Band gap opening of monolayer and bilayer graphene , phosphorus, and sulfur

Band gap opening of monolayer and bilayer graphene doped with aluminium,silicon,phosphorus,and sulfurPablo A.Denis *Computational Nanotechnology,DETEMA,Facultad de Química,UDELAR,CC 1157,11800Montevideo,UruguayCentro Interdisciplinario en Nanotecnología y Química Física de Materiales,Espacios Intersiciplinarios,UDELAR,Uruguaya r t i c l e i n f o Article history:Received 5March 2010In final form 15April 2010Available online 18April 2010a b s t r a c tThe chemical doping of monolayer and bilayer graphene with aluminium,silicon,phosphorus and sulfur was investigated.Si-doped graphene has the lowest formation energy although it is semimetallic.P-doped graphene has a magnetic moment of 1l B and for 3at.%of doping the band gap is 0.67eV.Al-doped graphene is very unstable but it is an attractive material because it is metallic.To reduce the formation energies of the substitutional defects we investigated the formation of interlayer bonds in bilayer graphene.Phosphorus forms the strongest bonds between layers giving particular stability to this material.P-doped bilayer graphene has a gap of 0.43eV but it is has no magnetic moment.Ó2010Elsevier B.V.All rights reserved.1.IntroductionThe synthesis of single layer graphene by Novoselov et al.[1]opened new avenues for the construction of field effect transistors (FET).However,the lack of a sizable band gap renders the con-struction of graphene based FET very difficult [2].A great amount of effort has been devoted to open a tunable band gap in graphene and different methods have been proposed:chemical functionali-zation [3–7],doping with heteroatoms [8,9],using electric fields [10,11],depositing graphene on substrates like SiO 2[12],SiC [13],or cubic BN (111)[14],and the adsorption of polar molecules like NH 3and H 2O [15].Our group is interested in using the chem-ical doping with heteroatoms approach.In effect,in a recent work we showed that using sulfur atoms it is possible to open a band gap in the band structure of graphene [8].We found that a band gap of 0.30eV could be opened when a sulfur atom replaces a carbon atom in a 5Â5graphene supercell.However,when the number of sulfur atoms was doubled the band gap closed and we obtained the semimetallic band structure of pristine graphene.The analysis of the partial density of states showed that the changes in the elec-tronic structure of graphene were due to the structural modifica-tion induced by the incorporation of the heteroatom.This property was used by Dai et al.[9]to suggest that sulfur doped graphene could be a good sensor for polluting gases,like NO and NO 2.Thus,opening a band gap in graphene by chemical doping is not only interesting to construct FET but also to adjust the sens-ing capabilities of graphene derived materials.For example,Ao et al.[16,17]showed that aluminium doped graphene would bean excellent candidate for sensing CO gas,although Dai et al.[9]showed that this material is too reactive and can bind many more gases.In recent work Kurmaev et al.[18]showed that it is possible to synthesize sulfur doped graphite.This material has very interest-ing properties because it has superconducting behavior below 35K [19].Thus,since sulfur doped graphite exists [18–20],it is rea-sonable to expect that sulfur doped graphene can be produced.However,to the best of our knowledge a single layer of sulfur doped graphene has not been synthesized yet.In our previous work [9]we showed that it may be possible to create the sulfur substitutional defect,although the superconducting properties may be lost because of the importance of the interlayer states formed in this material [18].One approach to synthesize sulfur doped graphene maybe the exfoliation of sulfur doped graphite.In addition to this route,we showed [21]that the adsorption of SH at the vacancy defect sites of graphene can create the sulfur substitutional defect.Considering the aforementioned interesting properties of sulfur doped graphene and the possibility of using doped graphene for sensing gases [9,16,17],we become interested in extending the characterization of graphene doped with second row atoms.Here-in,we investigated the effect of aluminium,phosphorus and silicon doping on the electronic structure of graphene.The results were compared with those obtained for sulfur.In addition,we have ex-tended