Dopants Control ElectronâHole Recombination at PerovskiteâTiO2

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Dopants Control Electron-Hole Recombination at Perovskite-TiO2 Interfaces: Ab Initio Time-Domain Study Run Long, and Oleg V. Prezhdo ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b05843 • Publication Date (Web): 11 Oct 2015 Downloaded from http://pubs.acs.org on October 13, 2015

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Dopants Control Electron-Hole Recombination at Perovskite-TiO2 Interfaces: Ab Initio Time-Domain Study Run Long1,2*, Oleg V. Prezhdo3† 1

College of Chemistry, Key Laboratory of Theoretical & Computational

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

School of Physics, Complex & Adaptive Systems Lab, University College Dublin, Ireland 3

Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA

ABSTRACT: TiO2 sensitized with organo-halide perovskites gives rise to solar-toelectricity conversion efficiencies reaching close to 20%. Nonradiative electron-hole recombination across the perovskite/TiO2 interface constitutes a major pathway of energy losses, limiting quantum yield of the photoinduced charge. In order to establish the fundamental mechanisms of the energy losses and to propose practical means for controlling the interfacial electron-hole recombination, we applied ab initio nonadiabatic (NA) molecular dynamics to pristine and doped CH3NH3PbI3(100)/TiO2 anatase (001) interfaces. We show that doping by substitution of iodide with chlorine or bromine reduces charge recombination, while replacing lead with tin enhances the recombination. Generally, lighter and faster atoms increase the NA coupling. Since the dopants are lighter than the atoms they replace, one expects a priori that all three dopants should accelerate the recombination. We rationalize the unexpected behavior of chlorine and bromine by three effects. First, the Pb-Cl and Pb-Br bonds are shorter * †

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

1 ACS Paragon Plus Environment

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than the Pb-I bond. As a result, Cl and Br atoms are farther away from the TiO2 surface, decreasing the donor-acceptor coupling. In contrast, some iodines form chemical bonds with Ti atoms, increasing the coupling. Second, chlorine and bromine reduce the NA electron-vibrational coupling, because they contribute little to the electron and hole wavefunctions. Tin increases the coupling, since it is lighter than lead and contributes to the hole wavefunction. Third, higher frequency modes introduced by chlorine and bromine shorten quantum coherence, thereby decreasing the transition rate. The recombination occurs due to coupling of the electronic subsystem to low-frequency perovskite and TiO2 modes. The simulation shows excellent agreement with the available experimental data and advances our understanding of electronic and vibrational dynamics in perovskite solar cells. The study provides design principles for optimizing solar cell performance and increasing photon-to-electron conversion efficiency through creative choice of dopants.

KEYWORDS:

Organo-halide

perovskites,

TiO2,

dopants,

electron-hole

recombination, nonadiabatic molecular dynamics, time-domain density functional theory.


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Following the first report of a perovskite solar cell with the solar energy conversion efficiency of 3.8%,1 organic-inorganic halide perovskites, such as CH3NH3PbI3 (MAPbI3), have attracted intense attention. Perovskites have unique geometric and electronic properties, are good light absorbers, and are cost-effective.214

Currently, the highest reported conversion efficiency of perovskite-sensitized TiO2

solar cells is 19.3%.9 The MAPbI3 band gap allows absorption over a wide range of the solar spectrum, from visible to near-infrared. MAPbI3 exhibits extremely long diffusion lengths for both electrons and holes,4 around 100 nm, which is larger than the typical charge diffusion lengths in other materials, on the order of 10 nm. The electron and hole diffusion lengths can increase with doping. For instance, mixed MAPbI3-xClx perovskites transport charge over distances exceeding 1 micrometer, an order of magnitude greater than in the pristine material.15 Cl doping is possible only at relatively low concentrations. Some experiments demonstrate that Cl doping concentration can reach only 0.1% to 1%, with Cl atoms localized preferentially on the surface.16, 17 Such doping levels have little effect on the band gap.18 Other papers report higher Cl doping concentrations.19 In contrast, the Br and Sn dopants are commensurate with the MAPbI3 lattice.20-22 MAPbI3-xClx can act as both light-harvester and electron conductor. Mesosuperstructured solar cells employing MAPbI3-xClx and a buffer layer composed of Al2O3 and sprio-MeOTAD reach 12.3% conversion efficiency.23 Recently, Han and co-workers reported a 12.8% efficiency in a mixed-cation configuration without a hole-conductor.24 Because the hole-conductor is expensive, this advance can significantly reduce the fabrication cost and make perovskite-based solar cells feasible for large-scale applications. Perovskites compete successfully with other


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modern materials used in solar energy applications, including organic molecules and polymers,25 semiconducting26, 27 and metallic28 nanoparticles, graphene,29 etc. The measured times of electron injection from MAPbI3 to TiO2 are 260-307 ps.30 This is three orders of magnitude longer than the hot carrier cooling time of 0.4 ps.4 Insertion of a layer of ultrathin graphene quantum dots between perovskite and TiO2 can accelerate the electron transfer to 90-106 ps,30 arguably by optimizing the interfacial morphology. The extremely slow electron-hole recombination time (1.71 ns)24 at the MAPbI3-TiO2 interface facilitates high photon-to-electricity conversion efficiency. Cl and Br-doped MAPbI3 (MAPbI3-xClx, MAPbI3-xBrx) can increase the conversion efficiency further.9,

20

In contrast, Sn-doped MAPbI3 (MAPb1-xSnxI3)

shows only a 4.18% conversion efficiency, even though the Sn dopant reduces the energy gap of MAPbI3, allowing the material to harvest a broader range of the solar spectrum.21 Many ab initio molecular dynamics simulations have been performed on the pristine MAPbI3 system. Carignano and co-authors studied the finite size effects on the structural and electronic properties of tetragonal phase MAPbI3.31 Others addressed the structural and electronic properties of cubic phase MAPbI3.32,

33

Classical Monte-Carlo simulation were used to investigate the ferroelectric properties of MAPbI3.34 Quarti et al. observed a localization of the valence and conduction band states in separate regions of bulk MAPbI3.33 The same result was highlighted by Ma and Wang using linear scaling ab initio approach with a large supercell.35 Quarti et al. emphasized further the dynamical nature of the charge localization.33,

36, 37

The

obtained charge localization timescales were in good agreement with the temperaturedependent UV-vis spectra, reflecting the screening between electrons and holes introduced by the motions of the methylammonium cations.38 To-date, no theoretical


