Chlorine Doping Reduces Electron–Hole ... - ACS Publications

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Chlorine Doping Reduces Electron−Hole Recombination in Lead Iodide Perovskites: Time-Domain Ab Initio Analysis Jin Liu† and Oleg V. Prezhdo*,‡ †

Department of Chemical Engineering, University of Rochester, Rochester, New York 14627, United States Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

‡

S Supporting Information *

ABSTRACT: Rapid development in lead halide perovskites has led to solutionprocessable thin film solar cells with power conversion efficiencies close to 20%. Nonradiative electron−hole recombination within perovskites has been identified as the main pathway of energy losses, competing with charge transport and limiting the efficiency. Using nonadiabatic (NA) molecular dynamics, combined with time-domain density functional theory, we show that nonradiative recombination happens faster than radiative recombination and long-range charge transfer to an acceptor material. Doping of lead iodide perovskites with chlorine atoms reduces charge recombination. On the one hand, chlorines decrease the NA coupling because they contribute little to the wave functions of the valence and conduction band edges. On the other hand, chlorines shorten coherence time because they are lighter than iodines and introduce highfrequency modes. Both factors favor longer excited-state lifetimes. The simulation shows good agreement with the available experimental data and contributes to the comprehensive understanding of electronic and vibrational dynamics in perovskites. The generated insights into design of higher-efficiency solar cells range from fundamental scientific principles, such as the role of electron−vibrational coupling and quantum coherence, to practical guidelines, such as specific suggestions for chemical doping.

T

perovskite/Al2O3 hybrids.27,32 The number depends on the wavelengths of the pump and probe pulses used to measure transient absorption decay. In this case, mismatch of the conduction bands of Al2O3 and perovskite prevents charge transfer from perovskite to Al2O3. Luminescence is observed at higher light intensities after trap states are mostly filled.28 It is slower than the nonradiative relaxation, taking 9.6 ns.8 Sandwiching perovskite thin films between TiO2 layers, which function as an electron extraction material, leads to rapid charge separation, reducing energy losses from both nonradiative27 and radiative8,9 pathways. On the downside, the multilayer structure leads to reduction of the open-circuit voltage, from 1.65 eV in pure MAPbI3 to about 1 eV,16 and introduction of additional recombination processes. Transient absorption spectra27 showed that charge separation at the perovskite− titania interface occurs within several picoseconds after photoexcitation. Charge transport from perovskite bulk to the interface can take nanoseconds or longer. The studies indicate that nonradiative electron−hole combination within perovskite competes with charge transport and is the most important mechanism of photovoltaic efficiency losses. Several research groups7,33−35 observed significant concentration of chlorine incorporated into pristine MAPbI3. The

he emergence of solar cells made of light-absorbing methylammonium lead halide perovskites (hereafter MAPbX3) has stimulated a wide range of studies over the past few years.1−7 Perovskites exhibit high carrier mobilities.8−10 Their band gap can be tuned by changes in fractional content of different halides.11 Inexpensive to manufacture and process, for instance, by low-cost solution casting,7,12 perovskites constitute a promising alternative to silicon solar cells, which currently dominate the industry. The current surge of interest can be traced to the 2009 work of the Miyasaka group,13 which reported 3.8% power conversion efficiency of MAPbI3 nanoparticles self-organized on a TiO2 substrate. Particular interest has been placed on developing cheaper thin film production methods.2,10,12,14−19 Currently, the efficiency has reached 19.3%.16 Fundamental research followed synthetic advances. Theoretical studies20−22 on perovskite optical and electronic properties provide important insights into overcoming problems with stability,23 toxicity,24,25 and energy losses.26,27 Experiments28 indicate that nonradiative electron−hole recombination governs energy losses at room temperature and low carrier density, limiting the solar cell efficiency. Nonradiative recombination is shown to be trap-assisted,29−31 exhibiting monomolecular kinetics. In comparison, radiative recombination requires participation of both a mobile electron and hole, and thus, it is bimolecular.7,28 The nonradiative recombination takes between 40 and 300 ps in multilayer © XXXX American Chemical Society

Received: October 21, 2015 Accepted: October 27, 2015

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DOI: 10.1021/acs.jpclett.5b02355 J. Phys. Chem. Lett. 2015, 6, 4463−4469

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The Journal of Physical Chemistry Letters

Figure 1. Geometric structures of (a) MAPbI3 and (b) MAPbI2Cl optimized at 0 K and (c,d) from a MD trajectory at 300 K. The zigzag Pb−I backbone seen at 0 K transforms into a straighter shape at 300 K, in both cases.

