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Cite this:Phys.Chem.Chem.Phys.,

2014, 16, 22861

Tunable electronic properties induced by adefect-substrate in graphene/BC3 heterobilayers

Sheng-shi Li, Chang-wen Zhang,* Wei-xiao Ji, Feng Li and Pei-ji Wang

We perform first-principles calculations to study the geometric, energetics and electronic properties of

graphene supported on BC3 monolayer. The results show that overall graphene interacts weakly with

BC3 monolayer via van der Waals interaction. The energy gap of graphene can be up to B0.162 eV in

graphene/BC3 heterobilayers (G/BC3 HBLs), which is large enough for the gap opening at room

temperature. We also find that the interlayer spacing and in-plane strain can tune the band gap of

G/BC3 HBLs effectively. Interestingly, the characteristics of a Dirac cone with a nearly linear band

dispersion relationship of graphene can be preserved, accompanied by a small electron effective mass,

and thus the higher carrier mobility is still expected. These findings provide a possible way to design

effective FETs out of graphene on a BC3 substrate.

I. Introduction

Graphene, due to its intriguing electronic properties as well asits high carrier mobility, has attracted enormous attentionsince its experimental realization in 2004.1,2 Unfortunately,the zero-gap property of graphene makes it very difficult toapply in electronic devices such as high-performance fieldeffect transistors (FETs) operating at room temperature. Con-siderable attempts have been made to open the band gap,3–8

among which the bilayer nanostructures are of particularinterest, including SiO2,9,10 SiC,11,12 MoSe2,13 WS2,14 and BN15

substrates. Despite these achievements, the search for idealsubstrates is still underway.

Recently, BC3, a two-dimensional (2D) defect-like graphene,has been realized in an epitaxial way on the NbB2 (0001)surface.16 The 2D BC3 is a semiconductor with an intermediateband-gap of 0.5–0.66 eV predicted within local density approxi-mation (LDA) using different basis sets.17 Chen et al.18 furtherinvestigated the Fermi surface nesting-derived magnetic phasesin BC3, suggesting BC3 as an experimentally feasible nano-system for exploring the nesting-driven quantum phases.

In the present work, we design new 2D G/BC3 HBLscomposed of graphene and BC3 monolayer, due to their similarcrystal geometries. It is revealed that overall graphene interactsweakly with BC3 monolayer via van der Waals interaction. Thus,the intrinsic properties of graphene, especially, high carriermobility, can be preserved in G/BC3 HBLs. We also find that thesizeable band gap would be induced by interlayer interactions,and all band gaps can be tuned effectively by changing the

interlayer spacing and in-plane strain. Our work is expected toprovide an effective way to tune the electronic properties oflayered graphene-related nanoelectronic devices.

II. Computational details

All the calculations were performed by means of first-principlescalculations as implemented in the Vienna Ab Initio SimulationPackage (VASP).19–21 Generalized gradient approximation (GGA)using the Perdew–Burke–Ernzerhof (PBE)22,23 exchange correlationfunctional was adopted to describe the exchange–correlationinteraction, which is developed for the calculations of surfacesystems. To properly take into account the van der Waals (vdW)interactions in the structures, the DFT-D2 method24 was usedthroughout all the calculations. The projector augmented wavemethod25 was used to describe the electron–ion interaction.The dipole corrections were also included considering thepossible charge redistribution in the HBLs. The plane-wavecutoff energy was set to 400 eV, and a supercell with the 20 Åvacuum layer was used to simulate the isolated sheet. TheMonkhorst–Pack (MP)26 scheme was used to sample the Brillouinzone, which adopted the 11 � 11 � 1 and 27 � 27 � 1 k-mesh forthe relaxation and static calculations, respectively. All the latticeconstants and atom coordinates were optimized until the conver-gence of the force on each atom is less than 0.01 eV Å�1.

