2D silicon carbide: computational insights and the observation of SiC nanograin assembly

6.2 MB·

by  Toma Susi

2D silicon carbide: computational insights and the
observation of SiC nanograin assembly
Toma Susi1,*, Viera Ska´kalova´1,2, Andreas Mittelberger1, Peter Kotrusz3, Martin Hulman3,
Timothy J. Pennycook1, Clemens Mangler1, Jani Kotakoski1, and Jannik C. Meyer1,*
1UniversityofVienna,FacultyofPhysics,Boltzmanngasse5,1090Vienna,Austria
2SlovakUniversityofTechnology(STU),CenterforNanodiagnostics,Vazovova5,81243Bratislava,Slovakia
7
3DanubiaNanoTech,Ilkovicova3,84104Bratislava,Slovakia
1
0 *[email protected]&[email protected]
2

n ABSTRACT
a
J

5 Whileanincreasingnumberoftwo-dimensional(2D)materials,includinggrapheneandsilicene,havealreadybeenrealized,
2 othershaveonlybeenpredicted. Aninterestingexampleisthetwo-dimensionalformofsiliconcarbide(2D-SiC).Here,we
presentanobservationofatomicallythinandhexagonallybondednanosizedgrainsofSiCassemblingtemporarilyingraphene

] oxideporesduringanatomicresolutionscanningtransmissionelectronmicroscopyexperiment. Eventhoughthesesmall
i
c grainsdonotfullyrepresentthebulkcrystal,simulationsindicatethattheirelectronicstructurealreadyapproachesthatof
s 2D-SiC. This is predicted to be flat, but some doubts have remained regarding the preference of Si for sp3 hybridization.
-
l Exploringanumberofcorrugatedmorphologies,wefindcompletelyflat2D-SiCtohavethelowestenergy. Wefurthercompute
r
t itsphonondispersion,withaRaman-activetransverseopticalmode,andestimatethecorelevelbindingenergies. Finally,we
m studythechemicalreactivityof2D-SiC,suggestingitislikesiliceneunstableagainstmolecularabsorptionorinterlayerlinking.
. Nonetheless,itcanformstablevanderWaals-bondedbilayerswitheithergrapheneorhexagonalboronnitride,promisingto
t
a furtherenrichthefamilyoftwo-dimensionalmaterialsoncebulksynthesisisachieved.
m
-
d
n
o
Introduction
c
[
Inthewakeofthe2004discoveryofgraphene,thesingle-atomthinformofhexagonalcarbon1,two-dimensional(2D)materials

1 have attracted increasing attention. They can be divided into two classes: inherently layered materials bound by van der
v
Waalsinteractions,includinghexagonalboronnitride(hBN)2,phosphorene3 andtransitionmetaldichalgonenidessuchas
7
molybdenumdisulphide4; andthosewithnon-planarcovalentbondingintheirbulkform. Animportantclassofthelatter
8
3 consists of the remaining group-IV elements, namely Si, Ge, Sn and Pb. The first of these, composed on Si and named
7 silicene5,6,wasrecentlysynthesizedonsilversubstrates7–9,andfurtherfabricatedintotransistors10. Unlikegraphene,silicene
0 exhibitsachair-likedistortionofthehexagonalrings,resultinginout-of-planecorrugation. Likegraphene,chargecarriersin
.
1 siliceneshowaDiracdispersionattheFermilevel6,althoughasmallgapdoesopenduetothestructuraldistortion10.
0 In addition to lattices of either pure C or Si, mixed stoichiometries are possible for 2D forms of silicon carbide (2D-
7 Si C )11,12. Althoughthes2p2 valenceshellstructureofSiissimilartoC,itsgreatercovalentbondingdistanceinmost
1 x 1−x
crystalsinhibitsp–poverlap,leadingtosp3hybridization. BulkSiCexistsinover200crystallineforms13,somewiththree-
:
v dimensionalhexagonalcrystalstructures. Fortheisoatomic2DformSi C (whichwewillsimplycall2D-SiC),aplanar
0.5 0.5
Xi structureidenticaltographenebutwithabonddistanceof1.77-1.79A˚—comparedto1.425A˚ forgraphene,1.89A˚ forbulk
SiC,and2.33A˚ forbulksilicon—andalargebandgap(2.5–2.6eV)havebeenpredicted14–16. Arecentclusterexpansionstudy
r
a exploredthespaceofpossibleC:Simixings,findingthelowestformationenergyfortheisoatomicstoichiometry17. Despitethe
explosionofinterestintwo-dimensionalmaterials,no2DformofSiChasyetbeenexperimentallyrealized.
