Lead Vacancy Can Explain the Suppressed Nonradiative Electron

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Energy Conversion and Storage; Plasmonics and Optoelectronics

Lead Vacancy Can Explain the Suppressed Nonradiative Electron-Hole Recombination in FAPbI3 Perovskite under Iodine-Rich Condition: A Time-Domain Ab Initio Study Jinlu He, and Run Long J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b03095 • Publication Date (Web): 01 Nov 2018 Downloaded from http://pubs.acs.org on November 1, 2018

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The Journal of Physical Chemistry Letters

Lead Vacancy Can Explain the Suppressed Nonradiative Electron-Hole Recombination in FAPbI3 Perovskite under Iodine-Rich Condition: A Time-Domain Ab Initio Study Jinlu He, Run Long College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875, P. R. China ABSTRACT: Experiments show that the excited-state lifetime of hybrid organicinorganic perovskite, synthesized under iodine-rich conditions, can be greatly enhanced. Ab initio nonadiabatic (NA) molecular dynamics demonstrates that a single lead vacancy, which constitutes a major defect with iodine-rich environment, significantly suppresses the nonradiative electron-hole recombination in HC(NH2)2PbI3 (FAPbI3) perovskite. The simulations show that electron-hole recombination in pristine FAPbI3 occurs within one nanosecond. Introduction of a single lead vacancy weakens the NA electron-phonon coupling and prolongs the coherence time simultaneously. The weaker NA coupling competes successfully with the longer coherence time, extending the lifetime over tens of nanoseconds. The calculated recombination time scales show excellent agreement with experiment. Our study rationalizes the microscopic mechanism responsible for experimental observations, suggests a rational choice of defect can modulate perovskite excited-state lifetimes, and improve the solar cell



Corresponding author, E-mail: [email protected]

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performance. TOC Only


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Hybrid organic−inorganic perovskites (HOIPs) solar cells have attracted enormous attention due to their high power conversion efficiencies.1-6 The remarkable performance stems from low trap density,7 high photoluminescence yields,8 long carrier lifetimes,9 and large carrier diffusion lengths.7 In addition to the application of solar cells, these excellent properties have motivated HOIPs into other areas, including photocatalytic water-splitting assemblies,10 optically pumped lasers,11 and lightemitting diodes.12 In all of these applications, nonradiative charge recombination always plays an important role because such process leads excess electronic energy of photogenerated charge carriers to dissipate into heat and shortens the devices lifetime. Thus, a long-lived excited state lifetime is needed to achieve better performance of the aforementioned devices. Among dozens of HOIPs,13-22 the research mainly focuses on methylammonium lead iodide CH3NH3PbI3 (MAPbI3) due to the rapid growing of power conversion efficiency from 3.8%23 to 23.2%3 within less ten years. Despite this remarkable progress, MAPbI3 suffers from instability stemming from the migration of the CH3NH3+ cation,24 moisture degradation,25 photoirradiation,25 and even decomposition under moderate temperature,26 and these issues are detrimental to their photovoltaic performance.25 In addition, the relatively large band gap27 of 1.69 eV is greater than the optimal value of 1.35 eV for a single-junction solar cell,28 which constitutes another issue to increase its power conversion efficiency further. As an alternative, formamidinium lead halide HC(NH2)2PbI3 (FAPbI3) shows higher thermal stability29 and smaller bandgap (1.47 eV),30 leading to FAPbI3-based solar cell achieving a 22.1%



power conversion efficiency.1 There is still a room to improve the efficiency approaching to the Schochkley-Queisser limit31 with optimized technologies for materials synthesis and devices fabrication. The maximum efficiency is found to be 30% based on photo-absorber with bandgap of 1.1 eV.32 The solution-processed FAPbI3 polycrystalline films exist inevitably various defects, which play a crucial role in determining excited-state lifetime and influencing devices performance. Usually, defects create mid-gap states that act as nonradiative recombination centers and which typically accelerate electron-hole recombination and are responsible for short minority carrier lifetime. Douhal and coauthors reported the electron–hole recombination time scales in FAPbI3 ranging from 700 ps to 1400 ps using femtosecond transient absorption spectrometry and sub-picosecond time-resolved terahertz spectrophotometry.33 Yang et al. have fabricated an efficient FAPbI3 perovskite solar cell via adding excess iodide ions into the precursor solution that give rise to the increased crystalline size, and achieved an impressive power conversion efficiency partially and extremely long carrier lifetime of 1105 ns.1 The lifetime in the FAPbI3 is long and has a very high open circuit voltage, 1 indicating that some certain kinds of defects are benign in the FAPbI3 perovskite. Petrozza and coauthors demonstrated that shallow electronic levels induced by defects dramatically slow down the electron−hole recombination, enhancing the open-circuit voltage of metal halide perovskite solar cells,34 arising from that the strong Pb lone-pair s orbital and I p orbital antibonding coupling as well as the high iconicity weaken the electron-phonon coupling.35 First-principles calculations showed that lead vacancy (Pb_v) is energetically favorable forming under iodine-rich condition due to