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work has reported atomistic investigation of the electron-hole recombination at the MAPbI3/TiO2 interface, in particular explicitly considering nonadiabatic transitions within the manifold of electronic states. The experimental results provide strong motivation for fundamental theoretical studies. Despite the rapid increase in efficiency associated with the evolution of different types of perovskites and device fabrication techniques, the mechanisms of electron-hole recombination and energy losses limiting device efficiency remain unclear. Most of the successes have been achieved by trial-anderror, and more often than not, the observed behavior is surprising and could not have been predicted a priori. To mimic such experimental observations in real time and at the atomistic level, we employ ab initio time-domain non-equilibrium simulation to explore in detail the mechanism of the electron-hole recombination at the perovskite MAPbI3/TiO2 interface with and without doping and to provide guidelines for minimizing charge losses. Our study shows, in excellent agreement with experiment, that the rate of the electron-hole recombination at the MAPbI3/TiO2 interfaces depends strongly on the following factors: the strengths of inelastic and elastic electron-vibrational interactions, location of the dopant electronic energy levels relative to the levels of the pristine system, and the extent of chemical interaction and donor-acceptor coupling at the interface. Inelastic electron-vibrational scattering constitutes the fundamental mechanism of energy loss and electron-hole recombination. Elastic electron-phonon scattering determines duration of quantum coherence, which is needed for the electronic transition to occur. Location of the dopant energy levels controls the states involved in the dynamics, and determines whether and how dopants affect electronvibrational interactions. Chemical interactions at the interface modify the donor-


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acceptor coupling between the electron and hole states. All factors show temperature dependence. The simulations demonstrate that thermal fluctuations perturb the perfect chemical structure of the interface, create opportunities for transient chemical bonding, e.g. between iodine and titanium, and increase the donor-acceptor interaction. By altering the perfect crystal structure of the perovskite, some dopants, such as Sn, open additional channels for interfacial interaction. Other dopants, such as Cl and Br, diminish bonding between the donor and acceptor subsystems, in particular, since the Pb-Cl and Pb-Br bonds are shorter than the Pb-I bond, Cl-Ti and Br-Ti bonds cannot be formed. The wavefunction of the electron is localized entirely within TiO2. In contrast, the wavefunction of the hole leaks from the perovskites into TiO2, creating the needed donor-acceptor wavefunction overlap. Chlorine and bromine contribute little to the donor and acceptor states, and as a result, they have little effect or even decrease the donor-acceptor interaction. Lighter and faster than iodine they replace, chlorine and bromine shorten quantum coherence time, and slow down electron-hole recombination. In contrast, tin contributes to the wavefunction of the hole, increases the electron-hole and charge-phonon interactions, and accelerates the recombination. The energy lost during the electron-hole recombination is accommodated primarily by low-frequency modes of perovskite’s inorganic backbone and TiO2. At the same time, fast motions of the organic component of the perovskite contribute to rapid coherence loss. By establishing the fundamental aspects of the electron-hole recombination mechanism, the study rationalizes why pervsokite/TiO2 solar cells have high photon-to-electron conversion efficiency and suggests specific guidelines for minimizing charge losses in MAPbI3/TiO2 systems by choice of suitable dopants.


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RESULTS AND DISCUSSIONS Figure 1a presents an energy level diagram for the MAPbI3/TiO2 interface, while Figure 1b gives the corresponding ab initio data in the form of the projected density of states (PDOS) obtained from the PBE calculation using the optimized structure at 0 K. The electron-hole recombination at the MAPbI3/TiO2 interface is associated with transfer of the excited electron from the TiO2 conduction band (CB) minimum (CBM) to the MAPbI3 valence band (VB) maximum (VBM). It takes place on a nanosecond timescale.24 Therefore, one can assume that the electron has already reached the bottom of the TiO2 CB prior to the recombination. Similarly, the hole has reached the top of the MAPbI3 VB. The PDOS is split into the CH3NH3, Pb, I, O, and Ti contributions, Figure 1b. It shows that primarily Ti 3d orbitals and I atomic orbitals contribute to the TiO2 CBM and MAPbI3 VBM, respectively. The CBM and VBM are separated by a large energy gap, and the excess electronic energy is accommodated by phonons. It is impossible for atomic motions to bring the initial and final electronic states in resonance, necessitating a NA transition. Thus, the electron-hole recombination at the MAPbI3/TiO interface definitely proceeds by the NA mechanism. The present work is motivated by the recent experiments9, 20, 24 showing that Cl and Br doped MAPbI3/TiO2 have higher photo-to-electricity conversion efficiency than neat MAPbI3/TiO2. In contrast, Sn-doped MAPbI3/TiO2 has lower efficiency than the neat system.21 The following two subsections consider in detail the model of the MAPbI3/TiO2 interface and its electronic structure, with and without Cl, Br, and Sn doping. Then, the focus shifts to electron-phonon interactions and phonon modes,


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which induce the NA transition and cause loss of quantum coherence in the electronic subsystem. Finally, the electron-hole recombination dynamics is discussed.

MAPbI3/TiO2 Interface Interactions between the MAPbI3 and TiO2 surfaces determine the electronhole recombination rate. The MAPbI3/TiO2 geometry and separation influence the strength of the interfacial interaction. The interface affects both geometric and electronic structure of the two subsystems. Figure 2 shows the top and side views (top and bottom panels, respectively) of the pristine system at the optimized geometry and during the MD trajectory at 300K (first and second columns, respectively). Comparing the two columns, we observe that thermal motions create binding opportunities. The donor-acceptor separation decreases and I-Ti chemical bonds are formed with increasing temperature. At 0K, TiO2 maintains perfect crystal structure, while the MAPbI3 layer exhibits minor distortions due to proximity to TiO2. The MAPbI3/TiO2 interaction is purely van der Waals at 0K. At the elevated temperature, the geometries of both slabs change significantly. The largest motions of the TiO2 structure are associated with displacements of inplane oxygen atoms, resulting in dissociation of some O-Ti bonds. More pronounced changes occur within the MAPbI3 layer, Figure 2. Several new I-Ti bonds form (side view at 300K), and the whole layer undergoes large-scale undulating motions (side and top views at 300 K). Pb-I bonds on the MAPbI3 surface contract and elongate. CH3NH3+ cations move closer to the TiO2 surface and rotate significantly. The purely van der Waals interactions of MAPbI3 with the TiO2 surface is too weak to maintain MAPbI3/TiO2 binding at room temperature. The new I-Ti covalent bonds facilitated


