2012_JPCC_Tuning Electronic Structure of Bilayer MoS2 by Vertical Electric Field
Tuning Electronic Structure of Bilayer MoS 2by Vertical Electric Field:A First-Principles Investigation
Qihang Liu,?,∥Linze Li,?,∥Yafei Li,§Zhengxiang Gao,?Zhongfang Chen,*,§and Jing Lu *,?
?State Key Laboratory of Mesoscopic Physics and Department of Physics,Peking University,Beijing 100871,P.R.China ?Department of Materials Science and Engineering,University of Michigan,Ann Arbor,Michigan 48109,United States
§Department of Chemistry,Institute for Functional Nanomaterials,University of Puerto Rico,San Juan 00931,Puerto Rico *Supporting Information
INTRODUCTION Graphene is just the tip of the iceberg of two-dimensional (2D)nanomaterials;explorations involving the discovery of the rest of this iceberg are becoming more and more attractive.1Through exfoliation,layered materials with strong covalent in-plane bonds and weak van der Waals-like coupling between layers,such as transition metal dichalcogenides and transition metal oxides,can be made into single-and few-layer ?akes.1,2With the relative fabrication easiness compared to one-dimensional materials,2D materials are expected to have a signi ?cant impact on next-generation nanoelectronic devices.MoS 2is a typical example of the layered transition-metal dichalcogenide family.It is composed of covalently bonded S ?Mo ?S sheets that are bound by weak van der Waals forces.In its bulk form,MoS 2is a semiconductor with an indirect bandgap of 1.2eV 3and has attracted attentions because of its distinctive electronic,optical,catalytic,and lubricant proper-ties.4The 2D MoS 2nanostructures exhibit even more
interesting properties.When the MoS 2crystal is thinned to monolayer,a strong photoluminescence emerges,and an indirect to direct bandgap transition is thus con ?rmed.5Notably,monolayer MoS 2transistor with room-temperature current on/o ?ratios of 108has been achieved and demonstrates a room-temperature mobility of at least 200cm 2V ?1s ?1,which is similar to that of graphene nanoribbons.6With such distinctive properties,2D MoS 2could substitute or
complement graphene in many aspects.Bandgap engineering is a powerful technique and an essential
part of nanoelectronics and nanophotonics.Recent advances in engineering a graphene bandgap have motivated our study of tuning the bandgap of the technologically important 2D semiconducting MoS 2materials.An e ?cient method to open a graphene bandgap
is to apply a perpendicular electric ?eld to its bilayer structure.7The mechanism lies in that the inversion symmetry of the bilayer graphene is broken in the presence of an external electric ?eld;an electrostatic screening between the two layers occurs;and the πand π*bands crossing each other at the Fermi level (E f )are split.This method avoids the problems of fabrication complexity and reduced mobility involved in some other bandgap engineering processes such as lateral con ?nement and functionalization.Recently,Yue et al.studied the bandgap modulation by a transverse and perpendicular electric ?eld in armchair MoS
2nanoribbons
(AMoS 2NRs)by ?rst-principles calculations 8and found that
the bandgap of monolayer AMoS 2NRs is insensitive to an external perpendicular ?eld,but that of multilayer AMoS 2NRs can be e ?ciently reduced by a perpendicular ?eld.In addition,Ramasubramaniam et al.theoretically investigated the bandgap manipulation by applied electric ?eld perpendicular to the
bilayer transition-metal dichalcogenides,such as MoS 2,MoSe
2,
MoTe 2,and WS
2,
and by imposing symmetry constraints,they predicted that the critical electric ?elds,at which the bilayer
structures transform from semiconductor to metal,are between 0.2?0.3V/?.9
However,MoS 2bilayers have ?ve di ?erent stacking patterns,which cause di ?erent interlayer distance,stability,and bandgap,Received:July 18,2012
Revised:September 10,2012
Published:September 17,2012
thus a systematic study over all the conformations is necessary. In addition,when an unreasonable symmetry constraint is imposed in the band structure calculations under?nite vertical electric?eld for a structure with z-symmetry,an arti?cial dependence of the bandgap on the electric?eld may emerge, and the critical?eld for the semiconducting-to-metallic transition is usually underestimated.Therefore,more reliable results are expected after considering the symmetry breaking for the z-symmetrical conformations under the applied?eld. In this article,by means of density functional theory(DFT) computations and non-equilibrium Green’s function(NEGF) method,we reveal that bandgaps of the bilayer MoS2with di?erent stacking patterns all decrease monotonically with increasing the electric?eld perpendicular to the layers,and ?nally,the systems turn to metallic.The more reliable critical electric?elds(in the range of1.0?1.5V/?depending on the stacked conformations)are obtained.The di?erence from the previous results is mainly because the inversion symmetry breaking under the electric?eld is taken into account in our calculations.Subsequently,we provide a quantum transport simulation of a dual-gated bilayer MoS2device and con?rm that the zero transmission gaps(ZTG)also decrease with the applied electric?eld.Our work is expected to stimulate the applications of such few-layered transition-metal dichalcoge-
nides in nanoelectronics and nanophotonics.