Wepresenthereatomicresolutionscanningtransmissionelectronmicroscopy(STEM)observationsofnanosizedgrains
ofSiC,foundtoassembleintheporesofgrapheneoxide(GO)18.GOisusefulherefortworeasons: itsdisorderedstructure
containsnanometer-sizedholes(asindisorderedgraphene19),andthesynthesisby-productsremainingevenafterpurification
provideanamplesourceofmobileCandSiadatoms. Theobservedpatcheswerestablefortensofsecondsundertheintense
60keVelectronirradiation,allowingustocapturehighqualityimagesoftheatomicconfigurations. Theobservedbonding
andthemeasuredannulardarkfielddetectorintensitiespreciselymatchaquantitativeimagesimulationbasedonadensity
functionaltheory(DFT)model. IncontrasttoearlierobservationsofpureSiclusterdynamicsinagraphenenanopore20,our
grainscontainasimilarnumberofCandSiatoms,predominantlyinanalternatingarrangement.
a b c d e f
5 Å
g h i j k l
m n o p q r
s t u v w x
Figure1. ObservedtimeseriesoftheassemblyofatomicallythinSiCnanograins. Theoverlaidreddashedlinesindicatethe
approximatelocationsoftheSiCregions. Thetriangularpatchinpanellwasusedasthebasisforelementalidentification.
Wedonotclaimtohavesynthesized2D-SiC,norsuggestthatgrainassemblyisapracticalroutetothebulkmaterial.
Nonetheless,itisremarkabletodirectlyobservetheformationofahexagonalSiClattice. Oursimulationsfurtherindicate
thattheelectronicstructureinthelargestpatchesdoesalreadyresemblethatofthebulkform,forwhichwecomputemany
importantcharacteristicstoguidefurtherexperimentalefforts.
Results and discussion
Samplesandmicroscopy
Our graphene oxide synthesis has been described in detail previously21 (see also Methods). In our transferred samples, a
goodcoverageofsingle-layerGOflakeswasfoundonthesupportgrid. Tostudytheirmorphology,weconductedelectron
microscopy in a Nion UltraSTEM100 scanning transmission electron microscope operated at 60 kV. While continuously
imagingacleanmonolayerareaofaflake,weweresurprisedtoobservetheconversionofadisorderedareasurroundinga
smallporeintoahexagonallatticeofalternatingheavierandlighteratoms(Fig.1,timebetweenpanels∼23s,panelssmoothed
forclaritywitha0.1A˚ Gaussiankernel). Heavieratomsappearbrighterinimagesrecordedwithanannulardarkfielddetector,
sincegreaterCoulombscatteringoftheprobeelectronsoccursfromthenucleiofatomswithmoreprotons(Z-contrast22). A
particularlywellresolvedstructureinpanellexhibitedatriangularcrystallinepatchof3×3units,whosestructurecouldbe
preciselydeducedfromtheimage. Bycomparisonwithsimulations(shownfurtherbelow)wecanidentifyalllighteratomsas
carbon,andtheheavieronesassilicon. Thelighteratomsinsidethepatchappearslightlybrighterthanthecarbonatomsinthe
graphenelattice,whichisawellknowneffectofprobetailsinpresenceoftheheavierneighbouringatoms22.
Undertheintenseelectronirradiation,thispatchwasnotstableforlong,butlaterintheseriesanotherlargerpatchformed
nearthetoprightcorneroftheview(Figure1panelsl,n,p,r-t,v). Thus,eventhoughtheirradiationcontinuouslyperturbs
theatomicstructure,thedynamicsarenotfullyrandomandthereseemstobeanenergetictendencytowardsthisperiodic
arrangementofatoms. TheassemblyoftheSiClatticemaythusbeconsideredastheresultofbeam-drivensamplingofthe
dynamicalpotentialenergylandscape. Interestingly,thelinesofSiatomsindifferentcrystallites,orinthesameoneatdifferent
times,donothavethesameangleswithrespecttothegraphenelattice. Thissuggeststhattheporesmerelyactassuitable
containingspaces23,anddonothaveastrongroleindirectingtheassembly. Anadditionalexample,startingwithheavieratoms
saturatingthereactiveedgeofapore24,25,isshownasSupplementaryFigure1.
