Chlorine Passivation of Grain Boundary Suppresses ElectronâHole

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Chlorine Passivation of Grain Boundary Suppresses Electron-Hole Recombination in CsPbBr3 Perovskite by Nonadiabatic Molecular Dynamics Simulation Yutong Wang, Jinlu He, Yaochun Yang, Zhenkui Zhang, and Run Long ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.9b00220 • Publication Date (Web): 03 Apr 2019 Downloaded from http://pubs.acs.org on April 3, 2019

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ACS Applied Energy Materials

Chlorine Passivation of Grain Boundary Suppresses ElectronHole Recombination in CsPbBr3 Perovskite by Nonadiabatic Molecular Dynamics Simulation Yutong Wang,1 Jinlu He,1 Yaochun Yang,2 Zhenkui Zhang,3 Run Long1 1College

of Chemistry, Key Laboratory of Theoretical & Computational

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

Laboratory of Materials Modification by Laser, Ion and Electron Beams

(Ministry of Education), Dalian University of Technology, Dalian 116024, P. R. China 3School



of Science, Langfang Normal University, Langfang 065000, P. R. China

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

ACS Paragon Plus Environment

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Abstract: Nonradiative charge recombination comprises a main pathway for energy losses that impedes the performance of all-inorganic perovskite solar cells. Grain boundaries (GBs) defects are unavoidable in low-temperature solution-processed perovskite polycrystalline films but their role remains unclear. By performing ab initio nonadiabatic (NA) molecular dynamics simulations, we illustrate that electron-hole recombination in CsPbBr3 takes place over 100 picoseconds, achieving a good agreement with experiment. Introduction of GBs into CsPbBr3 accelerates the recombination while GBs doping with chlorine notably slows it down. Importantly, GBs do not create deep electron traps because they only narrow the band gap slightly. GB localizes electron wave functions at boundaries and activate additional phonon modes, leading to an enhanced NA coupling and a shortened coherence time. Consequently, the interplay between the three competitive factors accelerates the recombination by a factor of 2. Chlorine doping diminishes the mixing of electron and hole wave functions and reduces the NA coupling, which also shortens the coherence time further by introducing higher frequencies phonons, notably delaying the recombination. Our study establishes the atomistic mechanism that the acceleration and retardation in electron-hole recombination induced by GBs and chlorine doping in CsPbBr3 perovskite, providing new insights to improve the material properties via passivating the GB by chemical doping. Keywords: All-inorganic Perovskite CsPbBr3, Grain Boundary, Electron-Hole Recombination, Nonadiabatic Molecular Dynamics, Time Domain Density Functional Theory 2


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1. INTRODUCTION Hybrid organic-inorganic lead halide perovskites (HOIPs) have attracted substantial interest because of their simple solution/vapor-chemistry process,1-4 suitable direct bandgap,5,6 strong optical absorption,7 long carrier diffusion length,8 lead to a prominent power conversion efficiency (PCE) of HOIP solar cell exceeding 23.7% recently.9 However, the thermal and moisture instability for HOIPs caused by organic components such as MA (CH3NH3+) constitutes a serious challenge for the further development and practicality target of perovskite solar cells.10-14 The disadvantages motivate experimental synthesis of all-inorganic halide perovskites CsPbX3 (X = Cl, Br, I) because they have simultaneous structure stability and outstanding optoelectronic properties,15-18 such as defect density, long carrier diffusion length and high charge mobility and collection efficiency. These advantages make the PCE of all-inorganic perovskite solar cells exceeds 15%,19 and extend the applications to X-ray20 and other photoelectronic devices.21,22 Similar to traditional semiconductors and HOIPs, all inorganic halide perovskites are typically polycrystalline films with unavoidable grain boundary (GB) defects. The role of GBs play in traditional semiconductors depends on materials. In principle, GBs are generally considered to be detrimental to silicon solar cells,23 because of the dangling bonds and associated midgap states which can accelerate nonradiative energy loss. However, GBs play benign role in CdTe,24 Cu(Ga,In)Se2,25,26 and black phosphorus,27 that can significantly enhance charge carrier collection and reduce charge recombination, due to absent of deep trap levels within their band gaps. 3