■MODEL AND METHODS
A supercell model is built.We use the lattice parameter a=b=
3.16?according to experimental value.10The geometry optimization and electronic properties are calculated by using DFT implemented in the Dmol3package.11To treat the long-range dispersion,two schemes are used:one is the local density approximation(LDA)to the exchange-correlation functional. In the minimum energy con?guration,the charge clouds overlap,and it turns out that the LDA tends to overestimate attractions.12The other scheme is the generalized gradient approximation to the exchange-correlation functional of Perdew,Burke,and Ernzerhof(PBE)form,13with the inclusion of dispersion correction(PBE+D)proposed by Ortmann, Bechstedt,and Schmidt.14The Dmol3code has been extended to include the static potentials arising from an externally applied electric?eld.The electric?eld can be featured as an additional sawtooth potential along the z direction with discontinuity at the mid plane of the vacuum region of the supercell.We place the subject structures in the bottom part of the supercell,and our supercells are large enough(35?)to ensure that the discontinuity of the sawtooth potential as well as the interaction with spurious replicas along the z direction can be safely avoided.The double numerical basis set plus polarization (DNP)is employed,and the?rst Brillouin zone is sampled on a 24×24×1k-point Monkhorst?Pack mesh15for the density optimizations.The geometries are optimized under zero electric?eld and kept?xed hereafter since the in?uence of the band structure caused by the geometry disturbance is negligible.The automatic symmetry constraint is switched o?, and the e?ects of the imposition of symmetry constraint will be discussed later.
A two-probe bilayer MoS2model with dual gate is fabricated to simulate the transport properties.Di?erent from a single-gated transportation model,a dual-gated device can control not only the doping level but also the vertical electric?eld applied to the channel.Electron transport properties are calculated by the DFT coupled with NGEF formalism implemented in the ATK11.8package.16Single-ζplus polarization(SZP)basis sets are employed.The k-points of the electrodes and central region,which are generated by the Monkhorst?Pack scheme as well,are set to1×50×50and1×50×1,respectively.We used LDA for the exchange-correlation functional.A dual-gated bilayer MoS2channel with SiO2dielectric bu?er layers is considered.17The e?ect of the gate voltages is calculated by solving the Poisson equation self-consistently,instead of simply shifting the central region’s chemical potential.The temper-ature is set to300K.The system is divided into three parts:left electrode,scattering region(SR),and right electrode.The transmission spectrum can be calculated from the Green’s function approach:
==ΓΓ
??
T E Tr t t Tr G G
()[][]
r r
L R(1) Here,t is the transmission matrix,and G r andΓL(R)represent the retarded Green’s function in the SR and coupling matrix between the left(right)electrode and the SR:
=??Σ?Σ?
G ES H
()
r
L R
1(2)Γ=Σ?Σ?
i()
L(R)L(R)L(R)(3)
whereΣL(R)is the corresponding self-energy term.■RESULTS AND DISCUSSION
Geometries,Stabilities,and Band Structures of MoS2 Bilayers with Di?erent Stacking Patterns under Zero Electric Field.We?rst present our results of the MoS2 monolayer.The band structures of the MoS2monolayer are shown in Figure S1,Supporting Information.A direct bandgap is located at the K point,and the1.80eV bandgap value is in agreement with the experimental data(about1.8eV)5b and previous LDA results(1.87eV).18When the MoS2monolayer is applied with an external perpendicular electric?eld of even up to E⊥=2.0V/?,its bandgap is almost unchanged.
