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October 11, 2015

C 2015 American Chemical Society

Dopants Control Electron�HoleRecombination at Perovskite�TiO2Interfaces:Ab InitioTime-DomainStudyRun Long*,†,‡ and Oleg V. Prezhdo*,§

†College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875,People's Republic of China, ‡School of Physics, Complex & Adaptive Systems Lab, University College Dublin, Dublin, Ireland, and §Department of Chemistry,University of Southern California, Los Angeles, California 90089, United States

Following the first report of a perovskitesolar cellwith thesolarenergyconversionefficiency of 3.8%,1 organic�inorganic

halide perovskites, such as CH3NH3PbI3(MAPbI3), have attracted intense attention.Perovskites have unique geometric andelectronic properties, are good light absor-bers, and are cost-effective.2�14 Currently,the highest reported conversion efficiencyof perovskite-sensitized TiO2 solar cells is19.3%.9 TheMAPbI3 bandgap allows absorp-tion over a wide range of the solar spectrum,from visible to near-infrared. MAPbI3 exhibitsextremely long diffusion lengths for bothelectrons and holes,4 around 100 nm, whichis larger than the typical charge diffusionlengths in other materials, on the order of

10 nm. The electron and hole diffusionlengths can increase with doping. For in-stance,mixedMAPbI3�xClxperovskites trans-port charge over distances exceeding 1 μm,an order of magnitude greater than in thepristine material.15 Cl doping is possibleonly at relatively low concentrations. Someexperiments demonstrate that Cl dopingconcentration can reach only 0.1% to 1%,with Cl atoms localized preferentially onthe surface.16,17 Such doping levels havelittle effect on the band gap.18 Other papersreport higher Cl doping concentrations.19

In contrast, the Br and Sn dopants are com-mensurate with the MAPbI3 lattice.

20�22

MAPbI3�xClx can act as both light harvesterandelectronconductor.Meso-superstructured

* Address correspondence torunlong.anh@gmail.com,prezhdo@usc.edu.

Received for review July 26, 2015and accepted October 11, 2015.

Published online10.1021/acsnano.5b05843

ABSTRACT TiO2 sensitized with organohalide perovskites gives rise to solar-to-

electricity 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 non-

adiabatic (NA) molecular dynamics to pristine and doped CH3NH3PbI3(100)/TiO2anatase(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 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 wave functions. Tin increases the coupling, since it is lighter than lead and contributes to the hole wave function. 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: organohalide perovskites . TiO2. dopants . electron�hole recombination . nonadiabatic molecular dynamics .

time-domain density functional theory

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solar cells employing MAPbI3�xClx and a buffer layercomposed of Al2O3 and spiro-MeOTAD reach 12.3%conversion efficiency.23 Recently, Han and co-workersreported a 12.8% efficiency in a mixed-cation config-uration without a hole conductor.24 Because the holeconductor is expensive, this advance can significantlyreduce the fabrication cost andmake perovskite-basedsolar cells feasible for large-scale applications. Perov-skites compete successfully with other modernmateri-als used in solar energy applications, including organicmolecules and polymers,25 semiconducting26,27 andmetallic28 nanoparticles, graphene,29 etc.The measured times of electron injection from

MAPbI3 to TiO2 are 260�307 ps.30 This is 3 orders ofmagnitude longer than the hot carrier cooling timeof 0.4 ps.4 Insertion of a layer of ultrathin graphenequantum dots between perovskite and TiO2 can accel-erate the electron transfer to 90�106 ps,30 arguably byoptimizing the interfacial morphology. The extremelyslow electron�hole recombination time (1.71 ns)24

at the MAPbI3�TiO2 interface facilitates high photon-to-electricity conversion efficiency. Cl- and Br-dopedMAPbI3 (MAPbI3�xClx, MAPbI3�xBrx) can increase theconversion efficiency further.9,20 In contrast, Sn-dopedMAPbI3 (MAPb1�xSnxI3) shows only a 4.18% conversionefficiency, even though the Sn dopant reduces theenergy gap of MAPbI3, allowing the material to harvesta broader range of the solar spectrum.21

Many ab initio molecular dynamics simulationshave been performed on the pristine MAPbI3 system.Carignano and coauthors studied the finite size effectson the structural and electronic properties of tetrago-nal phase MAPbI3.

31 Others addressed the structuraland electronic properties of cubic phase MAPbI3.

32,33

Classical Monte Carlo simulations were used to inves-tigate the ferroelectric properties of MAPbI3.

34 Quartiet al. observed a localization of the valence and con-duction band states in separate regions of bulkMAPbI3.

33 The same result was highlighted by Ma andWang using a linear scaling ab initio approach with alarge supercell.35 Quarti et al. emphasized further thedynamical nature of the charge localization.33,36,37 Theobtained charge localization time scales were in goodagreement with the temperature-dependent UV�visspectra, reflecting the screening between electronsand holes introduced by the motions of the methylam-monium cations.38 To date, no theoretical work hasreported atomistic investigation of the electron�holerecombination at the MAPbI3/TiO2 interface, in particu-lar explicitly considering nonadiabatic transitions with-in the manifold of electronic states.The experimental results provide strong motivation

for fundamental theoretical studies. Despite the rapidincrease in efficiency associated with the evolution ofdifferent types of perovskites and device fabricationtechniques, the mechanisms of electron�hole recom-bination and energy losses limiting device efficiency

remain unclear. Most of the successes have beenachieved by trial-and-error, and more often than not,the observed behavior is surprising and could not havebeen predicted a priori. To mimic such experimentalobservations in real time and at the atomistic level,we employ ab initio time-domain nonequilibriumsimulation to explore in detail the mechanism ofthe electron�hole recombination at the perovskiteMAPbI3/TiO2 interface with and without doping andto provide guidelines for minimizing charge losses.Our study shows, in excellent agreement with ex-

periment, that the rate of the electron�hole recombi-nation at the MAPbI3/TiO2 interfaces depends stronglyon the following factors: the strengths of inelasticand elastic electron�vibrational interactions, locationof the dopant electronic energy levels relative to thelevels of the pristine system, and the extent of chemicalinteraction and donor�acceptor coupling at the inter-face. Inelastic electron�vibrational scattering consti-tutes the fundamental mechanism of energy lossand electron�hole recombination. Elastic electron�phonon scattering determines duration of quantumcoherence, which is needed for the electronic transi-tion to occur. Location of the dopant energy levelscontrols the states involved in the dynamics anddetermines whether and howdopants affect electron�vibrational interactions. Chemical interactions at theinterface modify the donor�acceptor coupling be-tween the electron and hole states. All factors showtemperature dependence.The simulations demonstrate that thermal fluctua-

tions perturb the perfect chemical structure of theinterface, create opportunities for transient chemicalbonding, e.g., between iodine and titanium, and in-crease the donor�acceptor interaction. By alteringthe perfect crystal structure of the perovskite, somedopants, such as Sn, open additional channels forinterfacial interaction. Other dopants, such as Cl andBr, diminish bonding between the donor and acceptorsubsystems; in particular, since the Pb�Cl and Pb�Brbonds are shorter than the Pb�I bond, Cl�Ti and Br�Tibonds cannot be formed. The wave function of theelectron is localized entirelywithin TiO2. In contrast, thewave function of the hole leaks from the perovskitesinto TiO2, creating the needed donor�acceptor wavefunction overlap. Chlorine and bromine contributelittle 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 iodinethey replace, chlorine and bromine shorten quantumcoherence time and slow down electron�hole recom-bination. In contrast, tin contributes to the wave func-tion of the hole, increases the electron�hole andcharge�phonon interactions, and accelerates the re-combination. The energy lost during the electron�hole recombination is accommodatedprimarily by low-frequency modes of perovskite's inorganic backbone

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and TiO2. At the same time, fast motions of the organiccomponent of the perovskite contribute to rapid co-herence loss. By establishing the fundamental aspectsof the electron�hole recombination mechanism, thestudy rationalizes why pervsokite/TiO2 solar cells havehigh photon-to-electron conversion efficiency and sug-gests specific guidelines forminimizing charge losses inMAPbI3/TiO2 systems by choice of suitable dopants.