Although GBs in HOIPs have been extensively investigated,28-35 the influence of GBs on the excited-state lifetime and optoelectronic device performance remains elusive. Experiments have shown both negative28,29 and positive30-32 effect of GBs on the charge dynamics of the most studied MAPbI3 perovskite. Both Ginger group and Mohite group have demonstrated that GBs exhibit fast nonradiative decay in MAPbI3 perovskite because charge recombination often occurs at the boundary region due to high charge-trap densities at GBs.28,29 While Zhu and coauthors have shown that electron-hole recombination takes places primarily in the non-GB regions of MAPbI3,31,32 arguing that GBs are benign to excited-state carrier lifetimes because GBs are shallow defects attributing to the strong Pb 6s- I 5p orbital hybridization and high iconicity of the Pb-I bond.33,34 However, charge dynamics relies on not only the electronic energy gap of host material but also the electron-vibrational interaction and phonon-induced loss of quantum coherence,36-39 verified by our previous work that GBs suppress charge recombination because of the increased electron-phonon coupling and reduced electronic band gap.35 The reported contradictory results on both experimental and theoretical works on HOIPs MAPbI3 have motivated the research focusing on the influence of GBs and chemical doping affecting the excited-state charge dynamics and solar cell performance of all-inorganic perovskites. Duan et al.40

have reported that the reduced grain size

increases charge recombination at GBs and accelerates the energy and charge losses in the CsPbBr3-based photovoltaic devices. Song et al.41 have demonstrated that the performance of CsPbBr3 light-emitting diodes can be improved by passivation of 4


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detrimental nonradiative defects at both the GBs and the non-GBs using tetrabutylammonium bromide additive into perovskite precursors. Li et al.42 have shown for the first time that the Cl doping in cubic CsPbBr3 improves the photovoltaic performance attributing to the enhanced carrier lifetime, diffusion length, extraction rate and suppressed nonradiative recombination. Alternatively, Guo et al.43 have suggested that GBs are benign associated with the fact that GBs do not create deep levels in the midgap by first-principles calculations. The influence of GBs on the excited-state lifetimes and Cl doping effect play in the all-inorganic CsPbBr3 perovskite performance strongly calls theoretical studies in charge recombination dynamics in GB region with and without Cl doping. Stimulated by both the experimental and theoretical works,40-43 we carry out a theoretical simulation using a combination of time-dependent density functional (TDDFT)44-46 and nonadiabatic molecular dynamics (NAMD),47,48 to interpret the nonradiative electron-hole recombination in CsPbBr3, CsPbBr3 containing GBs, and Cl-doped GBs. The study demonstrates that in the pristine CsPbBr3, the nonradiative electron-hole recombination occurs over 100 p, in a good agreement with experiment.49 GBs only reduce the band gap slightly by introducing shallow defects near band edges and enhance NA coupling by introducing additional phonon modes that couple of the electronic subsystem. The broader and higher frequencies created by symmetry breaking in GBs shorten the coherence time. Consequently, the interplay between narrowed band gap, enhanced NA coupling and rapid loss of coherence accelerates electron-hole recombination by a factor of 2. GBs doping with chorines reduce electron 5



and hole wave functions mixing, lower the NA electron-phonon coupling. Furthermore, replacing heavier bromines with lighter chlorines introduces higher frequencies phonons, accelerating the phonon-induced loss of coherence further. As a consequence, the simultaneous contribution of the two factors slows the recombination by a factor of 4.6. Our simulations establish vital factors that GBs accelerate the nonradiative charge recombination of CsPbBr3 while chlorine doping retards it, providing critical insights for optimizing the performance of all-inorganic perovskite materials and devices.

