Why Chemical Vapor Deposition Grown MoS2 Samples OutperformPhysical Vapor Deposition Samples: Time-Domain ab Initio AnalysisLinqiu Li,† Run Long,§ and Oleg V. Prezhdo*,†,‡

†Department of Chemistry and ‡Department of Physics and Astronomy, University of Southern California, Los Angeles, California90089, United States§College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing NormalUniversity, Beijing 100875, PR China

*S Supporting Information

ABSTRACT: Two-dimensional transition metal dichalcogenides (TMDs)have drawn strong attention due to their unique properties and diverseapplications. However, TMD performance depends strongly on materialquality and defect morphology. Experiments show that samples grown bychemical vapor deposition (CVD) outperform those obtained by physicalvapor deposition (PVD). Experiments also show that CVD samples exhibitvacancy defects, while antisite defects are frequently observed in PVDsamples. Our time-domain ab initio study demonstrates that both antisitesand vacancies accelerate trapping and nonradiative recombination ofcharge carriers, but antisites are much more detrimental than vacancies.Antisites create deep traps for both electrons and holes, reducing energygaps for recombination, while vacancies trap primarily holes. Antisites also perturb band-edge states, creating significant overlapwith the trap states. In comparison, vacancy defects overlap much less with the band-edge states. Finally, antisites can create pairsof electron and hole traps close to the Fermi energy, allowing trapping by thermal activation from the ground state and stronglycontributing to charge scattering. As a result, antisites accelerate charge recombination by more than a factor of 8, while vacanciesenhance the recombination by less than a factor of 2. Our simulations demonstrate a general principle that missing atoms aresignificantly more benign than misplaced atoms, such as antisites and adatoms. The study rationalizes the existing experimentaldata, provides theoretical insights into the diverse behavior of different classes of defects, and generates guidelines for defectengineering to achieve high-performance electronic, optoelectronic, and solar-cell devices.

KEYWORDS: Transition-metal dichalcogenides, electron−hole recombination, antisite and vacancy defects,time-dependent density functional theory, nonadiabatic molecular dynamics

The success of single-layer graphene has opened upexploration and research into the physics of two-

dimensional materials.1−4 Due to the zero bandgap, chargecarriers rapidly recombine in graphene, limiting its optoelec-tronic and solar energy applications.5,6 Two-dimensionaltransition metal dichalcogenides (TMDs) of the generalformula MX2, where M = Mo or W and X = S, Se, or Te,have drawn strong attention as possible substitutes ofgraphene.7−12 The unique chemical, electrical, mechanical,and optical properties of TMDs, such as strong catalyticactivity, high current-carrying capacity, moderate flexibility,large charge-carrier mobility, and high photoluminescenceefficiency, are stimulating growing research efforts.13−18

MoS2 is the one of the most extensively studied TMDs.11 Itsmonolayer is composed of a plane of hexagonally arrangedmolybdenum atoms sandwiched between two planes ofhexagonally arranged sulfur atoms.19 The properties of single-layer MoS2 are superior to those of bulk MoS2 in many ways.Single-layer MoS2 is a direct bandgap semiconductor withhigher photoluminescence efficiency.20 It is marginally strongerthan the bulk crystal.21 Because of the true two-dimensional

nature, monolayer MoS2 outperforms three-dimensionalmaterials in transistor applications. The electronic transportof MoS2 field-effect transistors shows a steeper subthresholdswing and a higher on/off ratio.7 Furthermore, MoS2 has strongspin−orbit coupling and extra valley degrees of freedom, whichcan be exploited for the development of novel valleytronics.22

Owing to its excellent optical and electric properties, MoS2 isa promising building block for a new generation of electronicand optoelectronic materials. Devices based on mechanicallyexfoliated MoS2 exhibit good electric performance. However,the thickness, shape, and number of layers of mechanicallyexfoliated MoS2 are not controllable.23 For large-scaleapplications, though, large area and continuous thin films ofMoS2 are a must, limiting applicability of mechanicallyexfoliated MoS2. Physical vapor deposition (PVD) andchemical vapor deposition (CVD) enable the controlled growthof large area TMD films with precise atomic-scale thick-

Received: April 14, 2018Revised: May 17, 2018Published: May 18, 2018

Letter

pubs.acs.org/NanoLettCite This: Nano Lett. 2018, 18, 4008−4014

© 2018 American Chemical Society 4008 DOI: 10.1021/acs.nanolett.8b01501Nano Lett. 2018, 18, 4008−4014

