Electronic structures and edge effects of Ga2S2 nanoribbons

0.45 MB·

by  Bao-Ji Wang

Electronic structures and edgeeffects ofGa S nanoribbons
2 2
Bao-Ji Wang,1 Xiao-Hua Li,1 Li-Wei Zhang,1 Guo-DongWang,2 and San-HuangKe3,4,∗
1SchoolofPhysicsandChemistry,HenanPolytechnicUniversity,2001ShijiRoad,Jiaozuo454000, P.R.China
2SchoolofElectricalEngineering Automation,HenanPolytechnicUniversity,2001ShijiRoad,Jiaozuo454000,P.R.China
3MOEKeyLabortoray ofMicrostructured Materials, School ofPhysicsScience andEngineering,
Tonji University, 1239 Siping Road, Shanghai 200092, P. R. China
4BeijingComputational ScienceResearchCenter,10DongbeiwangWestRoad,Beijing100094, P.R.China
6 Abinitiodensityfunctionaltheorycalculationsarecarriedouttopredicttheelectronicpropertiesandrelative
1 stabilityof galliumsulfidenanoribbons (Ga2S2-NRs)witheitherzigzag- or armchair-terminatededges. It is
0 found that the electronic properties of the nanoribbons are very sensitive to the edge structure. The zigzag
2 nanoribbons(Ga2S2-ZNRs)aremetallicwithspin-polarizededgestatesregardlessoftheH-passivation,whereas
thebarearmchairones(Ga2S2-ANRs)aresemiconductingwithanindirectbandgap. Thisbandgapexhibits
n
anoscillationbehaviorasthewidthincreasesandfinallyconvergestoaconstantvalue.Similarbehaviorisalso
a
J foundinH-saturatedGa2S2-ANRs,althoughthebandgapconvergestoalargervalue. Therelativestabilities
ofthebareANRsandZNRsareinvestigatedbycalculatingtheirbindingenergies. Itisfoundthatforasimilar
7
widththeANRsaremorestablethantheZNRs,andbotharemorestablethansomeGa2S2 nanocluterswith
stableconfigurations.
]
l
l
a PACSnumbers:
h
-
s INTRODUCTION bulk form, GaS usually crystallizes into a layered structure,
e
m S-Ga-Ga-S(Ga2S2),inwhicheachlayerconsistsoftwoAA-
stacked hexagonal sublayers of Ga atoms sandwiched be-
. Low-dimensionalmaterials,especiallyone-dimensional(1-
t tweentwohexagonalsublayersofSatoms. Theselayersare
a D) nanoribbons,have attracted significant attentionfrom the
m boundinathree-dimensional(3-D)structurebythenonbond-
scientificcommunityduringthepasttwodecadesduetotheir
inginteractionthroughtheSatomsalongtheverticalaxis[11].
- interestingelectronicpropertiesassociatedwith theirlow di-
d Recently, the micromechanicalcleavage technique (as origi-
n mensionality and the resulting quantum confinement effect. nallyusedinpeelingoffgraphenefromgraphite)wassuccess-
o In the past few years, graphene nanoribbons (GNRs) – thin
fullyusedtofabricatesingle-layersheetsofGa2S2[12,13].A
c strips of graphene – have been extensively studied because
theoreticalcalculationbasedonthedensityfunctionaltheory
[
of their rich and exotic physical properties which depends (DFT)hasshowedthattheGa2S2 sheetisdynamicallystable
1 ontheirsizeandedgetermination[1,2]. First-principlescal-
andisaindirect-band-gapsemiconductorwithanunusualin-
v culations have revealed that GNRs with hydrogen saturated
vertedsombrerodispersionofholesnearthetopofthevalence
7
armchair-or zigzag-shapededges always have a nonzerodi-
3 band[14]. AsfortheelectronicpropertiesofGa2S2 nanorib-
rectbandgapwhichdecreasesastheribbonwidthincreases.
4 bons(Ga2S2-NRs)whichareimportantinrealisticdeviceap-
1 ThebandgapvariationforarmchairGNRs(AGNRs)exhibits plications, very few reports are available in the literature, to
0 distinct”familybehaviors”[3].ThebandgapsofAGNRsarise
thebestofourknowledge.