2. COMPUTATIONAL METHODS The simulations are carried out with the mixed quantum-classical decoherenceinduced surface hopping (DISH)47 NAMD technique,48 implemented within the TDDFT.44-46 The approach describes electrons quantum mechanically, and treats nuclei semi-classically. This approximation is reasonable because electrons are lighter and faster than nuclei. DISH incorporates decoherence within the electronic degrees of freedom arising from interactions with the nuclei. The decoherence is analogue to the pure-dephasing in optical response theory and whose time is calculated in the secondorder cumulant approximation.50 The decoherence correction is needed because the decoherence occurs significantly faster than the electron-hole recombination.49 This NAMD approach has been widely used to investigate photoexcitation charge dynamics in a wide range of systems, including perovskites doping with foreign atoms51 and containing intrinsic defect,52 lattice deformation,53 forming localized charge,54 and MoS2/ WSe2 junction,55 etc.36,38,56 6


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Geometry relaxation, finite temperature MD, and NA electron-phonon coupling calculations are performed using the plane-wave pseudopotential methods as implemented in the Vienna Ab initio Simulation Package (VASP).57 The PedrewBurke-Emzrhof functional is used to describe electron exchange-correlation effects,58 and the projector-augmented wave approach is employed to treat electron-core interactions.59 A 400 eV energy cutoff for plane-wave basis set has been employed for geometry optimization, electronic structure and NA coupling calculations. The geometry relaxation has been done for both lattice constants and atomic coordinates of the cubic CsPbBr3 unit cell. The simulation cell of CsPbBr3, GB, and Cl-doped GB is optimized with a 4 × 2 × 1 Monkhorst–Pack k-point mesh.60 The optimization stops until the force on each atom is less than 0.01 eV/Å. To stabilize all the systems during geometry optimization and MD simulations, the van der Waals interactions within the perovskites are taken into account with Grimme DFT-D3 method.61 All the structures are optimized at 0 K. Then the three systems are heated to 300 K with repeated velocity rescaling. After equilibration, 6 ps adiabatic MD trajectory was obtained in the microcanonical ensemble with a 1 fs atomic time step. Then, 1000 initial geometries were chosen from the adiabatic MD trajectory as initial configurations as the PYXAID code input for simulating nonradiative electron-hole recombination.48,62

3. RESULTS AND DISCUSSIONS In order to exclude the size effect on photoinduced dynamics since NA coupling 7



is tightly depending on the number of atoms in simulation cells, we constructed (1×2×10) CsPbBr3 supercell containing 100 atoms (Figure 1a) and same size Σ5 (210) GB structure (Figure 1b) based on the relaxed CsPbBr3. The optimized lattice constant of CsPbBr3 is 5.899 Å53 and which is approaching to the experimental value of 5.870 Å.63 In the case of Cl-doped GBs, we consider all possible dual doped-configurations and find that replacing two bromine atoms around dangling bonds at the GB with two chlorine atoms is energetically favorable (Figure 1c).

Figure 1. Simulation cell showing the optimized geometry (left panel) and a snapshot at 300 K (right panel) of (a) 100-atom (1×2×10) pristine CsPbBr3, (b) 100-atom Σ5 (210) GB, and (c) Cl-doped GB. Thermal motions impact the geometries, and thence, affect the charge localization and recombination dynamics.

The average Pb-Br bond length in the optimized CsPbBr3 is 2.950 Å, consistent with the experimental value of 2.935 Å.64 The GB geometry with and without Cl doping remains stable associated with that the average Pb-Br bond length changes into 2.977 Å and 2.966 Å, respectively. Upon heating to 300 K, the pristine CsPbBr3 geometry 8


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experiences a slight distortion thanks to the hard stiffness of inorganic Pb-Br framework. While both the GBs and Cl-doped GBs happen significant distortions because symmetry breaking activates additional phonon modes and improves movements of bromine and lead atoms, leading to a change in electron-hole interaction and affecting charge recombination because bromine and lead atoms constitute the band edge states, particularly including the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), respectively.65 In particular, replacing the two most active bromine atoms with chlorine atoms at GB could increase band gap relative to the GB system because Cl 3p orbital is lower than Br 4p orbital. Consequently, the NA electron-phonon coupling is expected to be decreased because electron and hole is inclined to decouple spatially.

