Charge Separation and Recombination in Two-Dimensional MoS2/WS2: Time-Domain ab Initio ModelingLinqiu Li,† Run Long,‡,§ and Oleg V. Prezhdo*,†

†Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States‡College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing NormalUniversity, Beijing 100875, People’s Republic of China§School of Physics, Complex & Adaptive Systems Lab, University College Dublin, Dublin 4, Ireland

ABSTRACT: With applications in high performance electronics,photovoltaics and catalysis, two-dimensional transition metaldichalcogenides (TMDs) attract strong attention. IsolatedTMDs, which are already remarkably complex, can stack insequence to make even more complex heterostructures. Surpris-ingly, charge separation is ultrafast in layered TMD hetero-structures, even though the interlayer interaction is weak. Alsosurprisingly, the charge separated state is long-lived, despite theclose proximity of electron and hole. Using real-time time-dependent density functional theory combined with nonadiabatic(NA) molecular dynamics, we model hole and electron transfer,and electron−hole recombination at a MoS2/WS2 heterojunction.Hole transfer is ultrafast, in excellent agreement with theexperiment, due to significant delocalization of the photoexcitedstate between the donor and acceptor materials. Electron transfer is 1 order of magnitude longer, due to weaker donor−acceptorand NA couplings, lower density of acceptor states, and shorter quantum coherence. The electron−hole recombination is 3−4orders of magnitude slower than the charge separation, because the initial and final states are localized strongly within differentmaterials, rationalizing the long-lived charge separation. The computed recombination time scale agrees with the experimentaldata on the closely related MoSe2/WSe2 system. All electronic processes are coupled to the characteristic out-of-plane 400 cm−1

motion of the MoS2 and WS2 layers. The atomistic, time-domain methodology provides theoretical insights into thephotoinduced electron−phonon dynamics in two-dimensional TMD heterostructures, and can be used for in silico design ofnovel functional materials operating under nonequilibrium conditions.

1. INTRODUCTION

Chemically versatile,1,2 two-dimensional dichalcogenides, withthe general formula MX2, M = Mo, W and X = S, Se, can findapplications in electronics,3−7 photovoltaics8−10 and cataly-sis.1,11,12 Compared with many existing materials, transitionmetal dichalcogenides (TMDs) have the advantages offlexibility, small thickness, high performance, low powerconsumption and low cost.3,13−15 TMD leads to flexibleelectronics with much better transport properties comparedto other materials, for example, organic semiconductors.3 Field-effect transistors fabricated with MoS2 conducting channelshave large on/off ratios and small subthreshold swing.3

Experiments find TMDs to be promising for hydrogenevolution reactions, as well as supercapacitors and batteries.14

About 40 different TMDs have been synthesized so far,1,10

though not all of them are layered solids. To be defined as alayered TMD, the metal atoms have to be sandwiched betweentwo hexagonally ordered planes of chalcogen atoms.16 Thestructure of layered MX2 is similar to the structure of graphite.Layered TMDs have strong in-plane covalent bonding within

each layer and weak out-of-plane van der Waals interactionsbetween layers.10

Most MX2 monolayers are direct-gap semiconductors, whosebandgap energy can be tuned by changes in composition andstructure.13 Most layered TMDs undergo direct to indirectbandgap transition with increasing number of layers.10 IsolatedMX2 monolayers, which are already chemically intriguing, canstack in sequence to make complex heterostructures. Theheterstructures are receiving broad interest as essential buildingblocks for high performance electronic, optoelectronic, photo-voltaic and catalytic devices.Numerous experiments have been carried out to investigate

the properties of TMD heterostructures and, in particular,MoS2/WS2. Ab initio analysis shows that the MoS2/WS2 bilayeris a direct bandgap semiconductor with the type-II band

Special Issue: Computational Design of Functional Materials

Received: September 3, 2016Revised: November 2, 2016Published: November 3, 2016

Article

pubs.acs.org/cm

© 2016 American Chemical Society 2466 DOI: 10.1021/acs.chemmater.6b03727Chem. Mater. 2017, 29, 2466−2473

Dow

nloa

ded

via

UN

IV O

F SO

UT

HE

RN

CA

LIF

OR

NIA

on

Nov

embe

r 9,

201

9 at

21:

32:1

4 (U

TC

).Se

e ht

tps:

//pub

s.ac

s.or

g/sh

arin

ggui

delin

es f

or o

ptio

ns o

n ho

w to

legi

timat

ely

shar

e pu

blis

hed

artic

les.

alignment, in which the valence band maximum (VBM) andthe conduction band minimum (CBM) reside in differentmonolayers, Figure 1. The VBM and CBM offsets between the

materials are 0.39 and 0.35 eV, respectively.16 The MoS2/WS2bandgap is 1.097 eV,17 which is significantly smaller than thebandgap of the individual monolayers.In recent experiments, Hong et al. investigated the dynamics

of hole transfer in MoS2/WS2 heterostructures using femto-second pump−probe spectroscopy.18 They reported that holetransfer from the MoS2 layer to the WS2 layer takes less than 50fs after photoexcitation. Other experiments showed subpico-second hole and electron transfer in MoS2/MoSe2

19 and anextremely long time scale for electron−hole recombination inMoSe2/WSe2 heterostructures, ranging from 240 ps19 to 1.8ns.20 Theoretical studies of the photoinduced charge separationand recombination dynamics in layered TDM heterostructureslag behind the extensive experimental efforts. A microscopicunderstanding of the dynamic processes is desired, in particular,in order to establish the mechanisms of the ultrafast sub-100 fscharge transfer, occurring despite the weak van der Waalscoupling between the layers, and the extremely long-livedcharge separation, observed despite the low dielectric screeningof Coulomb interactions and close proximity of the charges.In this paper, we model the photoinduced charge separation

and recombination dynamics at the MoS2/WS2 bilayerheterojunction at the ab initio, atomistic level of detail andexplicitly in the time-domain, directly mimicking the time-resolved optical experiments. We analyze the MoS2/WS2electronic structure, nuclear dynamics, elastic and inelasticelectron−phonon interactions, charge separation and chargerecombination. The charge transfer mechanisms are analyzedby considering the effects of electronic and electron−phononcoupling, acceptor state density and quantum coherence.

