Increased Lattice Stiffness Suppresses Nonradiative Charge

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Increased Lattice Stiffness Suppresses Nonradiative Charge Recombination in MAPbI3 Doped with Larger Cations: Time-Domain Ab Initio Analysis Jinlu He, Wei-Hai Fang, Run Long, and Oleg V. Prezhdo ACS Energy Lett., Just Accepted Manuscript • Publication Date (Web): 07 Aug 2018 Downloaded from http://pubs.acs.org on August 7, 2018

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ACS Energy Letters

Increased Lattice Stiffness Suppresses Nonradiative Charge Recombination in MAPbI3 Doped with Larger Cations: Time-Domain Ab Initio Analysis

Jinlu He,1 Wei-Hai Fang,1 Run Long1∗, Oleg V. Prezhdo2 1

College of Chemistry, Key Laboratory of Theoretical & Computational

Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875, P. R. China 2

Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

ABSTRACT: Hybrid organic-inorganic perovskites have attracted great attention as promising photovoltaic materials due to their excellent electronic and optical properties, and facile synthesis. Experiments report that halide perovskites containing several organic cations exhibit much longer charge carrier lifetimes than pristine CH3NH3PbI3 (MAPbI3). Using time-domain density functional theory combined with nonadiabatic (NA) molecular dynamics, we demonstrate that partial replacement of MA with formamidinium (FA) or guanidinium (GA) significantly reduces the NA electron-vibrational coupling. The effect arises due to stiffening of the inorganic Pb-I lattice, which exhibits strongly decreased fluctuations while maintaining its original structure and electronic bandgap. In addition to extending charge carrier lifetimes, reduced lattice motions, and particularly those of iodides, are indicative of decreased

∗

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

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ion diffusion that is responsible for formation of defects, such as iodine interstitials and vacancies, and current-voltage hysteresis. The obtained excited state lifetimes show good agreeement with experiments. The mechanistic insights into the effect of organic cation mixing on charge carrier lifetimes, provided by our simulations, contributes to the fundamental understanding of the halide perovskite properties and generates important principles for design of high-performance perovskite solar cells.

TOC only

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Hybrid organic-inorganic perovskite solar cells are under intense investigation due to their high power conversion efficiences.1-12 The excellent photovoltaic properties stem from high absorption coefficients,13 long charge carrier lifetimes,14-16 low trap density,17 and high photoluminescence (PL) yields.18 The most common lead halide perovskite, CH3NH3PbI3 (MAPbI3), has the advantage of harvesting both visible and near-infrared parts of the solar spectrum. Halide perovskites are also used in other applications, including light-emitting diodes19 and lasers.20,21 Poor stability is one of the major drawbacks of hybrid organic-inorganic perovskites, which exhibit intrinsic halide segregation22,23 and decomposition to the initial precursors.24 Poor stability leads to a significant reduction in efficiency of perovskites over time. Recently, several research groups have demonstrated that partial replacement of MA with other organic cations, such as CH3(NH2)2 (formamidinium, FA) or C(NH2)3 (guanidinium, GA), can increase both stability and carrier lifetime of perovskite solar cells.8, 23, 25-28 Zhang et al. have shown23 that crystallinity of the MAPbI3 perovskite is enhanced upon replacement of a fraction of MA cations with larger FA cations, resulting in reduced charge trapping and increased carrier diffusion length. The measured PL lifetimes and photo-current efficiencies (PCE) of the FAxMA1−xPbI3 perovskite are larger than those of MAPbI3 films. Yao and co-authors have reported24 that (FA)x(MA)1−xPbI3 perovskite films are highly uniform compared to FAPbI3 films and exhibit improved device performance. The carrier lifetimes are longer in the (FA)x(MA)1−xPbI3 films than in films with a single organic component. Pellet et al. 3