With di?erent stacking conformations,two MoS2monolayers can form?ve di?erent bilayer structures(Figure1).Note that, in each MoS2monolayer,every S atom in the upper S sublayer is right on top of one S atom in the lower S sublayer;thus,we represent one pair of S atoms by one yellow circle for a concise scheme.In this work,we refer to the di?erent bilayer structures by the notation introduced in Figure1.In the A-A and A-A′conformation(Figure1a,b),two monolayers are aligned.Their di?erence lies in that atoms of the same type are superimposed in the A-A case,while one type of atom is on top of the other type in the A-A′case,which is the most studied in the previous calculations.9,10In the A′-B conformation(Figure1c),the Mo atoms are superimposed,and the S atoms in the top monolayer are above the hexagon centers of the bottom monolayer;in the A-B′conformation(Figure1d),the S atoms are superimposed, and the Mo atoms in the top monolayer are above the hexagon centers of the bottom monolayer;and in the A-B conformation (Figure1e),the S atoms of the top monolayer are superimposed on the Mo atoms of the bottom monolayer, and the Mo atoms of the top monolayer are above the hexagon centers of the bottom monolayer.We also provide a perspective view of the optimized A-B stacked bilayer MoS2in Figure1f. The interlayer distances,relative energies,and binding energy based on the LDA and PBE-D functional of the?ve di?erent bilayer structures are given in Table1.According to LDA computations,the?ve bilayer con?gurations can be divided into two categories:the?rst has much longer interlayer
distances and consists of A-B ′(6.66?)and A-A (6.71?),and the second has three con ?gurations with shorter interlayer distances,namely,A-B (5.93?),A-A ′(5.99?),and A ′-B (5.98?).The larger interlayer distance in the A-B ′(6.66?)and A-A (6.71?)conformations is attributed to the stronger repulsion arising from the S atoms superimposing in the two conformations.These structural features highly correlate their relative stabilities.The lowest-energy conformation is the A-B stacking,closely followed by the A-A ′conformation (only 0.3meV per atom higher in energy),which is the most reported conformation for bulk MoS 2.The energy of the A ′-B conformation is slightly higher than those of the A-B and A-A ′conformations by about 4meV/atom.Because of the stronger repulsion caused by the superimposed S atoms,the A-B ′and A-A conformations are 9.8?14.5meV/atom higher in energy than the A-B,A-A ′,and A ′-B conformations.In the A-B and A-A ′conformations,di ?erent types of atoms are superimposed and thus generate more attractive potential,which leads to a lower energy.The calculated interlayer
distance of the A-A ′conformations at the LDA level is merely 0.15?smaller than the experimental value of 6.14?for bulk MoS 2.19
The PBE-D results also divide the ?ve conformations into two similar categories:one with larger interlayer distance and
higher relative energy,including A-B ′(6.82?)and A-A (6.83?),and the other with smaller interlayer distance and lower relative energy,including A-B (6.24?),A-A ′(6.27?),and A ′-B (6.33?).The interlayer distances given by PBE-D are about 0.2?larger than their respective LDA values.The interlayer
distance of the A-A ′conformation at the PBE-D level is 0.13?larger than the experimental value of bulk MoS 2.19Therefore,the experimental interlayer distance (6.14?)for the A-A ′conformation is roughly an average over the LDA (5.99?)and
PBE-D (6.27?)values.The relative stability of the ?ve conformations is similar to the LDA result except that the A-A ′conformation is 0.5meV per atom lower in energy than that of A-B conformation in the PBE-D calculations.Though in the actual MoS 2bulk,the A-A ′conformation is observed,19other
conformations probably exist in bilayer MoS 2.The binding energies based on the PBE-D level are among 20?35meV,which are about 10meV larger than their LDA counterparts.In
light of the small di ?erence between the LDA and PBE-D geometry and stability,in the electronic structure and transport calculations,we adopt the LDA method,and the discussions are
based on the LDA optimized geometry unless otherwise mentioned.