2. THEORYThe simulations are performed using mixed quantum-classicaltechniques with semiclassical corrections. The electronic structure isdescribed quantum mechanically, using ab initio density functionaltheory (DFT). The electronic evolution is obtained using real-timetime-dependent (TD) DFT.21 The nuclear evolutions are obtained byclassical molecular dynamics (MD), and the electron−nuclear

interactions are modeled using nonadiabatic (NA) MD. In particular,the ultrafast photoinduced electron and hole separation areinvestigated using fewest switching surface hopping (FSSH),22,23

which is the most common NAMD methodology. The chargerecombination dynamics is studied using decoherence induced surfacehopping24 (DISH), which includes loss of coherence within theelectronic subsystem induced by coupling to quantum phonons.Decoherence effects are insignificant for the ultrafast chargeseparation, which occurs by a succession of rapid quantum transitionswithin the conduction and valence bands; however, decoherence isessential for the slow charge recombination that involves a singlequantum transition across a large energy gap. The originalimplementation of FSSH within TDDFT in the Kohn−Sham (KS)formulation is described in ref 25 and tested further in ref 26. Thesimulations are performed using the Pyxaid software package,27,28

which describes the implementation of DISH within KS-TDDFT.28

The methodology has been applied successfully to model excitationdynamics in a broad range of materials.29−34

2.1. Real-Time Time-Dependent Density Functional Theory.The electron density, ρ(r, t), is expressed in the KS formulation ofDFT as a sum of the densities of the single-electron KS orbitals, Ψn(r,t), occupied by Ne electrons

∑ρ = |Ψ |=

t tr r( , ) ( , )n

N

n1

2e

(1)

Applying the time domain variational principle to the KS energygives equations-of-motion for the single-electron KS orbitals

ℏ ∂∂

Ψ = Ψit

t H t tr r R r( , ) ( , , ) ( , )n n (2)

Here, the Hamiltonian, H(r, R, t), depends on the total electrondensity, its gradient, etc. The Hamiltonian is time dependent due tothe external potential created by the moving atoms and electric field ofa laser. The time-dependent KS orbitals, Ψn(r, t), are expanded in thebasis of adiabatic KS orbitals, Φk(r; R, (t)), which are calculated aseigenstates of the KS Hamiltonian for the current atomic positions R,obtained from the MD

∑Ψ = Φt C t tr r R( , ) ( ) ( ; , ( ))nk

kn

k(3)

Combination of eq 2 and eq 3 gives equations-of-motion for theexpansion coefficients

∑ ε δℏ ∂∂

= +it

C t C t d( ) ( )( )jn

kk

nk jk jk

(4)

where εk is the energy of the adiabatic state k, and djk is the NAcoupling between adiabatic states k and j. The later arises from thedependence on the atomic motion R and is calculated numerically asthe overlap between wave functions k and j at sequential time steps

= − ℏ⟨Φ|∇ |Φ ⟩· = − ℏ Φ ∂∂

Φd it

it

Rddjk j k j kR

(5)

The many-particle formulation of the above formalism andimplementation details are given in ref 27.

2.2. Nonadiabatic Molecular Dynamics. The ultrafast electronand hole transfer processes are modeled using FSSH,22,23 which is themost popular NAMD technique. FSSH can be viewed as a masterequation, with time-dependent transition rates between states arisingfrom solution of the time-dependent Schrodinger equation. Inparticular, the probability of transition between adiabatic states j andk during time interval dt is defined in the FSSH approach through thewave function expansion coefficients and coupling as

=− *

= *A d

At A c cP

Rd

2Re( )d ;jk

jk jk

jjjk j k

(6)

Figure 1. (a) Electronic energy levels involved in the photoinducedcharge transfer and nonradiative charge recombination at the MoS2/WS2 interface. Absorption of a photon, hv, by either MoS2 or WS2leads to ① hole transfer or ② electron transfer. Following the chargetransfer, electron and hole can recombine at the interface ③. (b) Topand (c) side views of the MoS2/WS2 heterostructure. Mo is purple. Wis gray. S is yellow.