have demonstrated that introduction of the FA cation into the MAPbI3 perovskite reduces the bandgap, enabling harvesting of a broader sunlight spectrum.29,30 The mixed-cation perovskite MA0.6FA0.4PbI3 exhibits a longer carrier lifetime and a larger diffusion length than MAPbI3, both factors improving carrier collection efficiency.27 Similarly, Han and co-authors have shown that the bigger FA cation expands the crystal lattice and reduces the bandgap of MAPbI3 perovskite, leading to collection of longer-wavelength photons.8 The nonradiative electron-hole recombination channels are significantly inhibited in the mixed MA0.6FA0.4PbI3 perovskite.8 Recently, Marco et al. have demonstrated through PL and time-resolved PL measurements that the electron-hole recombination rate is decreased by addition of the GA cation into the pure MAPbI3 perovskite.28 The carrier lifetimes of the GA doped films are an order of magnitude greater than those of the pure MA films. The authors suggested that GA cations may reduce formation of iodide vacancies and passivate under-coordinated iodine species, located at grain boundaries and in bulk, by hydrogen bonding.28 Nazeeruddin and co-authors have shown that stability of the MAPbI3 perovskite is improved by incorporation of the large GA cation into the pure MAPbI3 crystal structure, enhancing the PCE to 19.3%.29 An atomistic rationalization of the demonstrated improvement in the device performance achieved by doping MAPbI3 with larger organic cations can advance fundamental understanding of halide perovskite properties and suggest routes towards better solar cells. In this letter we demonstrate that reduction of nonradiative electron-hole recombination in MAPbI3 doped with the larger FA and GA cations arises from 4


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stiffening of the perovskite crystal lattice and corresponding decrease in electron-phonon coupling. Motivated by the recent experimental findings,8, 27,28, 30 our

ab initio time-domain simulations demonstrate that fluctuations of the Pb and I atoms, which form the inorganic lattice and support electron and hole wavefunctions, decrease by 10 to nearly 50%, when 25% of MA cations are replaced with either FA or GA. The larger GA cation has a stronger effect on the dynamics of the inorganic lattice, and the effect is more pronounced for the I than Pb atoms. The nonadiabatic (NA) electron-phonon coupling decreases by up to a factor of 3, while the elastic electron-phonon scattering rate responsible for loss of coherence in the electronic subsystem is reduced by 30%, and the bandgap remains virtuall unchanged. As a result, the electron-hole recombination time increases by nearly an order of magnitude in MA0.75GA0.25PbI3 and by a factor of two in MA0.75FA0.25PbI3, relative to pristine MAPbI3. The strongly suppressed motions of Pb and especially I ions have a positive long-term effect on perovskite properties as well. They demonstrate increased stability of the doped systems, slow down ion diffision taking place under an electric bias, and reduce formation of defects, such as iodine interstitials and vacancies, that are common

in

halide

perovskites.

The

calculated

nonradiative

electron-hole

recombination times range from hunderds of picoseconds to nanoseconds, and show excellent agreement with the experimental data.31-33 The established mechanism responsible for increased lattice stiffness and reduced charge carrier losses provides means for improvement of performance and stability of halide perovskite solar cells and other devices. 5



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The NA molecular dynamics (NAMD) simulations are performed using the decoherence-induced surface hopping (DISH)34 approach implemented within the real-time time-dependent density functional theory (TDDFT).35,36 The lighter and faster electrons are treated quantum mechanically, whereas the heavier and slower nuclei are described semiclassically. It is essential to consider quantum decoherence, because the nonradiative electron-hole recombination takes hundreds of picoseconds, which is several orders of magnitude longer than the coherence time. The method has been applied succesfully to elucidate other properties of halide perovskites, including the dependence of excited state lifetime in 2D perovskites on number of layers,37 the influence of chemical composition on charge recombination in CsPbX3 quantum dots,38 the origin of hot luminescence in MAPbBr3,39 the effect of Lewis base passivation40 and water coverage41 on charge localization and recombination, the role of defects42 and doping43-45 on excited state dynamics, the influence of ferroelectric order on charge separation and recombination,46 etc. The technique has been applied to transition metal dichalcogenides,47-53 and a broad range of other systems.54-62

A

detailed description of the theoretical approach and its implementation can be round in.63,64 The geometry optimization, adiabatic MD, and NA coupling calculations are conducted with the Vienna Ab initio Simulation Package (VASP).65 The electron exchange

and

correlation

interactions

are

described

using

the

Pedrew-Burke-Ernzerhof (PBE) functional.66 The interaction between the ionic cores and the valence electrons are treated by the projector-augmented wave (PAW) 6