Unlike the MoS 2monolayer with a direct bandgap at the K
point,the ?ve conformations of MoS
2bilayers all have indirect
bandgaps.We choose the A-A and A-A ′conformations as the
representative for the category with a larger and smaller interlayer distance,respectively,to explore the relationship
between the interlayer distance and the corresponding bandgap.Figure 2a shows the band structures of the A-A and A-A ′bilayer
conformations under zero electric ?eld.In both cases,the direct
bandgap at the K point remains to be 1.80eV,while the Γpoint
energy level of the valence band becomes higher than the K
point of the valence band.Since the indirect bandgap of the
bilayer MoS 2is determined by the K point energy level of the
conduction band and the Γpoint energy level of the valence band,we now analyze the states at these two points.The states at the K point of the conduction band are primarily composed of the strongly localized d orbitals at the Mo atom sites,and the double degeneracy at the K point of the conduction band is nearly intact in MoS
2bilayer due to the very weak interaction between them.However,the states of the valence band at the Γpoint are mainly contributed by the outer p orbitals of the S atom sites and the internal d orbitals of the Mo atom sites.The stronger interaction between the outer p orbitals of the valence band at the Γpoint belonging to di ?erent MoS 2layers lifts their double level degeneracy.The uplifted energy level at the Γpoint of the valence band is even higher than that at the K point of the valence band,and thus,a direct to indirect bandgap transition occurs.
A smaller interlayer distance implies a stronger interlayer coupling interaction (Figure 2c),a larger energy level splitting at the Γpoint of the valence band (0.49eV for the A-A conformation and 0.85eV for the A-A ′conformation),and eventually a smaller band gap.Therefore,the structures
with
Figure 1.(a ?e)Drawing schemes of ?ve bilayer MoS 2structures.We represent one
pair of S atoms by one yellow circle for a concise scheme.(f)Perspective view of the optimized A-B stacked bilayer MoS 2.Table 1.Interlayer Distances (d ),Relative Energies (ΔE ),Binding Energies (E b ),Energy Level Splitting at the ΓPoint of the Valence Band (E s ),and Bandgaps (E g )of Five Di ?erent MoS 2Bilayer Structures Based on the LDA and PBE-D Methods structure A-B A-A ′A ′-B A-B ′A-A d (?)LDA 5.93 5.99a 5.98 6.66 6.71PBE-D 6.24 6.27 6.33 6.82 6.83ΔE (meV)LDA 00.3 4.013.814.5PBE-D 0.60 2.911.812.2E b (meV)LDA 26.225.922.212.411.7PBE-D 33.634.131.322.321.9E g (eV)LDA 1.01 1.09 1.06 1.47 1.47E s (eV)LDA 0.940.850.900.520.49a Experimental value:6.14?.19
smaller interlayer distances have smaller bandgaps.This trend holds true also for other bilayer con ?gurations (Table 1).E ?ect of External Electric Field to the Band Gaps of MoS 2Bilayers.Previous studies suggest that a bandgap can be opened by a perpendicular applied electric ?eld in bilayer or few-layer graphene;the gap collapses,and the system turns back to metallic when the electric ?eld is further increased.20Will the external electric ?eld also reduce the band gap of MoS 2bilayers?The answer is yes.In Figure 2a,we present the band structures of the A-A ′and A-A conformations of MoS 2bilayer under E ⊥=1.0V/?.The bandgap of the A-A ′conformation reduces to 0.4eV;while the A-A conformation has become metallic from semiconducting.Actually,the bandgaps of all ?ve MoS 2bilayer structures decrease monotonically with the increasing electric ?eld strength,as shown in Figure 3a.Similar to the case for interlayer distances (or band gaps),the bandgap versus electric ?eld relationship can also be divided into two groups,A-B ′pairs up with A-A to form the ?rst group,they have indistinguishable curves;in the second group,the curves for A-A ′and A ′-B are almost identical with that of the A-B (+z direction)conformation.Interestingly,applying E ⊥along +z direction and ?z directions has di ?erent e ?ects on the band gap of A-B layer,while it has the same e ?ect on the other four con ?gurations.This is because only in the A-B bilayer does the spontaneous polarization exist.When applying E ⊥on the A-B conformation along the +z direction,its bandgap decreases almost linearly to the ?eld strength,while applying the ?z direction E ⊥results in a nonlinear modulation on the bandgap.The critical ?elds are estimated to be 1.5V/?and 1.7V/?for the +z and ?z direction ?eld,respectively.Under a ?z direction ?eld below the threshold 0.2V/?,the bandgap of this system is almost unchanged.This threshold electric ?eld could be caused by a spontaneous polarization existing between the two monolayers.Under zero bias,each Mo atom has 0.4e positive charge and S atom has 0.2e negative charge in terms of Mullikan analysis.The S atoms of the top monolayer and the Mo atoms of
the
Figure 2.(a,b)Band structures under E ⊥=0(a)and 1.0V/?(b)of the A-A ′and A-A MoS 2bilayer conformations.(c)Electron density (isovalue,0.1au)at the Γpoint of the valence band under E ⊥=0V/?.The valence band top is set to zero.Yellow balls represent S
atoms.Figure 3.Bandgap of the bilayer MoS 2as a function of applied electric ?eld along +z and ?z directions with the symmetry constraint o ?(a)and on (b).For all the conformations except the A-B one,applying electric ?eld along +z direction and ?z directions have the same e ?ect.