function of Cl was demonstrated by the Zhao group,36 suggesting that Cl greatly facilitates the release of excess MA ions at a relatively low annealing temperature by forming the MACl compound. Both MACl and MAI can be formed and evaporated in a recrystallization process at high temperature, producing the mixed MAPbI3−xClx perovskite. Introduction of chlorine atoms into MAPbI3 slows the luminescence decay.8 The importance of Cl in improving the efficiency of perovskite solar cells motivates theoretical studies. Using the earlier theoretical work on perovskite structures with and without Cl doping,37−39 we apply nonadiabatic (NA) molecular dynamics to investigate in detail the nonradiative electron−hole recombination process. The Letter presents the first time-domain ab initio study of electron−hole recombination in lead halide perovskites, directly mimicking recent time-resolved experimental data and providing a detailed understanding of the mechanisms of energy losses in perovskite-based solar devices. The simulated time scales agree well with the experimental data. The study shows that nonradiative recombination within perovskites happens within tens of picoseconds, faster than radiative recombination and long-range charge transfer to an acceptor material. Doping lead iodide perovskites with chlorines reduces charge and energy losses due to a combination of two factors. Chlorines diminish the inelastic electron−phonon NA coupling matrix element between the lowest-energy electron and hole states. Qualitatively, the coupling is reduced because chlorines contribute little to the band gap states. By replacing iodines, they eliminate some of the needed wave function overlap. At the same time, chlorines introduce higher-frequency phonon

modes, which accelerate loss of quantum coherence due to elastic electron−phonon scattering. The role of coherence in quantum dynamics has received wide attention recently, and the current investigation provides an important, topical example of decoherence effects. The simulations are performed using a combination of timedependent density functional theory and NA molecular dynamics, developed in our group and applied to study excitation dynamics in a variety of systems.40−44 Quantum decoherence effects are implemented using the optical response theory45 and a semiclassical correction to the NA dynamics.46 The simulation details can be found in our previous publications47−49 and Supporting Information. MAPbX3 is a hybrid organic−inorganic perovskite. The lead and halide atoms define the band edge states and are responsible for photon absorption.37 The organic part, MA in this case, allows low-temperature processability. It is rather flexible and mobile, capable of rotating inside of the more rigid inorganic lead halide structure.7,50 MAPbX3 exhibits a wide range of vibrational motions,51 ranging from low-frequency phonons, associated with the inorganic Pb−X bonds, to highfrequency modes of the organic part. Because the band edge states are formed by lead and halide atoms, one expects that Pb−X bond motions are responsible for creating the NA electron−phonon coupling leading to electron−hole recombination and energy losses. The crystal structure of MAPbI3 shows strong temperature dependence.52,53 The lattice is tetragonal at temperatures between 162.2 and 327.4 K. At higher and lower temperatures, it transforms into cubic or orthorhombic structures, respec4464

DOI: 10.1021/acs.jpclett.5b02355 J. Phys. Chem. Lett. 2015, 6, 4463−4469

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Figure 2. Charge density for the HOMO and LUMO in MAPbI3 and MAPbI2Cl. The HOMO and LUMO localize primarily on iodine and lead atoms, respectively.

Figure 3. Projected density of states in (a) MAPbI3 and (b) MAPbI2Cl at the Γ point. The HOMO is supported primarily by iodine atoms, with notable contribution of lead. The LUMO localizes on lead atoms (cf. Figure 2). There is little involvement of chlorine in the HOMO and LUMO of MAPbI2Cl. As a result, chlorine motions do not contribute to the NA coupling that causes electron−hole recombination.

Table 1. Summary of NAMD Results for the Electron−Hole Recombination in MAPbI3 and MAPbI2Cl MAPbI3 MAPbI2Cl

NA coupling, meV

pure-dephasing, fs

linewidth, meV

recombination (FSSH), ps

recombination (DC-DSSH), ps

3.0 2.3

9.9 9.1

66 72

2.7 6.5

42.8 124.6

Both MAPbI3 and MAPbI2Cl are direct band gap semiconductors in the tetragonal phase, with the conduction band minimum and the valence band maximum located at the Γ point. The densities of the corresponding orbitals are shown in Figure 2. The NA transition resulting in the electron−hole recombination involves these orbitals. Our previous work55 on silicon quantum dots showed that transition from an indirect band gap in bulk Si to a direct band gap in Si quantum dots accelerates the electron−hole recombination rate by several orders of magnitude. Shown in Figure 2, the highest occupied (molecular) orbital (HOMO) is localized primarily on iodine atoms, while the lowest unoccupied (molecular) orbital (LUMO) is formed by lead atoms. This conclusion is more evident from the data of