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by thermal undulating motions of the MAPbI3 layer, decrease the MAPbI3-TiO2 separation and increase the electronic donor-acceptor coupling. Introduction of the substitutional dopants – Cl or Br in place of I, and Sn in place of Pb – causes additional distortions of the MAPbI3/TiO2 interface geometry, especially at room temperature, Figure 3. Considering the optimized (0 K) geometries, we observe that both Cl-Pb (2.636 Å) and Br-Pb (2.763 Å) bonds are notably shorter than the I-Pb bond (2.972 Å, Figure 2). Consequently, the Cl and Br atoms are farther away from the TiO2 slab than iodines. The number of halogentitanium bonds, and therefore, the donor-acceptor coupling, decrease. Moreover, the electro-negativities of Cl (3.16) and Br (2.96) are larger than of I (2.66).39 As a result, Cl and Br interact more strongly with CH3NH3+ ions than I does, and the ions are pulled away from TiO2, decreasing the donor-acceptor interaction further. Considering the Sn-doped system, we note that Sn2+ is smaller than Pb2+, and the Sn-I bond (2.886 Å) pointing towards TiO2 is also shorter than the corresponding Pb-I bond (2.972 Å). Similarly, the average bond length (3.129 Å) of the four Sn-I bonds in the outer layer are shorter than the average length of the four I-Pb bonds (3.174 Å) in the pristine system. Distortions induced by Sn are significant and do not eliminate the Ti-I bonding opportunities at room temperature. Strong donor-acceptor coupling is maintained in the Sn-doped system. The geometries of the doped systems undergo additional distortions at room temperature, compared to the pristine MAPbI3/TiO2 interface. The number of I-Ti bonds becomes smaller upon Cl and Br doping, indicating that the interaction between the donor and acceptor materials weakens. This finding is opposite to the previous static DFT calculations, showing that Cl doping enhances the interaction between MAPbI3 and TiO2 slab.40 The differences likely arise because the whole bottom layer


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of iodine atoms was replaced with chlorines in the above cited work, while we consider a much lower level of substitution doping. Further, we study the system at a finite temperature, which includes thermal disorder, while the above work considers the optimized structure corresponding to 0K. In contrast to Cl and Br doping, Sn doping maintains I-Ti bonds and even creates new bonding opportunities, for instance TiO2-CH3NH3+ hydrogen bonds, enhancing the donor-acceptor coupling. In order to confirm that the current model provides a reasonable description of the MAPbI3/TiO2 interface, we performed additional calculations on the pristine system employing a thicker perovskite layer. The results are presented in Supporting Information (SI).

Electronic Structure Figure 4 presents densities of the electron donor and acceptor states involved in the electron-hole recombination. The recombination dynamics depends on the electronic energy gap and donor-acceptor coupling. The strength of the coupling is related directly to the overlap between the donor and acceptor wave functions. Here, the donor state is localized completely within the TiO2 substrate. The acceptor state is localized mainly on the iodine atoms of MAPbI3. At the same time, it delocalizes onto the TiO2 slab, creating the required donor-acceptor wavefunction overlap. The extent of the delocalized tail decreases in the following order: Sn-doped > MAPbI3/TiO2 > Br-doped > Cl-doped. The donor-acceptor coupling decreases in the same order. Overall, the donor-acceptor wavefunction overlap is quite small, rationalizing the slow, nanosecond electron-hole recombination. Electrons and holes can recombine in pure materials both radiatively and nonradiatively. Here, luminescence from the CBM to the VBM is unlikely because the


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CBM and VBM are localized on the two different components, Figure 4, and the corresponding transition dipole moment is small. Instead, transitions from the CBM to the VBM transitions occurs non-radiatively. Figure 5 shows PDOS of the Cl, Br and Sn-doped MAPbI3/TiO2 systems that were calculated at 0 K using the optimized structure. The PDOS is split into contributions from MAPbI3, TiO2, and the dopants. The dopant component is magnified 10 times. Sn contributes to the hole density at the VBM, Figure 5d, modifying the VBM of the pristine systems, Figure 5a. In contrast, Cl and Br contribute little to either electron or hole wavefunction, Figures 5b and c, respectively. The PDOS analysis is consistent with the three-dimensional images of the state densities, Figure 4. It is known that pure DFT functionals, such as PBE, underestimate bandgaps, in particular, the TiO2 band gap. However, DFT calculations employing the PBE functional give a reasonable agreement with the experimental bandgap for hybrid halide perovskites.40,

41

The agreement can be attributed to cancellation of errors,

arising due to approximate description of electron exchange/correlation and lack of relativistic effects (spin-orbit coupling), as demonstrated in several publications.42-44 The canonically averaged bandgap computed here for the pristine MAPbI3/TiO2 system is 0.987 eV.

Doubling the length of the MD trajectory changed the

canonically averaged value to 0.972 eV. A 3ps MD trajectory for the system including a twice thicker perovskite layer, Figure S1 of SI, gave 0.961 eV. These values are to be compared to the experimental value of around 1.4 eV.24, 45 Different experimental samples and measurements produce a significant variation in the energy level alignment at the MAPbI3/TiO2 interface.

24, 45, 46

The canonically averaged bandgaps

for the Cl, Br, and Sn-doped systems are slightly smaller than the bandgap of the


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pristine system. They are equal to 0.834, 0.792, 0.796 eV, respectively. The experimental bandgaps for the Cl and Br-doped systems20, 24 should not be compared to the calculated values, since the doping concentrations are different. Experiment shows that Sn doping reduces the MAPbI3 bandgap very slightly.47 This agrees with the GW calculations demonstrating that MASnI3 has a smaller bandgap than MAPbI3.32 For better comparison with the experiments, we scale the bandgap of all four systems by adding the same constant, chosen to match the experimental bandgap of the pristine MAPbI3/TiO2 system.24

Electron-Vibrational Interactions Electron-vibrational interactions generate elastic and inelastic scattering. Both types of scattering affect the electron-hole recombination process. Inelastic energy exchange between the electronic and vibrational subsystems is required in order to accommodate the energy lost during the electronic transition from the CBM to the VBM. Elastic electron-phonon interactions destroy coherence formed between the CBM and VBM states. The coherence is formed when the states become coupled by the NA coupling during non-radiative relaxation. The coherence appears during radiative transitions when states become coupled via the transition dipole moment. Elastic electron-phonon scattering is known in optical measurements as puredephasing.48 In particular, it determines the linewidth of single particle luminescence. Figure 6 presents Fourier transforms (FT) of the VBM-CBM energy gaps in the four systems. FT characterizes the phonon modes that couple to the electronic subsystem, cause decoherence, and accommodate the excess energy released during the electron-hole recombination process. Only low frequency vibrations are involved


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in the non-radiative decay process in all four cases. Dopants increase the frequency range of active vibrations. The dominant peak in pristine MAPbI3/TiO2 can be attributed to Pb-I bond stretching at 94 cm-1.49 This frequency is the diagnostic mode of the inorganic cage. The peak can also be assigned to the librations of the organic cations at 119 cm-1.49 Even though the organic groups contribute to neither electron nor hole states, Figure 1b, they influence the electron and hole wavefunctions electrostatically. Rotation of organic groups leads to signficant changes of the generated electrostatic field.19 The second main peak can be related to the bending mode of Pb-I bonds at 62 cm-1,49 as well as to the low-frequency acoustic symmetrical spheroidal mode of anatase TiO2 at 33cm-1.50 The length of the MD trajectories is insufficient to resolve such low frequency modes more accurately. Both modes alter the MAPbI3 geometry, create the NA coupling, and promote electron-hole recombination. The medium frequency vibrations ranging from 200 to 400 cm-1 can be assigned to torsional motions of the CH3NH3+ cations.49 Just as the CH3NH3+ rotation, the tortional modes alter the generated electric field, though to a much lesser extent. The bandgap of pristine MAPbI3 reported in previous ab initio molecular dynamics simulations flucturates with frequencies similar to those found in our work. For instance, the dominat frequency shown in the first panel of Figure 6 in ref.37 corresponds to the first peark in Figure 6 here. Quarti et al.37 shows that spatial localization of the electron and hole states occurs on a 0.1ps time scale, roughly corresponding to the libration motions of the methylammonium cations.38 The electornic states of the current MAPbI3/TiO2 system couple primary to the 100 cm-1 mode, with a 0.3 ps period. This slower motion may arise from the interaction between MAPbI3 and TiO2 that supresses rotations of MA cations.