bottom monolayer are superimposed,while the Mo atoms of the top monolayer and the S atoms of the bottom monolayer are not,so there exists a spontaneous polarization along the+z direction.Thus,the bandgap of the A-B bilayer can only be increased by a?z direction electric?eld large enough to overcome the intrinsic electric polarization.
The bandgap modulation discussed above arises from the well-known Stark e?ect,which has been observed in the previous studies on BN and MoS2sheets and armchair nanoribbons.8,9,21External perpendicular electric?eld induces a potential di?erence between the two layers.As a result,the energy bands belonging to di?erent MoS2layers are separated from each other entirely.The potential di?erence U can be expressed approximately by U=?dE*e,where E*is the screened electric?eld(external?eld plus that caused by charge redistribution)and d is the interlayer distance.In MoS2bilayer, the stronger the electric?eld is,the larger the band splitting is, and thus the smaller the band gap.However,the Stark e?ects do not always reduce the band gap of a system.For example, there is a linear Stark e?ect in the zigzag BN nanoribbons (ZBNNRs),and the mechanism arises from the spontaneous electric polarization existing in ZBNNRs.21b The conducting electrons and holes in this system are localized separately at the B and N edges,respectively;thus,there is a strong intrinsic electric?eld even when no external?eld is applied.Applied ?elds along di?erent directions enhance or weaken the equivalent?eld,and thus,the bandgap increases or decreases due to the Stark e?ect.In our case,only the A-B conformation has the intrinsic symmetry broken and has slight spontaneous polarization,as discussed before.Therefore,the Stark e?ect leads to the bandgap reduction in the other four conformations, while the bandgap of the A-B conformation is almost unchanged below the threshold0.2V/?along the?z direction. Compared with the A-B,A-A′,and A′-B conformations,the A-A and A-B′conformations have larger interlayer distances.As a result,the potential di?erences in these two conformations are larger and so are the band https://www.sodocs.net/doc/911644922.html,rger band splittings result in a quicker decreasing of the bandgap.Therefore,the critical?elds for the A-A and A-B′conformations with larger interlayer distances are smaller.In fact,the critical?eld for the A-A and A-B′conformations are both1.0V/?;while the critical?eld for the A-B(+z direction),A-A′,and A′-B conformations are all1.5V/?.
The absence of the inversion symmetry along the z direction in the A-B conformation of MoS2bilayer leads to the spontaneous polarization and the bandgap dependence on the direction of E⊥.However,though the other four con?gurations have z-symmetry under zero electric?eld,their z-symmetry will be destroyed by the external electric?eld.If an unreasonable symmetry constraint is imposed in the band structure calculations under?nite vertical electric?eld for a structure with z-symmetry,an arti?cial dependence of the bandgap on the electrical?eld will be led to.We provide the calculated band gap of bilayer graphene as a function of the vertical electric?eld with and without imposition of symmetry constraint and compare them with the experimental values in Figure S2,Supporting Information.The theoretical curve without imposition of symmetry constraint is consistent with the experiment,while the theoretical bandgap with imposition of symmetry constraint is too sensitive to the vertical electric ?eld.On the basis of the physical picture and the comparison with the experimental values,we can conclude that the band gap values without imposition of symmetry constraint are more reliable than those with imposition of symmetry constraint.In MoS2bilayer structures,when the symmetry constraint is switched on,the response of the bandgap of the A-A′conformation to E⊥also become much more sensitive,and the critical?eld greatly reduces from1.5to0.26V/?(Figure 3).The latter arti?cial value is consistent with the recent calculations of Ramasubramaniam et al.,suggestive of imposition of symmetry constraint therein.9Because the A-B conformation has no z-symmetry under zero electric?eld, whether the symmetry constraint is used does not change the E g?E⊥relationship at all.