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a b
2 Å
c d
Figure2. ElementalidentificationoftheatomswithintheSiCnanograin. (a)CropofanunprocessedMAADF-STEMimage.
(b)SimplifiedatomicSiCmodel. (c)TheexperimentalimagewithnoiseremovedbyaGaussianblur(sigma=0.28A˚),with
higherintensitiescolouredtowardswhite. (d)CropofaquantitativeimagesimulationoftheSiCmodel(seetext).
Structureidentification
Usingtheexperimentalimage(Figure1l)asastartingpoint,wecreatedasimplifiedsymmetricalmodelstructureofsixSi
atomsembeddedina9×9supercellofgraphene(150atomsintotal,correspondingtosixatomicsubstitutionsand12missingC
atoms)andrelaxeditsatomicstructureviaDFTusingtheGPAWpackage26(Methods). ThebondlengthsbetweentheSiandC
variedbetween1.78and1.87A˚,dependingontheatompair. Tocreatealargerstructureforimagesimulations,werepeatedthe
cellperiodicallyandcroppedasquareof27.0×25.4A˚ (627atoms)surroundingthepatch. Inaddition,wecreatedaprimitive
2-atomunitcellfor2D-SiC.Byrelaxingthestructureandoptimizingthecellsizeusingthestresstensorinplane-wavemode
(Methods),wefoundaplanargroundstatewithaSi–Cbondlengthof1.792A˚.Supercellsofthiswereusedtocalculatea
numberofpropertiesofthematerialandcomparethemtothoseoftheprimarybulkforms(Table1).
ToidentifytheatomsinFig. 1l,weusedtheQSTEMsoftwarepackage27tofindaquantitativematchofintensitiesbetween
experimentalandsimulatedimages. Asweknowthatmostatomsinourfieldofviewarecarbon,wecouldusethegraphene
lattice contrast as reference and subtract a background value measured in vacuum in a large hole with the same imaging
conditionsfromtherawdatapriortomeasuringtheintensities. Theimagecontrastisinfluencedbylensaberrations(including
chromaticaberration28),thermaldiffusescattering29,finitesourcesizeand,importantly,theannulardarkfielddetectorangles.
AllthesecanbeaddressedbytheQSTEMsimulationandweresettovaluesrepresentingourexperimentalsetup(Methods).
Theimagethussimulated(Figure2d)leadstoaSi/Cintensityratioof2.15(averageforall6Siatomsand10Catoms
awayfromtheSiCpatch),withanincreasedintensityontheCatomsnexttoSiduetotheprobetails22(althoughthemodel
structurediffersfromtheexperimentalstructureatitsedges,thisdoesnotaffecttheintensitiesofthecentralatoms). Fromthe
experimentalimage,wemeasuredaSi/Cintensityratioof2.17,matchingthesimulationwithanerrorofonly1%. Noother
impurityelementprovidesasimilarratio. Two-dimensionalsilica30,ontheotherhand,hasamuchlargerlattice,andoxygen
atomswouldnotformthreebondsorbebeam-stable31. ThustheinvestigatedstructurecanonlybeSiC,whichisnotsurprising
sinceSiisfrequentlyfoundingraphenesamples25,32,especiallyingrapheneoxidepreparedviawetchemistry(althoughits
originisstillunknown). WecouldalsoverifythepresenceofSiasamajorcontaminationinthissamplebyelectronenergyloss
spectroscopy(SupplementaryFigure2),butindividualatomsweretoomobiletoreliablyconfirmtheiridentitybyspectroscopy.
Electronicstructureofthenanograins
Theelectronicbandstructureofbulk2D-SiChasalreadybeenextensivelydiscussedintheliterature14,16. Inourcase,the
electronicbandgapwasestimatedbyconvergingthebandstructureoftheprimitive2-atomcellupto8unoccupiedbands
(Methods),yieldingagapof2.58eV(predictedtobeashighas4.42eVduetounusuallystrongexcitoniceffectsincluded
at the G0W0 level of theory15). The overall band structure (Supplementary Figure 3) is in good agreement with earlier
simulations15,16.