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its low formation energy, which may be responsible for the decreased recombination rate and increased photovoltaic conversion efficiency of perovskite devices.36 To explore the microscopic mechanism responsible for the experimental observations of extended excited-state lifetime in FAPbI3 under iodine-rich environment, it is essential to conduct a real-time atomistic simulation of the nonradiative electron−hole recombination dynamics to mimic the experiment directly. Inspired by recent experimental and theoretical works,1,33,36 we perform simulations using a time-dependent density functional theory (TDDFT) combined with nonadiabatic molecular dynamics (NAMD) to study the nonradiative electron−hole recombination in pristine FAPbI3 with and without and a lead vacancy (Pb_v). The simulations demonstrate that the nonradiative electron−hole recombination in pristine FAPbI3 occurs within one nanosecond. Removing a lead atom significantly retards the recombination, extending the lifetime over tens of nanoseconds. The obtained time scales agree well with the experimental data.33 The increase in lifetime in the Pb_v system can be rationalized by the change in treads of NA electron-phonon coupling, band gap, and quantum decoherence time. The lead vacancy localizes the hole along the middle of Pb-atom column, lowers the overlap between the highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO), significantly decreasing the NA electron-phonon coupling. More importantly, lead vacancy only gives rise to shallow traps and merge into the valence band that the excited-state electron can thermally escape from the traps, remaining the band gap largely unaffected. As a result, the influence of band gap on the electron-hole recombination becomes insignificant. At



the same time, lead vacancy suppresses the atomic motions and prolongs coherence time between the HOMO and LUMO. Eventually, NA electron-phonon coupling constitutes the major factor influencing the electron-hole recombination, slowing down the recombination. The NAMD simulations employ the quantum-classical decoherence-induced surface hopping (DISH)37 implemented within the framework of time-dependent KohnSham theory.38 The approach describes nuclear degrees of freedom classically and electronic degrees of freedom quantum mechanically. DISH is developed based on the fewest switch surface hopping algorithm,39 which captures the nature of the nuclei wave functions branching and includes quantum decoherence correction in the quantum-classical approximation. Decoherence, known as pure-dephasing in the optical response theory,40 which is added in the charge recombination calculation, because the decoherence time is significantly shorter than the electron-hole recombination time.33 The approach has been used to investigate photoexcitation dynamics in a wide range of perovskite-based systems,41-50 including perovskite quantum dots,41 two-dimensional perovskites,42 perovskite passivated with water molecules43 and Lewis base,44 cation mixing,45 containing dopants46 and grain boundaries,47 forming localized charge,48-49 and interfaced with TiO2.50 A detailed theoretical method can be found elsewhere.51,52 The geometry optimization, adiabatic MD, and NA coupling calculations are performed using the Vienna ab initio Simulation Package (VASP).53 The projectedaugmented wave method is applied to describe the interactions between electron and


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ion cores.54 The Perdew-Burke-Ernzerhof (PBE) functional is employed to treat the electron exchange correlation energy.55 The plane-wave basis energy cutoff is set to 400 eV. The geometry optimization is performed at the Γ-point, because a large (3 × 3 × 2) supercell was used. A much denser Γ-centered k-meshes of 4× 4 ×4 is used to obtain accurate electronic properties.56 The adiabatic MD and NA coupling calculations are carried out at the M-point, because the direct HOMO-LUMO band gap of the pristine FAPbI3 and Pb_v systems is at the M-point. In order to stabilize the geometry optimization at 0 K and MD at 300 K, the Grimme DFT-D3 approach was used to describe the van der Waals interactions.57 After relaxing the geometry at 0 K, both the pristine FAPbI3 and Pb_v systems are heated to room temperature via repeated velocity rescaling. Then, 6 ps adiabatic MD trajectories are generated in the microcanonical ensemble with a 1 fs atomic time step. The nonradiative electron-hole recombination simulations are carried out using the PYXAID code.51,52 To simulate the electron-hole recombination, 1000 geometries are chosen randomly from the adiabatic MD trajectories as initial configurations for the NAMD simulations. The optimized lattice constants of ɑ-phase of FAPbI3 is 6.41 Å, agreeing well with experimental value of 6.36 Å.58 The 216-atom (3 × 3 × 2) supercell was created using the optimized unit cell, Figure 1a. The Pb_v system (Figure 1b) was constructed by removing a single Pb atom from the (3 ×3 × 2) supercell (Figure 1a) colored in green, corresponding to 5.6% lead vacancy concentration. Figure 1 shows geometries of the pristine FAPbI3 and Pb_v systems. The