Quantum Transport Simulation of a Dual-Gated A-A′Bilayer MoS2Structure.The modulation of the bandgap by vertical electric?eld in the bilayer MoS2should be re?ected in the transport properties.Here,we perform?rst-principles quantum transport simulation of a dual-gated A-A′bilayer MoS2structure as shown in Figure4a.
In the experiments,the MoS2monolayer channel is connected to metal leads(like Au)that serve as source and drain electrodes.6However,we cannot apply vertical electric ?eld on the electrode regions in the model.As a result,the metal leads here only provide an electron doping,causing E f of contacted bilayer MoS2to shift,and the states remain absent in the band gap of bilayer MoS2contacted with metal,which results in the failure of the observation of decrease of ZTG
with Figure4.Dual-gated?eld e?ect transistor based on the A-A′MoS2 bilayer comformation.(a)Schematic model.The channel is4.9nm long,and the electrodes are composed of doping homogeneous bilayer MoS2.Dark green ball,Mo;yellow ball,S;blue ball,N;light green ball, Cl.(b)Transmission spectrum under E⊥=0V/?(black line)and1.3 V/?(red line).Inset:ZTG as a function of the applied electric?eld.
(c)Transmission eigenstates at E f and at the(0,0)point of the k-space under E⊥=0V/?and1.3V/?.The isovalue is0.1au.
the increasing electric ?eld.In addition,the bonding between the metal and S atoms and the resulting contact resistance are complicated.22In order to observe the decrease of ZTG with increasing electric ?eld and avoid the complex interaction between the metal electrode and bilayer MoS 2,we generate the electrodes by doping homogeneous bilayer MoS 2.In the uppermost and lowest sulfur layers,a nitrogen and a chlorine atom substitute every other sulfur atom,respectively,so that the E f of the lead region is close to that of the pristine bilayer MoS 2(the middle point of the band gap).The top gate and bottom gate voltages are de ?ned as V t and V b .The distance between the two gates is d 0=41?in our model,and the thickness of the two identical dielectric regions is d i =13?.The dielectric constant of the dielectric region is ε=3.9,which models SiO 2.The length of the gated-channel is 4.9nm.The vertical electric ?eld and corresponding total doping level applied to the device are obtained as follows:17ε=??+⊥E V V d d d (2)2/b t
0i i (4)=+V V V g b t (5)where the total doping and bias voltage are both set to zero.The transmission spectra of the A-A ′bilayer MoS 2under a vertical electric ?eld of E ⊥=0and 1.3V/?(Figure 4b).Under no electric ?eld,the width of the ZTG region is 1.10eV,which coincides with the corresponding DFT bandgap (1.09eV).When the electric ?eld is applied,both edges of ZTG move toward E f ,and the gap decreases linearly with the applied ?eld except in the vicinity of the critical ?eld (see the inset of Figure 4b).The ZTG vanishes,and the whole device becomes metallic at E ⊥=1.3V/?,in agreement with the band calculation (1.5V/?)without imposition of symmetry constraint.This agreement once con ?rms the necessity of canceling the symmetry constraint in the band calculation for the z -symmetrical conformations.The di ?erence between the semiconducting and metallic state is also illustrated by the transmission eigenchannels at E f and at the (0,0)point of the k -space (Figure 4c).The transmission eigenvalue without E ⊥is 1.95×10?7,and the incoming wave function is almost completely scattered,so that it is unable to reach the other lead.In sharp contrast,the transmission eigenvalue at E ⊥=1.3V/?is 0.33;the incoming wave function is less scattered;and far more of the incoming wave is able to reach the other lead.