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The vibrational frequencies do not change in Cl-doped MAPbI3/TiO2. The dominant peak at 100 cm-1 increases, while the other peak at 40 cm-1 decreases in magnitude. FTs of the energy gap ACF presented in Figure 6 are most directly related to the pure-dephasing function, eqs 10 and 11. A larger number of contributing modes accelerates dephasing. The dephasing becomes faster upon Cl doping, insert in Figure 7, because the contributions of the two modes are nearly equal. Br doping introduces a broad range of modes. Although the magnitude of the main peaks decreases, two other peaks appear in the 200-400 cm-1 frequency range, providing new dephasing channels. The additional peaks can be assigned to the Eg mode and transverse optical Eu(1) mode of anatase TiO2 at 198 cm-1 and 262 cm-1, respectively.51,

52

Sn doping eliminates the 100 cm-1 peak, and decreases the

magnitude of the 40 cm-1 and 200-400 cm-1 peaks. Consequently, pure-dephasing slows down. TiO2 phonon modes contribute significantly to the electron-hole recombination because the MAPbI3 wave fuction is delocalized onto the TiO2 slab, both with and wihout doping, Figure 4. While high frequency NH stretching modes of MA cations are present in all of four systems, they are hard to detect. These frequencies can be observed if the FT data are magnified several thousand times. The signals arising form high frequency vibrations often average out in extended, bulk systems, since the observables are computed by integrating over wave functions delocalized over large parts of the system, Figure 4. The optical pure-dephasing functions, eq. 10, are shown in the inset of Figure 7. The functions characterize elastic electron-phonon scattering. The open circles represent Gaussian fits f(t) = Bexp(-0.5(t/τa)2)+C. The pure-dephasing times decrease in the sequence Sn-doped > MAPbI3/TiO2 > Br-doped > Cl-doped, and are equal to


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4.4, 4.3, 4.0, and 3.4 fs, respectively. The decoherence is caused primarily by coupling of the electronic subsystem to the 100 cm-1vibrational mode. The lower frequency peak in Figure 6 is the second main contributor. The presence of multiple frequencies in the vibrational influence spectrum accelerate decoherence. The 4.3 fs pure-dephasing time of the pristine system is dramatically shorter than the 1.71 ns electron-hole recombination time reported in the experiment,24 as it is expected for transitions across large energy gaps. Because the dopants are present at a low concentration, the pure-dephasing times differ little from each other, in agreement with the above phonon mode analysis. Sn has a small effect on decoherence, because it is not much lighter than iodine, which is the lightest atom in the inorganic subsystem of MAPbI3. Recall that the CBM and VBM arise from the inorganic backbone.41 In comparison, Cl and Br are lighter than iodine, and therefore, they have a larger effect on the decoherence time. The decoherence times computed here are significantly shorter than those obtained for TiO2 sensitized with PbSe and Au nanocrystals,53 because the latter systems contain no organic components and are formed by heavier elements. Shortlived coherence leads to long electron-hole recombination.

Electron-Hole Recombination Dynamics The electron-hole recombination at the TiO2/MAPbI3 interface occurs by a nonradiative transition of the photo-excited electron from the CBM localized on the TiO2 surface to the VBM localized on MAPbI3. The time-dependent population of the CBM is shown in Figure 7. The calculated 0.65 ns time, obtained using the short-time linear approximation, f(t) = aτ + b, to the exponential decay agrees well with the experimental data.24 Such slow electron-hole recombination is beneficial for


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maintaining solar cell current, which serves to the high conversion efficiency of MAPbI3/TiO2 solar cells.24 To reduce energy losses and increase performance of photovoltaic cells, one can tune and further minimize the electron-hole recombination by doping. Both Cl and Br doping give slower recombination dynamics, 2.0 and 0.84 ns, respectively; while Sn doping accelerates the recombination, 0.52 ns. The canonically averaged absolute values of the NA coupling decrease in the series Sn-doped > MAPbI3/TiO2 > Br-doped > Cl-doped, and are equal to 1.845, 1.475, 1.415, and 1.395 meV, respectively. The NA coupling strength is related to the wave function overlap between the donor and acceptor states, Figure 4. The overlap follows the same trend as the NA coupling. The reduced coupling between the MAPbI3 and TiO2 subsystems, together with the increased decoherence rate, Figure 7 insert, rationalize the effect of the dopants on the electron-hole recombination. In particular, Cl-doped MAPbI3-TiO2 gives the slowest recombination, which serves to explain the highest conversion efficiency, up to 20%, of MAPbI(3-x)Clx/TiO2 solar cells.9 In order to establish convergence of the reported results with respect to system size and simulation time, we performed the following tests, focusing on the system without defects. First, we increased the thickness of the perovskite layer and created a 366-atom MAPbI3/TiO2 interface with two layers of the MAPbI3 (001) surface. Note that NAMD simulation is more expensive than a regular MD simulation, in particular, since it requires NA couplings, which are computed using high precision wavefunctions. We performed the NAMD simulation only for the pristine system and for a shorter time. The structure, PDOS, and population dynamics are shown in Figures S1-S3 of SI. Figure S1 displays the optimized structure at 0 K and a geometry from MD at 300 K. The behaviour of the two perovskite layer system is similar to the