Dow

nloa

ded

via

UN

IV O

F SO

UT

HE

RN

CA

LIF

OR

NIA

on

Nov

embe

r 7,

201

9 at

16:

47:2

5 (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.

ness.24,25 However, the charge carrier mobility are much lowerin PVD- and CVD-grown samples than in mechanicallyexfoliated samples. The highest reported mobility reaches 81cm2 V−1 s−1 for mechanically exfoliated samples, 45 cm2 V−1 s−1

for CVD-grown samples, and <1 cm2 V−1 s−1 for PVD-grownsamples. This is significantly lower than the theoretical limit of410 cm2 V−1 s−1.7

Deterioration of the charge mobility has been attributed tocharge scattering off short-range disordered defects. Hong et al.reported that the antisite defects with one molybdenum atomreplacing one or two sulfur atoms (MoS or MoS2) are thedominant point defects in PVD-grown MoS2 monolayers, whilesulfur vacancies are predominant in mechanically exfoliated andCVD-grown samples.7,26−29 The work of Zhou et al. confirmedexistence of one sulfur vacancy (VS) and two sulfur vacancies,on the opposite (VS2_opp) or the same (VS2_same) side, in CVD-grown MoS2 monolayers.26 Having identified the defect types,one needs to estimate the rates of charge scattering and energylosses at these defects. Because it is very difficult to disentanglethe contributions of different defects experimentally, the taskcan be achieved by atomistic calculations.In this Letter, we use ab initio quantum dynamic calculations

to study the role of different point defects on charge-carrierdynamics in monolayer MoS2 and rationalize why CVD-grownsamples are superior to PVD samples. We demonstrate that alldefects are bad for MoS2 quality, but antisite defects are moredetrimental than vacancy defects. Antisites creates trap statesfor both electrons and holes deep within the bandgap, openingextra charge-carrier relaxation pathways. They also perturbwave functions of the band-edge states in a way that allows freecharge carriers to couple to the defect states. The simplestantisite defect generates a pair of electron and hole traps at theFermi energy, such that the traps can be populated already bythermal activation at room temperature. As a result, the excited-state lifetime is decreased by a factor of 8.3 due to antisitedefects. In contrast, vacancies decrease the lifetime only by afactor of 1.7. Conduction-band (CB) edge states are perturbedslightly by vacancies. Only shallow hole traps couple strongly tothe valence-band (VB) edge. Electron is hard to trap, and itsmobility remains high. Charge recombination in vacancy MoS2monolayers occurs primarily through hole traps. In general,misplaced atoms, including adatoms and antisite atoms, perturbcharge-carrier dynamics much more strongly than missingatoms and, therefore, should be avoided.The Quantum Espresso program was used to perform

geometry optimization, density functional theory (DFT)calculations and adiabatic molecular dynamics.30 Nonadiabatic(NA) molecular dynamics were modeled using the decoher-ence-induced surface hopping (DISH) method,31 which hadbeen implemented in the Pyxaid software package.31−33 DISHhas proven reliable in simulating excited-state dynamics inTMD systems, including MoS2 monolayers, MoS2/MoSe2 andMoS2/WS2 heterojunctions, and MoS2/TiO2 composites,34−37

as well as in many other systems.38−44 Simulation details areprovided in the Supporting Information.Figure 1 depicts a diagram of the charge carrier trapping and

relaxation dynamics in the perfect and defective MoS2monolayers. Defects generally bring in trap states within thebandgap, which provide extra pathways for charge-carrierrelaxation. Without trap states, electrons in the CB directlyrecombine with VB holes (process 1). In the presence ofdefects, electrons and holes get trapped (processes 2 and 4).Trapped electrons recombine with free or trapped holes

(processes 3 and 6) while CB electrons also recombine withtrapped holes (process 5). The population of a trap state isdetermined through competing trapping and detrappingprocesses.Figure 2 shows the side and top views of the pristine MoS2

monolayer, together with the antisite and vacancy defects,which are highlighted with red arrows and circles. Theconsidered defects include antisite defects, in which a Moatom replaces one (MoS) or two (MoS2) S atoms, as well assingle (VS) and double S vacancies, with the two vacanciesbeing on the same (VS2_same) or opposite (VS2_opp) sides of themonolayer. DFT calculations predict the formations energies ofthe antisite and vacancy defects to be in the ranges of 5.45−

