Density-functional calculations of multivalency-driven formation of Te-based monolayer materials with superior electronic and optical properties

0.82 MB·

by  Zhili Zhu

Density-functional calculations ofmultivalency-driven formationofTe-based monolayermaterials
withsuperior electronic and opticalproperties
Zhili Zhu1, Xiaolin Cai1, Chunyao Niu1, Seho Yi2, Zhengxiao Guo3,1,
Feng Liu4, Jun-Hyung Cho5,2,1, Yu Jia1∗, and Zhenyu Zhang5∗
1 International Laboratory for Quantum Functional Materials of Henan,
and School of Physics and Engineering, Zhengzhou University, Zhengzhou 450001, China
2 DepartmentofPhysics,HanyangUniversity,17Haengdang-Dong, Seongdong-Ku, Seoul133-791, Korea
7 3 Department of Chemistry, UniversityCollegeLondon, London WC1E6BT, UnitedKingdom
1 4 DepartmentofMaterialsScienceandEngineering, UniversityofUtah,SaltLakeCity,Utah84112, USA
0 5 ICQD, Hefei National Laboratory for Physical Sciences at the Microscale,
2 and Synergetic Innovation Center of Quantum Information and Quantum Physics,
University of Science and Technology of China, Hefei, Anhui 230026, China
n
(Dated:February1,2017)
a
J
Contemporary scienceiswitnessingarapidexpansion of thetwo-dimensional (2D) materialsfamily, each
0
memberpossessingintriguingemergentpropertiesoffundamentalandpracticalimportance.Usingtheparticle-
3
swarmoptimizationmethodincombinationwithfirst-principlesdensityfunctionaltheorycalculations,herewe

predictanewcategoryof2Dmonolayersnamedtellurene,composedofthemetalloidelementTe,withstable
l] 1T-MoS2-like(a -Te), andmetastabletetragonal (b -Te)and 2H-MoS2-like(g -Te)structures. Theunderlying
al formationmechanismofsuchtri-layerarrangementsisuniquelyrootedinthemultivalentnatureofTe,withthe
h central-layerTebehavingmoremetal-like(e.g.,Mo),andthetwoouterlayersmoresemiconductor-like(e.g.,
- S).Inparticular,thea -Tephasecanbespontaneouslyobtainedfromthemagicthicknessestruncatedalongthe
s [001]directionofthetrigonalstructureofbulkTe. Furthermore,boththea -andb -Tephasespossesselectron
e
and hole mobilitiesmuch higher thanMoS , aswell as salient optical absorption properties. These findings
m 2
effectivelyextendtherealmof2Dmaterialstogroup-VImonolayers,andprovideanewandgenericformation
t. mechanismfordesigning2Dmaterials.
a
m
PACSnumbers:73.20.At,61.46.-w,73.22.-f,73.61.Cw
-
d
n Thetwo-dimensional(2D)materialshavebeenintensively the two outer layers more semiconductor-like. In particular,
o investigated in recent years for their intriguingly emergent themonolayerandmultilayersofa -Tecanbereadilyobtained
c
propertiesthatcanbeexploitedforelectronic,photonic,spin- viaathickness-dependentstructuralphasetransitionfromthe
[
tronic, and catalytic device applications [1–10]. Various 2D trigonal bulk Te, with van der Waals-type coupling between

1 monolayers have been synthetized beyond the first member neighboring tri-layers. Furthermore, both the a - and b -Te
v
system of graphene [1–3], including the group-IV mono- phasespossessnotonlyhighercarriermobilitiesrangingfrom
5
7 layers of silicene [4] and stanene [8], the group-V mono- hundredstothousandsofcm2V−1s−1 comparedtoMoS2,but
8 layer of phosphorene [5], and the group-III monolayer of also significantlyenhancedopticalabsorptionpropertiesdue
8 borophene[6,7].Besidesthesegroup-III,-IV,and-Velemen- toanearlydirectordirectbandgap.Thesefindingseffectively
0
tal monolayers, transition metal dichalcogenides (TMDCs) extendtherealmof2Dmaterialstogroup-VImonolayers,and
.
1 have also been attracted much attention because of their rel- providea new and genericformationmechanismfor design-
0 atively wider, tunable, and direct band gaps and inherently ing2Dmaterials.