our characterization of sulfur doped graphene considering different levels of doping.Finally,we investigated possible solu-tions to reduce the formation energies of these doped graphenes.To that end,we considered bilayer graphene.The reason for using two layers is that because second row atoms protrude from the graphene plane,they may be able to form interlayer bonds without significantly altering the stacking interaction.The results showed0009-2614/$-see front matter Ó2010Elsevier B.V.All rights reserved.doi:10.1016/j.cplett.2010.04.038*Address:Computational Nanotechnology,DETEMA,Facultad de Química,UDELAR,CC 1157,11800Montevideo,Uruguay.E-mail address:pablod@.uy Chemical Physics Letters 492(2010)251–257Contents lists available at ScienceDirectChemical Physics Lettersj o ur na l h om e pa ge :w w w.e lse v ie r.c om /lo c at e /c pl ettthat phosphorus is the best choice to open a band gap in graphene and also to create interlayer bonds.In addition,to this,P-doped monolayer graphene showed a permanent magnetic moment.2.MethodsThe methodology applied herein is the same as the one we ap-plied to successfully study sulfur doped graphene [8],thiolated [21]and hydrogenated [22]graphene,thioepoxidated [23]and thi-olated [24,25]SWCNTs,hydrogenated DWCNTs [26],the addition of azomethine ylides to carbon nanostructures [27]and the adsorption of CH 4on SWCNTs [28].Briefly,we performed Density Functional Theory (DFT)calculations employing the PBE [29]and LDA [30]functionals,as implemented in SIESTA [31,32],which per-forms SCF calculations using numerical basis sets.For the latter we have selected the double-zeta basis set with polarization functions and fixed the orbital confining cut-off to 0.01Ry.The split norm used was 0.15.The DFT implementation in SIESTA can be prone to significant basis set superposition error (BSSE),even with rela-tively low degree of radial confinement [21].To avoid this problem,when we evaluated the interlayer interaction energies in bilayer graphene we used the counterpoise correction suggested by Boys and Bernardi [33].In all cases,we used relaxed structures to esti-mate the BSSE corrected binding energies and we took monomer deformation energies into account.The interaction between ionic cores and valence electrons was described by the Troullier–Martins norm conserving pseudopotentials [34].We have checked the con-vergence of the mesh cut-off;using a value of 200Ry we obtained converged binding energies (within 0.02eV).It is important to note that in our previous studies [8,21–28]we performed method-ology calibration against mesh cut-off and orbital confining cut-off values.By doing so,we were able to reproduce the results obtained without the use of pseudopotentials.For monolayer and bilayer graphene we used a Monkhorst–Packard k-point sampling scheme of 30Â30Â6k-points for all of the unit cells employed,which gave converged results in every calculations.Further increasing of the density of k-points did not change the results.Band struc-tures were calculated using 100points along the path C –M–K–C .In all cases we checked that the band gaps obtained from the bandstructure were similar to those obtained from the density of states.Geometry optimizations were pursued using the conjugate gradi-ent algorithm until all residual forces were smaller than 0.01eV/Å.We performed PBE periodic calculations for monolayer graphene using 4Â4,5Â5,6Â6,7Â7and 8Â8unit cells;the total num-ber of atoms is 32,50,72,98and 128,respectively.The lattice parameters along the a and b directions were optimized,although the non-periodic c axis was maintained frozen at 20Å.In the case of bilayer graphene we used an AB stacked 4Â4supercell which is composed by 64atoms and the functional used was LDA because it works better than GGA for stacking interactions.3.Results and discussion 3.1.Doped monolayer grapheneThe energetic cost to create the heteroatom substitutional de-fect was evaluated using the reaction:perfect-graphene þheteroatom !doped-grapheneþcarbon atomThe selection of the atomic forms to evaluate the formation en-ergy can be replaced by the chemical potential obtained using the bulk forms,molecules,etc.However,since we are interested in the relative values and because we used the same form in all cases we are able to conclude if the formation energy is larger or smaller than the one calculated for sulfur.Therefore,considering that