III. Results and discussion

In order to explore the interaction between graphene and theBC3 substrate, we consider three representational stackingpatterns as shown in the insets of Fig. 1(a)–(c). P-I exhibits

School of Physics and Technology, University of Jinan, Jinan, Shandong, 250022,

People’s Republic of China. E-mail: zhchwsd@163.com

Received 22nd July 2014,Accepted 29th August 2014

DOI: 10.1039/c4cp03248a

www.rsc.org/pccp

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hexagonal stacking arrangement (AA) with all C atoms ingraphene right above C and B atoms in the BC3 substrate;P-II has the Bernal stacking (AB) features, with the C atoms ofgraphene right above the C–B or C–C hexagonal center withinBC3 monolayer, while P-III can be achieved by translating

graphene a distance offfiffiffi3p �

6a, where a is the lattice constantof graphene, with respect to BC3 along C–B bond orientationfrom pattern AA. After structural relaxations, we find thatgraphene retains its original planar and hexagonal atomicnetwork, while the lattice constant of G/BC3 HBLs increasesfrom 2.44 to 2.565 Å, irrespective of the stacking types. Toevaluate the structural stability of the three stacking patterns,the binding energies are calculated as

Eb = E(G/BC3) � E(G) � E(BC3) (1)

where E(G/BC3), E(G) and E(BC3) are energies of G/BC3 HBLs,isolated graphene and BC3 monolayer, respectively. The evolu-tion of the binding energy (Eb) per C atom as a function of theinterlayer spacing is plotted in Fig. 1. We find that patterns I–IIIexhibit a similar equilibrium interlayer spacing of about 3.3 Å,as shown in the side view of P-II [see the inset in Fig. 1(d)]. Thestability of the HBLs follows the order of P-II 4 P-I 4 P-III,suggesting that the stacking pattern P-II is the most stable one.Furthermore, the lower Eb of�0.099 eV also indicates that thereis a weak van der Waals interaction between graphene and BC3

monolayer.Notice that the graphene retains its planar structure and the

interlayer distance is much larger than the sum of covalentradii of C and B atoms, which means that the C atoms ofgraphene and C or B atoms of BC3 are beyond the bondingrange. To explore whether the electronic structures of graphenecan be affected by the BC3 substrate, taking the energeticallyfavorable P-II as an example, we examine the projected bandstructures of the G/BC3 HBLs, which show that the contribu-tions from graphene and the BC3 substrate are separated, asshown in Fig. 2(a). For comparison, we also present the bandstructure of free-standing graphene (FSG) and BC3 monolayerin Fig. 2(b) and (c). It can be seen that a metal–semiconductortransition occurs in graphene due to the effect of the BC3

substrate. The valence band maximum (VBM) and the conduc-tion band minimum (CBM) in G/BC3 HBLs have the typicalp and p* characters, similar to the FSG one. According to thep-electron tight-binding (TB) model of bipartite lattices, the banddispersion relationship near the Fermi level can be expressed as

EðkÞj j ¼ �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 þ �hnFkð Þ2

q(2)

Here, k is the wave vector relative to the K point, vF is theFermi velocity, and D is the onsite energy difference betweentwo sublattices. For FSG, the onsite energies of A and B

Fig. 1 The variation in the binding energy for the three configurations as afunction of interlayer spacing. Top views of the relaxed atomic structuresof three stacking patterns of G/BC3: (a) P-I, (b) P-II, and (c) P-III. The sideview of the relaxed atomic structure of P-II (d).

Fig. 2 (a) The band structure of P-II: the cyan, green and red represent the component of graphene, B and C atoms in the BC3 substrate, respectively.(b) The band structure of FSG, and (c) the band structure of isolated BC3.