. frombothquantumconfinementandthe crucialeffectof the
1 The purpose of this work is to investigate the electronic
0 edges,whileforzigzagGNRs(ZGNRs),gapsappearbecause
structuresof Ga2S2-NRs by performingfirst-principlesDFT
6 ofastaggeredsublatticepotentialonthehexagonallatticedue
calculations. The effects of different ribbon widths and dif-
1 to edge magnetization[1, 3–5]. Besides GNRs, some other
ferentedge structures are studied. Also studied are the rela-
:
v layer-structured nanoribbons, such as boron nitride nanorib-
tive stabilities of these nanoribbons. In the next section, we
Xi bons(BNNRs) andMoS2 nanoribbons,havealso beenstud- describeour computationalmethod. Section III presentsour
iedintensively[6]. Itisfoundthatthebandgapofhydrogen-
r calculated results, and the last section is devoted to conclu-
a terminatedzigzagBNNRsisindirectanddecreasesmonoton- sions.
icallywiththeincreasingribbonwidth. Whereas,directband
gaposcillationisobservedforarmchairBNNRs[7,8],which
tendstoconvergetoaconstantvaluewhentheribboniswider
STRUCTUREANDCOMPUTATION
than3nm.Incontrast,zigzagedgedMoS2nanoribbonsshow
a metallic behavior irrespective of the ribbon width, while
The models of Ga2S2-NRs are constructed by cutting out
armchair edged ones are semiconducting and the band gaps
a stripe of Ga2S2 sheet with the desired edges and widths.
convergetoaconstantvalueastheribbonwidthincreases[9].
AdoptingasimilarnotationusedtodescribeGNRs[1,2,15],
As a wide indirect-band-gapsemiconductor with uniform weusethenumberofzigzaglines(Nz)ordimerlines(Na)to
layered structure, gallium sulfide (GaS) [10] has been used presentthe width of a zigzag-edgedribbon(Ga2S2-ZNR) or
inphotoelectricdevices,electricalsensors,andnonlinearop- aarmchair-edgedribbon(Ga2S2-ANR)anddenotetheribbon
tical applications and gained renewed interest [11]. In its byNz-Ga2S2-ZNR(asillustratedinFig.1(a))orNa-Ga2S2-
2
ANR(asillustratedintheFig.1(b)). tween Ga and S atoms varies depending on their position in
Calculations of structure optimization and band structure the ribbon. For the 6-Ga2S2-ZNR, the Ga-S bond lengths
are carried out by using a first-principles pseudopotential are2.36A˚ and2.37A˚ atinnersites,and2.41A˚ and2.24A˚ at
planewavemethodbasedonDFT,asimplementedintheVi- theGa-terminatedandS-terminatededges,respectively. The
enna ab initio simulation package (VASP)[16]. The projec- bond angles of Ga-Ga-S and S-Ga-S at the inner sites are
tor augmented wave method (PAW)[17] is used to describe 117.43◦and100.24◦,respectively.Becauseoftheedgerelax-
the ion-electroninteraction. The electron exchangeand cor- ation,thetwoangleschangeto105.60◦attheGa-terminated
relation are treated by the generalized gradient approxima- edge and 108.48◦ at the S-terminated edge. In the case of
tion (GGA)[18] in the version of Perdew-Burke-Ernzerhof the 11-Ga2S2-ANR, the edge S atoms tend to shift outward
(PBE)[19]. A kinetic energycutoffof 600eV is adoptedfor slightly.TheGa-Sbondlengthsare2.36A˚,2.37A˚ and2.41A˚
the plane-waveexpansionofthe wave function. The 4s24p2 at the inner sites and 2.21A˚ at the two edges. The Ga-Ga
electronsof Ga, and 3s23p4 electronsof Sare treated asva- bondlengthsare2.48A˚,2.47A˚ and2.50A˚ attheinnersites
lenceelectrons. Periodicboundaryconditions(PBC)areem- and2.48A˚ atthetwoedges.ThebondanglesofGa-Ga-Sand
ployedfor the infinitely longnanoribbonsystems and a vac- S-Ga-S are 117.50◦ and 100.36◦, respectively, at the inner
uumspaceof10A˚ ineachdirectionperpendiculartotherib-
bonis used to eliminatethe interactionbetweenthe periodic
images. The atomic structures of the systems, including the
lattice parameters and atomic positions, are fully relaxed by
theconjugategradientmethoduntiltheresidualforcesacting
oneachatomarelessthan0.001eV/A˚ .Forthestructureop-
timization a Monkhorst-Packs k-mesh of 1×1×12 is used
fortheBrillouinzone(BZ)sampling.Thebandstructuresare
presentedby45k-pointsalongtheX-axisintheBZ.