Chemistry of Materials Article

DOI: 10.1021/acs.chemmater.6b03727Chem. Mater. 2017, 29, 2466−2473

2467

Transitions between states take place in the form of “hops”. Thetransition probabilities are computed on the fly for the current nuclearconfiguration.The electron−hole recombination process is investigated using the

DISH method.24 Mixed quantum-classical simulation of slowtransitions across large energy gaps requires decoherence correc-tions.35−37 DISH is a practical technique developed upon the conceptthat decoherence provides the physical mechanisms for the hops.38

The classical-path approximation,39 in which the time-dependpotential is determined by a single molecular dynamics trajectorycomputed prior to the NAMD simulation, allows us to obtain verysignificant computational savings. The savings arise because hundredsof excited state trajectories are replaced with a single ground statetrajectory. The following references to the Pyxaid software provide adetailed description of the implementation of FSSH27 and DISH.28

Examples of application of the methodology to other nanoscalematerials can be found elsewhere.29−33,40−43

2.3. Simulation Details. The electronic structure and adiabaticMD trajectories were computed with the Quantum Espressoprogram44 using a converged plane-wave basis set. The generalizedgradient approximation of Perdew, Burke and Ernzerhof (PBE),45 andprojector-augmented wave (PAW)46 pseudopotentials were used. Thevan der Waals interaction was described by the semiempirical potentialintroduced by Grimme’s in the DFT-D2 method.47 The approachgives a good description of the electronic structure and intermolecularinteractions of the van der Waals heterojunction. Although moreadvanced electronic structure methodologies, such as hybrid andscreened-hybrid DFT functionals and GW theory, can provide a moreaccurate description of the electronic properties of the system underinvestigation,48,49 they are significantly more computationally demand-ing and cannot be combined with NAMD that requires thousands ofelectronic structure calculations. A vacuum layer of 9 Å was placed inthe direction perpendicular to the bilayer, Figure 1, in order to avoidspurious interactions between adjacent images. The calculations wereperformed with the 12 × 12 × 1 k-point mesh. The structure was fullyrelaxed until the calculated Hellmann−Feynman force was smallerthan 0.05 eV/Å. The system was then heated to 300 K throughrepeated velocity rescaling. A 6 ps adiabatic MD trajectory with a 1 fsatomic time-step was produced and used to perform the NAMDsimulations with the Pyxaid package.27,28 100 initial conditions weresampled randomly from the first 1 ps of the 6 ps trajectory, andNAMD simulations were performed starting from each initialcondition and using 1000 random number sequences to sample thesurface hopping probabilities.

3. RESULTS AND DISCUSSION

Our work is motivated by the recent experiment,18 showingthat hole transfer at the MoS2/WS2 interface takes less than 50fs. This was surprising, because the donor−acceptor interactionbetween the layers is weak, and because the driving force, givenby the energy offset between the VBMs of MoS2 and WS2, issmall according to the calculations.16 The mechanism for theultrafast charge transfer was unclear. Our work is also closelyrelated to the pump−probe experiments showing sub-pico-second hole and electron transfer in MoS2/MoSe2,

19 and long1.8 ns time scale for electron−hole recombination in MoSe2/WSe2.

20

The processes under investigation are depicted on the energylevel diagram shown in Figure 1a. Excitation of MoS2 induceshole transfer from MoS2 to WS2, ①. Excitation of WS2 leads toelectron transfer from WS2 to MoS2, ②. After the chargeseparation, the electron and hole can recombine at theinterface, ③. The top and side views of the MoS2/WS2simulation cell are shown in Figure 1b,c, respectively. Thetransition metal atoms of one layer are on the top of thechalcogen atoms of the other layer, which is consistent with theearlier theoretical studies.16,50

3.1. Electronic Structure of the MoS2/WS2 Hetero-structure. Figure 2a shows the projected density of states

(PDOS) of the MoS2/WS2 heterostructure at 300 K. Thecontribution of the MoS2 and WS2 monolayers are given by theblack and red lines. The PDOS demonstrates that MoS2/WS2 isa type-II heterojunction, which is consistent with theexperimental result.18 The lowest excited state is formed atthe interface when the electron is localized at the MoS2 CBMand the hole is localized at the WS2 VBM. The canonicallyaveraged VBM and CBM band offsets are 0.39 and 0.42 eV,respectively, indicating that about 0.4 eV of energy is lost tovibrational motions during the charge transfer events.To elucidate the origin of the fast charge separation

dynamics, charge distributions of the donor and acceptorstates in the MoS2/WS2 bilayer are shown in Figure 2b. Thearrows connecting top and bottom panels relate the chargedistributions with the state energies. The donor orbitalsinvolved in the separation dynamics are delocalized betweenthe MoS2 and WS2 monolayers. The delocalization can beconsidered surprising, because the layers are coupled onlyweakly by a van der Waals interaction. The delocalization of thephotoexcited donor state into the acceptor can be rationalizedby the fact that the acceptor has a significantly higher DOS thanthe donor, and even the weak coupling is sufficient to producethe effect. The delocalization of the photoexcited state onto thecharge acceptor material indicates that a fraction of the chargeis transferred during the excitation process. Note that the initialstate of the hole, state 1 in Figure 2b, contains density on thesulfurs of both bilayers pointing toward each other. In contrast,the initial state of the electron, state 4, has no density betweenthe bilayers. As a result, the interlayer coupling is stronger forhole than electron transfer.The final states of the charge separation processes, states 2

and 3 in Figure 2b, are localized strictly within a single material.

Figure 2. (a) Partial density of states (PDOS) of the MoS2 and WS2monolayers in the MoS2/WS2 heterostructure at 300 K. The donor−acceptor band edge energy offsets determine the driving force for thecharge separation and recombination. (b) Charge densities (red) ofthe key states at the MoS2/WS2 junction: (1) Valence band maximum(VBM) of MoS2. (2) VBM of WS2. (3) Conduction band minimum(CBM) of MoS2. (4) CBM of WS2. The electron and hole donororbitals are delocalized between MoS2 and WS2, indicating that somecharge transfer has already happened during the photoexcitationprocess. Mo is purple. W is gray. S is yellow.