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system with a single perovskite layer, Figure 2. The PDOS (Figure S2) and the electron-hole recombination timescale (Figure S3a) for the two-layer MAPbI3 system are nearly identical to the corresponding results obtained for TiO2 interfaced with one layer MAPbI3 (Figures 1b and 7, respectively). Second, we doubled the length of the MD trajectory and performed a longer NAMD simulation for the TiO2 anatase (001) surface interfaced with one layer MAPbI3 (100). The electron-hole recombination dynamics are characterized in the Figure S3b. The obtained time scale matches the shorter NAMD simulation, Figure 7. The tests performed with the pristine system indicate that the current model provides a good description of the perovskite/TiO2 interface, leading us to expect that the studies including the dopants produce reliable results. Experiments indicate that Cl dopants prefer to accumulate at the perovskite surface,16, 17 while the Br and Sn dopants provide a better match to the MAPbI3 lattice and enter perovskite bulk.20-22 Therefore, the same formal dopant concentration can have different effects on the interfacial charge recombination dynamics, depending on dopant concentration at the interface. In particular, even at low concentrations Cl dopants should have a strong effect on the interfacial electron-hole recombination, reducing its rate. This conclusion agrees with the fact that Cl doped MAPbI3 exhibits better photovoltaic performance. 16, 54, 55 In general, doping concertation can affect the donor-acceptor interaction, electron-phonon coupling, and the interface morphology. Smaller doping levels will decrease dopant effect on the donor-acceptor coupling for all three cases. The electron-hole recombination rate will change little at low doping concertation, compared to the pristine system. In contrast, doping level increase is expected to supress electron-hole recombination in the presence of Cl and Br doping because the dopants weaken the donor-acceptor coupling. In the specific case of Cl


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doping, using chlorine containing precursors, PbCl2 and MACl strongly improves the quality of perovskite and enhance the photovoltaic properties of MAPbI3, 16, 54, 55 16, 54, 55

suggesting that morphology of perovskites and solar cell performance can be

optimized via doping. In contrast to Cl and Br, increasing Sn doping concentration will further extends the tail of the perovskite wavefunction into the TiO2 slab, increase the donor-acceptor coupling, and accelerate the interfacial electron-hole recombination.

CONCLUSIONS We reported the first time-domain ab initio study of electron-hole recombination dynamics in TiO2 sensitized with methylammonium lead halide perovskites with and without doping. The material holds great promise for photovoltaic applications. The recombination constitutes the main channel for charge and energy losses, limiting light-to-current conversion efficiency. The simulated timescales and the phonon modes found to promote the relaxation agree well with the experimental data available for the MAPbI3/TiO2 system. The simulations show that doping with Cl and Br notably reduces the recombination rate, while doping with Sn increases the rate. These findings are rather surprising and would have been hard to predict a priori, in particular, since all three dopants are lighter than the atoms they substitute, and since higher frequency vibrations introduced by lighter atoms are expected to accelerate the relaxation. The established results are rationalized by a combination of the following three factors: (1) Cl and Br decrease the MAPbI3/TiO2 bonding interaction, while Sn increases the bonding; (2) Cl and Br diminish the donor-acceptor and NA coupling, while Sn makes the coupling stronger; (3) Cl and


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Br accelerate loss of quantum coherence, while Sn leaves the decoherence time largely unchanged. Compared with the optimized zero-temperature structures, both pristine and doped MAPbI3/TiO2 exhibit additional bonding at ambient temperature due to thermal fluctuations. In particular, transient I-Ti bonds are formed. Similar Cl-Ti and Br-Ti bonds cannot form, since Cl and Br are smaller than I, are closer to Pb and are farther from Ti. The electron donor state is strongly localized on TiO2, while the electron acceptor state (the hole state) has a tail extending from MAPbI3 into TiO2. The delocalization decreases in the series Sn-doped > MAPbI3/TiO2 > Br-doped > Cldoped. Correspondingly, the NA coupling exhibits the same trend. The simulations demonstrate that the electron-hole recombination is largely promoted by low-frequency bending and stretching modes of I-Pb bonds and TiO2 acoustic modes. Librational motions of the organic ligands facilitate the recombination indirectly, via changes in the electrostatic environment. Replacement of iodine by either Cl or Br increases the electron-phonon coupling magnitude and introduces higher frequency modes. As a result, the lifetimes of quantum coherence between the initial and final states involved in the electron-hole recombination decrease, and quantum transitions take more time. Substitution of Pb by Sn also introduces higher frequency vibrations; however, the electron-phonon coupling magnitude decreases, and the coherence time decrease slightly as well. The study highlights the importance of quantum coherence in the excited state dynamics of perovskite-based materials. The reported time-domain ab initio investigation establishes the fundamental mechanisms behind the energy losses: chemical bonding, wave function mixing, electron-vibrational coupling, and quantum coherence. It also generates practical


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guidelines on reduction of the interfacial charge recombination rate by appropriate choice of dopants. By pioneering a new class of theoretical investigations into the excited state dynamics of hybrid organic-inorganic perovskites, the research described in this paper advances our understanding of the key factors influencing and controlling the performance of hybrid organic-inorganic perovskite solar cells.

EXPERIMENTAL METHODS The simulations were carried out by the combination of nonadiabatic (NA) molecular dynamics (MD) and time-dependent (TD) density functional theory (DFT). NAMD is performed using the quantum-classical fewest-switches (FS) surface hopping (SH) technique56 implemented with the Kohn-Sham formulation of TDDFT.57-60 A semiclassical correction for quantum decoherence is included.61, 62 The correction is needed here, because the decoherence (pure-dephasing) time is significantly shorter than the quantum transition time. The pure-dephasing times were computed using the optical-response formalism.63 The approach has been applied to study electron transfer, energy relaxation, and electron-hole recombination in a variety of systems, including semiconducting64 and metallic65 nanocrystals, interfaces between fullerene and QD,66 QD and molecule,67 QD and TiO2,68 etc.

Time-Domain Density Functional Theory DFT maps an interacting many-body system onto a tractable system of noninteracting particles moving in an effective potential, using electron density as the variable to minimize the ground state energy. In practical implementations, the density is constructed from TD single-particle Kohn-Sham (KS) orbitals,


ϕ p (r, t )

.

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Ne

ρ (r, t ) = ∑| ϕ p (r, t ) |2

(1)

p =1

The evolution of the electron density is determined by the TD variational principle, leading to a set of single-electron equations for the evolution of the KS orbitals:

ih

∂ϕ p (r, t ) ∂t

= H (r, R, t )ϕ p (r, t ); p = 1,2,..., Ne

(2)

These equations are non-linear, since the Hamiltonian H(r, R,t) is a functional of the electron density, which is obtained by summing over occupied KS orbitals, eq 1. By expanding the time-dependent KS orbitals in the adiabatic KS orbital basis,

ϕ% p (r , R (t )) , obtained for a given nuclear configuration,

ϕ P (r, t ) = ∑ ck (t )ϕ%k (r; R (t ))

(3)

k

and inserting eq 3 into eq 2, one obtains equations for the expansion coefficients:

∂ c j (t ) = ∑ ck (t )(ε kδ jk + d jk ) ∂t k Here, ε k is the energy of the adiabatic state k, and d jk is the NA coupling between ih