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method.67 The van der Waals interactions are described by the Grimme DFT-D3 approach.68 The plane-wave energy cutoff of 400 eV is used in all calculations. The structure is optimized using the 4×4×4 Monkhorst-Pack k-point mesh.69 A denser k-point mesh of 8×8×8 is employed to obtain the density of states.69 The adiabatic and NAMD simulations are performed at the Γ-point, which gives the bandgap of the studied materials. Because intraband electron and hole relaxation occur much faster than elctron-hole recombination, it is sufficient to consider recombination across the direct band gap at the Γ-point. Since the simulation cell contains several unit cells of MAPbI3, the Γ-point calculation already includes multiple k-points of the Brillouine zone of the unit cell, for both electrons and phonons. After relaxing the geometry at 0 K, all three structures are heated to 300 K via velocity rescaling. Then, 6 ps adiabatic MD trajectories are generated in the microcanonical ensemble with a 1 fs time step. The PYXAID code63,64 is used to perform the NAMD simulations for the electron-hole recombination. The decoherence time is evaluated as the pure-dephasing time of the optical-response theory.70 The NA Hamiltonian obtained for the 6 ps trajectories, which are sufficient to sample the essential atomic motions, is iterated several times in order to obtain longer-time NA dynamics. 1000 initial configurations are selected randomly from the 6 ps trajectory and are used as initial conditions for NAMD. For each initial condition 100 stochastic processes are sampled for the DISH simulations.

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Figure 1. Geometries of (a) MAPbI3, (b) MA0.75FA0.25PbI3 and (c) MA0.75GA0.25PbI3 at 0 K (top) and 300 K (bottom).

The optimized lattice constant of the pseudocubic phase71 of MAPbI3 is 6.29 Å, agreeing well with the experimental value of 6.33 Å.72 The optimized MAPbI3 unit cell has been used to create the (2×2×2) 96-atom supercell, Figure 1a. The MA0.75FA0.25PbI3 and MA0.75GA0.25PbI3 structures are obtained by replacing two MA cations with either FA or GA cations, respectively, Figures 1b,c. The 25% doping concentration provides a good representation of the experiments27,28 that demonstrate 0 to 100% doping with FA27 and up to 1/6 (~17%) doping with GA.28 The FA and GA doping concentrations are kept the same in order to compare the dopants by focusing on their chemical indentity. The top panels of Figure 1 present the optimized geometries, while the bottom panels show the structures at the end of the 6 ps trajectories at 300 K. The geometries of MA0.75FA0.25PbI3 and MA0.75GA0.25PbI3 distort slightly relative to the perfect MAPbI3 geometry at 0 K, demonstrating that replacement of 25% of MA cations with either FA or GA maintains the perovskite crystal structure. The organic cations randomize their orientations, and the inorganic 8


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cages distort significantly at room temperature. The average length of the I-Pb bonds in MAPbI3 is 3.157 Å at 0 K. The average bond length increases to 3.364 Å at 300 K. These values are consistent with those obtained with other DFT calculations: 3.19-3.31 Å73 and 3.25 Å.74 The averaged length of the I-Pb bonds in MA0.75FA0.25PbI3 is 3.167 Å at 0 K, which is 0.01 Å greater than in MAPbI3. At room temperature, the average I-Pb bond length in MA0.75FA0.25PbI3 is 3.320 Å. The thermal expansion is 0.153 Å compared to 0.207 Å in MAPbI3, indicating that the mixed cation structure is stiffer than the pristine structure. The average I-Pb bond lengths in MA0.75GA0.25PbI3 are 3.179 Å at 0 K and 3.312 Å at 300 K. The thermal expansion is the smallest here, 0.133 Å, demonstrating that the GA doped structure is the stiffest.

Table 1. Standard deviations (Å) in positions of the Pb and I atoms in MAPbI3, MA0.75FA0.25PbI3 and MA0.75GA0.25PbI3. MAPbI3

MA0.75FA0.25PbI3

MA0.75GA0.25PbI3

Pb

0.537

0.492

0.452

I

0.768

0.602

0.523

In order to quantify the thermal fluctuations of the atoms forming the inorganic sublattice in the halide perovskites, we compute the standard deviation of the atomic ur

ur

ur

positions, σ i = 〈 ( ri − 〈 ri 〉 ) 2 〉 . where ri stands for the location of atom i, and the angular bracket represents canonical averaging. The values reported in Table 1 9



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characterize the lattice stiffness further, and provide important insights into nonradiative charge recombination, in particular, since electrons and holes are localized on the Pb and I atoms, and the NA coupling depends on nuclear velocity that correlates with nuclear fluctuation. The data lead to following three conclusions: first, iodine atoms fluctuate more than leads, since they are almost twice lighter; second, the fluctuations decrease significantly upon doping MAPbI3 with larger cations, the larger the dopant the smaller the fluctuations; and third, the fluctuations decrease more significantly for iodines than leads, compare factor of 1.47 vs. 1.27.

Besides

smaller NA electron-phonon coupling, the decreased iodine fluctuations indicate that the doped perovskites are much less prone to iodide diffusion that is responsible for the current-voltage hysteresis.75

Figure 2. Projected densities of states (PDOS) of (a) MAPbI3, (b) MA0.75FA0.25PbI3 and (c) MA0.75GA0.25PbI3.