RESULTS AND DISCUSSION

Figure 1a presents an energy level diagram forthe MAPbI3/TiO2 interface, while Figure 1b gives thecorresponding ab initio data in the form of the pro-jected density of states (PDOS) obtained from thePerdew�Burke�Ernzerhof (PBE) calculation using theoptimized structure at 0 K. The electron�hole recom-bination at the MAPbI3/TiO2 interface is associatedwith transfer of the excited electron from the TiO2

conduction band (CB) minimum (CBM) to the MAPbI3valence band (VB) maximum (VBM). It takes place ona nanosecond time scale.24 Therefore, one can assumethat the electron has already reached the bottom ofthe TiO2 CB prior to the recombination. Similarly, thehole 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 3dorbitals and I atomic orbitals contribute to the TiO2

CBM and MAPbI3 VBM, respectively. The CBM and VBMare separated by a large energy gap, and the excesselectronic energy is accommodated by phonons. It isimpossible for atomic motions to bring the initial andfinal electronic states in resonance, necessitating annonadiabatic (NA) transition. Thus, the electron�holerecombination at the MAPbI3/TiO interface definitelyproceeds by the NA mechanism.The present work is motivated by the recent experi-

ments9,20,24 showing that Cl- and Br-dopedMAPbI3/TiO2

have higher phototoelectricity conversion efficiencythan neat MAPbI3/TiO2. In contrast, Sn-doped MAPbI3/TiO2 has lower efficiency than the neat system.21

The following two subsections consider in detail themodel of the MAPbI3/TiO2 interface and its electronicstructure, with and without Cl, Br, and Sn doping. Then,the focus shifts to electron�phonon interactions andphonon modes, which induce the NA transition andcause loss of quantum coherence in the electronicsubsystem. Finally, the electron�hole recombinationdynamics is discussed.

MAPbI3/TiO2 Interface. Interactions between theMAPbI3 and TiO2 surfaces determine the electron�hole recombination rate. The MAPbI3/TiO2 geometryand separation influence the strength of the interfacialinteraction. The interface affects both the geometricand electronic structure of the two subsystems.

Figure 2 shows the top and side views (top andbottom panels, respectively) of the pristine system atthe optimized geometry and during the MD trajectoryat 300 K (first and second columns, respectively).Comparing the two columns, we observe that thermalmotions create binding opportunities. The donor�acceptor separation decreases and I�Ti chemicalbonds are formed with increasing temperature. At0 K, TiO2 maintains a perfect crystal structure, whilethe MAPbI3 layer exhibits minor distortions due toproximity to TiO2. The MAPbI3/TiO2 interaction ispurely van der Waals at 0 K.

At elevated temperature, the geometries of bothslabs change significantly. The largest motions of theTiO2 structure are associated with displacements of in-plane oxygen atoms, resulting in dissociation of someO�Ti bonds. More pronounced changes occur withinthe MAPbI3 layer, Figure 2. Several new I�Ti bondsform (side view at 300 K), and the whole layer under-goes large-scale undulating motions (side and topviews at 300 K). Pb�I bonds on the MAPbI3 surfacecontract and elongate. CH3NH3

þ cations move closerto the TiO2 surface and rotate significantly. The purelyvan der Waals interaction of MAPbI3 with the TiO2

surface is too weak to maintain MAPbI3/TiO2 bindingat room temperature. The new I�Ti covalent bonds

Figure 1. (a) Energy level diagramand (b) projected density of states (PDOS) of the optimizedMAPbI3(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 the perovskite valence band (VB)maximum. The DOS is split into the CH3NH3, Pb, I, O, andTi 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.

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facilitated by thermal undulatingmotions of theMAPbI3layer decrease the MAPbI3�TiO2 separation and in-crease the electronic donor�acceptor coupling.

Introduction of the substitutional dopants Cl or Brin place of I, and Sn in place of Pb, causes additionaldistortions of the MAPbI3/TiO2 interface geometry,especially at room temperature, Figure 3. Consideringthe optimized (0 K) geometries, we observe that bothCl�Pb (2.636 Å) and Br�Pb (2.763 Å) bonds are notablyshorter than the I�Pb bond (2.972 Å, Figure 2). Conse-quently, the Cl and Br atoms are farther away fromthe TiO2 slab than iodines. The number of halogen�titanium bonds and, therefore, the donor�acceptorcoupling decrease. Moreover, the electronegativitiesof Cl (3.16) and Br (2.96) are larger than that of I (2.66).39

As a result, Cl and Br interact more strongly withCH3NH3

þ ions than I does, and the ions are pulledaway from TiO2, decreasing the donor�acceptor inter-action further.

Considering the Sn-doped system, we note thatSn2þ is smaller than Pb2þ, and the Sn�I bond (2.886 Å)pointing toward TiO2 is also shorter than the corre-sponding Pb�I bond (2.972 Å). Similarly, the averagebond length (3.129 Å) of the four Sn�I bonds in theouter layer is shorter than the average length ofthe four I�Pb bonds (3.174 Å) in the pristine system.Distortions induced by Sn are significant and do noteliminate the Ti�I bonding opportunities at roomtemperature. Strong donor�acceptor coupling ismain-tained in the Sn-doped system.

The geometries of the doped systems undergoadditional distortions at room temperature, comparedto the pristine MAPbI3/TiO2 interface. The number ofI�Ti bonds becomes smaller upon Cl and Br doping,

indicating that the interaction between the donor andacceptor materials weakens. This finding is oppositethe previous static DFT calculations, showing thatCl doping enhances the interaction between MAPbI3and the TiO2 slab.

40 The differences likely arise becausethe whole bottom layer of iodine atoms was replacedwith chlorines in the above cited work, while weconsider a much lower level of substitution doping.Further, we study the system at a finite temperature,which includes thermal disorder, while the abovework considers the optimized structure correspond-ing to 0 K. In contrast to Cl and Br doping, Sndoping maintains I�Ti bonds and even creates newbonding opportunities, for instance TiO2�CH3NH3

þ

hydrogen bonds, enhancing the donor�acceptorcoupling.

In order to confirm that the current model providesa reasonable description of the MAPbI3/TiO2 interface,we performed additional calculations on the pristinesystem employing a thicker perovskite layer. The resultsare presented in Supporting Information (SI).

Electronic Structure. Figure 4 presents densities ofthe electron donor and acceptor states involved inthe electron�hole recombination. The recombinationdynamics depends on the electronic energy gap anddonor�acceptor coupling. The strength of the coupl-ing is related directly to the overlap between the donorand acceptor wave functions. Here, the donor stateis localized completely within the TiO2 substrate. Theacceptor state is localized mainly on the iodine atomsof MAPbI3. At the same time, it delocalizes onto theTiO2 slab, creating the required donor�acceptor wavefunction overlap. The extent of the delocalized taildecreases in the following order: Sn-doped > MAPbI3/TiO2 > Br-doped > Cl-doped. The donor�acceptorcoupling decreases in the same order. Overall, thedonor�acceptor wave function overlap is quite small,rationalizing the slow, nanosecond electron�holerecombination.

Electrons and holes can recombine in purematerialsboth radiatively andnonradiatively. Here, luminescencefrom the CBM to the VBM is unlikely because the CBMand VBM are localized on two different components,Figure 4, and the corresponding transition dipolemoment is small. Instead, transitions from the CBM tothe VBM occur nonradiatively.

Figure 5 shows PDOS of the Cl-, Br-, and Sn-dopedMAPbI3/TiO2 systems that were calculated at 0 Kusing the optimized structure. The PDOS is split intocontributions fromMAPbI3, TiO2, and the dopants. Thedopant component is magnified 10 times. Sn con-tributes to the hole density at the VBM, Figure 5d,modifying the VBMof the pristine systems, Figure 5a. Incontrast, Cl and Br contribute little to either electron orhole wave function, Figure 5b and c, respectively. ThePDOS analysis is consistent with the three-dimensionalimages of the state densities, Figure 4.