optimized geometries at 0 K are displayed in the top panels, while the representative structures of the 6 ps MD trajectories are shown in the bottom panels. Compared to the optimized geometries, the inorganic Pb-I framework at room temperature has slight distortions, The small distortions of geometries demonstrate that two systems are stable after heating to 300 K, leading to weak electron-vibrational interactions. The largest changes of the geometries upon heating are associated with the rearrangements of the organic FA+ cations. Although the FA+ cations do not directly contribute to the NA coupling, they perturb the Pb-I sublattice and affect the electron-phonon coupling indirectly. The averaged Pb-I bond length in the optimized pristine FAPbI3 is 3.174 Å , agreeing well with experimental (3.181 Å)58 and theoretical (3.177 Å)59 data. While thermal fluctuations increase it to 3.219 Å due at 300 K. After removing a Pb atom in the pristine FAPbI3, the averaged Pb-I bond length changes from 3.166 Å at 0 K to 3.196 Å at 300 K. The bond elongations caused by thermal expansion for pristine FAPbI3 and Pb_v systems are 0.045 Å and 0.030 Å, respectively. It is evident that the Pb vacancy suppresses the motions of inorganic sublattice, shortens the Pb-I bond length, and decreases the electron-vibrational interaction. Thus, smaller NA coupling and longer decoherence time are expected to exist in the Pb_v system compared to the pristine FAPbI3 system.


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Figure 1. Geometries of (a) pristine FAPbI3 and (b) Pb_v system created by removing the Pb atom colored in green at 0 K (top) and representative geometries at 300 K (bottom).

Figure 2 shows the projected density of states (PDOS) of the pristine FAPbI3 and Pb_v systems, which are calculated using the optimized geometries. The PDOS is split into the FA, Pb, and I contributions. The HOMO is dominated by the atomic orbitals of iodine, with small contributions of Pb orbitals, while the LUMO arises form the atomic orbitals of Pb. The analysis is in consistent with other theoretical work.60 The HOMO and LUMO is separated by a wide band gap of 1.47 eV in the pristine FAPbI3 system. This amount of electronic energy is accommodated by phonons during the nonradiative electron-hole recombination. Introduction of a single lead vacancy generates shallow defects that merge into the valence band. The LUMO and HOMO orbitals constitute initial and final states for electron-hole recombination, affecting the nonradiative electron-hole recombination across the energy gap. Although organic cations FA+ do not directly contribute to the HOMO and LUMO, the rearrangements of FA+ cations



can influence the I-Pb-I backbone and affect the electron-hole recombination electrostatically.61 The calculated direct band gap of pristine FAPbI3 system at the Mpoint is 1.52 eV using the PBE functional, agreeing well with the first-principles predicted value of 1.45 eV36 and experimental value of 1.47 eV.30 A lead vacancy only decreases slightly the band gap to 1.50 eV, indicating small change in band gap that has negligible impact on electron-hole recombination. The 5.6% lead vacancy under investigation is much higher than the predicted equilibrium ones of 0.4%.62 To directly mimic the 0.4% lead vacancy concentration requires 3000-atom supercell that significantly exceeds the computational capability for first-principles NAMD simulations. Importantly, the system containing high lead vacancy concentration only gives rise to a small deformation of the inorganic Pb-I sublattice and shallow defects, Figure 1 and 2. Reduced lead vacancy concentration further decreases the impact on the geometry and remains shallow electronic states. As a result, the electron-hole recombination is suppressed. The strength of NA coupling is influenced by the overlap between the HOMO and LUMO wave functions, ―iħ⟨ϕj│∇𝐑│ϕk⟩, which enters the NA coupling matrix element. The charge densities of the HOMO and LUMO are shown in the insets of Figure 2a and 2b, respectively. The inset of Figure 2a shows that in the pristine FAPbI3 the HOMO is delocalized onto the lead and iodine atoms, while the LUMO is distributed on the lead atoms. Such situation is beneficial for achieving an enhancement in wave functions mixing and thus in NA electron-phonon coupling. Lead vacancy makes the charge density of HOMO localize on iodine and lead atoms of the middle of