Figure 1. Electronic energy levels involved in charge carriers trappingand relaxation. Defects can create electron and hole trap within theband gap. After photoexcitation, electrons in the conduction band(CB) can directly recombine with holes in the valence band (VB)(label 1). Some electrons can get trapped by unoccupied defect levels(electron trap states, label 2) and then recombine with the VB holes(label 3). Similarly, holes can get trapped by occupied defect levels(hole trap states) (label 4) and then recombine with the CB electrons(label 5) or the trapped electrons (label 6). Electrons are shown inorange. Holes are shown in green.

Figure 2. Side and top views of the (a) perfect MoS2 monolayer, (b)MoS2 monolayer with one Mo replacing one S atom (MoS), (c) MoS2monolayer with one Mo replacing two S atoms (MoS2). (d) MoS2monolayer with one S vacancy (VS), (e) MoS2 monolayer with two Svacancies on the opposite sides (VS2_opp), and (f) MoS2 monolayerwith two S vacancies on the same side (VS2_same). Mo is green, and S isyellow. Defects are highlighted with red arrows and red circles in theside and top views, respectively.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.8b01501Nano Lett. 2018, 18, 4008−4014

4009

6.09 and 2.86−4.34 eV, respectively.7 The smaller formationenergies of the vacancy defects indicate that they are commonin MoS2 samples.26,28 This is true for mechanically exfoliatedand CVD-grown MoS2 monolayers, as confirmed, for instance,through the scanning transmission electron microscopy experi-ments by Zhou et al.26 In comparison, the PVD manufacturingprocess maintains S-deficient and Mo-rich conditions, resultingin a high probability of the antisite defects, with theexperimental probability density ratio of MoS2:MoS:VS =9:2.3:1, indicating that the antisite defects dominate PVD-grown MoS2.

7

In PVD-grown MoS2 monolayers, the antisite Mo atom isloosely bonded to the MoS2 monolayer and can undergo large-scale vibrations. Because Mo is heavier than S, the antisitedefects vibrates at low frequencies. In mechanically exfoliatedand CVD-grown MoS2 monolayers, the sulfur vacancies createunsaturated chemical bonds at the Mo atoms, which caninteract with adjacent S atoms and amplify their motions. Bothantisite and vacancy defects perturb the symmetry of the MoS2monolayer and bring in phonon modes that are not available inthe perfect system.Figure 3 shows the densities of states (DOS) of the perfect,

antisite, and vacancy MoS2 monolayers. The calculated bandgap

of the perfect MoS2 monolayer is 1.72 eV, which is consistentwith the previously published results.45−47 The antisite defectscreate a deep electron trap and two kinds of hole traps: ashallow hole trap attached to the VB edge and a deep hole trapclose to the electron trap near the Fermi energy. The gapbetween the deep electron trap and the deep hole trap isnarrowed down by a large extent, especially in MoS, in which itis almost zero. As a result, the NA couplings between theelectron and hole trap states are large. Trapped electrons canquickly recombine with trapped holes, and the electron−holerecombination is accelerated through both electron and holetrapping. The S vacancies create deep electron traps andshallow hole traps. The shallow hole traps can efficiently coupleto the VB edge states, in contrast to electron traps, which onlyweakly couple to the CB edge states. Hole trapping plays a

much more important role than electron trapping in MoS2 withS vacancies.Figure 4 presents the charge densities of states involved in

the charge-carrier trapping and relaxation dynamics for the

perfect and defective MoS2 monolayers. The VB and CB edgestates are delocalized within the whole monolayer, while thetrap states are localized around defects. In antisite MoS2, allstates are strongly perturbed by the misplaced Mo atom, eventhe VB and CB edge states gather more charge densities nearthe defect region. Consequently, the band-edge states overlapwell with the defect states, and the NA couplings leading tocharge trapping are relatively large; see Table 1. The MoSsystem has an unusually large NA coupling between theelectron and hole traps because these states are nearlydegenerate; see Figure 3b. In vacancy MoS2 monolayers, theCB edge states remain unperturbed. In comparison, the VBedges are perturbed because the vacancies create shallow holetraps next to VB edge states. The shallow hole trap stateshybridize with the VB edge and are more delocalized than thedeep electron trap states. Therefore, the NA coupling is largerfor hole than electron trapping in the S vacancy systems (Table1) and the nonradiative recombination of free charge carriers ismediated primarily by hole traps.Figure 5 depicts time evolution of populations of the key