Chemistry of Materials Article

DOI: 10.1021/acs.chemmater.6b03727Chem. Mater. 2017, 29, 2466−2473

2468

This is expected since the complementary materials have nostates at these energies. States 2 and 3 are the initial states ofthe recombining hole and electron. Because these states exhibitno appreciable overlap, the donor−acceptor interaction leadingto the electron−hole recombination is weak, and therecombination is slow.3.2. Electron−Phonon Interactions. The charge separa-

tion and recombination processes are governed by bothelectronic interactions between the donor and acceptor states,and electron−phonon interactions. The latter are particularlyimportant for the recombination process. The photoinducedelectron and hole transfer at the MoS2/WS2 interface lead tolosses of about 0.4 eV of electronic energy into heat. Theearliest stages of the transfer occur iso-energetically, becauseboth materials have states at the initial energy. However, it isenergy relaxation into phonons that prevents back-transfer ofthe charges and allows for a long-lived charge separation. Thenonradiative electron−hole recombination occurs across a 1 eVenergy gap. This energy is deposited into multiple phononquanta.Both elastic and inelastic electron−phonon interactions

contribute to the photoinduced charge transfer dynamics atthe MoS2/WS2 interface. Elastic interactions randomize phasesof electronic wave function phase, resulting in loss of quantumcoherence. Loss of coherence is key for the slow electron−holerecombination process. The quantum Zeno effect presents theextreme example of how quantum coherence loss decreases atransition rate.43 Inelastic electron−phonon scattering isresponsible for losses of electronic energy to heat. It takesplace during both charge separation and recombination.We estimate the time scale of elastic electron−phonon

scattering using the optical response theory formalism, bycomputing the pure-dephasing time51 for pairs of initial andfinal states for each process under consideration, Figure 1. Thepure-dephasing functions, D(t), shown in Figure 3, demon-strate that coherence is lost faster during electron than holetransfer. Generally, one can attribute fast decoherence to eithera rapid loss of correlation in the oscillation of the relevantenergy gap, or a large oscillation magnitude.52 Both factors are

reflected in the unnormalized autocorrelation functions(ACFs), Cun(t), also shown in Figure 3. Both ACFs decay onsimilar time scales; however, the initial ACF magnitude issignificantly larger for the electron ACF, 0.0037 eV2, than thehole ACF, 0.0015 eV2. The initial magnitude equals to thecanonically averaged squared gap, and characterizes the gapfluctuation. Thus, it is the larger charge−phonon coupling andrapid ACF decay, typically associated with involvement of abroader range of phonon modes, that makes decoherence fasterfor the electron transfer.The pure-dephasing functions were fitted by a combination

of a Gaussian and an exponent.51

τ τ

ω

= − + − −

++

⎡

⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜⎜

⎛⎝⎜⎜

⎞⎠⎟⎟

⎞

⎠⎟⎟⎤

⎦⎥⎥f t B

tB

t

A tA

( ) exp (1 )exp12

1 cos( )1

e g

2

(7)

In eq 7, B is the magnitude of exponential decay, whereas 1 − Brepresents the magnitude of the Gaussian component. Thenormalized cosine term accounts for oscillations thatcorrespond to the vibrational modes observed in the phononspectral density, Figure 3. The pure-dephasing time constant isdefined as the weighted average τ = Bτe + (1 − B)τg. The fittingresults are presented in Table 1.

Figure 3. Un-normalized autocorrelation functions (top panels), dephasing functions (middle panels) and influence spectra (bottom panels) for (a)hole transfer and (b) electron transfer. The dephasing functions are fitted by eq 7, giving time constants of 29.1 fs for hole transfer and 10.0 fs forelectron transfer. Both hole and electron transfer couple primarily to the optical phonon mode near 400 cm−1, characteristic of the out of plane A1gmotion of MoS2 and WS2.

Table 1. Pure-Dephasing (Decoherence) Time, AverageAbsolute Value of Nonadiabatic Coupling (NAC), and TimeScales for Hole Transfer, Electron Transfer and Electron−Hole Recombination

Holetransfer

Electrontransfer

Electron−holerecombination

Dephasing time(fs)

29.1 10.0 27.2

NAC (meV) 9.17 1.64 0.17Transfer time (ps) 0.061 0.747 2,200

Chemistry of Materials Article

DOI: 10.1021/acs.chemmater.6b03727Chem. Mater. 2017, 29, 2466−2473

2469

Table 1 also presents the canonically averaged absolutevalues of the NA coupling for the charge separation andrecombination processes. Charge separation involves transi-tions between multiple states within the conduction andvalence band manifolds, and the reported values are averagedover the transitions encountered during the NAMD simu-latoins. The NA electron−phonon coupling is five times largerfor the hole than electron transfer, and is 1 order of magnitudesmaller for the recombination than separation. These results areconsistent with the state densities depicted in Figure 2. Forinstance, there is practically no overlap between states 2 and 3,explaining why the NA coupling value for the recombination isso small, 0.17 meV.Fourier transforms (FT) of ACFs, or similarly, of the

corresponding energy gaps, characterize the phonon modesthat couple to the electronic subsystem. The resulting spectrumis known as the influence spectrum, or spectral density. TheACF FTs are presented in the bottom panels of Figure 3. Bothhole transfer and electron transfer couple primarily to phononsnear 400 cm−1. This frequency corresponds to the out-of-planeA1g modes of MoS2 (404.1 cm−1) and WS2 (420.4 cm−1).53,54