Figure 2. Top and side views of the simulation cell showinggeometry of the interface between the MAPbI3(100) andTiO2 anatase(001) surfaces at 0 K (top panel) and 300 K(bottom panel). Thermal atomic motions alter the geome-tries and affect the electron donor�acceptor interaction.

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It is known that pure DFT functionals, such as PBE,underestimate band gaps, in particular, the TiO2 bandgap. However, DFT calculations employing the PBEfunctional give a reasonable agreement with the ex-perimental band gap for hybrid halide perovskites.40,41

The agreement can be attributed to cancellation oferrors, arising due to an approximate description ofelectron exchange/correlation and lack of relativisticeffects (spin�orbit coupling), as demonstrated inseveral publications.42�44 The canonically averaged

Figure 3. Top and side views of the Cl-, Br-, and Sn-doped systems at 0 K (top panel) and 300 K (bottom panel). Cl andBr replace I, while Sn substitutes Pb inMAPbI3. The dopants are represented by green balls. Compared to the pristine system,Figure 2, the 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�holerecombination. While the electron state is localized completely within the TiO2 substrate, the hole state has a tail extendingfrom perovskite into TiO2. The tail decreases in the following order: Sn-doped > MAPbI3/TiO2 > Br-doped > Cl-doped. Largerdelocalization corresponds to stronger donor�acceptor coupling.

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band gap computed here for the pristine MAPbI3/TiO2

system is 0.987 eV. Doubling the length of the MDtrajectory changed the canonically averaged value to0.972 eV. A 3 ps MD trajectory for the system includinga twice thicker perovskite layer, Figure S1 of the SI,gave 0.961 eV. These values are to be compared tothe experimental value of around 1.4 eV.24,45 Differentexperimental samples and measurements produce asignificant variation in the energy level alignment atthe MAPbI3/TiO2 interface.

24,45,46 The canonically aver-aged band gaps for the Cl-, Br-, and Sn-doped systemsare slightly smaller than the band gap of the pristinesystem. They are equal to 0.834, 0.792, and 0.796 eV,respectively. The experimental band gaps for theCl- and Br-doped systems20,24 should not be comparedto the calculated values, since the doping concentra-tions are different. Experiment shows that Sn dopingreduces the MAPbI3 band gap very slightly.47 Thisagrees with the GW calculations demonstratingthat MASnI3 has a smaller band gap than MAPbI3.

32

For better comparison with the experiments, we scalethe band gap of all four systems by adding the sameconstant, chosen to match the experimental band gapof the pristine MAPbI3/TiO2 system.24

Electron�Vibrational Interactions. Electron�vibrationalinteractions generate elastic and inelastic scattering.Both types of scattering affect the electron�hole re-combinationprocess. Inelastic energy exchangebetweenthe electronic and vibrational subsystems is requiredin order to accommodate the energy lost during theelectronic transition from the CBM to the VBM. Elasticelectron�phonon interactions destroy coherence formedbetween the CBM and VBM states. The coherence is

formed when the states become coupled by the NAcouplingduring nonradiative relaxation. The coherenceappears during radiative transitions when states be-come coupled via the transition dipole moment. Elasticelectron�phononscattering is known inopticalmeasure-ments as pure dephasing.48 In particular, it determinesthe line width of single-particle luminescence.

Figure 6 presents Fourier transforms (FT) of theVBM�CBM energy gaps in the four systems. FT charac-terizes the phonon modes that couple to the electronicsubsystem, cause decoherence, and accommodatethe excess energy released during the electron�holerecombination process. Only low-frequency vibrationsare involved in the nonradiative decay process in allfour cases. Dopants increase the frequency range ofactive vibrations.

Figure 5. Densities of states of the optimizedpristine and dopedMAPbI3(100)/TiO2 anatase(001) interfaces at 0 K. The dopantcomponent ismagnified 10 times. Zero energy is set to the Fermi level.While Sn contributes to the hole density at the valenceband maximum. Cl and Br contribute little to either electron or hole wave function.

Figure 6. Fourier transforms of the donor�acceptor energygap.

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The dominant peak in pristine MAPbI3/TiO2 can beattributed to Pb�I bond stretching at 94 cm�1.49 Thisfrequency is the diagnostic mode of the inorganiccage. The peak can also be assigned to the librationsof the organic cations at 119 cm�1.49 Even though theorganic groups contribute to neither electron nor holestates (Figure 1b), they influence the electron and holewave functions electrostatically. Rotation of organicgroups leads to signficant changes of the generatedelectrostaticfield.19 The secondmainpeak canbe relatedto thebendingmodeof Pb�I bondsat 62 cm�1,49 aswellas to the low-frequency acoustic symmetrical spheroidalmode of anatase TiO2 at 33 cm�1.50 The length of theMD trajectories is insufficient to resolve such low-frequency modes more accurately. Both modes alterthe MAPbI3 geometry, create the NA coupling, andpromote electron�hole recombination. The medium-frequency vibrations ranging from 200 to 400 cm�1

can be assigned to torsional motions of the CH3NH3þ

cations.49 Just like the CH3NH3þ rotation, the tortional

modes alter the generated electric field, though to amuch lesser extent.

The band gap of pristine MAPbI3 reported in pre-vious ab initio molecular dynamics simulations fluctu-rates with frequencies similar to those found in ourwork. For instance, the dominat frequency shownin the first panel of Figure 6 in ref 37 correspondsto the first peark in Figure 6 here. Quarti et al.37 showsthat spatial localization of the electron and hole statesoccurs on a 0.1 ps time scale, roughly corresponding tothe librationmotions of themethylammonium cations.38

The electronic states of the current MAPbI3/TiO2 systemcouple primarily to the 100 cm�1 mode, with a 0.3 psperiod. This slowermotionmay arise from the interactionbetween MAPbI3 and TiO2 that suppresses rotations ofMA cations.

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 decreasesin magnitude. FTs of the energy gap autocorrelationfunction (ACF) presented in Figure 6 are most directlyrelated to the pure-dephasing function, eqs 10 and 11.A larger number of contributing modes acceleratesdephasing. The dephasing becomes faster upon Cldoping (inset in Figure 7) because the contributionsof the two modes are nearly equal. Br doping intro-duces a broad range of modes. Although the magni-tude of the main peaks decreases, two other peaksappear in the 200�400 cm�1 frequency range, provid-ing new dephasing channels. The additional peaks canbe assigned to the Eg mode and transverse optical Eu(1)mode of anatase TiO2 at 198 and 262 cm�1, res-pectively.51,52 Sn doping eliminates the 100 cm�1 peakand decreases the magnitude of the 40 and 200�400 cm�1 peaks. Consequently, pure dephasing slowsdown. TiO2 phonon modes contribute significantly tothe electron�hole recombination because the MAPbI3wave function is delocalized onto the TiO2 slab, bothwith and wihout doping, Figure 4.

While high-frequency NH stretching modes ofmethylammonium (MA) cations are present in all foursystems, they are hard to detect. These frequencies can

Figure 7. Electron�hole recombination dynamics across the MAPbI3(100)/TiO2 anatase(001) interface with and withoutdoping 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 byGaussians.

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be observed if the FT data are magnified severalthousand times. The signals arising from high-frequency vibrations often average out in extended,bulk systems, since the observables are computed byintegrating over wave functions delocalized over largeparts of the system, Figure 4.