states involved in the electron−hole recombination dynamics inthe perfect and defective MoS2 monolayers, including electrontrap states, hole trap states, states with electron and holetrapped simultaneously, and the ground state. In systems thatexhibit multiple electron or hole traps (Figure 3), thepopulations are added up to obtain the total population of allelectron traps, all hole traps, and all states with both electronsand holes trapped. The times presented in the figure areobtained through exponential fitting of the data as follows. Theground-state populations are fitted by a single exponent. Thepopulations of the trap states are characterized by thecompeting rise (trapping) and decay (detrapping) processes.

Figure 3. Density of states of (a) a perfect MoS2 monolayer, (b) MoS,(c) MoS2, (d) VS, (e) VS2_opp, and (f) VS2_same. The vertical blackdashed lines represent the Fermi energy. The antisite defects (MoS andMoS2) create a deep electron trap and two kinds of hole traps: ashallow hole trap state close to the VB edge and a deep hole trap nearthe Fermi energy. The vacancy defects (VS, VS2_opp, and VS2_same)create a shallow hole trap and deep electron traps.

Figure 4. Charge densities of (a) a perfect MoS2 monolayer, (b) MoS,(c) MoS2, (d) VS, (e) VS2_opp, and (f) VS2_same. The antisite defectscreate localized hole and electron trap states. The vacancy defects areless localized. In antisite MoS2, both VB and CB edge states areperturbed by the defects, with electron density gathering near thedefects. In vacancy MoS2, only the VB edge states are perturbed bydefects, and the CB edge states remain unchanged.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.8b01501Nano Lett. 2018, 18, 4008−4014

4010

The rise and decay parts are fitted separately, and the reportedtimes are the sum of the times of the two exponential fits.These time scales provide a measure of how long the trap statesare populated. The height of the curves represents themaximum average population of the traps.Nonradiative electron−hole recombination is a major

mechanism for charge losses and energy dissipation in solarand optoelectronic and other TMD applications. Thecalculation shows that the direct recombination of electronsand holes, corresponding to process 1 in Figure 1, needs 388 psin the perfect MoS2 monolayer. This time scale is consistentwith the previously reported experimental results of severalhundreds of picoseconds.48−50 Both antisite and vacancydefects introduce energy levels within the bandgap andaccelerate charge-carrier relaxation, but the degree of theaccelerations is different. The antisites can speed up therecombination by a factor of up to 8.3, while the vacanciesdecrease the time constants only by a factor of 1.7 (Figure 5).The enhancement of the electron−hole recombination rate

in antisite MoS2 monolayer is explained by efficientparticipation of both electron and hole traps as well as by the

larger NA coupling for defect trapping and detrapping, relativeto the S vacancy systems (Table 1). The root-mean-square ofNA coupling for electron−hole recombination in the perfectMoS2 is 2.8 meV. The NA coupling for electron−holerecombination directly between the CB and VB edges decreasesto 1.6−1.8 meV in the antisite MoS2 monolayers, particularlybecause the Mo atom is heavier than the S atom and antisiteMoS2 vibrates at lower frequencies. Although the NA couplingfor the direct recombination decreases, the NA coupling for thehole and electron trapping increases to 4.3−5.0 meV (Table 1).This is because the charge densities of the band-edge states areenhanced around the defective regions, which ensures efficientorbital overlap (Figure 4b,c). After trapping, electrons andholes recombine almost instantaneously in MoS because theenergy gap between the deepest electron and hole trapsnarrows down almost to zero (Figure 3b). The latter factexplains the oscillatory noise in the populations shown inFigure 5b. Because the electron and hole trap states originatingfrom the MoS defect reside very close to the Fermi energy, theycan be thermally populated from the ground state, even atroom temperature, providing an additional channel for

Table 1. Root-Mean-Square of Nonadiabatic Coupling (meV) for the Charge-Carrier Trapping and Recombination Dynamics

systemrecombination of CB electrons

and VB holeshole

trappingrecombination by hole

trappingelectrontrapping

recombination by electrontrapping

recombination by electron andhole trapping

perfect 2.78MoS 1.78 4.58 3.56 4.29 2.73 144.58MoS2 1.56 4.42 4.22 4.95 2.52 4.95VS 3.67 4.01 2.53 0.92 4.01 2.56VS2_opp 3.35 4.87 3.46 1.09 3.51 3.58VS2_same 3.62 3.97 1.74 0.82 3.61 1.70

