2024年5月11日发(作者：佳能90d镜头推荐)

CarbonantisiteclustersinSiC:apossiblepathwaytotheD

II

center

AlexanderMattausch,

∗

MichelBockstedte,andOlegPankratov

Lst.f¨urtheoretischeFestk¨orperphysik,Universit¨atErlangen-N¨urnberg,Staudtstr.7,D-91058Erlangen,Germany

(Dated:February2,2008)

2

0

0

4

ThephotoluminescencecenterD

II

isapersistentintrinsicdefectwhichiscommoninallSiC

fing

performab-initiocalculationsofvibrationalspectraforvariousdefectcomplexesandfindthatcarbon

antisiteclustersexhibitvibrationalmodesinthefrequencyrangeoftheD

II

sters

possessveryhighbindingenergieswhichguaranteetheirthermalstability—aknownfeatureofthe

D

II

arbonantisite(C

2

)

Si

(twocarbonatomssharingasiliconsite)isanimportant

b

e

buildingblockoftheseclusters.

F

PACSnumbers:61.72.-y,,78.55.-m

4

]

i

UCTION

c

s

-

l

ManyuniquefeaturesofSiC,suchasthewideband

r

t

gapandtheveryhighelectricalandthermalstability,

m

renderthissemiconductorespeciallyimportantforhigh

.

power,highfrequencyandhightemperatureapplica-

t

a

nysemiconductormaterial,theidentifi-

m

cationandunderstandingofstructuraldefectsandim-

-

puritiesisthekeytothetechnologicalcontrolofSiC.

d

Thisisespeciallyimportantinconnectionwiththeion-

n

implantation,whichisinevitablyaccompaniedbythe

o

thesedefects

c

[

ortantexamplesare

thephotoluminescence(PL)centersD

I

(Ref.1)andD

II

3

(Ref.2).Althoughthecentershavebeenextensively

v

2

studiedoverthepast30years,

1,2,3,4,5,6,7

theirmicroscopic

1

workwestudycarbon

1

antisiteclustersandtheirpossiblerelevancetoD

II

-type

9

centers.

0

D

II

centersarealwayspresentinion-implantedandan-

3

nealedSiCsamples,regardlessoftheimplantedspecies

0

realsofound(inlowcon-

/

t

a

centration)inas-grownmaterial.

4

TheabundanceofD

II

m

centersincreasessignificantlyathighannealingtemper-

atures(above

-

4

1300

)andthecenteristhermallystable

d

ropertiesimplythattheD

II

cen-

n

II

luminescence

originatesfromtherecombinationofanexcitonbound

c

o

ctraareusuallyidentifiedbythe

:

v

ortantspecificfeature

i

X

ofD

II

arecharacteristicphononreplicasabovetheSiC

riginalexperimentsin3C-

r

a

SiCthestrongest

6,7

fivereplicaswerehighlighted.

2

Inlater

experimentsin4Hand6H-SiCadditionallocalizedvi-

brationalmodes(LVMs)wereobserved(morethan12

LVMshavebeencountedin4H-SiC

6

).Manyofthese

ri-

sonofthespectrafromRef.7andtheearlierRef.2re-

vealsthatmorethanthefivehighlightedLVMsmayalso

pectraldensity

resemblesthephonondensityofstatesindiamond,indi-

catingthatacarbon-dominateddefectisresponsiblefor

theobservedspectrum.

Si

C

C

I

C

I

(C )

2Si

(C )

4Si

FIG.1:Structureofthedicarbonantisite(C

2

)

Si

andacarbon

clusterwithfouratomsonasiliconsite(C

4

)

Si

in3C-SiC.

Inthisworkweconsideranumberofcarbon-related

defectsinSiC:thecarbondi-interstitial,whichwasthe

firstsuggestedmodelfortheD

II

center,

2

thecarbonanti-

site,thecarbonsplit-interstitialsandseveralcarbonclus-

ingthecalculatedLVMswiththeexperi-

mentalD

II

spectraweareabletounequivocallyruleout

latteraretheonlydefectsthatprovidearichLVMspec-

trumsimilartothatoftheD

II

estruc-

tureofalltheseclustersisthedicarbonantisite(C

2

)

Si

(.1left)whichactsasanaggegationcenterfor

paperwewillfirstpresent

ourresultsforthedicarbonantisiteandthenconsider

u-

latetheLVMsassociatedwiththesedefectsandcompare

themwiththeD

II

ghtheoreticallyall

thesedefectscanacquiredifferentchargestates,wefo-

excitonsboundtoachargeddefectmorenon-radiative

recombinationchannelsareopen,andtheyareunlikely

tobeseeninPL-experiments.