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sublattices are identical (D = 0), and thus results in the Dirac-like linear dispersion relationship E(k) = ��hnF|k|. The positiveand negative solutions, which correspond to conduction andvalence bands, respectively, meet at k = 0, implying the absenceof a band gap. As shown in Fig. 2(a), when graphene isdeposited on the BC3 substrate, the symmetry of two C sub-lattices within graphene is broken, which induces a small gapof 0.162 eV at the K point, which is large enough for the gapopening at room temperature. Fig. 3 further shows the total andpartial densities of states (DOSs) for graphene and BC3 mono-layer. It can be seen that the C-2p orbital within graphenedominates the states near the Fermi level, and there is a gapwithin the range of [�0.08, 0.082] eV [Fig. 3(a) and (b)].Furthermore, the bands that originated from the C-2p orbitalare quite analogous to the FSG one, except for the downshift oftop valence bands at the K point. Similarly, for the bandscontributed by BC3 monolayer, while VBM at the K point movedup towards the Fermi level, the CBM from the B-2p orbital isdown-shifted. Thus, the gap of BC3 monolayer decreases fromthe pristine value of 0.56 eV to 0.45 eV [Fig. 3(c) and (d)].Overall, around the Fermi level, the band structures of G/BC3

HBL have the characteristic graphene feature of linear dis-persions, i.e., the merits of the Dirac system, such as the highFermi velocity and large carrier mobility, may be well retainedin the G/BC3 HBLs.

As mentioned above, the band gap is attributed to the onsiteenergy difference of C sublattices. To gain more insights into thisphenomenon, it is worthwhile to investigate the charge densitydifference (CDD) induced by the BC3 substrate, expressed as

Dr = r(G/BC3) � r(G) � r(BC3), (3)

where r(G/BC3), r(G), and r(BC3) are the total charge densitiesof the G/BC3 hybrid structure, isolated graphene, and BC3

monolayer, respectively. All stacking patterns exhibit a verysimilar CDD feature, thus we only present the P-II configuration.

As shown in the inset in Fig. 4, there is no charge accumulation inthe interspace between BC3 and graphene. However, in the gra-phene layer, there is evident charge redistribution by formingelectron-rich and hole-rich regions due to the different electrostaticpotentials induced by BC3 layer, which has also been found in theG/BN HBLs.14 According to the Bader charge analysis, the redis-tribution makes little charge (B0.12e) transfer from graphene to theBC3 substrate. However, the traces of charge transfer cannot dropthe Fermi level which still lies in the band gap as shown in Fig. 2(a).It induces an intrinsic electric field, which points from the BC3 layertowards graphene, and thus a sizable band gap opens at the Diracpoint. In addition, we also calculate the plane-integrated electrondensity difference to visualize the electron redistribution upon theformation of the interface in Fig. 4. The electron rearrangementlocalized at the interspace is visually revealed in the inset of Fig. 4.

Fig. 3 The calculated total and partial DOS for P-II of G/BC3 HBLs.

Fig. 4 Plane-integrated electron density difference of P-II. The insetshows the 3D isosurface of the charge density difference, the yellow andcyan areas represent electron accumulation and depletion, respectively.

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The trend of change in the band gap of P-II is furtherinvestigated by varying the interlayer distance between grapheneand BC3 monolayer, as shown in Fig. 5. When the distancedecreases, the charge begins to accumulate in the interspace ofgraphene and BC3 monolayer. Compared with the equilibriumstate, more charge transfers from graphene to the BC3 substrate.It means that there exists very strong hybridization betweengraphene and BC3 monolayer. Therefore, the onsite energydifference of graphene increases and thus results in a largerband gap opening. With the distance increasing, the interactionbetween graphene and BC3 becomes weak. In this case, thevan der Waals interaction will gain the main role in the system.The variation range is 145–84% of distance-free gap from 2.4 Å to3.4 Å. Similar results are also found for other configurations.By examining the Dirac point position near the Fermi level,however, unexpected semiconductor–metal transition is observedwhen the interlayer spacing is smaller than 2.5 Å or larger than3.4 Å [see the inset of Fig. 5]. Beyond the range of [2.5, 3.4] Å,although the gap is still opened at the K point, an interlayer-induced self-doping occurs due to the movement of bands at the Kpoint, which significantly reduces the gap for the whole bandstructure and renders graphene n or p-type metallic behaviors.

