, Table 2. The obtained recombination timescales are within several nanosecond, agreeing well with the previous experimental and theoretical carrier lifetimes.13,37-39 A longer nonradiative electron-hole recombination time scale means smaller charge and energy losses and a better photovoltaic performance for materials and optoelectronic devices. Interestingly, the electron-hole recombination in MAPbI3 at 300 K occurs slower than that at 150 K by a factor of over 2. The interplay between the NA coupling and pure-dephasing time can rationalize the unusual charge dynamics. The NA coupling in MAPbI3 system is 0.69 meV at 300 K and 0.96 meV at 150 K, while the corresponding pure-dephasing time is 9.13 fs and 10. 4 fs. The difference in the pure-dephasing time is smaller, a factor of 12%, compared to the NA coupling difference, a factor of 28%. Consequently, the decreased NA coupling in the MAPbI3 at higher temperature constitutes the major factor leading to the longer electron-hole recombination time. The above analysis advances our understanding of the key factors influencing the temperature-dependent excited-state lifetime of the hybrid organic-inorganic lead halide perovskites, and 15



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emphasizes the key role of charge localization induced by thermal effect.

Figure 6. Electron-hole recombination dynamics in MAPbI3 at 150 K and 300 K.

Table 2. Bandgap, Average NA coupling, Pure-Dephasing Time, and Nonradiative Electron-Hole Recombination Time for MAPbI3 at 150 K and 300 K. Bandgap

NA Coupling

Dephasing

Recombination

(eV)

(meV)

(fs)

(ns)

150 K

1.54

0.96

10.4

1.23

300 K

1.55

0.69

9.13

2.68

3. CONCLUSIONS In summary, we performed an ab initio NAMD combined with the TDDFT to 16


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investigate the temperature-dependent nonradiative electron-hole recombination process in MAPbI3 perovskites. Our simulations establish the key factors responsible for the suppressed charge recombination at high temperature. At low temperature, the octahedron distortion is mild and thus the inorganic framework remains largely intact. As a result, electrons and holes are supported by almost all I and Pb and the NA electron-phonon coupling is enhanced. Increasing temperature induces enhancement of thermal fluctuations and results in significant geometry distortion, giving rise to a charge separated state that electrons and holes are localized on the I and Pb atoms of different locations. The strong charge localization minimizes the overlap of electron and hole wave functions, decreasing the NA electron-phonon coupling. The enhanced atomic fluctuations increase the amplitude of phonon modes at high temperature, and thus shortens pure-dephasing time. Consequently, the reduced NA coupling and shortened decoherence time delays the electron-hole recombination at high temperature by a factor of 2 in comparison with low temperature. Promoted by low-frequency I-Pb vibrations, the electron-hole recombination occurring on several nanoseconds show excellent agreement with experiments.1,13,55 The study highlights the importance of thermal-driven charge localization on the unusual temperature-dependent excited-state lifetimes and provides crucial insights for improving the performance of HOIP materials.

4. COMPUTATIONAL DETAILS NAMD simulations are performed with mixed quantum-classical decoherence17



induced surface hopping (DISH) algorithm,35 implemented within the TDDFT.32-34 The approach treats the lighter and faster electrons quantum mechanically, while describes the heavier and slower nuclei classically. The algorithm provides a real time ab initio description of couple electron-vibrational dynamics35 and satisfies the detailed balance between transitions upward and downward in energy. The later ensures that the electron-vibrational energy equilibration is fully and properly achieved in the long-time limit.56 DISH algorithm carries the nature of nuclei wave functions branching. Typically, the decoherence time is much shorter than the nonradiative electron-hole recombinant time in perovskites that happens on several nanoseconds.1,13 And therefore, decoherence correction should be taken into account with the NAMD simulations. The decoherence time in DISH35 is estimated as the pure-dephasing in the optical response theory.50 The present NAMD approach has been widely applied on a broad range of systems, including perovskites with boundaries,37 containing dopants57,58 and defects,38,59 and forming heterojunction with other materials,60 black phosphorus and TiO2.61,62 A comprehensive description of the theoretical method is presented elsewhere.36,63 Geometry optimization, adiabatic MD and NA electron-phonon coupling calculations have been performed with the Vienna Ab initio Simulation Package (VASP),64 using the Perdew-Burke-Ernzerhof (PBE) functional for exchangecorrelation interactions65 and the projector-augmented wave pseudopotential for the electron-ion interactions.66 The plane-wave basis energy cutoff has been set to 400 eV to converge total energy. A 2 × 2 × 2 Monkhorst−Pack k-point mesh67 has been adopted 18


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for geometry optimization and a much denser 4 × 4 × 4 k-mesh has been used for electronic structure calculations. Furthermore, Grimme DFT-D3 method has been taken into account describing the van der Waals interactions in order to stabilize the perovskite during geometry optimization and MD simulations.68 After the geometry relaxing at 0 K, the system has been heated to 150 K and 300 K respectively with repeated velocity rescaling for 2 ps to equilibrate the structures. Then, a 5 ps adiabatic MD trajectory has been obtained in the canonical ensemble with a 1 fs atomic time step. Finally, 1200 geometries from the MD trajectory have been selected as initial configurations for NAMD simulation using the PYXAID code.36,63 Spin-orbital coupling (SOC) is important in MAPbI3 because it contains heavy Pb and I atoms. Previous calculations69 demonstrate that the bandgap obtained at the PBE level without SOC correction shows much better agreement with the experimental value of 1.61 eV44 than the PBE calculation with SOC. Furthermore, the calculated bandgap using hybrid functionals, such as PBE0 or HSE, is much larger than the experiment.44,69 In order to obtain an accurate bandgap, one needs to perform a combined calculation of hybrid functional/GW and SOC correction.43,44,69 However, such calculations are impossible for NAMD simulation because it requires to compute the NA coupling several thousand times. Therefore, we prefer to choose PBE functional because it has been successfully applied on studying the electron-hole recombination in MAPbI3 containing dopants70 and grain boundaries,37,71 and interfaced with water72 and TiO2.73

ASSOCIATED CONTENT 19



Supporting Information The Supporting Information is available free of charge on the ACS Publication website. Temperature-dependent evolution of HOMO and LUMO energy levels.

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS The work was supported by the National Natural Science Foundation of China, Grant Nos. 21573022 and 51861135101. R. L. acknowledges financial support by the Beijing Normal University Startup, the Recruitment Program of Global Youth Experts of China, and the Fundamental Research Funds for the Central Universities.

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