8

Wealsofindthatthefor-

mationkineticsofthecarbonclustersagreeswiththe

knownfeaturesoftheD

II

esultsindicate

thatalthoughneitheroftheconsidereddefectscanalone

explainallfeaturesoftheD

II

center,thecarbonantisite

clustersmayserveasacorestructureofD

II

-typedefects.

Weemployanabinitiodensityfunctionaltheory

(DFT)approachasimplementedinthesoftwarepackage

FHI96SPIN.

9

Smoothnorm-conservingpseudopotentials

oftheTroullier-Martintype

10

andaplane-wavebasis-set

withacut-offhange-

correlationpotentialisapproximatedwithintheLSDAin

theparametrizationofPerdewandZunger.

11

Inorderto

reducetheartificialdefect-defectinteraction,largesuper-

cellswith216latticesitesfor3C-SiCand128sitesfor4H-

SiCareusedforallcalculationsofthedefectenergetics.

Forthe216-sitecell,theBrillouinzoneissampledbythe

Γpoint,whereasforthehexagonal128-sitecellaspecial

MonkhorstandPack

12

2×2×ues

oftheformationenergiesaregivenassumingsilicon-rich

arbonrichconditionstheyshouldbe

reducedbyroughly3∆H

f

=1.74eV,where−∆H

f

isthe

rationalpropertiesare

am-

icalmatrix

Φ

1

∂

2

E

ij

=

m

i

m

j

√

∂Q

j

iscalculatedbyapplyingdisplacementsQ

j

fromtheequi-

libriumconfigurationandevaluatingtheforcederivatives

∂F

i

/∂Q

j

.Toobtainnoticeableenergychanges,thedis-

placementsQ

j

oughttobemuchlargerthanrealistic

oreitisimportanttoelimi-

natetheanharmoniccontributionwhenevaluatingΦ

ij

.

Wedothisbyapplyingthreedifferentvaluesofthedis-

placementandextractingthelinearforceconstantfroma

ceshavebeen

convergedtoarelativeaccuracyof10

−4

.For3C-SiC,

thedynamicalmatrixisevaluatedforasupercellwith64

erimentalbulkphononmodesare

po-

larizationsplittingoftheTOandtheLOmodesatthe

Γpointismissing,sincethemacroscopicpolarizationof

thecrystalisincompatiblewiththeperiodicboundary

inatriple

degeneratemodeat115.3meV,inplaceoftheTOmode

of98.7meVandtheLOmodeof120meV.

13

For4H-SiC

andforlargeclustersin3C-SiC,thecomputationalcost

ofevaluatingthedynamicalmatrixofthewhole128-site

ecases

weconstraintheLVMcalculationtothedefectmolecule

(bbellanditsnearestneighbors)embedded

examinedtheerrorresultingfrom

thedefectmoleculeapproximationandfromtheuncer-

ultsofthesetests

foradicarbonantisitein3C-SiC(seebelow)areshownin

esrepresentthefrequenciesoftheLVMs

versusthedefectmoleculesizecalculatedatthetheoreti-

cal(LSDA)quenciesshiftwithin

thegreyareawhenthelatticeconstantisincreasedto-

ck

barsarethesamefrequencyranges,butinthiscaseboth

2

180

5

5

)

V

e

m

160

(

s

M

V

L

4

f

o

y

c

140

n

3

3,4

e

u

q

e

r

F

2

120

2

1

1

100

050

Size of defect molecule (atoms)

100150200

FIG.2:Defectmodesof(C

2

)

Si

ectmoleculesize

aightlinedenotesthefrequency

atthetheoreticallatticeconstant,thegrayareaisthefre-

quencyshiftforthevariationofthelatticeconstantbetween

ckbarsarethe

correspondingvaluesforthe64sitescellasgiveninTab.I,

thearrowsindicatethephononreplicasoftheD

II

center.

2

theelectronicstructurecalculationandtheLVMcalcu-

alsoverifiedthatunderthepressureexertedbytheperi-

odicarrayofdefectsontothelatticethelatticeconstant

’svariation

duetotheuncertaintyinthelatticeconstantisthusless

soapparentthatthedefectmolecule

approximationaffectstheleastlocalizedmodes1and(to

amuchlesserextend)gesteffectontheaccu-

racyhastheinclusionofthefullsupercell,whichshifts

edto

thefull64sitescell,themode1isonly2meVhigher.

ARBONANTISITE

Letusnowconsideronebyonethecandidatesfor

theD

II

,wefindthatthe

originallysuggestedcarbondi-interstitialhasaforma-

extremelyhigheven

-

lardefectisthecarbonsplit-interstitialC

sp