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the simulation cell, while the charge density of LUMO remains largely unchanged. The circumstances diminishes the overlap of HOMO and LUMO wave functions and weakens NA electron-phonon coupling. Furthermore, the strength of NA coupling is also depending on the nuclear velocity, d𝐑/dt. And therefore, we compute the average magnitude of atomic fluctuations, 𝜎𝑖 =

⟨(𝑟 ― 〈𝑟 〉) ⟩ in the pristine FAPbI and Pb_v 2

𝑖

𝑖

3

systems. Here, 𝑟𝑖 represents for the location of atom 𝑖 at time t along the 6 ps MD trajectories, and the angular bracket gives canonically averaging. We average the standard deviations for all Pb and I atoms in the the two systems, because the HOMO and LUMO are composed by Pb and I orbitals. The obtained data summarized in Table 1 show that the standard deviations of Pb and I atoms in Pb_v are significantly smaller than those in the pristine FAPbI3, indicating lead vacancy suppresses atomic fluctuations and weakens the NA coupling further. At the same time, the decreased atomic motions lead to longer the decoherence time, Table 2.



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Figure 2. Projected density of states (PDOS) of (a) pristine FAPbI3 and (b) Pb_v systems. The inset represents the charge densities of HOMO and LUMO of each system. Zero energy is set to the Fermi level.

Table 1 Standard Deviations in the Positions of Pb and I Atoms in Pristine FAPbI3 and Pb_v systems. Pb

I

Pristine

0.439

0.762

Pb_v

0.401

0.504

Both elastic and inelastic electron-phonon scattering affect nonradiative electronhole recombination. Inelastic scattering creates the NA electron-phonon coupling, and accommodates the electronic energy lost since it induces transition from the LUMO to the HOMO. Elastic electron-vibrational interactions destroy coherence formed between the HOMO and LUMO, which affects the recombination in a subtle way. By performing the Fourier transforms (FTs) of the fluctuations for HOMO-LUMO energy gap in pristine FAPbI3 and Pb_v systems, we obtained the spectral densities that characterize the phonon modes participating in nonradiative electron-hole recombination. Figure 3 shows several modes in the 30-300 cm-1 frequency range, including phonon modes arising from inorganic Pb-I framework and the organic FA cations. In the case of the pristine FAPbI3, the main peak at 100 cm-1 can be attributed


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to the bending and stretching of the Pb-I bonds (Figure 3a).61 The mode are responsible for creating the NA electron-phonon coupling, because it originates from the inorganic sublattice. The peak at 166 cm-1 can be viewed as the libration of the organic cations.61 This mode contributes little to the NA coupling, because organic cations are lack of consisting of the band edge states. However, the organic cations influence the NA coupling though electrostatic interactions as well as the perturbation of inorganic atoms motion. Creation of a lead vacancy pushes the vibrational modes to lower frequencies due to the decreased atomic motions, leading to smaller NA electron-phonon coupling and longer pure-dephasing time, Table 2. Given the particular frequencies, the major peak at 33 cm-1 can be assigned to the octahedra distortion (Figure 3b).63 Similarly, the secondary peak at 100 cm-1 originates from the Pb-I stretching.61 Higher frequencies yield stronger electron-vibrational interactions, contributing to stronger NA coupling and faster pure-dephasing in the pristine FAPbI3 system, Table 2.

Figure 3. Fourier transforms of autocorrelation functions for the HOMO-LUMO energy gap in pristine FAPbI3 and Pb_v systems. Lead vacancy lowers frequencies,



resulting in a smaller NA electron-phonon coupling and longer dephasing time.

The pure-dephasing functions, characterizing the elastic electron-phonon scattering, are shown in Figure 4. It is computed from the autocorrelation function of the fluctuations of the HOMO-LUMO energy gaps using the second-order cumulant approximation in optical response theory.40 The calculated pure-dephasing times, τ, summarized in Table 2, are fitted the functions with a Gaussian, 𝑒𝑥𝑝( ― 0.5(𝑡/𝜏)2). The pure-dephasing times, less than 22 fs, which are significantly shorter than the electron-hole recombination times.33 Thus, it is needed to add decoherence correction into NAMD simulation. The pure-dephasing time for the pristine FAPbI3 system is shorter than that of Pb_v system, due to the higher frequencies (Figure 3) and faster atomic motions (Table 1). In order to further explore the origin of the phonon-induced pure-dephasing times between the two systems. We displayed the unnormalized autocorrelation functions (un-ACF) of the HOMO-LUMO energy gap fluctuations of the two systems, inset of Figure 4. Typically, bigger initial value and slower decay of un-ACF lead to shorter pure-dephasing time. The two un-ACFs decay on similar time scales with same oscillating period. In turn, the dephasing time is governed by the initial value. The initial value of un-ACF for pristine FAPbI3 system is dramatically larger than that in Pb_v system, giving rise to the shorter coherence time.