To further visualize the above theoretical model, we describethe CDD with different interlayer spacing as shown in Fig. 6.Owing to similar CDD features exhibited in all patterns, we justplot the P-II configuration as an example. As per the aboveanalysis, with the decrease of the interlayer spacing, the chargeaccumulation begins to occur between graphene and the BC3

substrate, also the G/BC3 HBL is still a semiconductor with aband gap of 0.294 eV when the spacing is 2.6 Å. However, forthe case of d = 2.5 Å [Fig. 6(a)], it can be observed that a strongorbital hybridization exists in the interspace of HBL, with alarge charge transfer from graphene to the substrate. Then itforms hole-rich regions, which can improve the Fermi level ofgraphene, leading to a metal state. When the distance isbetween 2.6 Å and 3.5 Å, all the CDD features are similar tothe case of the equilibrium state [Fig. 6(b)]. For d = 3.6 Å, it can

be obviously seen that no charge transfer and accumulationoccurs between graphene and BC3 layer. However, the largerdistance does not annihilate the effect of BC3 monolayer andthe defect-substrate induces a larger dipole moment in C atomswhich are located above the B atoms. This may be the mainreason for forming the phenomenon of electron-rich regions inG/BC3 HBLs. Hence, these results indicate that the bandstructure of graphene is sensitive to the interlayer spacingbetween graphene and BC3 monolayer, providing an intuitivetheory model. However, tuning the interlayer spacing of bilayerstructures in experiments is still an awkward question with agreat challenge. So we will introduce one suggestion for achievingthe distance variation. Experimentally, the interlayer spacing ofbilayer structures is usually modulated by inserting small organicmolecules (such as NH4

+) into them, which is considered in thestripping of boron nitride and bilayer graphene. So, we expectthat this way can be used to tune the interlayer spacing ofG/BC3 HBLs.

The band gap of G/BC3 HBLs can also be further tuned bythe strain which can be easily achieved in experiments, asshown in Fig. 7. The homogeneous in-plane strains are appliedto the HBLs by changing the lattices as e = (a � a0)/a0, where a(a0) is the lattice constant under the strain (equilibrium)conditions. Under the tensile strains, the graphene in G/BC3

HBLs preserves the planar plane clearly with the longer C–Cbond length in the horizontal direction, also the variations ofthe band gap for all HBLs exhibit the same trend. As ismentioned above, the C-2p orbitals in graphene dominate thestate around the Fermi level. When starting to implement atensile strain with e = 1%, the band gap will decrease due to thestretched C–C bonds, which will weaken the p state between theC atoms, leading to the energy shifting and the charge redis-tribution decrease. However, the continuous increase of tensilestrain and C–C bond lengths will enhance the localization ofthe electronic state on C atoms in graphene, resulting in theincrease of the band gap. Furthermore, we also investigate theband gap change in the case of compressive strains. Whenthe compressive strains are small enough, graphene in allG/BC3 HBLs can still maintain its planar structure. Neverthe-less, it will obtain corrugation (B0.6 Å) when the compressivestrains increase to 4%, and the BC3 substrate also gainsbuckling (B0.3 Å). For the variation of the band gap, compli-cated trends can be observed which are sensitive to the stackingpatterns. It does not increase monotonically as found in G/BNor G/WS2 HBLs. In the range of [�1%, �3%], the band gappresents a descending trend due to the average of the electronicstates between neighboring C atoms, which will result in thedecrease of the onsite energy difference. On the other hand, thefollowing change in the band gap will be complex, which ismainly attributed to the structural distortion of graphene andthe substrate induced by compressive strains. To reduce thedeformation of graphene and the substrate, experimentally, thebiaxial strain can be achieved by depositing G/BC3 HBLs on anelastic substrate. In addition, in the process of tuning the bandgap by strain, the phenomenon of self-doping can still beobserved in Fig. 7. So this suggests that the strain plays an

Fig. 5 The variation of band gap as a function of interlayer spacing for P-II.(a) and (b) are the band structures of P-II at different spacing. The blacksquare and red ring represent the band gap of the K point and entirety.