RESULTSANDDISCUSSION
We first optimize the atomic structure of an periodic 2-D
Ga2S2 sheet,inwhichGa-SandGa-Gaatomsarelinkedco-
valentlyinthequadruplelayer.Theoptimizedbondlengthsof
Ga-SandGa-Gaare2.37A˚ and2.47A˚,respectively.TheGa-
S-Ga(orS-Ga-S)andGa-Ga-Sbondanglesare100.38◦ and
117.50◦, respectively. The thickness of the quadruple layer
is4.76A˚.Thecomputedbindingenergyis3.64eVperatom.
TheGa2S2sheetisfoundtobeasemiconductorwithanindi-
rectbandgapof2.38eVontheDFT/PBElevel.Theseresults
areingoodagreementwithrecentDFTcalculations[14, 20].
We note that Kohn-ShamDFT calculations usually underes-
timate band gaps of semiconductors because of the lacking
of the derivative discontinuity in the energy functionals. A
hybrid DFT calculation[14] gives a larger value of the indi-
rectbandgap,3.28eV.AlthoughtheKohn-ShamDFThasthe
bandgapissue,itcanusuallygivereasonableshapesofenergy
bands and wave functions in the vicinity of the Fermi level,
comparedtoresultsfromquasiparticleGWcalculations.
We consider two different directions of termination for
Ga2S2-NRs, zigzag and armchair, and for each direction of
termination we consider the bare and H-saturated edge con-
figurations. In order to investigate the width dependence of
the electronic properties, we perform calculations for differ-
ent ribbonwidths, up to Nz=24 and Na=19 (i.e., 24-Ga2S2-
ZNRand19-Ga2S2-ANR).Sincequalitativelysimilarresults FIG. 1: Top and side views of the atomic structures of 6-Ga2S2-
areobservedforthedifferentwidths,herewefirsttakethe6- ZNR (a) and 11-Ga2S2-ANR (b). The ribbon width and 1-D unit
Ga2S2-ZNRwithwidthof17.37A˚ and11-Ga2S2-ANRwith cell distance are denoted by Wz (Wa) and dz (da) for the ZNRs
width of 18.37A˚ as prototypes to present our results (see (ANRs), respectively. Theribbons areextended periodically along
Fig.1). Afterthestructureoptimization,thebondlengthbe- thexdirection.
3
FIG.2: Calculatedspin-polarizedbandstructures(left:majorityspin;right: minorityspin)andcorrespondinglocaldensityofstates(LDOS)
neartheFermilevelforbare6-Ga2S2-ZNR((a),(b))andH-terminated6-Ga2S2-ZNR((c),(d)).

(a) (b)

FIG.3:Spin-dependenttotalandpartialdensityofstatesforbare6-Ga2S2-ZNR(a)andH-terminated6-Ga2S2-ZNR(b).
sites. These results show strong edge-inducedatomic relax- polarizationoriginatesfromthestatesneartheFermienergy.
ationwhichresultsinquitedifferentbondlengthsandangles
To understand the characteristics of these bands near the
attheedgescomparedtothosein2-DGa2S2 sheet. Thisbe- Fermi energy, we plot their local density of states (LDOS)
haviorisquitedifferentfromthecasesofGNRsandBNNRs
in Fig. 2(b),(d)forthe bareand H-saturatedribbons,respec-
wheretheedgedistortionismuchsmaller.
tively. Itcan be seen thatin both casesthe LDOSis located
Our calculations for the ZNRs show that their electronic aroundtheedges,indicatingthatthemetallicnatureofGa2S2-
ZNRs is mainly due to the spin-polarized edge states. To
structuresarespinpolarized. Asanexample,thebandstruc-
futhershowtheoriginofthesemetallicbands,wealsocalcu-
tures of 6-Ga2S2-ZNR with bare and H-saturated edges are
late the total density of states (TDOS) and projecteddensity
showninFigs.2(a),(c)forthetwospincomponents: up-spin
(majority) and down-spin (minority), respectively. One can of states (PDOS) of 6-Ga2S2-ZNR (see Fig. 3). The states
aroundtheFermilevelinbothspinchannelsaredominatedby
seethatthebandstructuresof6-Ga2S2-ZNRexhibitametal-
the 4s and 4p states of edgeGa atoms and3p states of edge
licnature:ThereareoneortwobandscrossingtheFermilevel
Satoms. FurtherMullikenpopulationanalysesshowthatthe
regardlessoftheH-passivation,whichissimilartothebehav-
spin polarization is mainly due to the ferromagneticstate of
iorof MoS2 Nanoribbons[21, 22]. We findthatthismetallic
theGa-terminatededgeregardlessoftheH-saturation.