The involvement of the out-of-plane mode in the interfacialcharge transfer dynamics is reasonable. By modulating theinterlayer distance, the out-of-plane motion influences theelectronic state energies and NA coupling, affects electron andhole transfer. A weak participation of low frequency modes,below 100 cm−1, is seen for both electrons and holes. Therelative contribution of the low frequency modes is greater forthe holes, rationalizing why the hole ACF decays slightly faster,Figure 3.Charge Separation. Figure 4 characterizes the photo-

induced charge separation processes that result from photo-

excitation of either MoS2 or WS2, Figure 1. The curves show aninitial Gaussian decay that rapidly turns into exponentialdynamics. The amplitude of the Gaussian component is small.Therefore, we fit the curves of Figure 4 using a exponent ratherthan a more complicated equation, such as eq 7. The 61 fs hole

transfer time agrees well with the experimental data, indicatinga 50 fs transfer time.18 Recall that, according to our simulations,a fraction of the hole is transferred from MoS2 to WS2 alreadyduring the photoexcitation process. In experiment, thephotoexcitation time scale is given by the width of the laserpulse, which was 250 fs in the experiment.18 The subpico-second electron transfer agrees with the experimental andtheoretical work on the closely related MoSe2/MoS2system.19,55

Several factors rationalize why the hole transfer is faster thanthe electron transfer. First, the donor−acceptor interaction isstronger for the hole transfer. The photogenerated hole hasdensity extending into the interlayer space, state 1 in Figure 2.This is not the case for the photogenerated electron, state 4 inFigure 2. Second, the NA coupling is stronger for the holetransfer, Table 1. Third, quantum coherence is longer lived.Finally, the acceptor state density is higher for the hole.Consider the peak in the WS2 DOS near the valence band edge,and the absence of a similar peak in the MoS2 DOS near theconduction band edge, Figure 2.

3.4. Electron−Hole Recombination. Nonradiative elec-tron−hole recombination constitutes the main source of chargelosses and energy dissipation in solar energy and electronicsapplications. The charge recombination across the MoS2/WS2interface is characterized in Figure 5. The calculated 2.2 nsrecombination time is consistent with the 1.8 ns time scalereported experimentally for the similar MoSe2/WSe2 inter-face.20 The shorter, 240 ps recombination time reported19 forMoSe2/WSe2 can be attributed to existence of defects in theexperimental samples. MoS2 defects are known56 and canaccelerate the charge recombination dynamics.57 We plan oninvestigating the role of defects in future work.Similarly to the charge separation, the nonradiative electron−

hole recombination is promoted primarily by the 400 cm−1 out-of-plane A1g modes of the two materials,53,54Figure 5c.Quantum coherence is maintained during the recombinationfor about 30 fs. This value is typical for electron−holerecombination in many nanoscale materials at room temper-ature.51,58,59

■ CONCLUSIONSUsing a combination of real-time time-dependent densityfunctional theory and nonadiabatic molecular dynamics, weinvestigated the photoinduced electron and hole transfer, andsubsequent nonradiative electron−hole recombination in aMoS2/WS2 heterojunction. The calculations rationalize whyexperiments observe ultrafast charge separation, despite only aweak van der Waals interaction between the layers, and why thecharge separated state is long-lived, even though the electronsand holes are located close to each other. The separation is fast,because the photoexcited charges are delocalized between thedonor and acceptor materials. The hole transfer is faster thanthe electron transfer, because the donor−acceptor interaction isstronger, the nonadiabatic coupling is larger, the quantumcoherence is longer-lived and the density of acceptor states ishigher. The nonradiative electron−hole recombination is slow,because the initial and final states are strongly localized withineach layer, and the nonadiabatic coupling is very small, about0.1 meV. In addition, the electron−phonon energy exchange isa high order process, requiring excitation of about 20vibrational quanta. Both charge separation and recombinationcouple to the 400 cm−1 out-of-plane motions of two-dimensional materials. In all cases, quantum coherence lasts

Figure 4. (a) Hole and (b) electron dynamics following photo-excitation. Hole transfer takes 61 fs, in agreement with theexperiment.18 Electron transfer is 1 order of magnitude longer, dueto weaker NA coupling, shorter coherence time, Table 1, and loweracceptor state density, Figure 2. Note that a fraction of electron or holeis transferred already during the photoexcitation, because the donorstates are delocalized between the two materials, Figure 2.

Chemistry of Materials Article

DOI: 10.1021/acs.chemmater.6b03727Chem. Mater. 2017, 29, 2466−2473

2470

for 10−30 fs. The reported time-domain ab initio calculationsagree well with the available experimental data, mimic the time-resolved experiments in a most direct manner, generatevaluable mechanistic insights into the photoinduced electron-vibrational dynamics, and provide a tool for screening andpredicting excited state dynamics in novel nanomaterials. Thefast photoinduced charge separation and the slow chargerecombination indicate that hetereojucnctions involving MoS2,WS2 and other two-dimensional transition metal dichalcoge-nide semiconductors are excellent candidates for applications inphotovoltaics, photocatalysis, electronics and related areas.

■ AUTHOR INFORMATION

ORCIDOleg V. Prezhdo: 0000-0002-5140-7500NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

L.L. and O.V.P. acknowledge financial support of the U.S.Department of Energy, grant no. DE-SC0014429. R.L.acknowledges support of the Science Foundation Ireland,grant no. 11/SIRG/E2172, the National Science Foundation ofChina, Grant No. 21573022, the Recruitment Program ofGlobal Youth Experts of China, and Beijing Normal UniversityStartup.