(4)

states k and j. The NA coupling arises because electronic wavefunctions depend parametrically on nuclear coordinates. It reflects the inelastic electron-vibrational interaction. The coupling is calculated numerically as the overlap of orbitals j and k at sequential time steps69

d jk = −ih < ϕ% j | ∇ R | ϕ%k > • ≈−

dR ∂ = −ih < ϕ% j | | ϕ%k > dt ∂t

ih (< ϕ% j (t ) | ϕ%k (t + ∆t ) > − < ϕ% j (t + ∆t ) | ϕ%k (t ) >) 2 ∆t

Nonadiabatic Dynamics by Fewest Switches Surface Hopping SH is a stochastic algorithm for switching electronic states in a mixed quantum-classical simulation. It introduces probabilistic hopping according to solution to the TD Schrodinger equation, i.e., eq 4 for the expansion coefficients in the present case. Only one potential energy surface is involved in nuclear dynamics at


(5)

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a given instance of time.70 FSSH is the most popular SH approach. It minimizes the number of hops, while maintaining consistency with the Schrodinger equation.56 Moreover, it satisfies approximately detailed balance between transitions upward and downward in energy,71 as required for proper description of electron-vibrational energy exchange and relaxation to thermodynamic equilibrium.72 FSSH can be regarded as the first order approximation within the class of methods that obtain hopping probabilities based on flux of quantum populations. Global flux SH generalizes FSSH to higher orders, in particular, to super-exchange and many-particles processes.73 The probability of a transition between states k and j within time interval δ t is given in FSSH by56

dPkj =

bkj akj

dt

(6)

where

akj = ck (t )c j (t ) and

bkj = 2h −1 Im(akj < ϕ%k | H | ϕ% j >) − 2 Re(akj d kj ) If the calculated dPkj is negative, the hopping probability is set to zero. A hop from state j to state k can occur only when the electronic occupation of state j decreases and the occupation of state k increases, minimizing the number of hops. To conserve the total electron-nuclear energy after a hop, the original FSSH technique56 rescales the nuclear velocities along the direction of the NA coupling. If a NA transition to a higher energy electronic state is predicted by eq 6, while the kinetic energy available in the nuclear coordinates along the direction of the NA coupling vector is insufficient to accommodate the increase in the electronic energy, the hop is rejected. This step gives the detailed balance between the upward and downward transitions in energy, leading to Boltzmann statistics and quantum-classical thermodynamic equilibrium.71


(7)

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The current simulation uses a simplified and more efficient version of FSSH, employing the classical path approximation, as detailed in ref 59, 74

Decoherence-Corrected Surface Hopping FSSH

is a quantum-classical approximation employing independent

trajectories. Consequently, it makes no attempt to reconstruct nuclear wavefunctions (wavepackets), and as a result, it neglects decoherence induced in the electronic subsystem by quantum nuclei. FSSH overestimates the rates of NA transitions that take significantly longer than the decoherence time for the corresponding pairs of states. In the limit of infinitely fast decoherence, this phenomenon is illustrated by the quantum Zeno effect.75 In such cases, FSSH should be corrected for decoherence.61, 76 Since decoherence is the physical mechanism of trajectory branching, more advanced formulations establish SH algorithms based on decoherence directly,72,

77-80

rather

than introducing decoherence corrections. The phonon-induced decoherence time associated with the electron-hole recombination process is calculated using the optical response theory.48 The electronhole recombination occurs in MAPbI3 across a wide energy gap on a nanosecond time scale.24 It is significantly longer than the decoherence time, requiring a decoherence correction to FSSH. In the current simulation, the time-dependent KS wavefunction

ϕ P (r, t ) is collapsed to an adiabatic eigenstate ϕ%k (r; R (t )) , eq 3, on the decoherence time scale, as implement in ref61. The decoherence procedure collapses the wavefunction coefficeints, ck (t ) in eq 4. The collapse times are determined by a sequence of random numbers sampled from the Poisson distribution with the characteristic time determined by the decoherence time. The probability of collapse onto eigenstate k is given by the square of the coefficient ck (t ) at the collapse time.


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The decoherence time was computed as the pure-dephasing time in the optical response formalism. The phonon-induced fluctuations in the energy gap between the electron and hole states are characterized by the autocorrelation function (ACF).

C (t ) = ∆E (t )∆E (0)

(8)

T

The brackets indicate canonical averaging. The ACF is normalized ∆E (t ) E ∆ (0)

C norm (t ) =

∆E 2 (0)

T

(9)

T

by its initial value C (0) = ∆E 2 (0) . The square root of this value gives the average T

fluctuation of the excitation energy. The pure-dephasing function is computed using the second-order cumulant expansion to the optical response function.48

Dcumu (t ) = exp(− g (t ))

(10)

where g (t ) t

τ1

0

0

g (t ) = ∫ dτ1 ∫ dτ 2C (τ 2 )

(11)

Fitting eq 11 by a Gaussian gives the pure-dephasing time. Fourier transform of an ACF produces the spectral density,

I (ω ) =

1 2π

∫

∞

−∞

2

dte

− iωt

C (t )

(12)

which identifies frequencies of the vibrational modes involved in the electron-hole recombination process.

Simulation Details

Experiments have identified orthorthombic, tetragonal, and cubic polymorphs of MAPbI3. It has been suggested that MAPbI3 undergoes a tetragonal to orthorhombic transition at close to 161 K, and transforms to a high-temperature cubic phase at around 330 K.81 We used the pseudocubic phase82 with the optimized lattice


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constant of 6.29 Å, providing a satisfactory match to the TiO2 periodicity. To create a periodically repeated slab involving the two materials, a 150-atom anatase TiO2-(5×5) (001) surface was chosen to match a 108-atom MAPbI3 (3×3)(100) surface terminated with MA. The supercell parameters are 18.88 Å in both a and b directions, leading to a lattice mismatch between the two slabs of only 0.01Å. We also considered a TiO2/MAPbI3 interface terminated with PbI2, and the calculation showed it to be unstable. Experiments have indicated that the anatase TiO2(001) surface is particularly advantageous for the photovoltaic applications.10, 24 Cl, Br and Sn dopants were introduced into MAPbI3, replacing I, I, and Pb atoms respectively. The slabs were separated from their images along the surface normal by a vacuum region of 20 Å. The simulation cells are shown in Figures 2-4. The geometry optimization, electronic structure and adiabatic MD calculations were performed using the Vienna ab initio simulation package (VASP).83 The Perdew-Burke-Ernzerhof (PBE)84 functional was used to describe the exchange and correlation effects. The interaction of the ionic cores with the valence electrons was treated by the projector-augmented wave (PAW) approach.85 The electron wave function was expanded in plane waves up to the 500 eV cutoff energy, to converge the total energy for geometry optimization and electronic wavefunctions for calculation of the NA couplings. A higher cutoff energy brings negligible differences. A lower energy cutoff of 200 eV as sufficient for performing the ground state MD simulation in order to represent thermal nuclear motions. The structure optimization and MD were performed at the Γ-point, since a large supercell was used. To obtain accurate density of states, a much denser Monkhorst−Pack k-point mesh of 8 × 8 × 1 was used.86 The geometry relaxation was carried out until the residual forces were below 0.01 eV/Å. The van der Waals interactions, in particular those between