The optical pure-dephasing functions, eq 10, areshown in the inset of Figure 7. The functions character-ize elastic electron�phonon scattering. The open cir-cles represent Gaussian fits f(t) = B exp(�0.5(t/τa)

2)þ C.The pure-dephasing times decrease in the sequenceSn-doped > MAPbI3/TiO2 > Br-doped > Cl-dopedand are equal to 4.4, 4.3, 4.0, and 3.4 fs, respectively.The decoherence is caused primarily by coupling ofthe electronic subsystem to the 100 cm�1 vibrationalmode. The lower frequency peak in Figure 6 is thesecond main contributor. The presence of multiplefrequencies in the vibrational influence spectrum ac-celerates decoherence. The 4.3 fs pure-dephasing timeof the pristine system is dramatically shorter than the1.71 ns electron�hole recombination time reported inthe experiment,24 as expected for transitions acrosslarge energy gaps. Because the dopants are present ata low concentration, the pure-dephasing times differlittle from each other, in agreement with the abovephonon mode analysis.

Sn has a small effect on decoherence, because itis not much lighter than iodine, which is the lightestatom in the inorganic subsystem of MAPbI3. Recall thatthe CBM and VBMarise from the inorganic backbone.41

In comparison, Cl and Br are lighter than iodine, andtherefore, they have a larger effect on the decoherencetime. The decoherence times computed here are sig-nificantly shorter than those obtained for TiO2 sensi-tized with PbSe and Au nanocrystals,53 because thelatter systems contain no organic components andare formed by heavier elements. Short-lived coherenceleads to long electron�hole recombination.

Electron�Hole Recombination Dynamics. The electron�hole recombination at the TiO2/MAPbI3 interfaceoccurs by a nonradiative transition of the photoexcitedelectron from the CBM localized on the TiO2 surfaceto the VBM localized on MAPbI3. The time-dependentpopulation of the CBM is shown in Figure 7. Thecalculated 0.65 ns time, obtained using the short-timelinear approximation, f(t) = aτ þ b, to the exponentialdecay agrees well with the experimental data.24 Suchslow electron�hole recombination is beneficial formaintaining solar cell current, which serves the highconversion efficiency of MAPbI3/TiO2 solar cells.

24

To reduce energy losses and increase performanceof photovoltaic cells, one can tune and further mini-mize the electron�hole recombination by doping.Both Cl and Br doping give slower recombinationdynamics, 2.0 and 0.84 ns, respectively, while Sndoping accelerates the recombination, 0.52 ns. Thecanonically averagedabsolute values of theNAcoupling

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 couplingstrength is related to the wave function overlap be-tween 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 decoherencerate, Figure 7 inset, rationalizes the effect of the dopantson the electron�hole recombination. In particular, Cl-doped MAPbI3�TiO2 gives the slowest recombination,which serves to explain the highest conversion effi-ciency, up to 20%, of MAPbI(3�x)Clx/TiO2 solar cells.

9

In order to establish convergence of the reportedresults with respect to system size and simulation time,we performed the following tests, focusing on thesystem without defects. First, we increased the thick-ness of the perovskite layer and created a 366-atom MAPbI3/TiO2 interface with two layers of theMAPbI3(001) surface. Note that NAMD simulationis more expensive than a regular MD simulation,in particular since it requires NA couplings, which arecomputed using high-precision wave functions. Weperformed the NAMD simulation only for the pristinesystem and for a shorter time. The structure, PDOS, andpopulation dynamics are shown in Figures S1�S3 inthe SI. Figure S1 displays the optimized structure at 0 Kand a geometry from molecular dynamics (MD) at300 K. The behavior of the two-perovskite-layer systemis similar to the system with a single perovskite layer,Figure 2. The PDOS (Figure S2) and the electron�holerecombination time scale (Figure S3a) for the two-layerMAPbI3 system are nearly identical to the correspond-ing results obtained for TiO2 interfaced with onelayer of MAPbI3 (Figures 1b and 7, respectively).Second, we doubled the length of the MD trajectoryand performed a longer NAMD simulation for theTiO2 anatase(001) surface interfaced with one-layerMAPbI3(100). The electron�hole recombination dy-namics are characterized in Figure S3b. The obtainedtime scale matches the shorter NAMD simulation,Figure 7. The tests performed with the pristine systemindicate that the current model provides a gooddescription of the perovskite/TiO2 interface, leadingus to expect that the studies including the dopantsproduce reliable results.

Experiments indicate that Cl dopants prefer toaccumulate at the perovskite surface,16,17 while theBr and Sn dopants provide a better match to theMAPbI3 lattice and enter perovskite bulk.20�22 There-fore, the same formal dopant concentration can havedifferent effects on the interfacial charge recombina-tion dynamics, depending on dopant concentration atthe interface. In particular, even at low concentrations,Cl dopants should have a strong effect on the inter-facial electron�hole recombination, reducing its rate.This conclusion agrees with the fact that Cl-doped

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MAPbI3 exhibits better photovoltaic performance.16,54,55

In general, doping concentration can affect the donor�acceptor interaction, electron�phonon coupling, andthe interface morphology. Smaller doping levels willdecrease the dopant effect on the donor�acceptorcoupling for all three cases. The electron�hole recom-bination rate will change little at low doping concentra-tion, compared to the pristine system. In contrast,doping level increase is expected to suppress electron�hole recombination in the presence of Cl and Br dopingbecause the dopants weaken the donor�acceptor cou-pling. In the specific case of Cl doping, using chlorine-containingprecursors, PbCl2 andMACl strongly improvethe quality of perovskite and enhance the photovoltaicproperties of MAPbI3,

16,54,55,16,54,55 suggesting thatthe morphology of perovskites and solar cell perfor-mance can be optimized via doping. In contrast toCl and Br, increasing the Sn doping concentration willfurther extend the tail of the perovskite wave func-tion into the TiO2 slab, increase the donor�acceptorcoupling, and accelerate the interfacial electron�holerecombination.

CONCLUSIONS

We reported the first time-domain ab initio study ofelectron�hole recombination dynamics in TiO2 sensi-tized with methylammonium lead halide perovskiteswith and without doping. The material holds greatpromise for photovoltaic applications. The recombina-tion constitutes the main channel for charge andenergy losses, limiting light-to-current conversionefficiency. The simulated time scales and the phononmodes found to promote the relaxation agree wellwith the experimental data available for the MAPbI3/TiO2 system. The simulations show that doping with Cland Br notably reduces the recombination rate, whiledoping with Sn increases the rate. These findings arerather surprising and would have been hard to predicta priori, in particular since all three dopants are lighterthan the atoms they substitute and since higherfrequency vibrations introduced by lighter atoms areexpected to accelerate the relaxation. The establishedresults are rationalized by a combination of the follow-ing three factors: (1) Cl and Br decrease the MAPbI3/TiO2 bonding interaction, while Sn increases the bond-ing; (2) Cl and Br diminish the donor�acceptor and NA

coupling, while Sn makes the coupling stronger; (3) Cland Br accelerate loss of quantum coherence, while Snleaves the decoherence time largely unchanged.Compared with the optimized zero-temperature

structures, both pristine and doped MAPbI3/TiO2

exhibit additional bonding at ambient temperaturedue to thermal fluctuations. In particular, transientI�Ti bonds are formed. Similar Cl�Ti and Br�Ti bondscannot form, since Cl and Br are smaller than I, arecloser to Pb, and are farther from Ti. The electron donorstate is strongly localized on TiO2, while the electronacceptor state (the hole state) has a tail extendingfrom MAPbI3 into TiO2. The delocalization decreasesin the series Sn-doped > MAPbI3/TiO2 > Br-doped >Cl-doped. Correspondingly, the NA coupling exhibitsthe same trend.The simulations demonstrate that the electron�

hole recombination is largely promoted by low-frequency bending and stretching modes of I�Pbbonds and TiO2 acoustic modes. Librational motionsof the organic ligands facilitate the recombinationindirectly, via changes in the electrostatic environment.Replacement of iodine by either Cl or Br increases theelectron�phonon coupling magnitude and introduceshigher frequency modes. As a result, the lifetimes ofquantum coherence between the initial and final statesinvolved in the electron�hole recombination decrease,and quantum transitions take more time. Substitutionof Pb by Sn also introduces higher frequency vibrations;however, the electron�phonon coupling magnitudedecreases and the coherence time decreases slightly aswell. The study highlights the importance of quantumcoherence in the excited-state dynamics of perovskite-based materials.The reported time-domain ab initio investigation

establishes the fundamental mechanisms behind theenergy losses: chemical bonding, wave function mixing,electron�vibrational coupling, and quantum coherence.It also generates practical guidelines on reduction of theinterfacial charge recombination rate by appropriatechoice of dopants. By pioneering a new class of theore-tical investigations into the excited-state dynamics ofhybrid organic�inorganic perovskites, the research de-scribed in this paper advances our understanding of thekey factors influencing and controlling the performanceof hybrid organic�inorganic perovskite solar cells.