■ REFERENCES(1) Chhowalla, M.; Shin, H. S.; Eda, G.; Li, L.-J.; Loh, K. P.; Zhang,H. The chemistry of two-dimensional layered transition metaldichalcogenide nanosheets. Nat. Chem. 2013, 5, 263−275.(2) Tedstone, A. A.; Lewis, D. J.; O’Brien, P. Synthesis, Properties,and Applications of Transition Metal-Doped Layered Transition MetalDichalcogenides. Chem. Mater. 2016, 28, 1965−1974.(3) Fiori, G.; Bonaccorso, F.; Iannaccone, G.; Palacios, T.; Neumaier,D.; Seabaugh, A.; Banerjee, S. K.; Colombo, L. Electronics based ontwo-dimensional materials. Nat. Nanotechnol. 2014, 9, 768−779.(4) Luo, H. X.; Xie, W. W.; Tao, J.; Pletikosic, I.; Valla, T.;Sahasrabudhe, G. S.; Osterhoudt, G.; Sutton, E.; Burch, K. S.; Seibel, E.M.; Krizan, J. W.; Zhu, Y. M.; Cava, R. J. Differences in Chemical

Doping Matter: Superconductivity in Ti1‑xTaxSe2 but Not inTi1‑xNbxSe2. Chem. Mater. 2016, 28, 1927−1935.(5) Gong, C.; Zhang, H.; Wang, W.; Colombo, L.; Wallace, R. M.;Cho, K. Band alignment of two-dimensional transition metaldichalcogenides: Application in tunnel field effect transistors. Appl.Phys. Lett. 2013, 103, 053513.(6) Pan, Y. Y.; Wang, Y. Y.; Ye, M.; Quhe, R. G.; Zhong, H. X.; Song,Z. G.; Peng, X. Y.; Yu, D. P.; Yang, J. B.; Shi, J. J.; Lu, J. MonolayerPhosphorene-Metal Contacts. Chem. Mater. 2016, 28, 2100−2109.(7) Lee, C.-H.; Lee, G.-H.; van der Zande, A. M.; Chen, W.; Li, Y.;Han, M.; Cui, X.; Arefe, G.; Nuckolls, C.; Heinz, T. F.; Guo, J.; Hone,J.; Kim, P. Atomically thin p−n junctions with van der Waalsheterointerfaces. Nat. Nanotechnol. 2014, 9, 676−681.(8) Peng, B.; Ang, P. K.; Loh, K. P. Two-dimensional dichalcogenidesfor light-harvesting applications. Nano Today 2015, 10, 128−137.(9) Xue, Y.; Zhang, Y.; Liu, Y.; Liu, H.; Song, J.; Sophia, J.; Liu, J.; Xu,Z.; Xu, Q.; Wang, Z.; Zheng, J.; Liu, Y.; Li, S.; Bao, Q. ScalableProduction of a Few-Layer MoS2/WS2 Vertical Heterojunction Arrayand Its Application for Photodetectors. ACS Nano 2016, 10, 573−580.(10) Britnell, L.; Ribeiro, R. M.; Eckmann, A.; Jalil, R.; Belle, B. D.;Mishchenko, A.; Kim, Y.-J.; Gorbachev, R. V.; Georgiou, T.; Morozov,S. V.; Grigorenko, A. N.; Geim, A. K.; Casiraghi, C.; Neto, A. H. C.;Novoselov, K. S. Strong Light-Matter Interactions in Heterostructuresof Atomically Thin Films. Science 2013, 340, 1311−1314.(11) Ouyang, Y. X.; Ling, C. Y.; Chen, Q.; Wang, Z. L.; Shi, L.;Wang, J. L. Activating Inert Basal Planes of MoS2 for HydrogenEvolution Reaction through the Formation of Different IntrinsicDefects. Chem. Mater. 2016, 28, 4390−4396.(12) Ding, J. B.; Zhou, Y.; Li, Y. G.; Guo, S. J.; Huang, X. Q. MoS2Nanosheet Assembling Superstructure with a Three-Dimensional IonAccessible Site: A New Class of Bifunctional Materials for Batteriesand Electrocatalysis. Chem. Mater. 2016, 28, 2074−2080.(13) Jariwala, D.; Sangwan, V. K.; Lauhon, L. J.; Marks, T. J.; Hersam,M. C. Emerging Device Applications for Semiconducting Two-Dimensional Transition Metal Dichalcogenides. ACS Nano 2014, 8,1102−1120.(14) Pumera, M.; Sofer, Z.; Ambrosi, A. Layered transition metaldichalcogenides for electrochemical energy generation and storage. J.Mater. Chem. A 2014, 2, 8981−8987.(15) Gholamvand, Z.; McAteer, D.; Harvey, A.; Backes, C.; Coleman,J. N. Electrochemical Applications of Two-Dimensional Nanosheets:The Effect of Nanosheet Length and Thickness. Chem. Mater. 2016,28, 2641−2651.

Figure 5. Electron−hole recombination dynamics: (a) population of the excited state; (b) pure-dephasing function; and (c) phonon influencespectrum. The recombination data is fitted by the short-time linear approximation to the exponential decay, giving the time-constant of 2.2 ns, inagreement with the experimental data on the closely related MoSe2/WSe2 system.

20 The pure dephasing-function is fitted to eq 7, giving the timescale is 27.2 fs. Similarly to the electron and hole transfer, Figure 3, the recombination process is facilitated by the 400 cm−1 out of plane A1g modes.