sul-fur doped graphene is likely to be synthesized [8,18–21],if the for-mation energy of the heteroatoms is lower than that of sulfur it will be easier to create the defect whereas if it is larger it will be more difficult.In Table 1we present the formation energies calcu-lated for the second row atoms considered.We can appreciate a ra-pid convergence of the formation energy with respect to the size of the supercell.In effect,the largest deviation between the values calculated employing the 4Â4model and the 8Â8one is 0.20eV,observed for aluminium,although it is worth noticing that for the remaining atoms the differences are close to 0.1eV.Thus,the 4Â4model seems to be adequate to estimate formation ener-gies.The energetic cost to introduce silicon or a phosphorus atom is very similar,being in the case of silicon about 0.2eV lower.How-ever,for sulfur the energy required is 1.4eV larger than that of sil-icon.Aluminium is an interesting case because it has the largest formation energy,close to 10eV.This may be the explanation of the unusual reactivity observed by Dai et al.[9]for Al-doped graphene.Therefore,from an energetic standpoint,the chemical doping with silicon or phosphorus is expected to the easier than that of sulfur and the kinetic effects are not expected to be a prob-lem as we explained in our previous works [8,21,25].The structural changes caused by the substitution are signifi-cant,as we can appreciate in Fig.1.In all cases the second rowTable 1Energetic cost to create a heteroatom substitutional defect for graphene,determined at the GGA level (eV).aGraphene model Atomic %of doping Al Si P S 4Â4 3.1310.06 6.997.148.335Â5 2.009.99 6.917.088.306Â6 1.399.98 6.907.128.327Â7 1.029.90 6.877.058.288Â80.789.866.857.058.30aIn all cases we used a 30Â30Â6sampling.Fig.1.Optimized unit cell for 6Â6graphene doped with a single second row atom,aluminium,silicon,phosphorus or sulfur.252P.A.Denis /Chemical Physics Letters 492(2010)251–257atom is too large tofit in the sp2framework and protrudes out of the sheet.As observed for the formation energies the carbon–het-eroatom bond distances determined with the four graphene mod-els selected are very similar,being the differences smaller than 0.005Å.The largest X–C bond distance was observed for alumin-ium1.860Å,and it is followed by phosphorus,1.783Å(8Â8mod-el).The latter value is0.003and0.016Ålarger than those determined for sulfur and phosphorus,respectively.The long Al–C bond distance was expected because Al has the largest formation energy and thus forms the weakest bond with carbon.In all cases, the second row atom protrudes from the sheet and the ripple in-duced by the heteroatom is significant,being up to1.8Å(alumin-ium)above the carbon atoms located in the lowest points.It is worth noticing that the carbon atoms surrounding the heteroatomTable2Band gap determined at the GGA level(eV)for graphene doped with second row atoms.bGraphene model Atomic%of doping Al Si P S4Â4 3.13Metal0.00(0.02)a0.67up/0.66down(0.60up/0.58down)0.57(0.57)5Â5 2.00Metal0.060.53up/0.40down0.45 6Â6 1.39Metal0.080.14up/0.15down0.01 7Â7 1.02Metal0.020.45up/0.18down0.25 8Â80.78Metal0.010.34up/0.27down0.22a Values in parenthesis denote LDA values.b In all cases we used a30Â30Â6sampling.Fig.2.Band structure of4Â4P-doped monolayer graphene(0eV is the Fermi level).P.A.Denis/Chemical Physics Letters492(2010)251–257253are also lifted.The three carbon atoms bonded to the heteroatom are elevated up to 0.7Åwhereas the second nearest carbon atoms are located 0.4Åabove.This structural modification should have profound implications for the reactivity of graphene because the deviation of the perfect sp 2hybridization makes these atoms more reactive.Therefore,doping with heteroatoms could not only open a band gap,but also is expected to increase the reactivity of graphene [9].The band gaps determined for doped graphene are presented in Table 2and the band structures in Figs.2–5.The largest band gap is observed for phosphorus.In the case of the 4Â4supercell,which corresponds to 3at.