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a
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at
st
of
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sit
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al
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E–E (eV)
F
b
Figure3. Localdensitiesofelectronicstates(LDOS)forSiCnanograinsofdifferentsizesandfor2D-SiC.a)LDOSes
projectedontoSi-orC-centredWigner-Seitzcellsof2D-SiCcomparedtothoseoftheSiC-likeatomsinsmallerpatches
embeddedintographene(thelegendidentifiesthesizeofthecalculatedSiCgrainandappliestobothpanels). b)Structure
modelsusedfortheLDOSprojections(Catomsshowninblack,Siinyellow;framecolourscorrespondtothelinecoloursina).
Usingthisbandstructureasastartingpointtoassesswhetherthenanograinsresemblethebulkformintheirproperties,
wecalculatedtheWigner-Seitzlocaldensitiesofstate(LDOS,Fig.3a)oftheSiC-likeatomsinasingleSisubstitutionand
triangularpatchesofSiCwith3,6and10Siatoms(Fig.3b),andcomparedthemto2D-SiC.Acleartrendtowardsthebulk
electronicstructurecanbeobserveddespitethedistortionsintheatomicstructureduetotheembeddingstrain(whichisknown
toaffectthebandgapof2D-SiC16),withthe10-Sipatchexhibitingaclearbandgap. Thusitappearsthatdespitetheirsmall
size,thelargestpatchesweobservedcouldalreadybeconsideredasnanosizedgrainsofthematerial.
Theplanarityandhybridizationof2D-SiC
Asidefromtheclearhexagonalbonding,theprojectedbondlengthsinourexperimentalimagesareconsistentwithaplanar
2D-SiCstructure. Intheliterature,simulated2D-SiChastypicallybeencharacterizedasflat14–17,butithasnotbeenclearif
therehavebeenenoughatomsinthechosenunitcellstoallowforcorrugation,andwhetherornotthechosencellsizeshave
beenimposingstrainthatpreventsbuckling. TheflatnessissomewhatsurprisingconsideringthepropensityofSitoprefersp3
bonding,whichleadstopuckeringinthegroundstateofsilicene6. Furthermore,thelowestenergystructureofananalogous
material—two-dimensionalphosphoruscarbide(2D-PC)—wasveryrecentlypredictedtobehighlycorrugated33.
Toaddressthis,werancalculationsinrectangular4and8-atomunitcells,startingfromdifferentdegreesofcorrugation
andcellsizes,includingstructureswithalternatingC–CandSi–Sibonds(analogoustotheproposedgroundstateof2D-PC).In
allcases,thetotalenergyoftherelaxedstructurewasminimizedforSi–Cbonding(consistentwithShietal.17),andlowest
foranentirelyplanarstructure(SupplementaryFigure4). Thus,whiletheremaybecompetitionbetweensp2hybridization
preferredbyCinitsplanarformandsp3preferredbySi,thegroundstateof2D-SiCisindeedplanar.
Baderanalysis34furtherrevealsthattheSi–Cbondin2D-SiCisratherpolarized16,17,withSidonatingalmost1.2electrons
toitsthreeCneighbours. Tounderstandthebondhybridizationinmoredetail,weprojectedtheKohn-Shamorbitalsofa
48-atomrectangularsupercelltothemaximallylocalizedWannierorbitals35ofthesp2-bondedcarbosilaneanalogueofethene
(SiH CH ),withitsSiandCatomsfixedtothelocationscorrespondingtoasingleSi–Cbond. Theresultingprojectoroverlaps
2 2
wereclosetounity,indicatingthatthesesp2molecularorbitalsprovideagoodrepresentationofthebond.
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V)
e
y (
g
er
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n
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o
h
P
Γ Γ
Figure4. Thephononbandstructureof2D-SiCandthecorrespondingdensityofstates(in-planeandout-of-plane
componentsareshowninredandblue,respectively).