7
stronger spin-orbit coupling [9, 10]. Yet to date, somewhat
1
surprisingly, no prediction or fabrication of group-VI ele- We perform the particle-swarm optimization (PSO)
:
v mentalmonolayershasbeenmade,whosepotentialexistence searches [11] in combination with the DFT calculations us-
Xi wouldnotonlyfurtherenrichourunderstandingoftherealm ingtheViennaabinitiosimulationpackage(VASP)withinthe
ofthe2Dmaterialsworld,butcouldalsooffernewapplication projectoraugmentedwavemethod[12,13].Fortheexchange-
r
a potentialsstemmingfromtheiruniquelyphysicalandchemi- correlation energy, we employ the PBE functional[14] with
calproperties. thevanderWaals(vdW)correctionproposedbyGrimme[15]
and the screened hybrid functional, HSE06, which can typ-
InthisLetter,weaddanattractivenewcategorytotheever ically describe the band gaps better [16, 17]. Unless other-
increasing2Dmaterialsfamilybypredictingtheexistenceand wise specified, theTemonolayersaremodeledbya periodic
fabricationofgroup-VIelementalmonolayerscenteredonthe 1×1×1slabgeometrywithavacuumthicknessof20A˚.The
metalloidelementTe. Ourtheoreticalcalculationsrevealthat kinetic-energy cutoff for the plane wave basis set is chosen
2D monolayers of Te, named tellurene, can exist in the sta- to be 500 eV, and the k-space integration is done using the
ble1T-MoS -like(a -Te)structure,andmetastabletetragonal Monkhorst-Pack scheme with the 21×21×1 meshes in the
2
(b -Te)and2H-MoS -like(g -Te)structures.Thesetri-layerar- Brillouinzones. Alltheatomsareallowedtorelaxalongthe
2
rangements are driven by the unique multivalency nature of calculated forcesof less than 0.01 eV/A˚. The phononcalcu-
Te, with the central-layer Te behaving more metal-like, and lationisperformedusinglargersupercells,asimplementedin
TypesetbyREVTEX
2
thePhonopycode[18]. furtherinvestigatedusing ab initio moleculardynamicssim-
ulations. We findthattheequilibriumstructuresofa -Teand
(cid:11)(cid:68)(cid:12) (cid:11)(cid:69)(cid:12) b -Tehardlychangeatroomtemperature,whileg -Tebecomes
unstableat temperaturesabove∼200K.In the moviesof the
a
aa SupplementalMaterial,we illustratethedynamicstabilityof
y b b eachphaseat300Kuptoatimeperiodof3pswith1fstime
x
step.
d
z z
x
(cid:11)(cid:70)(cid:12) (cid:11)(cid:71)(cid:12) TABLEI: Structural parameters of tellurene, together with the co-
(cid:11)(cid:19)e(cid:17)(cid:18)(cid:20)(cid:99)(cid:19)(cid:22)(cid:12) hesiveenergyEc andthechargetransferD Qfromthecentral atom
(cid:19)(cid:17)(cid:19)(cid:27) (cid:60) (cid:48) totheourteratoms: aandbarethelatticeconstants, d isthebond
(cid:19)(cid:17)(cid:19)(cid:25)
(cid:19)(cid:19)(cid:17)(cid:17)(cid:19)(cid:19)(cid:23)(cid:21) (cid:46) length, anddz istheintervaldistancebetweentheupper andlower
(cid:19)(cid:17)(cid:19)(cid:19) (cid:573) (cid:48) (cid:573) (cid:59) Telayers(seeFig. 1). Forcomparison,thestructuralandenergetic
(cid:16)(cid:19)(cid:17)(cid:19)(cid:21)
(cid:16)(cid:19)(cid:17)(cid:19)(cid:23) propertiesofbulkTearealsolisted.