Figure 5. Charge-carrier trapping and recombination dynamics in (a) a perfect MoS2 monolayer, (b) MoS, (c) MoS2, (d) VS, (e) VS2_opp, and (f)VS2_same. Shown are time-dependent populations of the ground state and three types of trap states involving either electron, hole, or both electronand hole trapping. When multiple hole or electron traps are present, their populations are summed up for clarity. The corresponding processes aredepicted schematically in Figure 1.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.8b01501Nano Lett. 2018, 18, 4008−4014

4011

deteriorating device performance. Perhaps unexpectedly, theMoS2 defect is less detrimental than the MoS defect. Theelectron and hole trap states are separated by 0.5 eV in theMoS2 system, and both are relatively far from the band edges.As a result, the charge recombination is 2.5 times slower in theMoS2 system relative to the MoS system, but still, it is 3 timesfaster than in pristine MoS2. Because electrons and holes caneasily get trapped and quickly recombine with each other inantisite MoS2 monolayers, the mobilities of free positive andnegative charge carriers are greatly reduced, and excited-statelifetime is decreased by a large extent.Hole trap assisted recombination dominates in MoS2

monolayers with the S vacancies. First, the shallow hole trapis populated (shown in red lines in Figure 5d−f). Second, thedeep electron trap is populated (shown in purple lines). At thesame time, the trapped holes start recombining with freeelectrons. Recombination of trapped holes with free andtrapped electrons gives rise to the ground-state population(shown in black lines in Figures 5d−f). The electron trapping isslow due to the small NA coupling of the electron trap with theCB edge (Table 1) originating from relatively large energyseparation and differences in the charge-density localization. Inaddition, the quantum coherence (pure-dephasing) times forelectron trapping are shorter than for hole trapping and otherdynamics (Table S1). As a result, less than half ofrecombination events involve electron trapping. In contrast,hole trapping is involved in most recombination events in theMoS2 monolayers with the S vacancies. The NA couplingvalues are around 4 meV for transitions involving hole traps,and the corresponding pure-dephasing times are fairly long(Table S1). Hole trapping accelerates electron−hole recombi-nation by a factor of 1.4−1.7 (Figure 5d,e) and can even delaythe ground-state recovery; see Figure 5f. The mobility of freepositive charge carriers is reduced by trapping in vacancy MoS2,while the mobility of free negative charge carriers changes little.The excited-state lifetime is decreased by a small extent.A recent publication51 reported an increase in the photo-

luminescence quantum yield of monolayer MoS2 to nearlyunity following treatment with organic super-acids thatprobably passivate defect sites. The corresponding photo-luminescence lifetime increased to up to 10 ns for low-excitation fluences, at which point bimolecular exciton−excitonannihilation is negligible. Our calculated nonradiative lifetimefor pristine MoS2 is shorter than the measured lifetime, mostlikely due to the small simulation cell size. The small cellsconfine electrons and hole to an area that is less than theexciton size in the infinite material, thereby enhancing bothelectron−hole and electron−phonon interactions. Further-more, the small cell size does not allow for exciton dissociationinto free charge carriers that is possible in a large sample due toentropic effects because two free charges have a larger entropythan an exciton does. The simulation cell size is sufficient tocapture the defect properties because the defects are stronglylocalized.The reported calculations use a pure DFT functional used

that tends to underestimate energy gaps and does not includeexplicitly excitonic effects. More-accurate hybrid DFT func-tionals are expensive with periodic systems. Excitonic effects,described by the Bethe-Salpether theory, are extremelyexpensive to incorporate into MD dynamics. Nevertheless,the methodology provides correct semiquantitative description.The DFT functional allows us to distinguish between deep andshallow trap states and between electron and hole traps because