nature holdsfor all Ga2S2-ZNRs studied (up to Nz= 24) re-
gardless of the ribbon width. One should note that the dif- In contrast, our calculations for the ANRs show that their
ference between the up-spin and down-spin band structures electronicstructuresarespin unpolarized. Both thebareand
exists only aroundthe Fermi energy,indicating that the spin H-saturated Ga2S2-ANRs exhibit a semiconducting nature.
4
FIG.4: BandstructuresandcorrespondingLDOSforCBMandVBMofthe11-Ga2S2-ANR.(a),(b),(c)correspondtothebareGa2S2-ANR,
(d),(e),(f)correspondtotheH-terminatedGa2S2-ANRs. EachLDOSfigurecontainsatopview(left)andasideview(right)oftheLDOS
isosurfaceofthespecifiedstatesatCBMorVBM.TheFermilevelissettobezero.
the VBM and CBM are now located at the Γ and K point,
respectively.
To analyze the characteristics of the VBM and CBM and
theinfluenceoftheedges,wecalculatetheLDOSisosurfaces
for the energies around the VBM and CBM of the bare and
H-saturated 11-Ga2S2-ANR (see Fig. 4(b),(c),(d), and (e)).
In the bare system the large edge relaxation (reconstruction)
mayweakenthedangling-bondstates. However,thestatesof
VBMandCBMarestillmainlydeterminedbythedangling-
bond-relatedstateswhicharedrivenfromGa-4pandS-3por-
bitals. Therefore,theirLDOSaremainlylocalizedaroundthe
edgesoftheribbon(seeFig.4(b),(c))andformflatbands[21].
Because of this edge-state effect, the converged band gap
(1.45eV) (seethe discussionlater) ofbareGa2S2-ANRsbe-
comessmallerthanthatofthe2-DGa2S2sheet(2.38eV).
Whenthe edgeGa and Satomsaresaturatedby H atoms,
thedangling-bondedgestatesdisappearandthusthebandgap
increases. AscanbeseeninFig.4(d),nowtheLDOSofthe
CBM are mainly located near the center of the ribbon. For
FIG.5: BandgapsofaseriesofbareGa2S2-ANRs(3≤Na ≤13)
theVBM,itsLDOSarenearlyuniformlydistributedthrough-
asafunctionoftheribbonwidths(filledredlozenges). Foracom-
parison,theresultforthecorrespondinghydrogensaturatedGa2S2- out the ribbon though very weak edge states are remained
ANRsisalsoshown(voidedbluelozenges). (see Fig. 4(e)). In contrast with the bare systems, now the
convergedbandgap(2.45eV)(seethediscussionlater)ofH-
AsanexampleshowninFig.4(a),bare11-ZGa2S2-ANRisa saturated Ga2S2-ANRs becomes slightly larger than that of
typicalsemiconductorwithanindirectbandgapof1.44eV.In the2-DGa2S2(2.38eV).
thiscase,thevalence-bandmaximum(VBM)occursalongthe Next let us look at the variation of band gap as a func-
Γ−K direction,andtheconductionbandminimum(CBM) tionofribbonwidthforboththebareandH-sturatedANRs.
liesattheK point. Wenotethatthelowestconductionband As shown in Fig. 5, all the Ga2S2-ANRs are semiconduct-
andhighestvalencebandareveryflat,whichissimilartothe ing and their band gaps are sensitive to the structural sym-
caseofBNNRs[23]. WhentheedgeGaandSatomsaresat- metry and ribbon width. Generally, owing to the quantum
urated by H atoms, Ga2S2-ANRs are still indirect band gap confinementeffectthebandgapEG shoulddecreasewithin-
semiconductorsbutwith alagerbandgap(seeFig. 4(f))and creasing ribbon width Na. However, here the variation of
5
EG with Na shows an oscillatory (or family) behavior, es- important to note that although the binding energies of the
peciallyfor thenarrowribbons(Na < 8). Specifically, anti- nanoribbons(exceptforNa=3)issmallerthanthe2-DGa2S2
symmetric Ga2S2-ANRs (Na =2m, where m is an integer) sheet, it is larger than that of Ga2S2 nanocluterswith stable
have larger band gaps than the neighboring symmetric ones configurations[26]. Therefore, it is reasonableto expectthat
(Na=2m−1).This’familybehavior’wasalsoobservedpre- stablebareGa2S2-NRsarepossibletomakeexperimentallyin
viouslyinarmchair-edgedGNRs[3], BNNRs[23],andMoS2 thefuture. SincedanglingbondsaresaturatedbyHatomsin
nanoribbons[9, 24], where a width-dependentoscillation in H-saturatedGa2S2-NRs,theirstabilityshouldbeevenbetter.