THEORETICAL METHODSThe simulations were carried out by the combination of

nonadiabatic molecular dynamics and time-dependent (TD)density functional theory (DFT). NAMD is performed using thequantum-classical fewest-switches (FS) surface hopping (SH)technique56 implemented with the Kohn�Sham formulation ofTDDFT.57�60 A semiclassical correction for quantum decoher-ence is included.61,62 The correction is needed here, because thedecoherence (pure-dephasing) time is significantly shorter than

the quantum transition time. The pure-dephasing times werecomputed using the optical-response formalism.63 The approachhas been applied to study electron transfer, energy relaxation,and electron�hole recombination in a variety of systems, includ-ing semiconducting64 and metallic65 nanocrystals, interfaces be-tween fullerene and quantum dots (QDs),66 QDs and molecule,67

QDs and TiO2,68 etc.

Time-Domain Density Functional Theory. DFTmaps an interactingmany-body system onto a tractable system of noninteractingparticlesmoving in an effective potential, using electron density

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as the variable tominimize the ground-state energy. In practicalimplementations, the density is constructed from TD single-particle Kohn�Sham (KS) orbitals, jp(r, t).

F(r, t) ¼ ∑Ne

p¼ 1jjp(r, t)j2 (1)

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

ipDjp(r, t)

Dt¼ H(r,R, t) jp(r, t); p ¼ 1, 2, :::, Ne (2)

These equations are nonlinear, since the HamiltonianH(r, R, t) is a functional of the electron density, which is obtainedby summing over occupied KS orbitals, eq 1. By expanding thetime-dependent KS orbitals in the adiabatic KS orbital basis,j~p(r, R(t)), obtained for a given nuclear configuration,

jp(r, t) ¼ ∑k

ck(t) j~k (r;R(t)) (3)

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

ipDDtcj(t) ¼ ∑

k

ck(t)(εkδjk þ djk ) (4)

Here, εk is the energy of the adiabatic state k, and djk is the NAcoupling between states k and j. TheNA coupling arises becauseelectronic wave functions depend parametrically on nuclearcoordinates. It reflects the inelastic electron�vibrational inter-action. The coupling is calculated numerically as the overlap oforbitals j and k at sequential time steps69

djk ¼�ipÆj~j jrRjj~kædRdt ¼ �ip Æj~jj DDtjj~kæ� � ip

2Δt(Æj~j(t)jj~k(tþΔt)æ�Æj~j(tþΔt)jj~k (t)æ)

(5)

Nonadiabatic Dynamics by Fewest Switches Surface Hopping. SH is astochastic algorithm for switching electronic states in a mixedquantum-classical simulation. It introduces probabilistic hopp-ing according to the solution to the TD Schrodinger equation,i.e., eq 4 for the expansion coefficients in the present case. Onlyone potential energy surface is involved in nuclear dynamicsat a given instance of time.70 FSSH is the most popular SHapproach. It minimizes the number of hops while maintain-ing consistency with the Schrodinger equation.56 Moreover,it satisfies approximately detailed balance between transitionsupward and downward in energy,71 as required for properdescription of electron�vibrational energy exchange and re-laxation to thermodynamic equilibrium.72

FSSH can be regarded as the first-order approximationwithin the class of methods that obtain hopping probabilitiesbased on flux of quantum populations. Global flux SH genera-lizes FSSH to higher orders, in particular, to superexchange andmany-particle processes.73

The probability of a transition between states k and j withintime interval δt is given in FSSH by56

dPkj ¼ bkjakj

dt (6)

where

akj ¼ ck(t) cj(t) and

bkj ¼ 2p�1 Im(akjÆj~k jHjj~jæ)� 2Re(akjdkj)(7)

If the calculated dPkj is negative, the hopping probability is setto zero. A hop from state j to state k can occur only when theelectronic occupation of state j decreases and the occupation ofstate k increases, minimizing the number of hops. To conservethe total electron�nuclear energy after a hop, the original FSSHtechnique56 rescales the nuclear velocities along the direc-tion of the NA coupling. If an NA transition to a higher energy

electronic state is predicted by eq 6, while the kinetic energyavailable in the nuclear coordinates along the direction of theNA coupling vector is insufficient to accommodate the increasein the electronic energy, the hop is rejected. This step gives thedetailed balance between the upward and downward transi-tions in energy, leading to Boltzmann statistics and quantum-classical thermodynamic equilibrium.71 The current simulationuses a simplified and more efficient version of FSSH, employingthe classical path approximation, as detailed in refs 59 and 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 decoherenceinduced in the electronic subsystem by quantum nuclei. FSSHoverestimates the rates of NA transitions that take signifi-cantly longer than the decoherence time for the correspondingpairs of states. In the limit of infinitely fast decoherence, thisphenomenon is illustratedby the quantumZeno effect.75 In suchcases, FSSH should be corrected for decoherence.61,76 Sincedecoherence is the physical mechanism of trajectory branching,more advanced formulations establish SH algorithms based ondecoherence directly,72,77�80 rather than introducing decoher-ence corrections.

The phonon-induced decoherence time associated with theelectron�hole recombination process is calculated using theoptical response theory.48 The electron�hole recombinationoccurs in MAPbI3 across a wide energy gap on a nanosecondtime scale.24 It is significantly longer than the decoherence time,requiring a decoherence correction to FSSH. In the currentsimulation, the time-dependent KS wave function jp(r, t) iscollapsed to an adiabatic eigenstate j~k(r; R(t)), eq 3, on thedecoherence time scale, as implement in ref 61. The decoher-ence procedure collapses the wave function coefficeints, ck(t)in eq 4. The collapse times are determined by a sequence ofrandom numbers sampled from the Poisson distribution withthe characteristic time determined by the decoherence time.The probability of collapse onto eigenstate k is given by thesquare of the coefficient ck(t) at the collapse time.

Thedecoherence timewas computed as thepure-dephasingtime in the optical response formalism. The phonon-inducedfluctuations in the energy gap between the electron and holestates are characterized by the autocorrelation function.

C(t) ¼ ÆΔE(t) ΔE(0)æT (8)

The brackets indicate canonical averaging. The ACF is normalized

Cnorm(t) ¼ ÆΔE(t) EΔ(0)æTÆΔE2(0)æT

(9)

by its initial value C(0) = ÆΔE2(0)æT. The square root of this valuegives the average 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) ¼ exp( �g(t)) (10)

where

g(t) ¼Z t

0dτ1

Z τ1

0dτ2 C(τ2) (11)

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

I(ω) ¼�����

1ffiffiffiffiffiffi2π

pZ ¥

�¥dt e� iωtC(t)

�����2

(12)

which identifies frequencies of the vibrational modes involvedin the electron�hole recombination process.