(cid:16)(cid:19)(cid:17)(cid:19)(cid:25)
(cid:16)(cid:19)(cid:17)(cid:19)(cid:27)
(cid:16)(cid:19)(cid:17)(cid:20)(cid:19) a,b(A˚) d(A˚) dz(A˚) Ec(eV/atom) D Q(e)
FIG.1:(Coloronline)Topandsideviewsoftheoptimizedstructures
oftellureneindifferentphases: (a)a -Te,(b)b -Te,and(c)g -Te.The a -Te a=b=4.15 3.02 3.67 2.62 0.41
Brillouinzonesfora (org )andb phasesaredrawnin(d).Thedashed
a=4.17 3.02
lineindicatestheunitcellofeachstructure.Fordistinction,thelarge, b -Te b=5.49 2.75a 2.16 2.56 0.11
medium, andsmallcirclesrepresentTeatomslocatedintheupper,
central, and lower layers, respectively. Thetotal charge density of g -Te a=b=3.92 3.08 4.16 2.46 0.29
eachstructureisplottedatthehorizontalandverticalcrosssections
a=b=4.33
indicatedbythebluedottedlines. Te-I 2.90 – 2.79 –
c=6.05
Figure1 presentsthe optimizedstructuresof Te monolay- abondlengthbetweentwoTeatomswithnc=3.
ers or tellurene. We identify three different phases denoted
bya -,b -,andg -Te,asshowninFig. 1(a),1(b),and1(c),re- InFigs. 1(a)-1(c),the totalchargedensitiesofa -, b -, and
spectively. Thestructuralparametersandcohesiveenergyof g -Terevealtheirbondingcharacteristics,respectively. Fora -
eachoptimizedstructurearelistedinTableI.Itisseenthata - andg -Te,thereexistsametal-ligand-likebondingbetweenthe
Te hasthe1T-MoS -like structurecontainingthreeTe atoms central atom and the outer atoms. On the other hand, for b -
2
perunitcell. Here,whencomparedwith1T-MoS monolayer, Te, the outer atoms with are bonded to each other with the
2
therearethetwodistincttypesofTeatomswithdifferentco- s bond,whilethecentralatomsinteractwiththeouteratoms
ordinationnumbers(n ): acentralTeatomlocatedattheMo intheformofametal-ligand-likebonding.Consequently,the
c
site has n = 6, while a Te atom in the upper or lower layer formerbondlength(2.75A˚)ismuchshorterthanthelatterone
c
at the S sites has n = 3. Meanwhile, b -Te is composed of (3.02A˚).AccordingtotheBaderchargeanalysis,thecharge
c
theplanarfour-memberedandchair-likesix-memberedrings transferfromthe centralto the outeratomsamountsto 0.41,
arrangedalternatelywiththelattice constantsa= 4.17andb 0.11, and 0.29e in a -, b -, and g -Te, respectively (see Table
=5.49A˚ [TableI];inthisstructure,acentralTeatomhasn I),andthereforethecentralTeatomsbehavemoremetal-like
c
=4,whileanupperorlowerTeatomhasn =3. g -Tehasthe withalargern whiletheouterTeatomsmoresemiconduct-
c c
2H-MoS -like structure, with smaller lattice constants a = b ingwithasmallern . Thestructuralfeaturesoftellurenecan
2 c
= 3.92 A˚ than those (a = b = 4.15 A˚) of a -Te. Correspond- befurtherassociatedwiththebondingcharactersofgroup-VI
ingly, the bondlength(d = 3.08A˚) and intervaldistance (d elements,wherethenonmetalliccharacterisweakenedinthe
z
= 4.16A˚)betweentheupperandlowerTe atomsin g -Teare order of O > S > Se > Te, leading to a complete metallic
larger than those (d = 3.02 A˚ and d = 3.67 A˚) in a -Te. To characterof Po. In particular,Te hasthe dualcharacteristics
z
examinetherelativestabilityofdifferenttellureneallotropes, of both metal and nonmetal. It is thus feasible that the two
thecohesiveenergy(E )peratomwithrespecttotheenergy dimensionalmonolayersof Te canadoptthe tri-layeratomic
c
ofanisolatedTeatomiscalculated. Accordingtotheresults structures,, e.g. MoS -likestructure. Withthe dimensional-
2
in Table1, a -Te is energeticallythe most stable phase, while ityreduction,themultivalency-dominated2Dstructureswith
b -,andg -Tearethemeta-stablephases. heterogeneouscoordinationnumbersbecomelowerinenergy.