Phononbandstructureandcohesiveenergy
Wethencalculatedthephononbandstructureof2D-SiCthroughitsdynamicalmatrix,estimatedbydisplacingeachprimitive
cellatombya0.08A˚ displacementinthethreeCartesiandirectionsandcalculatingviaDFTtheforcesonallotheratomsina
7×7supercell(theso-called’frozenphonon’approximation;Methods). Unlikethatofanearliercalculation14,theresulting
phononbandstructure(Fig.4)containsnoimaginaryfrequencies,demonstratingthestabilityofthematerial17. Theenergyof
theRaman-activetransverseopticalbranchatΓis127meV,anticipatingaG-band-likefeatureat1024cm−1. Itthusseems
clearthatfullyplanar2D-SiCindeedisstable,andwhileitscohesiveenergy(PBEfunctional)is0.50eV/atomlowerthanthat
of3C-SiC(themainbulkSiCpolymorphshaveverysimilarenergies36),thatdifferenceissmallerthanthatbetweensilicene
andmonocrystallineSi(0.64eV/at.).
Otherproperties
Furtherpropertiesof2D-SiCcanbecomputationallypredicted. Intermsofelectronirradiationstability,Siistooheavyto
bedisplacedfromtheSiCstructureataccelerationvoltagesbelow100kV.Wecalculatedthedisplacementthresholdenergy
T fortheCatomviaDFTmoleculardynamics(MD),describedindetailpreviously32,37–40. Inbrief, weestimatedT by
d d
increasingthestartingout-of-planekineticenergyofaselectedCatomuntilitescapedthestructureduringthecourseofan
MDsimulation. ForthestructureshowninFig. 2,theenergyrequiredtodisplaceaCatomfromtheSiCpatchisapproximately
13.25eV.Althoughthisishigherthanwhatcanbetransferredtoastaticnucleus,itislowenoughthatatomicvibrationscan
enabledisplacements32,40,41 andbondrotations37. ForaCatominbulk2D-SiC(7×7supercell),thethresholdisinstead
15.75eV,leadingtoanegligibledisplacementprobabilityby60keVelectronsatroomtemperature. Thusamacroscopicflake
of2D-SiCshouldproveratherstableforlow-voltagemicroscopy. Wealsocalculateditsbulkmodulusbyuniaxiallystraining
theoptimal2D-SiCunitcellandfindingtheminimumoftheresultingtotalenergycurve,resultingin98.3GPa.
Finally,weestimatedtheC1sandSi2pcorelevelbindingenergiesof2D-SiCviadeltaKohn–Sham(∆KS)totalenergy
differencesincludinganexplicitcore-hole42,43 (Methods). TheC1senergywascalculatedat283.265eVandtheSi2pat
101.074eV.Althoughtheabsolutevaluesaresensitivetotheaccuracyofthedescriptionofcore-holescreening,theenergy
separationC1s–Si2pof182.19eVshouldcharacterize2D-SiCwell.
Table1. Comparisonof2D-SiCpropertieswecalculatedtothoseofthemajorbulkpolytypesreportedintheliterature(from
Ref.44unlessotherwiseindicated).
Polytype 2D-SiC 6H(α) 4H 3C(β)
Symmetry hexagonal hexagonal hexagonal cubic
In-planelatticeconstant(A˚) 3.104 3.0810 3.0730 4.3596
Si-Cbondlength(A˚) 1.792 1.89 1.89 1.89
Bandgap(eV) 2.58 3.05 3.23 2.36
Bulkmodulus(GPa) 98.3 220 220 250
Opticalphononenergy(meV) 127 102.8 104.2 104.2
C1s–Si2p(eV) 182.19 181.945 182.346 182.1747
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a b
2.32 Å
c d
3.52 Å
e f
3.37-3.67 Å
Figure5. Calculatedequilibriumstructuresofbilayersof2D-SiCwithitself(a-b),graphene(c-d)andhexagonalboronnitride
(hBN,e-f). (a-b)Twolayersof2D-SiCinAA’stackingspontaneouslybondcovalently(all-electronchargedensityisosurface
showninthecornerofthecellinb),resultinginaninterlayerdistanceof2.32A˚.Whentheotherlayerisgraphene(c-d)or
hBN(e-f),theequilibriumdistancesandbindingenergiesaretypicalforvanderWaalsbonding. (NotethattheresultinghBN
structureisslightlybuckledduetolatticemismatchinthechosenunitcell.)