Chemistry of Materials Article

DOI: 10.1021/acs.chemmater.6b03727Chem. Mater. 2017, 29, 2466−2473

2471

(16) Kang, J.; Tongay, S.; Zhou, J.; Li, J.; Wu, J. Band offsets andheterostructures of two-dimensional semiconductors. Appl. Phys. Lett.2013, 102, 012111.(17) Su, X.; Ju, W.; Zhang, R.; Guo, C.; Zheng, J.; Yong, Y.; Li, X.Bandgap engineering of MoS2/MX2 (MX2 = WS2, MoSe2 and WSe2)heterobilayers subjected to biaxial strain and normal compressivestrain. RSC Adv. 2016, 6, 18319−18325.(18) Hong, X.; Kim, J.; Shi, S.-F.; Zhang, Y.; Jin, C.; Sun, Y.; Tongay,S.; Wu, J.; Zhang, Y.; Wang, F. Ultrafast charge transfer in atomicallythin MoS2/WS2 heterostructures. Nat. Nanotechnol. 2014, 9, 682−686.(19) Ceballos, F.; Bellus, M. Z.; Chiu, H.-Y.; Zhao, H. UltrafastCharge Separation and Indirect Exciton Formation in a MoS2−MoSe2van der Waals Heterostructure. ACS Nano 2014, 8, 12717−12724.(20) Rivera, P.; Schaibley, J. R.; Jones, A. M.; Ross, J. S.; Wu, S.;Aivazian, G.; Klement, P.; Seyler, K.; Clark, G.; Ghimire, N. J.; Yan, J.;Mandrus, D. G.; Yao, W.; Xu, X. Observation of long-lived interlayerexcitons in monolayer MoSe2−WSe2 heterostructures. Nat. Commun.2015, 6, 6242.(21) Runge, E.; Gross, E. K. U. Density-Functional Theory for Time-Dependent Systems. Phys. Rev. Lett. 1984, 52, 997−1000.(22) Tully, J. C. Molecular dynamics with electronic transitions. J.Chem. Phys. 1990, 93, 1061−1071.(23) Parandekar, P. V.; Tully, J. C. Mixed quantum-classicalequilibrium. J. Chem. Phys. 2005, 122, 094102.(24) Jaeger, H. M.; Fischer, S.; Prezhdo, O. V. Decoherence-inducedsurface hopping. J. Chem. Phys. 2012, 137, 22A545.(25) Craig, C. F.; Duncan, W. R.; Prezhdo, O. V. Trajectory SurfaceHopping in the Time-Dependent Kohn-Sham Approach for Electron-Nuclear Dynamics. Phys. Rev. Lett. 2005, 95, 163001.(26) 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 surfacehopping. J. Chem. Phys. 2011, 134, 024102.(27) 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.(28) Akimov, A. V.; Prezhdo, O. V. Advanced Capabilities of thePYXAID Program: Integration Schemes, Decoherenc:e Effects,Multiexcitonic States, and Field-Matter Interaction. J. Chem. TheoryComput. 2014, 10, 789−804.(29) Akimov, A. V.; Prezhdo, O. V. Nonadiabatic Dynamics ofCharge Transfer and Singlet Fission at the Pentacene/C60 Interface. J.Am. Chem. Soc. 2014, 136, 1599−1608.(30) Hyeon-Deuk, K.; Prezhdo, O. V. Multiple Exciton Generationand Recombination Dynamics in Small Si and CdSe Quantum Dots:An Ab Initio Time-Domain Study. ACS Nano 2012, 6, 1239−1250.(31) Long, R.; Prezhdo, O. V. Instantaneous Generation of Charge-Separated State on TiO2 Surface Sensitized with Plasmonic Nano-particles. J. Am. Chem. Soc. 2014, 136, 4343−4354.(32) Duncan, W. R.; Prezhdo, O. V. Nonadiabatic moleculardynamics study of electron transfer from alizarin to the hydratedTi4+ ion. J. Phys. Chem. B 2005, 109, 17998−18002.(33) Fischer, S. A.; Duncan, W. R.; Prezhdo, O. V. Ab InitioNonadiabatic Molecular Dynamics of Wet-Electrons on the TiO2

Surface. J. Am. Chem. Soc. 2009, 131, 15483−15491.(34) Zhu, H. M.; Yang, Y.; Hyeon-Deuk, K.; Califano, M.; Song, N.H.; Wang, Y. W.; Zhang, W. Q.; Prezhdo, O. V.; Lian, T. Q. Auger-Assisted Electron Transfer from Photoexcited SemiconductorQuantum Dots. Nano Lett. 2014, 14, 1263−1269.(35) Bittner, E. R.; Rossky, P. J. Quantum Decoherence in MixedQuantum-Classical Systems - Nonadiabatic Processes. J. Chem. Phys.1995, 103, 8130−8143.(36) Schwartz, B. J.; Bittner, E. R.; Prezhdo, O. V.; Rossky, P. J.Quantum decoherence and the isotope effect in condensed phasenonadiabatic molecular dynamics simulations. J. Chem. Phys. 1996,104, 5942−5955.(37) Prezhdo, O. V.; Rossky, P. J. Evaluation of quantum transitionrates from quantum-classical molecular dynamics simulations. J. Chem.Phys. 1997, 107, 5863−5878.