Figure 2. PDOS of (a) pristine CsPbBr3, (b) Σ5 (210) GB, and (c) Cl-doped GB calculated from the optimized geometry. The component of the chlorine atoms is enlarged by 10 times. Zero energy is set to the Fermi level. The HOMO is composed of Br and Pb orbitals, and LUMO is mainly contributed by Pb orbitals. The defective systems with and without Cl doping create only shallow trap states.

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The projected density of states (PDOS), calculated from optimized structures, of the pristine CsPbBr3, CsPbBr3 with a Σ5 (210) GB, and a Cl-doped GB is shown in Figure 2. The PDOS of the CsPbBr3 with and without GBs is plotted into the contributions of Cs, Pb, and Br atoms. In the case of Cl-doped GB, the contribution of Cl is also included in the PDOS that is magnified 10 times. Figure 2a shows that in the pristine CsPbBr3, Br atoms contribute primarily to the HOMO and Pb atoms contribute secondarily while the LUMO arises primarily from Pb atoms. Importantly, Cs atoms do not directly contribute to the HOMO and the LUMO, and thus they have little effect on the NA electron-phonon coupling. In turn, they affect electron–hole recombination in an indirect way via inducing Pb-Br octahedral tilting.53 The calculated 1.59 eV direct band gap of pristine CsPbBr3 is in consistent with previous first-principles calculation.66 but smaller than the experimental value of 2.36 eV.67 The underestimation arises due to semilocal PBE functional overestimating electron delocalization effect. Although the band gap calculated by means of HSE06 functional with spin-orbit coupling (SOC)68 correction or the GW method69 has achieved good agreement with experiment, which need an extremely high computational cost. NAMD requires thousands of electronic structures from a long trajectory, it is impossible to use GW+SOC method to study photoinduced charge dynamics. And hence, we employ PBE functional to investigate the electron-hole recombination process because which

generated comparable charge

recombination times53,70 to experiments71,72 for all-inorganic perovskites. The calculated band gap of the Σ5 (210) GB and Cl-doped GB is 1.39 and 1.42 eV (Figure 2 b and c), respectively. Importantly, in the both cases GBs avoid midgap states. 10


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Generally, smaller band gap makes the electron-hole recombination time shorter if chemical environments are same in two systems, because NA coupling is proportional to the inverse energy gap. The nonradiative electron-hole recombination is primarily determined by the NA electron-vibrational coupling, and which is depending on the overlap of electron and hole wave functions. The charge densities of the key orbitals, such as HOMO and LUMO, for the pristine CsPbBr3, Σ5 (210) GB and Cl-doped GB are shown in Figure 3. For the pristine CsPbBr3, the HOMO and LUMO are nearly uniformly delocalized on the Pb/Br and Br atoms (Figure 3a) in the simulation cell. Figure 3b shows that in the case of GB system the HOMO remains delocalized on the Pb/Br atoms. In contrast, the LUMO is localized on the GBs region due to symmetry breaking. Doping Cl into the GB system remains the LUMO largely unaffected, while reduces the charge distribution on the HOMO, particularly on the two Cl atoms (Figure 3c). One should be noted that the electron and hole wave functions are supported primarily by the Pb and Br atoms, respectively, minimizing HOMO-LUMO overlap. On the contrary, symmetry breaking activates additional phonons contributing to NA coupling despite the HOMO-LUMO overlap is even smaller in the GB system, allowing to enhance the NA coupling (Table 1). Cl doping reduces the HOMO-LUMO overlap further and as a result decreases the NA coupling relative to the GB system (Table 1). The strength of NA coupling decreases from the GB (3.01 meV), to the pristine CsPbBr3 (2.58 meV), and to the Cl-doped GB (1.86 meV), because it relies on the mixing of HOMO-LUMO wave functions, ―iħ⟨ϕj│∇𝐑│ϕk⟩. 11



Figure 3. Charge densities of the photoexcited states showing HOMO and LUMO of (a) pristine CsPbBr3, (b) Σ5 (210) GB, and (c) Cl-doped GB at 0 K. GBs localize electron at the boundary and Cl dopants reduce the electron and hole charge densities and then decrease NA coupling.