%of doping,the spin up gap is 0.67eV,and the spin down gap has a nearly identical value.When the level of dop-ing is decreased to 1atom per 50(5Â5)the band gaps are slightly changed,0.53eV for the spin up channel and 0.40eV for the spin down.Interestingly,for the 6Â6model the band gaps are signifi-cantly reduced to 0.14and 0.15eV for spin up and down channels,respectively.The reduction of the band gap for the 6Â6model is not only observed for phosphorus,but also for sulfur and silicon.When the level of doping is further decreased the band gap is in-creased again.For the P-doped 7Â7and 8Â8models the band gaps are 0.45(up)/0.18(down)and 0.34(up)/(0.27)down eV,respectively.Therefore,employing P atoms it is possible to tune the band gap of graphene from 0.67to 0.14eV just varying the amount of P introduced.Another interesting property of this mate-rial is that it has a permanent magnetic moment of 1l B ,so it is possible to have the semiconducting and magnetic properties in one material,something quite unusual.We have investigated the effect on increasing the P concentration on the magnetic properties by considering 2P atoms on a 6Â6model.The cases considered were:(a)2P atoms belong into different sublattices,(b)2P atoms belonging to the same sublattice.When the atoms belong to the same sublattice (case b)there is a tendency to maintain the mag-netic moment.However,when they belong to different lattice the magnetic moment tends to be quenched.There is only one case in which the X-doped graphene is metal-lic,aluminium,although,as said before,it is very difficult to syn-thesize this material due to the high energetic cost.TheinclusionFig.3.Band structure of 4Â4Si-doped monolayer graphene (0eV is the Fermilevel).Fig.4.Band structure of 4Â4S-doped monolayer graphene (0eV is the Fermi level).254P.A.Denis /Chemical Physics Letters 492(2010)251–257of the Al atom shifts downwards the Fermi level by 0.8eV and thus the p band now crosses the Fermi level,lifting the degeneration at the K point.As the level of Al-doping is decreased the shift of the Fermi level towards lower energies is smaller,although the mate-rial remains metallic for the 8Â8unit cell.For the latter cell the shift of the Fermi level is 0.2eV smaller.The results obtained for sulfur are in agreement with our previous work,in which we sug-gested that using sulfur it is possible to open and close a band gap in graphene.Indeed,for the 4Â4,5Â5,7Â7and 8Â8models,the material has a sizable band gap and it is larger than the thermal energy at 298K,which is 0.025eV.However,in all cases the band gaps are smaller than those observed for P.Silicon is the least effec-tive second row atom to open a band gap in graphene,inducing very few changes on its band structure,probably because it has the same number of valence electrons,and thus the occupation of the bands may not be changed.In the case of the 4Â4model the system is semimetallic,the p *band slightly crosses the Fermi level,and for the other models the system is metallic with a pseudogap of 0.01–0.08eV.3.2.Doped bilayer grapheneDoped monolayer graphene showed interesting properties such us magnetism and semicontuctivity.However,the large formation energies may be an obstacle for synthesizing this material.For this reason,we searched for different alternatives to lower the ener-getic cost necessary to introduce a heteroatom.Considering that the heteroatom protrudes from the sheet it may be possible to form interlayer bonds between heteroatoms located in different sheets of bilayer graphene.In the case of sulfur we were not able to locate a structure with an S–S linkage.However,for aluminium,silicon,phosphorus we succeed.In Fig.6we present the optimized unit cells.The P–P bond distance is 2.230Åwhereas for Si and Al they are 2.360and 2.528Å,respectively.The BSSE corrected inter-layer binding energies between both sheets are 1.72,0.99and 1.53eV,for P,Al and Si,respectively.These values can be compared with the stacking interaction determined for bilayer graphene at the LDA level of theory,namely,0.64eV.Thus,the interaction be-tween both sheets has two components,the stacking interaction and the weak covalent bond between the heteroatoms.The substi-tution with the heteroatoms displaces the graphene layers from the optimal stacking distance.Indeed,for pristine bilayer graphene the stacking distance that we determined is 3.1Åand in the case of P,Al and Si-doped bilayer graphene it is about 0.3–0.4Ålonger.Thus,the stacking interaction must be smaller than for pristine graphene and the formation of the X–X bond X =P,Al,Si must compensate the reduction of the stacking interaction.Keeping the latter information in mind,the true X–X binding energies must be larger than those obtained by subtracting