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MAPbI3 and TiO2, were described by the DFT-D2 method of Grimme using the standard parameters for each kind of atom for both geometry optimization and MD.87 After geometry optimization 0 K, the pristine and doped MAPbI3/TiO2 systems were heated to 300 K via repeated velocity rescaling, corresponding to the temperature used in the experiments.24 After that, 3 ps adiabatic MD trajectories were generated in the microcanonical ensemble with a 1 fs time step. Additional tests were performed on the pristine system using a twice longer adiabatic MD trajectory. To show rotation of methylammonium ions, we included a movie in the SI. Due to the journal limits on the size of the files which can be uploaded as SI, the movie is 1 ps in duration. Already during 1 ps one can observe significant rotation of methylammonium ions. The movie shows 3 rows and 3 columns of the ions. Focusing on the MA ion at the intersection of the 2nd row and 3rd column, we observe several (3-4) 180 degree rotations/librations interrupted by brief stops. The overall 6 ps MD provides reasonable sampling of the rational motion of the methylammonium ions. To simulate the electron-hole recombination, 500 hundred geometries were selected randomly from each adiabatic MD trajectory. They were used as initial conditions for NAMD, which was performed using fewest-switches surface hopping in the classical path approximation and with the decoherence correction. The nuclear time step for the equilibration and production runs was set to 1.0 fs. The electronic time step for NAMD was 1.0 attosecond. A detailed description of the NAMD method can be found in refs.59, 60

ACKOWLEDGEMENTS


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R.L. is grateful to the National Science Foundation of China (21573022) and the Science Foundation Ireland (SFI) SIRG Program (grant number 11/SIRG/E2172). O.V.P. acknowledges support from the NSF grant CHE-1300118.

Supporting Information Available. Geometric and electronic structure and electron-

hole recombination dynamics for the pristine MAPbI3/TiO2 system with a twice thicker perovskite layer, and a 1ps molecular dynamics movie. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES

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C.; Marks, T. J. “Supersaturated” Self-Assembled Charge-Selective Interfacial Layers for Organic Solar Cells. J. Am. Chem. Soc. 2014, 136, 17762-17773. 26. Callejas, J. F.; McEnaney, J. M.; Read, C. G.; Crompton, J. C.; Biacchi, A. J.; Popczun, E. J.; Gordon, T. R.; Lewis, N. S.; Schaak, R. E. Electrocatalytic and Photocatalytic Hydrogen Production from Acidic and Neutral-pH Aqueous Solutions Using Iron Phosphide Nanoparticles. ACS Nano 2014, 8, 11101-11107. 27. Sinito, C.; Fernee, M. J.; Goupalov, S. V.; Mulvaney, P.; Tamarat, P.; Lounis, B. Tailoring the Exciton Fine Structure of Cadmium Selenide Nanocrystals with Shape Anisotropy and Magnetic Field. ACS Nano 2014, 8, 11651-11656. 28. Manjavacas, A.; Liu, J. G.; Kulkarni, V.; Nordlander, P. Plasmon-Induced Hot Carriers in Metallic Nanoparticles. ACS Nano 2014, 8, 7630-7638. 29. Boota, M.; Hatzell, K. B.; Alhabeb, M.; Kumbur, E. C.; Gogotsi, Y. Graphene-Containing Flowable Electrodes for Capacitive Energy Storage. Carbon 2015, 92, 142-149. 30. Zhu, Z.; Ma, J.; Wang, Z.; Mu, C.; Fan, Z.; Du, L.; Bai, Y.; Fan, L.; Yan, H.; Phillips, D. L.; Yang, S. Efficiency Enhancement of Perovskite Solar Cells through Fast Electron Extraction: The Role of Graphene Quantum Dots. J. Am. Chem. Soc. 2014, 136, 3760-3763. 31. Carignano, M. A.; Kachmar, A.; Hutter, J. Thermal Effects on CH3NH3PbI3 Perovskite from Ab Initio Molecular Dynamics Simulations. J. Phys. Chem. C 2015, 119, 8991-8997. 32. Lindblad, R.; Bi, D.; Park, B.-w.; Oscarsson, J.; Gorgoi, M.; Siegbahn, H.; Odelius, M.; Johansson, E. M. J.; Rensmo, H. Electronic Structure of TiO2/CH3NH3PbI3 Perovskite Solar Cell Interfaces. J. Phys. Chem. Lett. 2014, 5, 648653. 33. Mosconi, E.; Quarti, C.; Ivanovska, T.; Ruani, G.; De Angelis, F. Structural and Electronic Properties of Organo-Halide Lead Perovskites: a Combined IRSpectroscopy and Ab Initio Molecular Dynamics Investigation. Phys. Chem. Chem. Phys. 2014, 16, 16137-16144. 34. Frost, J. M.; Butler, K. T.; Walsh, A. Molecular Ferroelectric Contributions to Anomalous Hysteresis in Hybrid Perovskite Solar Cells. APL Mater. 2014, 2, 081506. 35. Ma, J.; Wang, L.-W. Nanoscale Charge Localization Induced by Random Orientations of Organic Molecules in Hybrid Perovskite CH3NH3PbI3. Nano Lett. 2015, 15, 248-253. 36. Quarti, C.; Mosconi, E.; De Angelis, F. Interplay of Orientational Order and Electronic Structure in Methylammonium Lead Iodide: Implications for Solar Cell Operation. Chem. Mater. 2014, 26, 6557-6569. 37. Quarti, C.; Mosconi, E.; De Angelis, F. Structural and Electronic Properties of Organo-Halide Hybrid Perovskites from Ab Initio Molecular Dynamics. Phys. Chem. Chem. Phys. 2015, 17, 9394-9409. 38. Even, J.; Pedesseau, L.; Katan, C. Analysis of Multivalley and Multibandgap Absorption and Enhancement of Free Carriers Related to Exciton Screening in Hybrid Perovskites. J. Phys. Chem. C 2014, 118, 11566-11572. 39. CRC Handbook of Chemistry and Physics, 87th ed. Taylor & Francis:: London, 2006. 40. Mosconi, E.; Amat, A.; Nazeeruddin, M. K.; Grätzel, M.; De Angelis, F. FirstPrinciples Modeling of Mixed Halide Organometal Perovskites for Photovoltaic Applications. J. Phys. Chem. C 2013, 117, 13902-13913. 41. Umebayashi, T.; Asai, K.; Kondo, T.; Nakao, A. Electronic Structures of Lead Iodide Based Low-Dimensional Crystals. Phys. Rev. B 2003, 67, 155405.