they are determined by chemical properties of the atoms. Inparticular, the S vacancies create deep electron traps becausethe MoS2 CB arises due to Mo atoms, and unsaturated Mobonds create empty states within the gap. Perturbation to theVB caused by S vacancies is small because the VB arises from Satomic orbitals, and all S atoms remain chemically saturated. Incomparison, the occupied and vacant orbitals of the antisite Moatoms interact strongly with the surrounding atoms, perturbingthe MoS2 VB and CB edges. The antisite defects create deeptrap states for electrons and holes because the extraneous Moatoms contain both occupied and vacant orbitals separated bygaps that are much smaller than the MoS2 bandgap.In summary, we have used NA molecular dynamics and time-

dependent DFT to investigate the influence of two defect types,antisites and vacancies, on charge-carrier recombinationdynamics in MoS2 monolayers. We have found that defectsgenerally accelerate electron−hole recombination, but antisitedefects are much more detrimental than vacancy defects. Onthe one hand, antisites can speed up the recombination bymore than a factor of 8. On the other hand, vacancies acceleratethe recombination by less than a factor of 2 and even delay theground-state recovery. This is because the antisite defects createboth electron and hole traps deep within the bandgap, reducingthe energy gaps for the phonon-mediated charge relaxation. Inaddition, the CB and VB edge states are perturbed by theantisite defects in a way that creates significant overlap with thetrap states. In comparison, vacancies create deep electron butnot hole traps, and the CB and VB edge states remaindelocalized, showing a weaker overlap with the defect wavefunctions. Moreover, the simplest antisite defect with one Moatom replacing one S atom creates a pair of electron and holetraps close to the Fermi energy, allowing charge trapping bythermal activation from the ground state.Our simulations rationalize the better performance of CVD-

grown MoS2 monolayers over PVD-grown monolayers. PVDsamples contain many antisite defects, which greatly decreasecharge-carrier lifetimes and mobilities. In contrast, CVDsamples contain primarily vacancy defects that have a muchweaker effect on carrier lifetimes and influence primarily holesbut not electrons. Our analysis suggests that the performance ofPVD-grown MoS2 samples can be improved by introduction ofextra S during the growth process or post-growth treatment tominimize the appearance of Mo atoms in place of S atoms. Atthe same time, our previous publication shows that S adatomcan greatly, by a factor of 8, accelerate charge recombination,36

which is comparable to the acceleration induced by MoS.Therefore, the manufacturing process should be tuned toprevent the formation of both antisite and adatom defects. Inother words, missing atoms are more benign than misplacedatoms. The conclusions obtained in this work for MoS2 shouldbe applicable to the other closely related materials, such as WS2,WSe2, and MoSe2, because the chemistries during their PVDand CVD production are similar. Showing good agreementwith the existing experimental data, our results providetheoretical insights into defect engineering in TMDs andsuggest routes for improving MoS2 quality for applications inlow-dimensional electronic, optoelectronic, and solar-energydevices.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.8b01501Nano Lett. 2018, 18, 4008−4014

4012

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.nano-lett.8b01501.

Description of the theoretical methodology and simu-lation details. A table showing pure-dephasing times. Afigure showing electron−phonon influence spectra.(PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: prezhdo@usc.edu. Phone: +1-213-821-3116.

ORCIDRun Long: 0000-0003-3912-8899Oleg V. Prezhdo: 0000-0002-5140-7500NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors are grateful to Kuang Liu and Subodh Tiwari fortheir help with high-performance computing and to Prof.Aiichiro Nakano and Prof. Priya Vashishta for multiple fruitfuldiscussions. The work was supported as part of the Computa-tional Materials Sciences Program funded by the U.S.Department of Energy, Office of Science, Basic EnergySciences, under award no. DE-SC00014607.