The projected densities of states (PDOS) of MAPbI3, MA0.75FA0.25PbI3 and MA0.75GA0.25PbI3 are shown in Figure 2. The PDOS are separated into contributions from the organic cations (MA, FA, GA), Pb and I. The highest occupied molecular 10


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orbital (HOMO) is formed by I 5p atomic orbitals, with some contributions from Pb 6s orbitals. The lowest unoccupied molecular orbital (LUMO) arises from Pb 6p orbitals, with contributions from I 5p orbitals. The PDOS of the three systems are consistent with the charge densities shown in Figure 3. The densities undergo virtually no change upon substition of MA with either FA or MA, with the only visible difference being a slighly higher localization of the LUMOs on the Pb atoms in the regions near the dopants. The calculated bandgap for the MAPbI3 system is 1.53 eV, which shows good agreement with the experimental bandgap of 1.55 eV.71 The 1.49 eV bandgap of MA0.75FA0.25PbI3 is smaller than in pure MAPbI3, because replacing MA with FA changes the metal−halide−metal bond angle.76 The bandgap increases in MA0.75GA0.25PbI3 to 1.59 eV, due to reduction in antibonding interactions between the Pb and I atoms.77

Figure 3. HOMO and LUMO charge densities in (a) MAPbI3, (b) MA0.75FA0.25PbI3 and (c) MA0.75GA0.25PbI3, in their optimized geometries.

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Figure 4. Fourier transforms of autocorrelation functions for the HOMO−LUMO gap fluctuations in (a) MAPbI3, (b) MA0.75FA0.25PbI3, and (c) MA0.75GA0.25PbI3.

Fourier transforms (FT) of the HOMO-LUMO energy gaps shown in Figure 4 characterize the phonon modes that couple to the electronic subsystem during the nonradiative electron-hole recombination. Electron-vibrational interactions give rise to both elastic and inelastic scattering. Elastic electron-phonon scattering causes loss of coherence between the excited and ground electronic states, formed during the NA transition, while inelastic scattering leads to energy exchange between the electronic and vibrational subsystems. The FT directly characterize the modes involved in elastic scattering, since both the FT and the decoherence function are obtained from the energy gap autocorrelation function (ACF).70, 78 The FT provide a less direct measure of the modes contributing to the NA coupling. Nevertheless, they characterize these modes as well, in particular, since the NA transition rate can be related to the curvature (i.e. frequency) of the energy gap.79 Only low-frequency vibrations participate in the nonradiative decay in all three systems. The spectra in Figure 4 show several modes with frequencies under 300 cm−1. 12


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The major peak slightly below 100 cm−1 can be attributed to the Pb−I stretching mode.80 The weak higher frequencies features around 150 cm−1, Figure 4c, and 250 cm−1, Figure 4a,b, can be ascribed to librations of the organic cations.71, 80,81 Since the cations do not contribute to the HOMO and LUMO, which are formed entirely by the Pb and I atoms, Figures 2 and 3, they couple to the electron and hole via long-range electrostatic interactions and by mixing with vibrations of the inorganic lattice. The frequency of the major peak is slightly higher in MAPbI3 than MA0.75FA0.25PbI3 and MA0.75GA0.25PbI3. The small redshift upon doping with the heavier FA and GA species indicates that the organic cations couple weakly to the vibrations of the inorganic lattice, whose vibrational frequency depends slighly on the cation mass.

Figure 5. Pure-dephasing functions for the HOMO−LUMO transition in the three systems. The inset shows the unnormalized autocorrelation functions of the bandgap fluctuation. Their initial values are equal to the bandgap fluctuation squared. Larger initial values result in faster dephasing.78

Figure 5 shows the optical pure-dephasing functions obtained with the 13



second-order cumulant approximation,70, 78 The pure-dephasing times, τ, summarized in Table 2, are obtained by Gaussian fitting, exp 0.5 / . As one can anticipate, replacing MA with the heavier FA and GA slows down pure-dephasing, with the heavier GA producing a slightly longer time than FA. Perhaps unexpectedly, the difference does not stem from the fact that FA and GA move more slowly than MA. Rather, pure-dephasing gets decelerates upon doping because the amplitude of the fluctuation of the electronic energy gap is decreased. The inorganic Pb-I lattice, supporting both HOMO and LUMO, becomes stiffer with insertion of the larger organic cations and moves less. This is evidenced by the HOMO-LUMO gap ACF shown in the insert of Figure 5. The ACF decay and oscillate with similar frequencies, because the key phonon modes are the same in all three systems, Figure 4. However, the ACF initial value, corresponding to the gap fluctuation squared,78 is notably higher for MAPbI3.