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Figure 4. Pure-dephasing functions for the HOMO-LUMO transition in the two systems. The inset shows the unnormalized autocorrelation functions (un-ACF), whose initial values represent the energy gap fluctuations. The bigger the initial value of the un-ACF, the faster the pure-dephasing.

Figure 5 presents the electron-hole recombination dynamics for the pristine FAPbI3 and Pb_v systems. To mimic directly the experiment,1,33 we adjust the calculated bandgap 1.52 eV of pristine FAPbI3 system to the experimental value of 1.47 eV30 by subtracting a constant. The HOMO –LUMO energy gap of the Pb_v system is scaled to 1.45 eV with the same constant. The obtained recombination time scales, τ, are summarized in Table 2, which are fitted the population decay functions in Figure 5 to

an

exponent,

( ) 𝑡

𝑃(𝑡) = 𝑒𝑥𝑝 ― 𝜏 = 1 ― 𝑡/𝜏.

The

obtained

electron-hole

recombination time in the pristine FAPbI3 system is 0.75 ns, agreeing excellently with the experimental data.46 Introduction of a single Pb vacancy significantly extends the recombination time to tens of nanoseconds. The conclusion is notably important for



solar cell applications because that shallow defects may be benign for the perovskite photovoltaic properties. The increased lifetime can be explained by the competition between NA coupling and pure-dephasing time. As shown in Table 2, the influence of NA coupling and pure-dephasing of each system is opposite to the electron-hole recombination times, and NA coupling constitutes the major factor for steering the electron-hole recombination dynamics, leading to a delayed recombination in the system in the presence of Pb vacancy compared to the pristine FAPbI3. The study reveals the microscopic mechanism responsible for the delayed electron-hole recombination in HOIPs under iodine-rich condition, and shows that defects could be beneficial for suppressing electron-hole recombination. The obtained results are very important because intrinsic defects are often considered to be detrimental to perovskite properties,64 and significant efforts are dedicated to elimination of point defects by various methods, including ligand passivation65 and slow sample growth.66

Figure 5. Electron-hole recombination dynamics in the pristine FAPbI3 and Pb_v


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systems.

Table 2. Experimental Bandgap, Absolute Averaged Value of NA Coupling, PureDephasing Time, Nonradiative Electron-Hole Recombination Time for Pristine FAPbI3 and Pb_v Systems.

Bandgap

NA coupling

Dephasing

Time

(eV)

(meV)

(fs)

(ns)

Pristine

1.47

1.21

7.3

0.75

Pb_v

1.45

0.22

21.9

16

System

By performing time-domain ab initio simulations, we investigated the nonradiative electron-hole recombination in the pristine FAPbI3 with and without a lead vacancy and established the factors responsible for the significantly delayed charge recombination in the defective system compared with the pristine FAPbI3. Understanding of these factors is significant important for successful application of the FAPbI3 perovskite and related systems in solar cell application. The simulations show that the nonradiative electron-hole recombination of pristine FAPbI3 occurs within one nanosecond. Introduction of a single lead vacancy extends the recombination time to tens of nanoseconds. The significant increase in lifetime can be rationalized by the NA electron-phonon coupling and dephasing time. Lead vacancy localizes hole charge density, diminishes overlap of electron and hole wave functions,



weakens the atomic motions, and as a consequence of reducing the NA electron-phonon coupling. At the same time, the reduced atomic fluctuations decrease electron-vitational interactions, leading to a longer pure-dephasing time. Eventually, weaker NA coupling competes successfully with longer pure-dephasing time, suppressing electron-hole recombination and achieving long-lived excited-state lifetime. The calculated time scales achieve excellent agreement with experiment. The study demonstrates that shallow defect, like lead vacancy, can be benign to the perovskite solar cells, advances our understanding of excited-state properties of perovskite, and provides useful knowledge to optimize perovskite photovoltaic properties via defect engineering.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the National Science Foundation of China, grant Nos. 21573022 and 51861135101. 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.

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