bandgapoccurs. Whentheribbonbecomeswideenough(>
13A˚ orNa>8),thebandgapstendtoconvergetoaconstant
value (∼ 1.45eV), being smaller than the bulk band gap of CONCLUTION
the2-DGa2S2 sheet(2.38eV).Tocarefullyconfirmthisten-
dency,wefurtherdoacalculationfor19-Ga2S2-ANRs(width In summary, by performing first-princeples DFT calcula-
33A˚),whichalsoshowsabandgapof1.45eV.Inthecaseof tionswehaveinvestigatedsystematicallytheelectronicprop-
H-terminatedANRs(seeFig.5),similarbehaviorisfoundal- ertiesofGa2S2nanoribbonswhichhavenotbeenrealizedyet
thoughtheirbandgapsconvergetoa largervalueof2.46eV butthe corresponding2-Dsheethas beensuccessfully fabri-
duetothediminishingedgestates. Thevariationoftheband cated experimentally. We have considered the bare and H-
gap with Na may be an important advantage for their appli- saturated zigzag- and armchair-edged nanoribbons with dif-
cations in nanotechnologybecause it may lead to formation ferent ribbon widths (up to 3 nm). It is found that the elec-
ofquantumdotormultiplequantumwellsthroughthewidth tronicpropertiesofthenanoribbonsstronglydependsontheir
modulation[9,25]. edge structures. The Ga2S2-ZNRs are metallic with spin-
polarized edge states while the Ga2S2-ANRs are indirect-
band-gapsemiconductorswithoutspinpolarization.Theband
gapofbareGa2S2-ANRsexhibitsanoscillationbehaviorwith
increasingribbonwidthandultimatelyconvergestoaconstant
value of 1.45eV when the ribbon becomes wide enough (>
13A˚).TheH-saturatedGa2S2-ANRshavethesimilarbehav-
iorbutwithlargerconvergedbandgapof2.46eV dueto the
saturationofthedanglingbondsattheedges.Finally,wehave
studiedtherelativestabilitiesofthebareZNRsandANRsby
calculatingtheirbindingenergyperatom,andfoundthatthe
ANRs are more stable than the ZNRs with a similar width.
Thebindingenergiesarefoundtobeslightlysmallerthanthat
ofthe2-Dsheet,butislargerthanthatofGa2S2 nanocluters
withstableconfigurations,indicatingthatthebareribbonscan
beexpectedtoberealizedexperimentallyinthefuture.
FIG. 6: Binding energy of bare Ga2S2-ZNRs(3 ≤ Nz ≤ 8) and
Ga2S2-ANRs(6≤Na ≤13)asafunctionoftheribbonwidth. ACKNOWLEDGMENTS
Finally, we would like to discuss the stability of Ga2S2- Thiswork was supportedby the NationalNaturalScience
NRs,whichisquiteimportantbecauseitdetermineswhether FoundationofChina(No. 11174220and11374226),andby
thisnanostructurecanberealizedexperimentally. Thestabil- theKeyScientificResearchProjectoftheHenanInstitutions
ities of different nanoribbons and nanoclusters can be eval- of Higher Learning (No. 16A140009), and by the Program
uated with their binding energies; those with larger binding forInnovativeResearch Team ofHenanPolytechnicUniver-
energieswould be more stable. To estimate the stability, we sity(No. T2015-3),aswellasbytheDoctoralFoundationof
calculate the binding energy per atom as a function of the HenanPolytechnicUniversity(No. B2015-46).
ribbon width for bare Ga2S2-NRs in the following way[9]:
Eb=(nEGa+mES−EGanSm)/(n+m)whereEGa,ES,and
EGanSm are the total energies of Ga, S atoms, and GanSm,
respectively, with n and m being the number of Ga and S
atoms, respectively. As is shown in Fig. 6, the binding en- ∗ Correspondingauthor,E-mail:[email protected]
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