Reactivityandbilayers
Consideringthelargechargetransferandunconventionalhybridizationoftheflatstructure,wesuspectedthat2D-SiCmightbe
chemicallyreactive. Tostudythiscomputationally,wefirsthydrogenatedamonolayerof2D-SiCwithatomicH(inanalogyto
graphane48). TheHpreferentiallybondswithC,withaformationenergyof0.79eVwithrespecttothechemicalpotentialof
H . However,asecondHbondstoSiontheoppositesideoftheplane,resultinginahighlycorrugatedstructurewhenthecell
2
isallowedtorelax,bringingtheformationenergydownto-1.23eV.Thus,similartosiliceneandphosphorene49,50,2D-SiC
likelyisunstableinair.
Finally,toestimatethestabilityof2D-SiCinbilayers,wecompletedseveralcalculationsusingavanderWaalsexchange
correlationfunctional51 (intheplane-wavemode,seeMethods). First,weinitializedasimulationwithtwo2D-SiClayers
4A˚ apartineachofthefivepossiblestackingorders(inanalogytohBN52).AlthoughAB,AB’,A’BandAAstackingresulted
instablebilayers,thelowestenergy(by34,41,54and55meV/atom,respectively)isobtainedforAA’stackingwheretheSi
arelocatedovertheCandviceversa(Fig. 5a). Minimizingtheforcesbringsthetwolayerstowithin2.32A˚ ofeachother,
inducingaslightcorrugationoftheplanes. Theresidualstressesoftheunitcellindicatethatitssizepreventsthestructure
fromreachingits(three-dimensional)groundstate,andanalysisoftheall-electrondensitybetweenthelayersclearlyindicates
covalentbonding(Fig. 5b),inalmostperfectanalogytobilayersilicene53. ThisconfirmsthatnovanderWaalsbondedlayered
equivalentof2D-SiCcanexist,inagreementwithitsabsenceamongtheknownphasesofbulkSiC.However,whentheother
layerisinsteadeithergraphene(a5×5supercellofgraphenehasonlya0.5%latticemismatchtoa4×4supercellof2D-SiC)
orhBN(-1.4%mismatch),theequilibriumdistancesare∼3.5A˚ withbindingenergiesof∼56meVperatom(finite-difference
mode,seeMethods),bothconsistentwithvanderWaalsbonding. Thissuggeststhatencapsulationcouldbeusedtoprotect
2D-SiCfromtheatmospherewithoutseriouslyaffectingitsproperties.
Conclusions
Inconclusion,ouratomicresolutionscanningtransmissionelectronmicroscopyobservationsprovidethefirstdirectexperimental
indicationthatatwo-dimensionalformofsiliconcarbidemayexist. Poresingrapheneoxideactastemplatingspaces,with
theelectronbeameffectivelyprovidinganenergyinputsothattheSi-Cconfigurationspaceisexplored. Duringthisprocess,
mobileadatomsofCandSiprovideachemicalsource. Asrevealedbyextensivesimulations,thegroundstateofbulk2D-SiC
isindeedcompletelyplanar,withsp2hybridizationoftheSi–Cbond. ThelargechargetransferfromSitoCandthepreference
ofSiforsp3hybridizationrenderthelayerchemicallyreactiveandunstableinbilayers,similartoseveralother2Dmaterials.
However,oursimulationsindicatethatbilayersof2D-SiCwitheithergrapheneorhexagonalboronnitridearestable,makingit
apromisingcandidateforincorporationintolayeredvanderWaalsheterostructures54.
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Methods
Samplepreparation
Graphitepowder(purity99.9995%,2-15µmflakes,AlfaAesar)wasmixedintosulphuricacid,andthenpotassiumperman-
ganateandsodiumnitrateaddedportion-wise. Fortheoxidation,waterwasaddedandthereactionmixtureheatedto98◦Cfor
3weeks. Terminatingthereactionwasfollowedbyfiltering,washing,anddrying. Toexfoliatetheresultinggraphiteoxide
powderintosingle-layerflakes,itwasmixedwithdeionizedwater,vigorouslystirredfor24h,followedbybathsonication
for3h,tipsonicationfor30min,andfinallybathsonicationforafurther1h. TopreparetheTEMsamples,aAusupport
gridcoveredwithaholeycarbonfilm(Quantifoil(cid:13)R)wasdippedintoawater-baseddispersionfor1minandthenrinsedin
isopropanolanddriedinair55.