Figure 6. Electron-hole recombination dynamics in the MAPbI3, MA0.75FA0.25PbI3 and MA0.75GA0.25PbI3 systems.

14


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Figure 6 presents time-dependent population of the first excited state for the three perovskite systems. The electron-hole recombination times, τ, summarized in Table 2, are obtained via the short-time linear approximation to the exponential decay,

= exp / ≈ 1 / . The calculated recombination times are in the hunderds of picoseconds to nanoseconds range, in good agreement with the experimental data.31-33 The replacement of a quarter of MA cations with FA slows down the nonradiative decay of the excited state by a factor of 2. The replacement of MA with GA increases the lifetime by a factor of 7. Considering the three factors that govern the excited state lifetime, namely, the energy gap, the NA coupling and the pure-dephasing time, Table 2, we observe the biggest difference with the coupling, which changes by a factor of 3. The bandgaps differ very little, while the pure-dephasing time varies by 30%. Thus, we conclude that it is the decreased NA electron-phonon coupling which is responsible for the increased nonradiative charge carrier lifetime. The weaker NA coupling competes successfully with the slighly longer coherence time, which by itself favors faster dynamics. The NA coupling decreases, Table 2, because the fluctuations of the Pb and I atoms, and particularly iodines, Table 1, diminish strongly upon doping MAPbI3 with the larger organic cations.

Table 2. Experimental bandgap, average absolute nonadiabatic (NA) coupling, pure-dephasing time, and nonradiative electron-hole recombination time in the MAPbI3, MA0.75FA0.25PbI3 and MA0.75GA0.25PbI3 systems. 15



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Bandgap

NA coupling

Dephasing

Recombination

(eV)

(meV)

(fs)

(ps)

MAPbI3

1.53

2.02

4.5

315

MA0.75FA0.25PbI3

1.49

1.40

5.7

600

MA0.75GA0.25PbI3

1.59

0.67

6.0

2310

. In summary, our TDDFT-NAMD simulations of nonradiative electron-hole recombination in methylammonium lead halide perovskites doped with larger organic cations have rationalized the observed enhancement in the charge carrier lifetimes. The nonradiative recombination is the major cause of charge and energy losses in these materials, decreasing efficiencies of perovskite solar cells and other devices. The simulations show that the enhanced lifetime arises from significant stiffening of the inorganic Pb-I lattice upon insertion of the larger cations. The NA electron-phonon coupling is greatly decreased, while at the same time, the Pb-I lattice maintains its structure, and the fundamental electronic bandgap remains essentially unchanged. Fluctuations of iodine atoms are reduced most significantly, and this fact is also important for long-term perovskite stability and elimination of iodide diffusion, which is responsible for current-voltage hysteresis and induces formation of defects, such as iodine interstitials and vacancies. The nonradiative electron-hole recombination is promoted by electronic coupling to Pb-I vibrations, which interact weakly with motions of the organic cations. The pure-dephasing time, the inverse of which determines homogeneous optical linewidth, extends slightly in the presence of the heavier cations. The calculated nonradiative recombination times range from 16


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hundreds of picoseconds to a few nanoseconds, in good agreement with the experimental data. The simulations rationalize how a judical choice of the organic cation mixture in lead-halide perovskites can be used to improve its stability, and enhance charge carrier lifetimes and diffusion lengths. The fundamental principles formulated in this work apply to other perovskite structures. For instance, one can consider simultaneous changes in composition of both organic (MA+, FA+, GA+) or inorganic (Cs+) cations, and halides (I-, Br-, Cl-), in order to achieve stiff and stable structures with desireable bandgaps. The inorganic lattice stiffening can be engineered for Pb-free perovskties as well. The study formulates and rationalizes mechanistically an effective way for suppressing nonradiative carrier recombination and raising performance of perovskite solar cells.

Notes The authors declare no competing financial interests.

Acknowledgements This work was supported by the National Science Foundation of China (Grant Nos. 21573022 to R. L. and 21520102005, 21421003 to W.-H.F.), and the U.S. Department of Energy (Grant DE-SC0014429 to O.V.P.). R.L. acknowledges financial support by the Fundamental Research Funds for the Central Universities, the Recruitment Program of Global Youth Experts of China, and the Beijing Normal University Startup. O.V.P. thanks the 1000 Talents plan for support during his visit to 17



Beijing Normal University.

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Increased Lattice Stiffness Suppresses Nonradiative Charge

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