Simulation Details. Experimentshave identifiedorthorthombic,tetragonal, and cubic polymorphs of MAPbI3. It has been sug-gested that MAPbI3 undergoes a tetragonal to orthorhombictransition at close to 161 K and transforms to a high-temperaturecubic phase at around 330 K.81 We used the pseudocubicphase82 with the optimized lattice constant of 6.29 Å, providing

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a satisfactory match to the TiO2 periodicity. To create a periodicallyrepeated slab involving the two materials, a 150-atom anataseTiO2-(5�5)(001) surface was chosen to match a 108-atom MAPbI3(3�3)(100) surface terminated with MA. The supercell parametersare 18.88 Å in both the a and b directions, leading to a latticemismatchbetween the two slabsof only 0.01Å.Wealso considereda TiO2/MAPbI3 interface terminated with PbI2, and the calculationshowed it to be unstable. Experiments have indicated that theanatase TiO2(001) surface is particularly advantageous for photo-voltaic applications.10,24 Cl, Br, andSndopantswere introduced intoMAPbI3, replacing I, I, and Pb atoms, respectively. The slabs wereseparated from their images along the surface normal by a vacuumregion of 20 Å. The simulation cells are shown in Figures 2�4.

The geometry optimization, electronic structure, and adia-batic MD calculationswere performed using the Vienna ab initiosimulation package (VASP).83 The Perdew�Burke�Ernzerhof84

functional was used to describe the exchange and correlationeffects. The interaction of the ionic cores with the valenceelectrons was treated by the projector-augmented wave (PAW)approach.85 The electron wave function was expanded in planewaves up to the 500 eV cutoff energy, to converge the totalenergy for geometry optimization and electronic wave functionsfor calculation of the NA couplings. A higher cutoff energy bringsnegligible differences. A lower energy cutoff of 200 eV wassufficient for performing the ground-stateMD simulation in orderto represent thermal nuclear motions. The structure optimizationand MD were performed at the Γ-point, since a large supercellwas used. To obtain accurate density of states, a much denserMonkhorst�Pack k-point mesh of 8 � 8 � 1 was used.86 Thegeometry relaxationwas carried out until the residual forceswerebelow 0.01 eV/Å. The van der Waals interactions, in particularthose between MAPbI3 and TiO2, were described by the DFT-D2method of Grimme using the standard parameters for each kindof atom for both geometry optimization and MD.87

After geometry optimization at 0 K, the pristine and dopedMAPbI3/TiO2 systems were heated to 300 K via repeatedvelocity rescaling, corresponding to the temperature used inthe experiments.24 After that, 3 ps adiabatic MD trajectorieswere generated in themicrocanonical ensemblewith a 1 fs timestep. Additional tests were performed on the pristine systemusing a twice longer adiabatic MD trajectory. To show rotationof methylammonium ions, we included a movie in the SI.Due to the journal limits on the size of the files which can beuploaded as SI, themovie is 1 ps in duration. Already during 1 psone can observe significant rotation of methylammoniumions. The movie shows 3 rows and 3 columns of the ions.Focusing on the MA ion at the intersection of the second rowand third column, we observe several (3�4) 180 deg rotations/librations interrupted by brief stops. The overall 6 ps MDprovides reasonable sampling of the rational motion of themethylammonium ions.

To simulate the electron�hole recombination, 500 geome-tries were selected randomly from each adiabatic MD trajectory.They were used as initial conditions for NAMD, which wasperformed using fewest-switches surface hopping in the classi-cal path approximation and with the decoherence correction.The nuclear time step for the equilibration and productionruns was set to 1.0 fs. The electronic time step for NAMD was1.0 attosecond. A detailed description of the NAMDmethod canbe found in refs 59 and 60.

Conflict of Interest: The authors declare no competingfinancial interest.

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

Supporting Information Available: The Supporting Informa-tion is available free of charge on the ACS Publications websiteat DOI: 10.1021/acsnano.5b05843.

Geometric and electronic structure and electron�hole re-combination dynamics for the pristine MAPbI3/TiO2 systemwith a twice thicker perovskite layer (PDF)1 ps molecular dynamics movie (MPG)

REFERENCES AND NOTES1. Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal

Halide Perovskites as Visible-Light Sensitizers for Photo-voltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050–6051.

2. You, J.; Hong, Z.; Yang, Y.; Chen, Q.; Cai, M.; Song, T.-B.; Chen,C.-C.; Lu, S.; Liu, Y.; Zhou, H.; Yang, Y. Low-TemperatureSolution-Processed Perovskite Solar Cells with High Effi-ciency and Flexibility. ACS Nano 2014, 8, 1674–1680.

3. Dualeh, A.; Moehl, T.; Tétreault, N.; Teuscher, J.; Gao, P.;Nazeeruddin, M. K.; Grätzel, M. Impedance SpectroscopicAnalysis of Lead Iodide Perovskite-Sensitized Solid-StateSolar Cells. ACS Nano 2014, 8, 362–373.

4. Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.;Grätzel, M.; Mhaisalkar, S.; Sum, T. C. Long-Range BalancedElectron- and Hole-Transport Lengths in Organic-InorganicCH3NH3PbI3. Science 2013, 342, 344–347.

5. Yu, Y.; Li, J.; Geng, D.; Wang, J.; Zhang, L.; Andrew, T. L.;Arnold, M. S.; Wang, X. Development of Lead IodidePerovskite Solar Cells Using Three-Dimensional TitaniumDioxide Nanowire Architectures. ACS Nano 2015, 9, 564–572.

6. Christians, J. A.; Manser, J. S.; Kamat, P. V.Multifaceted ExcitedState of CH3NH3PbI3. Charge Separation, Recombination,and Trapping. J. Phys. Chem. Lett. 2015, 6, 2086–2095.

7. Schaak, R. E.; Mallouk, T. E. Perovskites by Design: AToolbox of Solid-State Reactions. Chem. Mater. 2002, 14,1455–1471.

8. Leijtens, T.; Stranks, S. D.; Eperon, G. E.; Lindblad, R.;Johansson, E. M. J.; McPherson, I. J.; Rensmo, H.; Ball,J. M.; Lee, M. M.; Snaith, H. J. Electronic Properties ofMeso-Superstructured and Planar Organometal HalidePerovskite Films: Charge Trapping, Photodoping, andCarrier Mobility. ACS Nano 2014, 8, 7147–7155.

9. Zhou, H.; Chen, Q.; Li, G.; Luo, S.; Song, T.-b.; Duan, H.-S.;Hong, Z.; You, J.; Liu, Y.; Yang, Y. Interface Engineering ofHighly Efficient Perovskite Solar Cells. Science 2014, 345,542–546.

10. Etgar, L.; Gao, P.; Xue, Z.; Peng, Q.; Chandiran, A. K.; Liu, B.;Nazeeruddin, M. K.; Grätzel, M. Mesoscopic CH3NH3PbI3/TiO2 Heterojunction Solar Cells. J. Am. Chem. Soc. 2012,134, 17396–17399.

11. Kobayashi, Y.; Tian, M.; Eguchi, M.; Mallouk, T. E. Ion-Exchangeable, Electronically Conducting Layered PerovskiteOxyfluorides. J. Am. Chem. Soc. 2009, 131, 9849–9855.

12. Zhao, Y.; Zhu, K. Charge Transport and Recombinationin Perovskite (CH3NH3)PbI3 Sensitized TiO2 Solar Cells.J. Phys. Chem. Lett. 2013, 4, 2880–2884.

13. Yamada, Y.; Nakamura, T.; Endo, M.; Wakamiya, A.;Kanemitsu, Y. Photocarrier Recombination Dynamics inPerovskite CH3NH3PbI3 for Solar Cell Applications. J. Am.Chem. Soc. 2014, 136, 11610–11613.

14. Dhanker, R.; Brigeman, A. N.; Larsen, A. V.; Stewart, R. J.;Asbury, J. B.; Giebink, N. C. Random Lasing in Organo-LeadHalide Perovskite Microcrystal Networks. Appl. Phys. Lett.2014, 105, 151112.

15. Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.;Alcocer, M. J. P.; Leijtens, T.; Herz, L. M.; Petrozza, A.; Snaith,H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micro-meter in an Organometal Trihalide Perovskite Absorber.Science 2013, 342, 341–344.