■ REFERENCES(1) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183−191.(2) Balandin, A. A.; Ghosh, S.; Bao, W.; Calizo, I.; Teweldebrhan, D.;Miao, F.; Lau, C. N. Nano Lett. 2008, 8, 902−907.(3) Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.;Velamakanni, A.; Jung, I.; Tutuc, E.; Banerjee, S. K.; Colombo, L.;Ruoff, R. S. Science 2009, 324, 1312−1314.(4) Schwierz, F. Nat. Nanotechnol. 2011, 6, 135−136.(5) Ohta, T.; Bostwick, A.; Seyller, T.; Horn, K.; Rotenberg, E.Science 2006, 313, 951−954.(6) Novoselov, K. S.; Falko, V. I.; Colombo, L.; Gellert, P. R.;Schwab, M. G.; Kim, K. Nature 2012, 490, 192−200.(7) Hong, J.; Hu, Z.; Probert, M.; Li, K.; Lv, D.; Yang, X.; Gu, L.;Mao, N.; Feng, Q.; Xie, L.; Zhang, J.; Wu, D.; Zhang, Z.; Jin, C.; Ji, W.;Zhang, X.; Yuan, J.; Zhang, Z. Nat. Commun. 2015, 6, 6293.(8) Brennan, C. J.; Ghosh, R.; Koul, K.; Banerjee, S. K.; Lu, N.; Yu, E.T. Nano Lett. 2017, 17, 5464−5471.(9) Hsieh, K.; Kochat, V.; Zhang, X.; Gong, Y.; Tiwary, C. S.; Ajayan,P. M.; Ghosh, A. Nano Lett. 2017, 17, 5452−5457.(10) Miller, B.; Steinhoff, A.; Pano, B.; Klein, J.; Jahnke, F.;Holleitner, A.; Wurstbauer, U. Nano Lett. 2017, 17, 5229−5237.(11) Ganatra, R.; Zhang, Q. ACS Nano 2014, 8, 4074−4099.(12) Lin, Y.-C.; Dumcenco, D. O.; Huang, Y.-S.; Suenaga, K. Nat.Nanotechnol. 2014, 9, 391−396.(13) Chia, X.; Ambrosi, A.; Sofer, Z.; Luxa, J.; Pumera, M. ACS Nano2015, 9, 5164−5179.(14) Mannebach, E. M.; Li, R.; Duerloo, K.-A.; Nyby, C.; Zalden, P.;Vecchione, T.; Ernst, F.; Reid, A. H.; Chase, T.; Shen, X.; Weathersby,S.; Hast, C.; Hettel, R.; Coffee, R.; Hartmann, N.; Fry, A. R.; Yu, Y.;Cao, L.; Heinz, T. F.; Reed, E. J.; Durr, H. A.; Wang, X.; Lindenberg,A. M. Nano Lett. 2015, 15, 6889−6895.(15) Mai, C.; Barrette, A.; Yu, Y.; Semenov, Y. G.; Kim, K. W.; Cao,L.; Gundogdu, K. Nano Lett. 2014, 14, 202−206.(16) Bernardi, M.; Palummo, M.; Grossman, J. C. Nano Lett. 2013,13, 3664−3670.