the stacking interac-tion determined for pristine bilayer graphene.By doing so we ob-tain the following lower limits for the covalent part of the interaction,1.08,0.35and 0.89eV,for P,Al and Si,respectively.Fig.5.Band structure of 4Â4Al-doped monolayer graphene (0eV is the Fermilevel).Fig.6.Optimized unit cell for 4Â4bilayer graphene doped with aluminium,silicon or phosphorus atom.P.A.Denis /Chemical Physics Letters 492(2010)251–257255The latter binding energies are very weak for a covalent bond but they serve to our purpose of reducing the formation energy of bi-layer doped graphene.For comparative purposes we performed PBE calculations for P-doped bilayer graphene.At the latter level of theory the interlayer binding energy is 0.8eV and it can be solely attributed to the covalent bond because the interaction between two sheets is repulsive at the PBE level.The binding energy of 0.8eV is close to the aforementioned lower limit for the P–P bond energy.The discrepancy is due to the overestimation of the binding energies by LDA and to the repulsive interaction at the PBE level.Therefore LDA and GGA confirm that it is possible to create inter-layer P–P,Al–Al and Si–Si bonds.Phosphorus doped bilayered graphene has a band gap equal to 0.43eV at the LDA level (0.37eV PBE)for both spin channels as it can be observed on Fig.7,although the magnetic moment is quenched by the bond formed.Therefore,P-doped bilayer graph-ene could have an important role in graphene derived electronic materials because the formation of the P–P link lowers the forma-tion energies and increases the stability of the material.In the case of Al-doped bilayer graphene we found that the system is metallicas observed for the monolayered material whereas Si-doped bi-layer graphene is semimetallic.Finally,we would like to note that the band gaps of these materials are expected to be larger than those calculated at the LDA and GGA level because the latter meth-ods systematically underestimate band gaps.However,this issue is not a problem for us because we are interested in opening large band gaps for graphene.4.ConclusionsWe have employed first principle periodic calculations to study the doping of monolayer and bilayer graphene with aluminium,sil-icon,phosphorus and sulfur.The following are considered to be the most important findings of this work:1.Phosphorus is the second row atom that can open the largest band gap in graphene and it is possible to tune the band gap of graphene from 0.66to 0.1eV just varying the amount of P intro-duced.The material showed a magnetic moment depending on the location of the P atoms.In the case of 2P atomsintroducedFig.7.Band Structure determined for P-doped bilayer graphene.The model used is that presented in Fig.6(0eV is the Fermi level).256P.A.Denis /Chemical Physics Letters 492(2010)251–257in a6Â6supercell,if they belong to different sublattice the mag-netic moment tend to be quenched.However,there is a strong tendency to be maintained if they belong to the same sublattice.2.Silicon has the lowest formation energy.However it is not effec-tive enough for opening a band gap in the band structure of graphene.3.The formation energy of the P substitutional defect is smallerthan that of sulfur.Since sulfur doped graphene is likely to be synthesized,based in experimental[18–20]and theoretical evi-dence[21],and also considering that P-doped nanotubes[35] and P-carbide thinfilms[36]were prepared,we can expect that P-doped graphene can be produced without major problems.4.Aluminium has the largest formation energy and the longest X–C bond distance.Thus,that maybe the explanation for the hugereactivity observed for that material[9].It is not expected to be easy to synthesize,although it is very attractive because it is a metallic system.5.The formation of interlayer Al–Al,P–P and Si–Si bonds betweendifferent layers strongly lowers the formation energy of these materials and making easier the synthesis of P and Si-doped bilayer graphene.For sulfur we were unable to optimize a struc-ture with an interlayer bond.In the case of P the magnetic moment is quenched by the weak covalent bond formed.The material has a band gap of0.43,making it very attractive to designfield effect transistors.AcknowledgmentsThe author thanks to the PEDECIBA-Quimica,ANII and CSIC Uruguayan institutions forfinancial 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