■CONCLUSIONS In summary,by means of DFT computations,we have demonstrated that the vertical electric ?eld can continuously tune the electronic structure of MoS 2bilayers.The bandgaps of the two-dimensional structures decrease monotonically with increasing electric bias and fall to zero eventually when the electric ?eld is in the range of 1.0?1.5V/?,depending on the bilayer stacking patterns.After considering the inversion symmetry breaking under the electric ?eld,the critical ?eld is 4?5times larger than that reported in the previous calculations.The e ?ects of the vertical electric ?eld are also veri ?ed by the ab initio quantum transport simulation of a dual-gated bilayer MoS 2device.A sizable transmission gap,which is comparable with the bandgap,and its monotonic decrease with the electric ?eld are observed.Our work is expected to promote the applications of such few-layered transition-metal dichalcoge-nides in the next-generation nanoelectronic devices.■ASSOCIATED CONTENT *Supporting Information
Band
structures of the monolayer MoS 2under a vertical electric ?eld of 0and 2.0V/?;comparison of the calculated (with the
symmetry constraint switched on and o ?)and observed bandgap of the bilayer graphene as a function of applied vertical electric ?eld.This material is available free of charge via
the Internet at https://www.sodocs.net/doc/911644922.html,.■AUTHOR INFORMATION Corresponding Author *E-mail:jinglu@https://www.sodocs.net/doc/911644922.html, (J.L.);zhongfangchen@https://www.sodocs.net/doc/911644922.html,
(Z.C.).Author Contributions
∥These authors contributed equally to this work.Notes
The
authors declare no competing ?nancial interest.■ACKNOWLEDGMENTS This work was supported in China by the NSFC (Grant Nos.90206048,20771010,10774003,90606023,11274016,and 20731160012),National 973Projects (Nos.2006CB932701,
2007AA03Z311,and 2007CB936200,2013CB932604MOST
of China),Fundamental Research Funds for the Central Universities,National Foundation for Fostering Talents of Basic Science (No.J1030310/No.J1103205),Program for New
Century Excellent Talents in University of MOE of China,and in USA by Department of Defense (Grant W911NF-12-1-0083)
and partially by NSF (Grant EPS-1010094).■REFERENCES (1)For selected recent reviews,see (a)Osada,M.;Sasaki,T.J.Mater.Chem.2009,19,2503?2511.(b)Golberg,D.;Bando,Y.;Huang,Y.;Terao,T.;Mitome,M.;Tang,C.;Zhi,C.ACS Nano 2010,4,2979.(c)Mas-Balleste ,R.;Go m ez-Navarro,C.;G οm ez-Herrero,J.;Zamora,F.Nanoscale 2011,3,20?30.(d)Rao,C.N.R.;Ramakrishna Matte,
H.S.S.;Subrahmanyam,K.S.Acc.Chem.Res.2012,DOI:10.1021/ar300033m.(2)For
example,
(a)Novoselov,K.S.;Jiang,D.;Schedin,F.;Booth,
T.J.;Khotkevich,V.V.;Morozov,S.V.;Geim,A.K.Proc.Natl.Acad.Sci.2005,102,10451.(b)Coleman,J.N.;Lotya,M.;Neil,A.O.;
Bergin,S.D.;King,P.J.;Khan,U.;Young,K.;Gaucher,A.;De,S.;Smith,R.J.;et al.Science 2011,331,568.(c)Lin,Y.;Williams,T.V.;Xu,T.B.;Cao,W.;Elsayed-Ali,H.E.;Connell,J.W.J.
Phys.Chem.C
2011,115,2679.(3)Kam,K.K.;Parkinson,B.A.J.Phys.Chem.1982,86,463.
(4)(a)Gourmelon,E.;Lignier,O.;Hadouda,H.;Couturier,G.;Bernede,J.C.;Tedd,J.;Pouzet,J.;Salardenne,J.Sol.Energy Mater.Sol.Cells
1997,46,115.(b)Ho,W.K.;Yu,J.C.;Lin,J.;Yu,J.G.;Li,P.S.
Langmuir 2004,20,5865.(c)Bernede,J.C.;Pouzet,J.;Gourmelon,E.;Hadouda,H.Synth.Met.1999,99,45.(d)Muratore,C.;Voevodin,A.
A.Surf.Coat.Technol.2006,201,4125.(e)Kim,Y.;Huang,J.L.;Lieber,C.M.Appl.Phys.Lett.1991,59,3404.(5)(a)Splendiani,A.;Sun,L.;Zhang,
Y.B.;
Li,T.S.;Kim,J.;Chim,
C.Y.;Galli,G.;Wang,F.Nano Lett.2010,10,1271.(b)Mak,K.F.;Lee,C.;Hone,J.;Shan,J.;Heinz,T.F.Phys.Rev.Lett.2010,105,
136805.(6)Radisavljevic,B.;Radenovic,A.;Brivio,J.;Giacometti,V.;Kis,A.