Electron-vibrational interactions create NA electron-phonon coupling and induce loss of quantum coherence, corresponding to inelastic and elastic electron-phonon scattering. Both of them affect electron-hole recombination. By performing Fourier transforms (FTs) of the fluctuations for the energy gaps between the HOMO and LUMO in the three systems, we obtained the spectral densities that characterize the phonon modes participating in the electron-hole recombination. Shown in Figure 4, low-frequency phonon modes play major roles in creating NA electron-phonon coupling and promote the nonradiative charge relaxation. Since GBs break the symmetry, additional phonon modes available in the higher frequencies region engage in the electron-hole recombination process. Replacing heavier bromines with lighter chlorines activate the range of vibration frequencies further. Focusing on particular 12


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phonon modes can correlate the lattice vibrations with the charge dynamics. The dominant peak in the pristine CsPbBr3 at 140 cm-1 is the diagnostic mode of the inorganic Pb-Br framework.73,74 The minor peak at 100 cm-1 can be associated with the vibrations of the [PbBr6]4- octahedra.73,74 These vibrational modes modulate the geometries, generate

the NA electron-phonon coupling, induce loss of quantum

coherence, and cause nonradiative charge relaxation. Symmetry breaking in the presence of GBs leads to the major peak redshift as well as introduces many additional modes, inducing rapid decoherence. Chlorine doping broadens the range of modes as well as create higher-frequency vibrations that couple to the electronic subsystem, accelerating decoherence process further.

Figure 4. Phonon modes involved in the photoinduced electron-hole recombination in the pristine CsPbBr3, Σ5 (210) GB, and Cl-doped GB. The data are obtained by 13



performing Fourier transforms of autocorrelation functions of the fluctuations of the HOMO-LUMO energy gap.

Besides the NA electron-phonon coupling and electronic energy gap, quantum decoherence time is another factor influencing electron-hole recombination. The decoherence time, known as pure-dephasing time in optical response theory,50 can be calculated using the second-order cumulant approximation.75 Figure 5 shows the puredephasing functions. Fitting the data to a Gaussian, exp[-0.5(t/τ)2], gives the puredephasing times τ (Table 1). The very short, sub-5fs, coherence times are responsible for long-lived excited-state lifetime in all-inorganic perovskites. It is manifested by the quantum Zeno effect that rapid decoherence suppresses quantum dynamics, in which the quantum transition stops in the limit of infinitely fast decoherence.76-78 The inset of Figure 5 shows the unnormalized autocorrelation functions (ACF) of fluctuations of the HOMO-LUMO energy gap. The very short pure-dephasing times arise due to involvement of a broad range of phonon modes (Figure 4). The inset of Figure 5 demonstrates that the pure-dephasing time is short if the initial value of the unnormalized ACF is large.79 The initial value of the unnormalized ACF decreases in the sequence: Cl-doped GB > GB > CsPbBr3, leading to an opposite change trend in the pure-dephasing time.

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Figure 5. Pure-dephasing functions obtained from the unnormalized ACFs of the energy gap fluctuations for the HOMO and LUMO states in the pristine CsPbBr3, Σ5 (210) GB, and Cl-doped GB. The pure-dephasing functions are fitted by Gaussian, and the fitted pure-dephasing times are presented in Table 1. The inset shows the unnormalized ACF. Generally,75 the larger initial value is responsible for shorter puredephasing time.