tively. The detailed parameters for the space group and lattice structure can be found in Table 1 of ref 52. The structural transition is also observed in our simulation upon temperature increase from 0 K to room temperature. The structures of MAPbI3 and MAPbI2Cl at 0 and 300 K are shown in Figure 1. At 0 K, the lead halide lattice is highly distorted, likely due to strong hydrogen bonding between the ammonium group and the halides.37 Upon heating to 300 K, the zigzag Pb−I backbone transforms into a more regular shape, indicating that thermal fluctuations at room temperature destroy some hydrogen bonding.39 Figure 1c reproduces the structural transition from low to room temperature.51,53,54 MAPbI2Cl shows similar transition between two structures, Figure 1b and d. 4465

DOI: 10.1021/acs.jpclett.5b02355 J. Phys. Chem. Lett. 2015, 6, 4463−4469

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The Journal of Physical Chemistry Letters Figure 3, which presents the projected density of states for both perovskites. Most interestingly, chlorine atoms contribute little to either the HOMO or LUMO, Figure 3b, indicating that the wave functions of chlorine atoms do not participate in the NA coupling. This is an important observation because chlorines are lighter than iodines, and therefore, they could create larger NA coupling, which is proportional to nuclear velocity. The data of Table 1 show that indeed the NA coupling decreases rather than increases in MAPbI2Cl compared to MAPbI3. The NA coupling depends on overlap of the initial and final wave functions at adjacent NAMD time steps. By replacing iodines and reducing their contribution to LUMO, Figure 3, chlorines decrease the HOMO−LUMO overlap. The role of coherence in quantum dynamics has achieved significant attention recently.56−59 The focus is primarily on biological systems,60−64 with only a few examples available for materials.65−67 Here, we show that quantum coherence has a strong effect on electron−hole recombination in perovskites. Decoherence effects enter NAMD simulation via a semiclassical correction, as described in ref 46 and the Supporting Information. Superpositions of ground and first excited states are formed and decay during nonradiative recombination. Generally, shorter coherence time leads to slower dynamics, exemplified by the quantum Zeno effect, in which the dynamics stops in the limit of infinitely fast decoherence.68 Overall, decoherence effects slow down the calculated electron−hole recombination dynamics by a factor of 20, Table 1, bringing the results in agreement with the experiment.27 The coherence time is shorter for MAPbI2Cl compared to that for MAPbI3. In combination with the smaller NA coupling, shorter coherence favors slower electron−hole recombination in MAPbI2Cl. The decoherence time is associated with the pure-dephasing time of the optical response theory.45,69−73 Pure-dephasing is responsible for elastic electron−hole scattering and determines the homogeneous line width of luminescence, which can be observed experimentally. Previous calculations of pure-dephasing times and line widths in other systems showed excellent agreement with the experimental results.69−73 Photoluminescence experiments on MAPbI3 give approximately a 100 meV full width at half-maximum.8,74−78 The 66 meV obtained in our calculations, Table 1, agree well with the experiments. The experimental line widths are larger likely due to incomplete elimination of inhomogeneous contributions. We predict that the homogeneous line width of luminescence should be slightly higher in MAPbI3 doped with chlorines, Table 1. The faster pure-dephasing/decoherence in MAPbI2Cl compared to MAPbI3 can be rationalized by analysis of the phonon modes involved in this process. The phonons can be identified by Fourier transforms (FTs) of the fluctuation of the energy gap between the initial and final states or by FT of the gap autocorrelation function.69−73 The latter is shown in Figure 4. Compared to the carbon-based materials,42,69,70 the phonon modes that determine the luminescence line width are much slower. This is because the light, organic component of MAPbX3 does not contribute to the dephasing process; the relevant orbitals are localized on the heavy elements, Figures 2 and 3. Most importantly, a broader spectrum of vibrations participate in the pure-dephasing process in MAPbI2Cl compared to MAPbI3. Even though the lighter chlorine atoms contribute little to the HOMO and LUMO wave functions, they modulate the HOMO and LUMO energies. The Pb−I modes of MAPbI3 couple to chlorine motions and split into lower- and higher-frequency components, Figure 4. A