16. Grancini, G.; Marras, S.; Prato, M.; Giannini, C.; Quarti, C.;De Angelis, F.; De Bastiani, M.; Eperon, G. E.; Snaith, H. J.;Manna, L.; Petrozza, A. The Impact of the CrystallizationProcesses on the Structural and Optical Properties ofHybrid Perovskite Films for Photovoltaics. J. Phys. Chem.Lett. 2014, 5, 3836–3842.

17. Yu, H.; Wang, F.; Xie, F.; Li, W.; Chen, J.; Zhao, N. The Role ofChlorine in the Formation Process of “CH3NH3PbI3‑xClx”Perovskite. Adv. Funct. Mater. 2014, 24, 7102–7108.

18. Colella, S.; Mosconi, E.; Fedeli, P.; Listorti, A.; Gazza, F.;Orlandi, F.; Ferro, P.; Besagni, T.; Rizzo, A.; Calestani, G.;Gigli, G.; De Angelis, F.; Mosca, R. MAPbI3‑xClx Mixed HalidePerovskite for Hybrid Solar Cells: The Role of Chloride asDopant on the Transport and Structural Properties. Chem.Mater. 2013, 25, 4613–4618.

ARTIC

LE

LONG AND PREZHDO VOL. 9 ’ NO. 11 ’ 11143–11155 ’ 2015

www.acsnano.org

11154

19. Nie, W. Y.; Tsai, H. H.; Asadpour, R.; Blancon, J. C.; Neukirch,A. J.; Gupta, G.; Crochet, J. J.; Chhowalla, M.; Tretiak, S.;Alam, M. A.; Wang, H. L.; Mohite, A. D. High-EfficiencySolution-Processed Perovskite Solar Cells with Millimeter-Scale Grains. Science 2015, 347, 522–525.

20. Noh, J. H.; Im, S. H.; Heo, J. H.; Mandal, T. N.; Seok, S. I.Chemical Management for Colorful, Efficient, and StableInorganic�Organic Hybrid Nanostructured Solar Cells.Nano Lett. 2013, 13, 1764–1769.

21. Ogomi, Y.; Morita, A.; Tsukamoto, S.; Saitho, T.; Fujikawa, N.;Shen, Q.; Toyoda, T.; Yoshino, K.; Pandey, S. S.; Ma, T.;Hayase, S. CH3NH3SnxPb(1�x)I3 Perovskite Solar Cells Cover-ing up to 1060 nm. J. Phys. Chem. Lett. 2014, 5, 1004–1011.

22. Mosconi, E.; Umari, P.; De Angelis, F. Electronic and OpticalProperties of Mixed Sn-Pb Organohalide Perovskites: aFirst Principles Investigation. J. Mater. Chem. A 2015, 3,9208–9215.

23. Ball, J. M.; Lee, M. M.; Hey, A.; Snaith, H. J. Low-TemperatureProcessed Meso-Superstructured to Thin-Film PerovskiteSolar Cells. Energy Environ. Sci. 2013, 6, 1739–1743.

24. Mei, A.; Li, X.; Liu, L.; Ku, Z.; Liu, T.; Rong, Y.; Xu, M.; Hu, M.;Chen, J.; Yang, Y.; Grätzel, M.; Han, H. A Hole-Conductor�Free, Fully Printable Mesoscopic Perovskite Solar Cell withHigh Stability. Science 2014, 345, 295–298.

25. Song, C. K.; Luck, K. A.; Zhou, N.; Zeng, L.; Heitzer,H. M.; Manley, E. F.; Goldman, S.; Chen, L. X.; Ratner,M. A.; Bedzyk, M. J.; Chang, R. P. H.; Hersam, M. C.; Marks,T. J. Supersaturated” Self-Assembled Charge-SelectiveInterfacial 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 HydrogenProduction fromAcidic andNeutral-pHAqueous SolutionsUsing 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 Structureof Cadmium Selenide Nanocrystals with Shape Anisotropyand 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 CapacitiveEnergy 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 ofPerovskite 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 onCH3NH3PbI3 Perovskite fromAb InitioMolecular DynamicsSimulations. 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 SolarCell Interfaces. J. Phys. Chem. Lett. 2014, 5, 648–653.

33. Mosconi, E.; Quarti, C.; Ivanovska, T.; Ruani, G.; De Angelis,F. Structural and Electronic Properties of Organo-HalideLead Perovskites: a Combined IR-Spectroscopy andAb Initio Molecular Dynamics Investigation. Phys. Chem.Chem. Phys. 2014, 16, 16137–16144.

34. Frost, J. M.; Butler, K. T.; Walsh, A. Molecular FerroelectricContributions to Anomalous Hysteresis in Hybrid Perov-skite Solar Cells. APL Mater. 2014, 2, 081506.

35. Ma, J.; Wang, L.-W. Nanoscale Charge Localization Inducedby Random Orientations of Organic Molecules in HybridPerovskite CH3NH3PbI3. Nano Lett. 2015, 15, 248–253.

36. Quarti, C.; Mosconi, E.; De Angelis, F. Interplay of Orienta-tional Order and Electronic Structure inMethylammoniumLead Iodide: Implications for Solar Cell Operation. Chem.Mater. 2014, 26, 6557–6569.

37. Quarti, C.; Mosconi, E.; De Angelis, F. Structural andElectronic 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 andMultibandgap Absorption and Enhancement of Free Car-riers 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. First-Principles Modeling of Mixed HalideOrganometal Perovskites for Photovoltaic Applications.J. Phys. Chem. C 2013, 117, 13902–13913.

41. Umebayashi, T.; Asai, K.; Kondo, T.; Nakao, A. ElectronicStructures of Lead Iodide Based Low-Dimensional Crystals.Phys. Rev. B: Condens.MatterMater. Phys.2003, 67, 155405.

42. Even, J.; Pedesseau, L.; Jancu, J.-M.; Katan, C. Importance ofSpin�Orbit Coupling in Hybrid Organic/Inorganic Perov-skites for Photovoltaic Applications. J. Phys. Chem. Lett.2013, 4, 2999–3005.

43. Brivio, F.; Butler, K. T.; Walsh, A.; van Schilfgaarde, M.Relativistic Quasiparticle Self-Consistent Electronic Struc-ture of Hybrid Halide Perovskite Photovoltaic Absorbers.Phys. Rev. B: Condens.MatterMater. Phys.2014, 89, 155204.

44. Umari, P.; Mosconi, E.; De Angelis, F. Relativistic GWCalculations on CH3NH3PbI3 and CH3NH3SnI3 Perovskitesfor Solar Cell Applications. Sci. Rep. 2014, 4, 4467.

45. Qin, P.; Kast, H.; Nazeeruddin, M. K.; Zakeeruddin, S. M.;Mishra, A.; Bauerle, P.; Gratzel, M. Low Band Gap S,N-Heteroacene-Based Oligothiophenes as Hole-Transportingand Light Absorbing Materials for Efficient Perovskite-Based Solar Cells. Energy Environ. Sci. 2014, 7, 2981–2985.

46. Schulz, P.; Edri, E.; Kirmayer, S.; Hodes, G.; Cahen, D.; Kahn,A. Interface Energetics in Organo-Metal Halide Perovskite-Based Photovoltaic Cells. Energy Environ. Sci. 2014, 7,1377–1381.

47. Navas, J.; Sanchez-Coronilla, A.; Gallardo, J. J.; Cruz Hernandez,N.; Pinero, J. C.; Alcantara, R.; Fernandez-Lorenzo, C.; De losSantos, D. M.; Aguilar, T.; Martin-Calleja, J. New Insights intoOrganic-Inorganic Hybrid Perovskite CH3NH3PbI3 Nano-particles. An Experimental and Theoretical Study of Dopingin Pb2þ Sites with Sn2þ, Sr2þ, Cd2þ and Ca2þ. Nanoscale2015, 7, 6216–6229.