Electronmicroscopy
The Nion UltraSTEM100 scanning transmission electron microscope was operated at 60 kV in near-ultrahigh vacuum
(∼2×10−7Pa). ThebeamcurrentduringtheexperimentswasafewtensofpA,correspondingtoadoserateofapproximately
1×107e−/A˚2s. Thebeamconvergencesemianglewas35mradandthesemi-angularrangeofthemedium-angleannulardark
field(MAADF)detectorwas60–80mrad.
Densityfunctionaltheory
ThelargercellcalculationswereconductedusingtheGPAWfinite-differencemodewitha0.18A˚ gridspacingand3×3×1
Monkhorst-Packk-points. Fortheplane-wavecalculations,weusedacutoffenergyof600eV(increasedto700eVforthe
bandstructure)and45×45×1k-points. ThePerdew-Burke-Ernzerhof(PBE)functionalwasusedtodescribeexchangeand
correlation,exceptforthebilayersimulationswhereweusedtheC09functional51.
Forcalculatingthephononbandstructure,weusedinsteadthelocaldensityapproximation(LDA)andaΓ-centredk-point
mesh of 42×42×1 was used to sample the Brillouin zone. A fine computational grid spacing of 0.16 A˚ alongside strict
convergencecriteriaforthestructuralrelaxation(forces<10−5 eV/A˚ peratom)andtheself-consistencycycle(changein
eigenstates<10−13eV2perelectron)ensuredaccurateforces.
Forthecorelevelcalculations,anextraelectronwasintroducedintothevalencebandtoensurechargeneutrality,and
supercellsupto9×9insizeusedtoconfirmthatspuriousinteractionsbetweenperiodicimagesofthecoreholewereminimized.
Althoughspin-orbitinteractionwasnotincludedintheSi2pcalculation,itsbindingenergycanbetakentocorrespondtothe
2p levelandasplittingof0.63eVinferredfromtheory.
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Imagesimulation
OurQSTEMparameterswere: chromaticaberrationcoefficientof1mmwithanenergyspreadof0.3eV;sphericalaberration
coefficientof1µm;thermaldiffusescatteringincludedviafrozenphononmodellingwithatemperatureof300K;additional
instabilities(suchassamplevibration)simulatedbyblurringtheresultingimage(Gaussiankernelwithasigmaof0.39A˚);
andthemedium-angleannulardark-fielddetectoranglerangesettotheexperimentalrangeof60–80mrad. Shotnoisewas
removedfromthefilteredexperimentalimageofFig. 2cbyblurringitwithaGaussiankernel(sigmaof0.28A˚).
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Acknowledgements
WethankMichaelWalterandMiguelCaroforusefuldiscussions. T.S.acknowledgesfundingfromtheAustrianScienceFund
(FWF)viaprojectP28322-N36andtheViennaScientificClusterforcomputationalresources. V.S.wassupportedbythe
FWFviaprojectAI0234411/21,andthroughprojectsVEGA1/1004/15andUVP,OPVaV-2011/4.2/01-PN.A.M.andJ.C.M.
acknowledgefundingbytheFWFprojectP25721-N20andtheEuropeanResearchCouncilGrantNo. 336453-PICOMAT.T.J.P.
wassupportedbytheEuropeanUnion’sHorizon2020researchandinnovationprogrammeundertheMarieSkłodowska-Curie
grant agreement No. 655760 – DIGIPHASE, and J.K. by the Wiener Wissenschafts-, Forschungs- und Technologiefonds
(WWTF)viaprojectMA14-009.
Author contributions statement
T.S.conductedtheDFTsimulationsanddraftedthemanuscript. V.S.conceivedofthestudy,conductedelectronmicroscopy,
andsupervisedthesamplesynthesis. A.M.simulatedtheSTEMimages. P.K.andM.H.synthesizedthesamples. T.J.P.and
C.M.participatedinelectronmicroscopy. J.K.andJ.C.M.supervisedthestudy. Allauthorsreviewedthemanuscript.
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Additional information
CompetingfinancialinterestsTheauthorsdeclarenocompetingfinancialinterests.
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