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58. Fischer, S. A.; Habenicht, B. F.; Madrid, A. B.; Duncan, W. R.; Prezhdo, O. V. Regarding the Validity of the Time-Dependent Kohn–Sham Approach for Electron-Nuclear Dynamics via Trajectory Surface Hopping. J. Chem. Phys. 2011, 134, 024102. 59. Akimov, A. V.; Prezhdo, O. V. The PYXAID Program for Non-Adiabatic Molecular Dynamics in Condensed Matter Systems. J. Chem. Theory Comput. 2013, 9, 4959-4972. 60. Akimov, A. V.; Prezhdo, O. V. Advanced Capabilities of the PYXAID Program: Integration Schemes, Decoherence Effects, Multiexcitonic States, and FieldMatter Interaction. J. Chem. Theory Comput. 2014, 10, 789-804. 61. Habenicht, B. F.; Prezhdo, O. V. Nonradiative Quenching of Fluorescence in a Semiconducting Carbon Nanotube: A Time-Domain Ab Initio Study. Phys.Rev. Lett. 2008, 100, 197402. 62. Jaeger, H. M.; Fischer, S.; Prezhdo, O. V. Decoherence-Induced Surface Hopping. J. Chem. Phys. 2012, 137, 22A545. 63. Madrid, A. B.; Hyeon-Deuk, K.; Habenicht, B. F.; Prezhdo, O. V. PhononInduced Dephasing of Excitons in Semiconductor Quantum Dots: Multiple Exciton Generation, Fission, and Luminescence. ACS Nano 2009, 3, 2487-2494. 64. Kilina, S. V.; Kilin, D. S.; Prezhdo, V. V.; Prezhdo, O. V. Theoretical Study of Electron–Phonon Relaxation in PbSe and CdSe Quantum Dots: Evidence for Phonon Memory. J. Phys. Chem. C 2011, 115, 21641-21651. 65. Neukirch, A. J.; Guo, Z.; Prezhdo, O. V. Time-Domain Ab Initio Study of Phonon-Induced Relaxation of Plasmon Excitations in a Silver Quantum Dot. J. Phys. Chem. C 2012, 116, 15034-15040. 66. Chaban, V. V.; Prezhdo, V. V.; Prezhdo, O. V. Covalent Linking Greatly Enhances Photoinduced Electron Transfer in Fullerene-Quantum Dot Nanocomposites: Time-Domain Ab Initio Study. J. Phys. Chem. Lett. 2012, 4, 1-6. 67. Long, R.; English, N. J.; Prezhdo, O. V. Defects Are Needed for Fast PhotoInduced Electron Transfer from a Nanocrystal to a Molecule: Time-Domain Ab Initio Analysis. J. Am. Chem. Soc. 2013, 135, 18892-18900. 68. Long, R.; English, N. J.; Prezhdo, O. V. Minimizing Electron–Hole Recombination on TiO2 Sensitized with PbSe Quantum Dots: Time-Domain Ab Initio Analysis. J. Phys. Chem. Lett. 2014, 5, 2941-2946. 69. Hammes-Schiffer, S.; Tully, J. C. Proton Transfer in Solution - Molecular Dynamics with Quantum Transtions. J. Chem. Phys. 1994, 101, 4657-4667. 70. Tully, J. C.; Preston, R. K. Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H+ with D2. J. Chem. Phys. 1971, 55, 562-572. 71. Parandekar, P. V.; Tully, J. C. Mixed Quantum-Classical Equilibrium. J. Chem. Phys. 2005, 122, 094102. 72. Prezhdo, O. V. Mean Field Approximation for the Stochastic Schrödinger Equation. J. Chem. Phys. 1999, 111, 8366-8377. 73. Wang, L. J.; Trivedi, D.; Prezhdo, O. V. Global Flux Surface Hopping Approach for Mixed Quantum-Classical Dynamics. J. Chem. Theory Comput. 2014, 10, 3598-3605. 74. Duncan, W. R.; Craig, C. F.; Prezhdo, O. V. Time-Domain ab Initio Study of Charge Relaxation and Recombination in Dye-Sensitized TiO2. J. Am. Chem. Soc. 2007, 129, 8528-8543.


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Figure Captions

Figure 1. (a) Energy level diagram and (b) projected density of states (PDOS) of the

optimized MAPbI3(100)/TiO2-anatase(001) interface at 0 K from the DFT calculation. The electron-hole recombination occurs by electron transfer from the TiO2 conduction band (CB) minimum to perovskite valence band (VB) maximum. The DOS is split into the CH3NH3, Pb, I, O, and Ti contributions. Zero energy is set to the Fermi level. The PDOS shows that the CB minimum is formed by titanium (3d) orbitals, while the VB maximum is due to iodine orbitals.

Figure 2. Top and side views of the simulation cell showing geometry of the interface

between the MAPbI3 (100) and TiO2 anatase (001) surfaces at 0 K (top panel) and 300 K (bottom panel). Thermal atomic motions alter the geometries and affect the electron donor-acceptor interaction.

Figure 3. Top and side views of the Cl, Br, and Sn-doped systems at 0 K (top) and

300 K (bottom panel). Cl and Br replace I, while Sn substitutes Pb in of MAPbI3. The dopants are represented by green balls. Compared to the pristine system, Figure 2, the


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doped systems exhibit additional geometric distortions, especially at room temperature.

Figure 4. Charge densities of the states supporting electron (top panel) and hole

(bottom panel) prior to the electron-hole recombination. While the electron state is localized completely within the TiO2 substrate, the hole state has a tail extending from perovskite into TiO2. The tail decreases in the following order: Sn-doped > MAPbI3/TiO2 > Br-doped > Cl-doped. Larger delocalization corresponds to stronger donor-acceptor coupling.

Figure 5. Densities of states of the optimized pristine and doped MAPbI3(100)/TiO2-

anatase(001) interfaces at 0 K. The dopant component is magnified 10 times. Zero energy is set to the Fermi level. While Sn contributes to the hole density at the valence band maximum. Cl and Br contribute little to either electron or hole wavefunction.

Figure 6. Fourier transforms of the donor–acceptor energy gap.

Figure 7. Electron-hole recombination dynamics across the MAPbI3(100)/TiO2-

anatase(001) interface with and without doping MAPbI3 by Cl, Br, or Sn. The circles are linear fits. The inset shows the pure-dephasing functions for the donor–acceptor transition in each system, representing elastic electron–phonon scattering. The dephasing functions are fitted by Gaussians.


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Figure 1

CB

(a)

(b)

CB 1.09 eV

EF

-0.23 eV

VB

VB

TiO2

MAPbI3


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Figure 2


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Figure 3

Cl-doped

Br-

Sn-doped

Cl-doped

Br-

Sn-doped

0K 300 K


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Figure 4


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Figure 5


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Figure 6


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Figure 7


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