48. Mukamel, S. Principles of Nonlinear Optical Spectroscopy;Oxford University Press: New York, 1995.

49. Quarti, C.; Grancini, G.; Mosconi, E.; Bruno, P.; Ball, J. M.; Lee,M. M.; Snaith, H. J.; Petrozza, A.; Angelis, F. D. The RamanSpectrum of the CH3NH3PbI3 Hybrid Perovskite: Interplayof Theory and Experiment. J. Phys. Chem. Lett. 2014, 5,279–284.

50. Mankad, V.; Gupta, S. K.; Jha, P. K. Low Frequency RamanScattering of Anatase TitaniumDioxide nanocrystals. Phys.E (Amsterdam, Neth.) 2011, 44, 614–617.

51. Giarola, M.; Sanson, A.; Monti, F.; Mariotto, G.; Bettinelli, M.;Speghini, A.; Salviulo, G. Vibrational dynamics of anataseTiO2: Polarized Raman Spectroscopy and Ab initio Calcula-tions. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81,174305.

52. Gonzalez, R. J.; Zallen, R.; Berger, H. Infrared Reflectivityand Lattice Fundamentals in Anatase TiO2. Phys. Rev. B:Condens. Matter Mater. Phys. 1997, 55, 7014–7017.

53. Long, R.; English, N. J.; Prezhdo, O. V. Minimizing Electron-Hole Recombination on TiO2 Sensitized with PbSe Quan-tum Dots: Time-Domain Ab Initio Analysis. J. Phys. Chem.Lett. 2014, 5, 2941–2946.

54. Williams, S. T.; Zuo, F.; Chueh, C.-C.; Liao, C.-Y.; Liang, P.-W.;Jen, A. K. Y. Role of Chloride in theMorphological Evolutionof Organo-Lead Halide Perovskite Thin Films. ACS Nano2014, 8, 10640–10654.

55. Zhao, Y.; Zhu, K. CH3NH3Cl-Assisted One-Step SolutionGrowth of CH3NH3PbI3: Structure, Charge-Carrier Dynamics,and Photovoltaic Properties of Perovskite Solar Cells. J. Phys.Chem. C 2014, 118, 9412–9418.

56. Tully, J. C. Molecular Dynamics with Electronic Transitions.J. Chem. Phys. 1990, 93, 1061–1071.

ARTIC

LE

LONG AND PREZHDO VOL. 9 ’ NO. 11 ’ 11143–11155 ’ 2015

www.acsnano.org

11155

57. Craig, C. F.; Duncan, W. R.; Prezhdo, O. V. Trajectory SurfaceHopping in the Time-Dependent Kohn-Sham Approachfor Electron-Nuclear Dynamics. Phys. Rev. Lett. 2005, 95,163001.

58. Fischer, S. A.; Habenicht, B. F.; Madrid, A. B.; Duncan, W. R.;Prezhdo, O. V. Regarding the Validity of the Time-DependentKohn�Sham Approach for Electron-Nuclear Dynamicsvia Trajectory Surface Hopping. J. Chem. Phys. 2011, 134,024102.

59. Akimov, A. V.; Prezhdo, O. V. The PYXAID Program forNon-Adiabatic Molecular Dynamics in Condensed MatterSystems. J. Chem. Theory Comput. 2013, 9, 4959–4972.

60. Akimov, A. V.; Prezhdo, O. V. Advanced Capabilities ofthe PYXAID Program: Integration Schemes, DecoherenceEffects, Multiexcitonic States, and Field-Matter Interaction.J. Chem. Theory Comput. 2014, 10, 789–804.

61. Habenicht, B. F.; Prezhdo, O. V. Nonradiative Quenchingof 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. Phonon-Induced Dephasing of Excitons in Semicon-ductor QuantumDots: 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 PbSeand 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-DomainAb Initio Study of Phonon-Induced Relaxation of PlasmonExcitations in a Silver Quantum Dot. J. Phys. Chem. C 2012,116, 15034–15040.

66. Chaban, V. V.; Prezhdo, V. V.; Prezhdo, O. V. CovalentLinking Greatly Enhances Photoinduced Electron Transferin Fullerene-QuantumDot Nanocomposites: Time-DomainAb Initio Study. J. Phys. Chem. Lett. 2013, 4, 1–6.

67. Long, R.; English, N. J.; Prezhdo, O. V. Defects Are Neededfor Fast Photo-Induced Electron Transfer from a Nano-crystal 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�HoleRecombinationonTiO2 SensitizedwithPbSeQuantumDots: 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 HoppingApproach to Nonadiabatic Molecular Collisions: The Reac-tion of Hþ with D2. J. Chem. Phys. 1971, 55, 562–572.

71. Parandekar, P. V.; Tully, J. C. Mixed Quantum-ClassicalEquilibrium. J. Chem. Phys. 2005, 122, 094102.

72. Prezhdo, O. V. Mean Field Approximation for the StochasticSchrödinger Equation. J. Chem. Phys. 1999, 111, 8366–8377.

73. Wang, L. J.; Trivedi, D.; Prezhdo, O. V. Global Flux SurfaceHopping 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-Domainab Initio Study of Charge Relaxation and Recombination inDye-Sensitized TiO2. J. Am. Chem. Soc.2007, 129, 8528–8543.

75. Kilina, S. V.; Neukirch, A. J.; Habenicht, B. F.; Kilin, D. S.;Prezhdo, O. V. Quantum Zeno Effect Rationalizes thePhonon Bottleneck in Semiconductor Quantum Dots.Phys. Rev. Lett. 2013, 110, 180404.

76. Bittner, E. R.; Rossky, P. J. Quantum Decoherence in MixedQuantum-Classical Systems - Nonadiabatic Processes.J. Chem. Phys. 1995, 103, 8130–8143.

77. Bedard-Hearn, M. J.; Larsen, R. E.; Schwartz, B. J. Mean-FieldDynamics with Stochastic Decoherence (MF-SD): A NewAlgorithm for Nonadiabatic Mixed Quantum/ClassicalMolecular-Dynamics Simulations with Nuclear-InducedDecoherence. J. Chem. Phys. 2005, 123, 234106.

78. Hack, M. D.; Truhlar, D. G. A Natural Decay of MixingAlgorithm for non-Born-Oppenheimer Trajectories. J. Chem.Phys. 2001, 114, 9305–9314.

79. Cheng, S. C.; Zhu, C. Y.; Liang, K. K.; Lin, S. H.; Truhlar, D. G.Algorithmic Decoherence Time for Decay-of-Mixing non-Born-Oppenheimer Dynamics. J. Chem. Phys. 2008, 129,024112.

80. Larsen, R. E.; Bedard-Hearn, M. J.; Schwartz, B. J. Exploringthe Role of Decoherence in Condensed-Phase Non-adiabatic Dynamics: A Comparison of Different MixedQuantum/Classical Simulation Algorithms for the ExcitedHydrated Electron. J. Phys. Chem. B 2006, 110, 20055–20066.

81. Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F.;Mhaisalkar, S. G.; Graetzel, M.; White, T. J. Synthesis andCrystal Chemistry of the Hybrid Perovskite (CH3NH3)PbI3for Solid-State Sensitised Solar Cell Applications. J. Mater.Chem. A 2013, 1, 5628–5641.

82. Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Semi-conducting Tin and Lead Iodide Perovskites with OrganicCations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties. Inorg. Chem. 2013,52, 9019–9038.

83. Kresse, G.; Furthmüller, J. Efficient Iterative Cchemes forAb Initio Total-Energy Calculations using a Plane-WaveBasis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996,54, 11169–11186.

84. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized GradientApproximation Made Simple. Phys. Rev. Lett. 1996, 77,3865–3868.

85. Blöchl, P. E. Projector Augmented-WaveMethod. Phys. Rev.B: Condens. Matter Mater. Phys. 1994, 50, 17953–17979.

86. Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188–5192.

87. Grimme, S. Semiempirical GGA-type Density FunctionalConstructed with a Long-Range Dispersion Correction.J. Comput. Chem. 2006, 27, 1787–1799.

ARTIC

LE