Nat.Nanotechnol.2010,6,147.(7)(a)Yu,E.K.;Stewart,D.A.;Tiwari,S.Phys.Rev.B 2008,77,
195406.(b)McCann,E.Phys.Rev.B 2006,74,161403.(c)Min,H.K.;Sahu,B.;Banerjee,S.K.;MacDonald,A.H.Phys.Rev.B 2007,75,
155115.(d)Castro,E.V.;Novoselov,K.S.;Morozov,S.V.;Peres,N. M.R.;Dos Santos,J.M.B.L.;Nilsson,J.;Guinea,F.;Geim,A.K.; Neto,A.H.C.Phys.Rev.Lett.2007,99,216902.(e)Castro,E.V.; Novoselov,K.S.;Morozov,S.V.;Peres,N.M.R.;Dos Santos,J.M.B. L.;Nilsson,J.;Guinea,F.;Geim,A.K.;Neto,A.H.C.J.Phys.: Condens.Matter2010,22,175503.
(8)Yue,Q.;Chang,S.;Kang,J.;Zhang,X.;Shao,Z.;Qin,S.;Li,J.J. Phys.:Condens.Matter2012,24,335501.
(9)Ramasubramaniam,A.;Naveh,D.;Towe,E.Phys.Rev.B2011, 84,205325.
(10)Boker,T.;Severin,R.;Muller,A.;Janowitz,C.;Manzke,R.; Voss,D.;Kruger,P.;Mazur,A.;Pollmann.J.Phys.Rev.B2011,64, 235305.
(11)Delley,B.J.Chem.Phys.1990,92,508.
(12)Meijer,E.J.;Sprik,M.J.Chem.Phys.1996,105,8684.
(13)Perdew,J.P.;Burke,K.;Ernzerhof,M.Phys.Rev.Lett.1996,77, 3865.
(14)Ortmann,F.;Bechstedt,F.;Schmidt,W.G.Phys.Rev.B2006, 73,205101.
(15)Monkhorst,H.J.;Pack,J.D.Phys.Rev.B1976,13,5188.
(16)(a)ATOMISTIX Toolkit and D.Copenhagen,2011;http:// https://www.sodocs.net/doc/911644922.html,.(b)Brandbyge,M.;Mozos,J.L.;Ordejon,P.; Taylor,J.;Stokbro,K.Phys.Rev.B2002,65,165401.(c)Taylor,J.; Guo,H.;Wang,J.Phys.Rev.B2001,63,245407.
(17)Ni,Z.Y.;Liu,Q.H.;Tang,K.C.;Zheng,J.X.;Zhou,J.;Qin,R.; Gao,Z.X.;Yu,D.P.;Lu,J.Nano Lett.2011,12,113.
(18)Ataca,C.;Sahin,H.;Akturk,E.;Ciraci,S.J.Phys.Chem.C2011, 115,3934.
(19)Mathur,H.;Baranger,H.U.Phys.Rev.B2001,64,235325.
(20)(a)Zhang,Y.B.;Tang,T.T.;Girit,C.;Hao,Z.;Martin,M.C.; Zettl,A.;Crommie,M.F.;Shen,Y.R.;Wang,F.Nature2009,459, 820.(b)Tang,K.;Qin,R.;Zhou,J.;Qu,H.;Zheng,J.;Fei,R.;Li,H.; Zheng,Q.;Gao,Z.;Lu,J.J.Phys.Chem.C2011,115,9458. (21)(a)Tang,K.;Ni,Z.;Liu,Q.;Quhe,R.;Zheng,Q.;Zheng,J.; Fei,R.;Gao,Z.;Lu,J.Eur.Phys.J.B2012,85,301.(b)Zheng,F.;Liu, Z.;Wu,J.;Duan,W.;Gu,B.-L.Phys Rev.B2008,78,085423.
(c)Zhang,Z.;Guo,W.Phys.Rev.B2008,77,075403.
(22)Basch,H.;Cohen,R.;Ratner,M.A.Nano Lett.2005,5,1668.