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important role in tuning the band gap of graphene, which canprovide a viable route for the design of graphene-based func-tional nanostructures.

To realize the practical applications of G/BC3 HBLs in FETs,higher carrier mobility and linear band dispersion are veryessential. So we investigate the electron effective mass (me*)and the hole effective mass (mh*) at the Dirac point of G/BC3

HBLs. As we have mentioned before, the G/BC3 HBLs preservethe linear band dispersion relationship of graphene. Accordingto the graphene dispersion relationship, the me* and mh* canbe expressed as27–31

m� � p

vg� �hk

vF(4)

where k is the wave vector and vF is the Fermi velocity. Table 1presents the calculated fitting value of vF for all G/BC3 HBLs.Fortunately, it can be seen that all the stacking patterns attaina considerable vF value (B0.76 � 106 m s�1), which is

Fig. 6 Charge density difference for the P-II stacking pattern at the interlayer spacing of d = 2.5, 3.3, 3.5 Å, respectively.

Fig. 7 The variation of band gap as a function of strain for all stacking patterns,where positive(negative) values of strain represent tensile(compressive) strains.The red points represent the gap in the K point with self-doping. The insetshows the schematic diagram.

Table 1 The calculated binding energy per C atom (Eb), lattice constants (a0), interlayer distance (d0), energy band gap (Eg), effective masses of electronsand holes, and the maximum Fermi velocity (vF) for all stacking patterns

Pattern Eb (eV) a0 (Å) d0 (Å) Eg (eV) Effective mass G–K K–M VF (m s�1)

P-I �0.095 2.565 3.24 0.141 me* 6.75 � 10�19 6.14 � 10�19 0.77 � 106

mh* 6.85 � 10�19 6.3 � 10�19

P-II �0.099 2.565 3.29 0.162 me* 7.26 � 10�19 6.47 � 10�19 0.73 � 106

mh* 7.38 � 10�19 6.85 � 10�19

P-III �0.097 2.565 3.34 0.109 me* 6.47 � 10�19 6.22 � 10�19 0.76 � 106

mh* 6.65 � 10�19 6.56 � 10�19

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comparable to that of FSG (1 � 106 m s�1). Moreover, accordingto eqn (4), we also investigate the calculated me* and mh* alongG–K and K–M directions of all the stacking patterns, as shownin Table 1. It can be observed that the me* and mh* at theVBM and CBM of the G/BC3 HBLs are very small, which isstill more superior to other graphene-based nanoelectronics.This indicates that the G/BC3 HBLs may have a higher carriermobility which is necessary in the application of FETs. Thelarge value of vF and the small value of m* are indispensable forthe design of applications and this can be analyzed qualitativelyby the interaction between graphene and the BC3 substrate. Thesmall binding energies indicate the weakening of electroniccoupling between graphene and BC3 and enable the grapheneto preserve linear band dispersion similar to that of FSG,suggesting that the vF in this case may be comparable to thatof graphene. As a result, an ideal FET with the high carriermobility and a certain band gap on G/BC3 HBL based nano-electronics can be expected to be achieved.

IV. Conclusion

A comprehensive first principles study is performed on thestructural and electronic properties of G/BC3 HBLs. Threepossible stacking patterns have been considered. The calcu-lated band gaps of different stacking patterns are considerablylarger than kBT (26 meV) at room temperature; this may overcomeone of the main obstacles to apply graphene as an electronicdevice, namely, the lack of intrinsic band gaps. We also find thatthe interlayer spacing and in-plane strain can tune the band gapof G/BC3 HBLs effectively. Interestingly, the characteristics of aDirac cone with a nearly linear band dispersion relationship ofgraphene can be preserved, accompanied by a small electroneffective mass, and thus the carrier mobility is expected not todegrade much. These findings may stimulate the experimentaldevelopments in the graphene/BC3 HBLs with small energy gapsand enable their use in novel integrated functional nanodevices.

Acknowledgements

This work was supported by National Natural Science Founda-tion of China (Grant no. 11274143, 60471042 and 11304121).

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