Toexaminethestructuralstabilityoftellurene,weperform Collectively,thesefindingsamplyreflectthedistinctmultiva-
thephononcalculations,whichcanidentifythepotentialpres- lentnatureofTeanditsvitalroleintheformationoftellurene.
ence of soft phonon modes that may lead to structure insta- Figures2(a)-2(c)showthebandstructuresofa -,b -,andg -
bility. The calculated phonon spectra of tellurene are dis- Te,respectively,obtainedusingthePBEcalculation. Wefind
playedinFig. S1oftheSupplementalMaterial. Wefirstcon- thata - andb -Tearesemiconductorswith indirectbandgaps
firm thatall hephasesare thermodynamicallystable without ofE =0.76and1.17eV,respectively,whileg -Teisametal.
g
imaginary-frequencyphononmodes.Thedynamicstabilityis It is well-known that the semi-local PBE scheme underesti-
3
(a) (b) locatedbetweenthebandgaps(∼0.7and∼1.1eV)ofbulkGe
andSi[19],andthatofb -Teis1.47eV,whichisclosetothat
of GaAs. These physically realistic values of the band gaps
4 ofthestableandmeta-stabletellurenephasesmayofferdesir-
able(e.g.,ohmic)contactswhensuchmaterialsareintegrated
)V 2 fordeviceapplications.
e
(
y 0
g
r
enE -2 106(a) (b)
armchair chain
-4 -1)cm 105 zigzag chain
(cid:42) (cid:48) (cid:46) (cid:42) (cid:56) (cid:42) (cid:38) (cid:48) (cid:46) nt (
(c) (d) cie 104
2.5 effi
)Ve( ygrenE 024 Energy (eV)112...050 )67.0()64.0)51.1()57.0( )71.1()30.1()97.1()74.1( Absorption co 1110001230 1 E2nergy3 (eV)4 50 1 En2ergy 3(eV) 4 5
-2 0.5 (
FIG.3: (Coloronline)Calculatedopticalabsorptioncoefficientsfor
-4 0.0 (a)a -Te,(b)b -Te.In(b),thepolarizationisalongthezigzagorarm-
(cid:42) (cid:48) (cid:46) (cid:42) (cid:68)(cid:16)(cid:55)e (cid:69)(cid:16)(cid:55)e chairchaindirection.
FIG. 2: (Color online) Band structures of (a) a -Te, (b) b -Te, and
(c) g -Te, obtained using the PBE scheme without (solid) and with For potential technological applications in electronic de-
(dashed)inclusionoftheSOC.Thecontourplotsoftheelectronden- vices, the newly discovered 2D materials should have suffi-
sities for the valence states within 0.5 eV below the valence band ciently high carrier mobilities. To estimate the carrier mo-
maximumorFermilevelEF aredrawnonthesamehorizontaland bilityofthetellurenemonolayers,wecalculatetheireffective
verticalcrosssectionsasmarkedinFig.1.Theintervalofthecharge masses,whicharerelativelysmallerthanthose(m∗=0.47,and
contoursis1×10−3 electrons/A˚3. (d)Bandgapsobtainedusingthe ∗ e
m =0.58m )ofmonolayer2H-MoS (seeTableII).Thesere-
PBE(PBE+SOC)andHSE(HSE+SOC),asrepresentedbythecyan h e 2
sultssuggestthattellurenemaypossesshighelectronandhole
(cyanmeshed)andred(redmeshed)bars,respectively.
mobilities. Using the acoustic phonon limited method [20],
the room-temperature carrier mobilities of a - and b -Te are
found to range from hundreds to thousands of cm2V−1s−1,
matesthe bandgap. Inorderto remedysuch a deficiencyin muchhigherthan those of monolayer2H-MoS (see Table II
2
PBE,weperformthehybridDFTcalculationwiththeHSE06 andthe SupplementalMaterial). Here, µ andµ show large
e h
functional,whichisknowntoprovidebetterpredictionsofthe differencesinmagnitude,indicatingasymmetricmobilitiesof
bandgaps.AsshowninFig. 2(d),theHSEcalculationsfora - electronsandholesduetotheirdifferenteffectivemasses. In
andb -TegiveincreasedEg = 1.15and1.79eV, respectively. addition,b -Tehasanisotropiccharactersofelectronandhole
GiventheheavymetalnatureofTe, we also examinetheef- mobilitiesalongtheydirection.