(17) Amani, M.; Burke, R. A.; Ji, X.; Zhao, P.; Lien, D.-H.; Taheri, P.;Ahn, G. H.; Kirya, D.; Ager, J. W.; Yablonovitch, E.; Kong, J.; Dubey,M.; Javey, A. ACS Nano 2016, 10 (7), 6535−6541.(18) Voiry, D.; Yang, J.; Chhowalla, M. Adv. Mater. 2016, 28, 6197−6206.(19) Chhowalla, M.; Shin, H. S.; Eda, G.; Li, L.-J.; Loh, K. P.; Zhang,H. Nat. Chem. 2013, 5, 263−275.(20) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.-Y.;Galli, G.; Wang, F. Nano Lett. 2010, 10, 1271−1275.(21) Bertolazzi, S.; Brivio, J.; Kis, A. ACS Nano 2011, 5, 9703−9709.(22) Schmidt, H.; Wang, S.; Chu, L.; Toh, M.; Kumar, R.; Zhao, W.;Castro Neto, A. H.; Martin, J.; Adam, S.; Ozyilmaz, B.; Eda, G. NanoLett. 2014, 14, 1909−1913.(23) Wang, X.; Feng, H.; Wu, Y.; Jiao, L. J. Am. Chem. Soc. 2013, 135,5304−5307.(24) Chen, W.; Zhao, J.; Zhang, J.; Gu, L.; Yang, Z.; Li, X.; Yu, H.;Zhu, X.; Yang, R.; Shi, D.; Lin, X.; Guo, J.; Bai, X.; Zhang, G. J. Am.Chem. Soc. 2015, 137, 15632−15635.(25) Muratore, C.; Hu, J. J.; Wang, B.; Haque, M. A.; Bultman, J. E.;Jespersen, M. L.; Shamberger, P. J.; McConney, M. E.; Naguy, R. D.;Voevodin, A. A. Appl. Phys. Lett. 2014, 104, 261604.(26) Zhou, W.; Zou, X.; Najmaei, S.; Liu, Z.; Shi, Y.; Kong, J.; Lou, J.;Ajayan, P. M.; Yakobson, B. I.; Idrobo, J.-C. Nano Lett. 2013, 13,2615−2622.(27) Gonzalez, C.; Biel, B.; Dappe, Y. J. Nanotechnology 2016, 27,105702.(28) Santosh, K. C.; Roberto, C. L.; Rafik, A.; Robert, M. W.;Kyeongjae, C. Nanotechnology 2014, 25, 375703.(29) Liu, D.; Guo, Y.; Fang, L.; Robertson, J. Appl. Phys. Lett. 2013,103, 183113.(30) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.;Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.;et al. J. Phys.: Condens. Matter 2009, 21, 395502.(31) Jaeger, H. M.; Fischer, S.; Prezhdo, O. V. J. Chem. Phys. 2012,137, 22A545.(32) Akimov, A. V.; Prezhdo, O. V. J. Chem. Theory Comput. 2013, 9,4959−4972.(33) Akimov, A. V.; Prezhdo, O. V. J. Chem. Theory Comput. 2014,10, 789−804.(34) Long, R.; Prezhdo, O. V. Nano Lett. 2016, 16, 1996−2003.(35) Li, L.; Long, R.; Prezhdo, O. V. Chem. Mater. 2017, 29, 2466−2473.(36) Li, L.; Long, R.; Bertolini, T.; Prezhdo, O. V. Nano Lett. 2017,17, 7962−7967.(37) Wei, Y.; Li, L.; Fang, W.; Long, R.; Prezhdo, O. V. Nano Lett.2017, 17, 4038−4046.(38) Chaban, V. V.; Prezhdo, V. V.; Prezhdo, O. V. J. Phys. Chem.Lett. 2013, 4, 1−6.(39) Liu, L. H.; Fang, W. H.; Long, R.; Prezhdo, O. V. J. Phys. Chem.Lett. 2018, 9, 1164−1171.(40) Long, R.; English, N. J.; Prezhdo, O. V. J. Am. Chem. Soc. 2013,135 (50), 18892−18900.(41) Long, R.; Prezhdo, O. V. Nano Lett. 2014, 14, 3335−3341.(42) Wang, L. J.; Long, R.; Prezhdo, O. V. Time-Domain Ab InitioModeling of Photoinduced Dynamics at Nanoscale Interfaces. Annu.Rev. Phys. Chem. 2015, 66, 549.(43) Zhang, Z. S.; Long, R.; Tokina, M. V.; Prezhdo, O. V. J. Am.Chem. Soc. 2017, 139, 17327−17333.(44) Zhou, Z. H.; Liu, J.; Long, R.; Li, L. G.; Guo, L. J.; Prezhdo, O.V. J. Am. Chem. Soc. 2017, 139, 6707−6717.(45) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Phys. Rev.Lett. 2010, 105, 136805.(46) Krivosheeva, A. V.; Shaposhnikov, V. L.; Borisenko, V. E.;Lazzari, J.-L.; Waileong, C.; Gusakova, J.; Tay, B. K. J. Semicond. 2015,36, 122002.(47) Lu, S.-C.; Leburton, J.-P. Nanoscale Res. Lett. 2014, 9, 676.(48) Korn, T.; Heydrich, S.; Hirmer, M.; Schmutzler, J.; Schuller, C.Appl. Phys. Lett. 2011, 99, 102109.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.8b01501Nano Lett. 2018, 18, 4008−4014

4013

(49) Shi, H.; Yan, R.; Bertolazzi, S.; Brivio, J.; Gao, B.; Kis, A.; Jena,D.; Xing, H. G.; Huang, L. ACS Nano 2013, 7, 1072−1080.(50) Sun, D.; Rao, Y.; Reider, G. A.; Chen, G.; You, Y.; Brezin, L.;Harutyunyan, A. R.; Heinz, T. F. Nano Lett. 2014, 14, 5625−5629.(51) Amani, M.; Lien, D. H.; Kiriya, D.; Xiao, J.; Azcatl, A.; Noh, J.;Madhvapathy, S. R.; Addou, R.; KC, S.; Dubey, M.; Cho, K.; Wallace,R. M.; Lee, S. C.; He, J. H.; Ager, J. W.; Zhang, X.; Yablonovitch, E.;Javey, A. Science 2015, 350, 1065−1068.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.8b01501Nano Lett. 2018, 18, 4008−4014

4014