Figure 6 presents the population evolution of LUMO for the pristine CsPbBr3, Σ5 (210) GB, and a Cl-doped GB. Since the experimental band gap of CsPbBr3 is known as 2.36 eV,67 we simulated electron-hole recombination dynamics of the pristine system by scaling the calculated band gap to this value by adding a constant, in order to compare with the experimentally measured time scale directly. We supposed that PBE 15



functional generates an identical error for the three system, and thus we scaled the band gap of the other two system by applying the same constant. The electron-hole recombination process was fitted at short times to a linear approximation, f(t) = exp(−t/τ) ≈ 1-(t/τ). The values of these fitting summarized in Table 1, give the recombination times. The calculated 160 ps electron-hole recombination time for the pristine CsPbBr3shows a good agreement with the experimental data.49 Importantly, we observe that GB accelerates the charge recombination by a factor of 2. The acceleration arises from the reduced band gap and increased NA coupling because GBs split symmetry and activate a broad range of phonon modes. More importantly, doping GBs with chlorines delays the recombination by a factor of 4.6. The deceleration stems from the reduced NA coupling and decreased coherence time. The change is associated with that Cl dopants decrease the overlap of HOMO/LUMO wave functions and introduce higher-frequency vibrations. The results rationalize the experiments showing that CsPbBr3 in the presence of GBs decreases the excited-state lifetime while Cl doping can efficiently extend the lifetime and enhance the solar cells performance due to suppressing the nonradiative charge and energy losses. In contrast to chlorine, iodine is heavier and slower than bromine and suppresses the loss of quantum coherence. At the same time, I 5p orbitals are higher than that of Br 4p orbitals, replacing bromine with iodine decreases the bandgap of CsPbBr3. However, larger iodine substituting to small bromine distorts the geometry of CsPbBr3 and reduces the mixing of HOMO/LUMO wave functions, making NA coupling decrease.70 Our previous work has demonstrated that the smaller NA electron-phonon coupling competes successfully with reduced band 16


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gap and slower quantum decoherence, leading to a retarded recombination in the Idoped CsPbBr3 system,70 verified by many Experiments.49,80 And therefore, it is expected that bromine replacing with iodine in CsPbBr3 containing GB decreases the electron-hole recombination operating by a different mechanism, such as charge localization.70

Figure 6. Population evolution of LUMO of the pristine CsPbBr3, Σ5 (210) GB, and Cl-doped GB.

Table 1. Bandgap, Average Absolute NA coupling, Pure-Dephasing Times, and Recombination Times for the Pristine CsPbBr3, Σ5 (210) GB, and Cl-doped GB. Bandgap

NA Coupling

Dephasing

Recombination

(eV)

(meV)

(fs)

(ps)

17



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Pristine

2.36

2.58

3.77

160

Σ5(210) (0,0) GB

2.13

3.01

2.50

75

Cl-doped GB

2.16

1.86

2.22

730

4. CONCLUSIONS Phonon-assisted the nonradiative electron-hole recombination dynamics in pristine CsPbBr3, CsPbBr3 with GBs, and Cl-doped GBs have been explored using a combination of nonadiabatic molecular dynamics and ab initio time-domain density functional theory. In agreement with previous relative time scales obtained experimentally,49 the simulations show that electron-hole recombination in pristine CsPbBr3 takes place over one hundred picoseconds. Results obtained from the GBs with and without Cl doping demonstrate that GBs accelerate charge recombination while Cl doping could suppress the recombination, resolving the long-term debate that the GBs are benign or detrimental to the excited-state lifetime and device performance of all-inorganic perovskite. On the one hand, GBs slightly reduce band gap with only introducing of shallow defects and localize electron at the boundaries for enhancing the NA coupling. On the other hand, GBs break symmetry as a result of activating more phonon modes. Consequently, GBs increase NA coupling and shorten coherence time simultaneously. They have opposite effect on excited-state lifetime and only accelerate recombination by a factor of 2. Choline doping decreases NA coupling arising due to the reduced overlap between electron and hole wave functions, and shortens the coherence time further because of introducing boarder and higher frequencies, thereby 18


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slowing the recombination down by a factor of 4.6. The results advance our understanding of the key factors affecting the excited-state lifetimes and encourage the study of these features in other all-inorganic perovskites in order to optimize the solar cell performance by precisely chemical doping strategies for device fabrication technology.

Notes The authors declare no competing financial interest.

Acknowledgements The work was supported by the National Science Foundation of China, Grant Nos. 21573022 and 51861135101. R. L. is grateful to 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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