fectsofSOConthebandstructure.Theresultsobtainedusing
thePBE+SOCcalculationareplottedwiththedashedlinesin
Figs. 2(a)-2(c). We findthatthe inclusionofSOCin a -and TABLEII:Effectivemassesm∗ andcarriermobilitiesµofa -Te,b -
b -Teinducesatransformationfromanindirecttoanearlydi- Te, and 2H-MoS , obtained using the PBE+SOC calculation. For
2
rect and a direct band gap at the G point, respectively. This thetetragonalstructureofb -Te,thecomponentsalongthearmchair
indirect-to-directband-gapchangeina -andb -Temaysignif- chain(x)andzigzagchain(y)directionsareseparatelygiven.
icantly enhance their optical absorbance. Indeed, as seen in
Fig. 3, both a - and b -Te exhibit superb optical absorptions, m∗(me) µ(103cm2V−1s−1)
whichcanbeexploitedforoptoelectronicsandphotondetec-
tion. b -Te also exhibits optical anisotropies, with stronger electron hole electron hole
absorbance along the zigzag chain direction, which can be a -Te 0.11 0.17 2.09 1.76
exploited for developing polarized optical sensors. Further-
0.83(x) 0.39(x) 0.05(x) 1.98(x)
more, it is noted that the PBE+SOC (HSE+SOC) band gaps b -Te
0.19(y) 0.11(y) 0.10(y) 0.45(y)
ofa -andb -Tearereducedby0.30(0.40)and0.26(0.32)eV,
comparedtothe PBE (HSE)ones: see Fig. 2(d). Therefore, 2H-MoS 0.47 0.58 0.08 0.29
2
the HSE+SOC band gap of a -Te becomes0.75 eV, which is
4
Now, we turn to discuss possible fabricationroute for tel- (a) (b)
0.6 4
lurene and its multilayers. To date, the existing 2D materi- 0.5 0.4 dzi,i+1: Interlayer spacing
aacslhsagncraiacnpahlbleyeneedxaivfnoiddlieMadteoidSnt2fo;rotthmweoiottcshaletaery,geaorcrekideinsb:guoalknleacyotehuranettdecrbapunalkrbt,ecsomuucneh-- E(eV/atom)f 000...234 (cid:21)(cid:39)(cid:40)f-000...202 3 6 9N 1U2Sntsatb1a5lbele18 z d ()(cid:99)i,i+1 23 bulk
0.1
terpart,hastobegrownepitaxiallyonapropersubstrate,such 1
0.0
assiliceneandstanene.Meanwhile,theTe-Ibulkhastheform 3 6 9 N 12 15 18 3 6 9N 12 15 18
(c) (d)
ofhelicalchainsalongthec axis, andtheTe filmsmosteas-
Before relaxation After relaxation Before relaxation After relaxation
ilygrowinthe[001]direction[21],totallydifferentfromthe N=8 N=9
structure of tellurene. Surprisingly, the monolayer or mul-
tilayers of tellurene can be generated via the new formation 3 Å
mechanismcharacterizedbyathickness-dependentstructural 3 Å
phasetransitionintheultrathinfilmregime,asdiscussedbe-
low.
Wereachtheaboveimportantfindingthroughasystematic
FIG.4: (Coloronline)Formationenergies,stabilities,andinterlayer
study of the Te film stability with increasing film thickness, spacingsofTeslabsatdifferentthicknesses. (a)Formationenergies
determinedbytheformationenergy(E )asafunctionofthe of the fullyrelaxed Teslabs asafunction of thickness. Theinsert
f
number of atomic layers, N. Here the initial configurations represents the second-order difference of Ef, with positive values
of the slabs are taken by truncating the trigonal structure of indicatingstablesystems. (b)Distributionofthelayer-resolvedin-
terlayerspacingofrelaxedTeslabsasafunctionofthickness. The
bulkTe(hereaftertermedTe-I)alongthe(001)direction.The
dashedlinedenotestheatomiclayerspacingofbulkTe. (c)and(d)
formation energy is given by the cohesive energy difference
arethe geometric structures of Teslabs at N = 8and 9before and
Ef =(Eslab(N)−NEbulk)/N,whereEslab(N)andEbulkarethe afterstructuraloptimization,respectively.