(38) Prezhdo, O. V. Mean field approximation for the stochasticSchrodinger equation. J. Chem. Phys. 1999, 111, 8366−8377.(39) Miller, W. H. Classical Path Approximation for the BoltzmannDensity Matrix. J. Chem. Phys. 1971, 55, 3146−3149.(40) Long, R.; Fang, W. H.; Prezhdo, O. V. Moderate HumidityDelays Electron-Hole Recombination in Hybrid Organic-InorganicPerovskites: Time-Domain Ab Initio Simulations Rationalize Experi-ments. J. Phys. Chem. Lett. 2016, 7, 3215−3222.(41) Akimov, A. V.; Asahi, R.; Jinnouchi, R.; Prezhdo, O. V. WhatMakes the Photocatalytic CO2 Reduction on N-Doped Ta2O5Efficient: Insights from Nonadiabatic Molecular Dynamics. J. Am.Chem. Soc. 2015, 137, 11517−11525.(42) Long, R.; Prezhdo, O. V. Time-Domain Ab Initio Analysis ofExcitation Dynamics in a Quantum Dot/Polymer Hybrid: AtomisticDescription Rationalizes Experiment. Nano Lett. 2015, 15, 4274−4281.(43) Kilina, S. V.; Neukirch, A. J.; Habenicht, B. F.; Kilin, D. S.;Prezhdo, O. V. Quantum Zeno Effect Rationalizes the PhononBottleneck in Semiconductor Quantum Dots. Phys. Rev. Lett. 2013,110, 180404.(44) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.;Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.;Dal Corso, A.; de Gironcoli, S.; Fabris, S.; Fratesi, G.; Gebauer, R.;Gerstmann, U.; Gougoussis, C.; Kokalj, A.; Lazzeri, M.; Martin-Samos,L.; Marzari, N.; Mauri, F.; Mazzarello, R.; Paolini, S.; Pasquarello, A.;Paulatto, L.; Sbraccia, C.; Scandolo, S.; Sclauzero, G.; Seitsonen, A. P.;Smogunov, A.; Umari, P.; Wentzcovitch, R. M. QUANTUMESPRESSO: a modular and open-source software project for quantumsimulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502.(45) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized GradientApproximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868.(46) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to theprojector augmented-wave method. Phys. Rev. B: Condens. MatterMater. Phys. 1999, 59, 1758−1775.(47) Grimme, S. Semiempirical GGA-type density functionalconstructed with a long-range dispersion correction. J. Comput.Chem. 2006, 27, 1787−1799.(48) Kang, J.; Tongay, S.; Zhou, J.; Li, J. B.; Wu, J. Q. Band offsetsand heterostructures of two-dimensional semiconductors. Appl. Phys.Lett. 2013, 102, 012111.(49) Debbichi, L.; Eriksson, O.; Lebegue, S. Electronic structure oftwo-dimensional transition metal dichalcogenide bilayers from abinitio theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89,205311.(50) Kosmider, K.; Fernandez-Rossier, J. Electronic properties of theMoS2-WS2 heterojunction. Phys. Rev. B: Condens. Matter Mater. Phys.2013, 87, 075451.(51) Nelson, T. R.; Prezhdo, O. V. Extremely Long NonradiativeRelaxation of Photoexcited Graphane Is Greatly Accelerated byOxidation: Time-Domain Ab Initio Study. J. Am. Chem. Soc. 2013, 135,3702−3710.(52) Akimov, A. V.; Prezhdo, O. V. Persistent Electronic CoherenceDespite Rapid Loss of Electron−Nuclear Correlation. J. Phys. Chem.Lett. 2013, 4, 3857−3864.(53) Chen, S.-Y.; Zheng, C.; Fuhrer, M. S.; Yan, J. Helicity-ResolvedRaman Scattering of MoS2, MoSe2, WS2, and WSe2 Atomic Layers.Nano Lett. 2015, 15, 2526−2532.(54) Molina-Sanchez, A.; Wirtz, L. Phonons in single-layer and few-layer MoS2 and WS2. Phys. Rev. B: Condens. Matter Mater. Phys. 2011,84, 155413.(55) Long, R.; Prezhdo, O. V. Quantum Coherence FacilitatesEfficient Charge Separation at a MoS2/MoSe2 van der Waals Junction.Nano Lett. 2016, 16, 1996−2003.(56) Zhou, W.; Zou, X.; Najmaei, S.; Liu, Z.; Shi, Y.; Kong, J.; Lou, J.;Ajayan, P. M.; Yakobson, B. I.; Idrobo, J.-C. Intrinsic Structural Defectsin Monolayer Molybdenum Disulfide. Nano Lett. 2013, 13, 2615−2622.(57) Wang, H.; Zhang, C.; Rana, F. Ultrafast Dynamics of Defect-Assisted Electron−Hole Recombination in Monolayer MoS2. NanoLett. 2015, 15, 339−345.

Chemistry of Materials Article

DOI: 10.1021/acs.chemmater.6b03727Chem. Mater. 2017, 29, 2466−2473

2472

(58) Kamisaka, H.; Kilina, S. V.; Yamashita, K.; Prezhdo, O. V. Abinitio study of temperature- and pressure dependence of energy andphonon-induced dephasing of electronic excitations in CdSe and PbSequantum dots. J. Phys. Chem. C 2008, 112, 7800−7808.(59) Habenicht, B. F.; Kamisaka, H.; Yamashita, K.; Prezhdo, O. V.Ab initio study of vibrational dephasing of electronic excitations insemiconducting carbon nanotubes. Nano Lett. 2007, 7, 3260−3265.

Chemistry of Materials Article

DOI: 10.1021/acs.chemmater.6b03727Chem. Mater. 2017, 29, 2466−2473

2473