Figure 4. FTs of autocorrelation functions for the HOMO−LUMO gap in MAPbI3 and MAPbI2Cl. Most peaks are below 200 cm−1, indicating that low-frequency modes are responsible for nonradiative electron−hole recombination. MAPbI2Cl shows more modes and higher intensity than MAPbI3. As a result, the elastic electron−phonon scattering is stronger, and the pure-dephasing (decoherence) time is shorter for MAPbI2Cl, Table 1.

broader spectrum of participating modes results in faster puredephasing. The MAPbI3 data show a broad peak at 50−90 cm−1, Figure 4, consistent with the 62 cm−1 I−Pb−I bending and 94 cm−1 Pb−I stretching modes determined from Raman spectroscopy.51 In comparison, MAPbI2Cl shows multiple peaks at 45, 120, and 260 cm−1, indicating that chlorine atoms perturb the MAPbI3 crystal structure and introduce more phonon modes. While no Raman spectra are available for MAPbI2Cl, the Raman spectra for metal lead chlorine perovskite79 show multiple peaks between 32 and 121 cm−1, in agreement with our calculations. Figure 5 shows the calculated decay of the first excited-state population, leading to electron−hole recombination. Data with

Figure 5. Decay of the excited-state population at 300 K. MAPbI3 shows faster decay compared to MAPbI2Cl due to larger NA coupling and longer coherence time, Table 1. The data obtained with the decoherence correction show good agreement with experiment.

and without the decoherence correction are presented. The results of the standard NAMD calculation without decoherence show Gaussian-like initial decay, giving rise to the quantum Zeno effect in the presence of decoherence.68 We thus estimate the relaxation time using a combination of Gaussian and exponential function, as described in the Supporting 4466

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Information. The relaxation times obtained by the quantum− classical NAMD are 2.7 and 6.5 ps for MAPbI3 and MAPbI2Cl, respectively, Table 1. They are both much longer than the puredephasing times, indicating the need for the decoherence correction. The relaxation times increase to 42.8 and 124.6 ps, respectively, with the decoherence correction. The 42.8 ps electron−hole recombination time for MAPbI3 lies at the lower end of the 40−300 ps experimental range,27,32 most likely due to the small size of the simulation cell leading to larger electron−phonon coupling. Our results indicate that the nonradiative recombination within the MAPbI3 layer is the main pathway of energy loss because it happens faster than radiative recombination and long-range charge transfers. The latter requires 400 ps for the [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) electron acceptor and 660 ps for the 2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenylamino)-9,9′-spirobifluorene (spiro-OMeTAD) hole acceptor.9 There is no report on the nonradiative recombination rate for MAPbI2Cl up to date. Indirectly, the larger diffusion constant and longer diffusion length reported for MAPbI2Cl8 suggest a reduced recombination rate, in agreement with our data. In summary, we reported the first ab initio time-domain study of nonradiative electron−hole recombination in methylammonium lead halide perovskites, which hold great promise for solar energy applications. The recombination constitutes the main mechanism of charge and energy losses in these materials, limiting solar light conversion efficiencies. The obtained recombination rate, luminescence line width, and vibrational modes are in good agreement with the available experimental data. The simulations show that doping MAPbI3 with chlorines notably reduces the recombination rate and establish the basic mechanisms for this effect. Replacement of iodine atoms with chlorines extends the lifetime of the charge-separated state for two fundamental reasons. First, the NA electron−phonon coupling is reduced. Chlorine atoms contribute little to the wave functions of the two electronic states involved in the recombination. At the same time, by replacing iodine atoms, they reduce the wave function overlap that determines the NA coupling matrix element. Second, lighter than iodines, chlorines introduce higher-frequency modes into the inorganic lattice of the hybrid organic−inorganic perovskite and broaden the range of vibrations that couple to the electronic states. As a result, the lifetime of quantum coherence between the initial and final states involved in the electron−hole recombination decreases, and the quantum transition time increases. The latter effect highlights the importance of quantum coherence in the excitedstate dynamics of perovskites. Our work both characterizes the fundamental mechanisms behind the energy losses (wave function overlap, quantum coherence) and provides practical guidelines (doping, mixed halides) for reducing charge recombination and improving efficiencies of multilayer thin film solar panels based on hybrid organic−inorganic perovskites.

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Letter

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by the U.S. Department of Energy, Grant Number DE-SC0014429. O.V.P. is grateful to the Photochemistry Center of the Russian Science Foundation, Project No. 14-43-00052, for financial support during the visit at the initial stages of the investigation. The computations were performed at the University of Southern California’s Center for High-Performance Computing (hpcc.usc.edu).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.5b02355. Full description of the material (PDF) 4467

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