totalenergiesoftheslabandasinglelayerinbulkTe,respec-
tively. For these multilayerd systems, we have included the
vdWinteractionsusingtheDFT-D2method[15]. of bulk Te obtained using the vdW-DF2 scheme show more
Figure 4(a) shows the formation energy variations of the severe deviation from the experimentalvalues (see Table S1
fully relaxed Te slabs with increasing N, exhibiting a dis- of the Supplemental Material), while the DFT-D2 and DFT-
tinctoscillatorybehavior. Therearefivehighlypreferred(or TS schemes agree better with experiments. Together, these
magic)thicknessesofN=3,6,9,12,15whenthethicknessof resultsconvincinglyindicatethatatleastafewmonolayersof
theTe-IslabsincreasesfromN =1to20. Strikingly,wefind the 2D tellurene structure will be readily obtained in a typi-
that the Te slabs automatically transform into multilayered calyetthickness-controlledfabricationapproachonaproper
structuresof-Teatthemagiclayerthicknesses,whiletheTe substratefavoringlayeredgrowth.
slabswillkeepthechain-likestructuresofbulkTeawayfrom Insummary,ourstate-of-the-artglobalstructuralsearching
thesemagicthicknesses. TheinsertinFig. 4(a)highlightsthe combinedwithfirst-principlescalculationshasresultedinthe
stabilityofthedifferentslabsbytheseconddifference,while discoveryofanewcategoryof2Dmaterialscomposedofthe
Fig. 4(c)and(d)highlightthedifferentstructuralpreferences group-VIelementof Te. These new 2D materialscalled tel-
ofTeslabswithN =8and9,respectively. Wefurtherobtain lurenecanbestabilizedintheMoS -like(a -,g -Te)ortetrag-
2
thattheinterlayercouplingstrengthbetweentwoneighboring onal(b -Te)structures,andtheirunderlyingformationmecha-
tellurenemonolayers(or,equivalently,twoTetrilayers)ofTe nismisinherentlyrootedinthemultivalencynatureofTe.The
is26meV/A˚2,whichisonthesameorderasthatofMoS2(21 a -Teandb -Temonolayersnotonlyexhibitsuperbopticalab-
meV/A˚2)[22],suggestingthatasingletellurenelayercanbe sorptions,butalsopossessmuchhighercarriermobilitythan
readilyexfoliatedonceitisformed. MoS2. Thea -Te multilayerscan be achievedspontaneously
Atpresent,thereisnoaprioriknowledgeaboutwhichvdW fromthebulktruncatedfilmsviaanovelthickness-dependent
schemeismoreaccurateforagivensystem. Ascrosschecks, structural phase transition. The coupling between neighbor-
we have also examined the Te film stability as a function of ingtellurenelayersisofvdWtype,allowingeasyseparation
thefilmthicknesswiththevdWinteractionstreatedwithinthe of a tellurenelayer via mechanicalexfoliation. The superior
widelyadoptedfirst-principles-basedschemesofTkatchenko electronic and optical propertiesof tellurene are expected to
andScheffler[23](DFT-TS)andvdW-DF2[24],respectively. findbroadtechnologicalapplications.
Foreitherscheme,theresultsqualitativelyalsosupporttheex-
istenceofastructuralphasetransitionfromthebulk-truncated We thank Dr. Xiaoyu Han and Prof. Qiang Sun for
Te structure to multilayered tellurene at the identical film helpful discussions. This work was partially supported
thicknesses,butthenumberofsuchmagicthicknessesisvar- by the NSFC (Nos. 11274280, 11504332, 11634011,
ieddependingonthespecificversionofthevdWscheme.For 61434002), the National Basic Research Program of China
DFT-TS(vdW-DF2),thelayered(orcloseshelled)structures (Nos. 2012CB921300and 2014CB921103). Z.X.G. is sup-
arefoundtobehighlypreferredatthethicknessesofN=3,6, ported by the UK EPSRC (No. EP/K021192/1). J.-H.C.
9 (3, 6). Here, we notethat the optimizedlattice parameters is supported by the National Research Foundation of Ko-
5
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(2014).
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