Adsorption of Si and C Atoms over SiC (111) Surfaes
P. G. Vivas,E. E. daSilva, L.C. de Carvalho, J.L. A. Alves, H. W. Leite Alves,
DepartamentodeCi^eniasNaturais-FUNREI,
C.P.: 110, CEP:36300-000, S~aoJo~aodelRei-MG,BRAZIL
L. M. R.Solfaro, and J. R. Leite
LNMS,Departamento deFsiadosMateriaiseMe^ania, USP,
C.P.: 66.318,CEP:05389-970, S~aoPaulo,SP, Brazil
Reeivedon23April,2001
Inthiswork,usingDensityFuntional,Hartree-FokandExtendedHukelTheoriestogether
with thesuperellandlustermodelapproahes,wepresentourpreliminaryresultsforthe
simulationof theadsorption of Si and C atoms overthe (111) SiC surfaes aswell asthe
torsion of SiC moleules at that surfaes. Our results shown that, before and after the
adsorption,theubistruturearethemoststableone,whenomparedwiththehexagonal
ones. However,thetorsionalenergybarrierbetweentheubiandthehexagonalstruturesis
smallenoughthat,attheonditionsofSiCgrowth,itfailitatestheSiCpolytypeformation.
I Introdution
ThereentinterestonthephysialpropertiesofSiC,is
duetothefatthatthisompoundisthemost
promis-ing substratefor the growth ofIII-Nitrides. Also,the
material is the ideal one for the fabriation of
semi-ondutor deviesoperatingunder extreme onditions
[1,2℄. Moreover, SiC has alarge numberof polytypes
and the knowledge of their properties is a key for
bothsuessfulgrowthoftheIII-Nitridesandthe
high-temperature miroeletroni devies. The polytypes,
orstablelong-rangeorder modiations,aredesribed
asdierent staking sequenesof SiC layersalongthe
[111℄orthe[0001℄diretionsoftheorrespondingubi
orhexagonalstrutures[3-6℄.
DespitetheprogressahievedonthegrowthofSiC
by MOCVD(or by MBE), lots of small triks(suh as
heating the substrate or reating buer layers) have
beenemployedtoobtainaspeimodiationofsuh
material[7,8℄. Moreover,there isnoexperimental SiC
thermodynami phase diagram, whih it ould be a
goodguidefortheknowledgeofthemehanismsofthe
polytypeformation.
On the theoretial side, there have been some
progresson the understanding thestrutural,
dynam-ialand eletroni properties ofSiC and itspolytypes
[3-6℄. However,muh ofthese eortsarebasedonthe
statipituresandequilibriumapproahesforthe
pro-In this ase, total energy dierenes alulations
be-tweenpolytypeshavebeendone, aswell asIsing
sim-ulations, and, until now, thereis not areal onsensus
aboutthemehanismsofpolytypeformation[10℄.
In this work, we present our preliminary results
for the atomi and eletroni strutures of the Si and
C atoms adsorbed over both C-terminated and
Si-terminated SiC (111) surfaes in order to understand
the mehanisms of the polytype formation. The
ob-tained results were alulated by means of the
on-jugation of the Density Funtional(DFT),
Hartree-Fok(HF) and Extended Hukel(EHT) Theories
to-getherwiththesuperellandlustermodelapproahes.
Themodels, separately,havebeensuessfullyusedto
haraterizetheIII-Nitridessurfaes[11℄andnow,they
willbeappliedtogethertostudySi-andC-terminated
SiC(111)surfaes ina(11) reonstrutionpattern.
Inourlustermodelalulations,wehaveused
Un-restrited HF method with single-zeta basis
set(STO-3G), within the Gaussian94 ode [12℄. We have
then alulated the optimised uppermost atomi
po-sitions and the resulting eletroni strutures of the
Si6C4H13, C6Si4H13(simulating, respetively, the
Si-and C-terminated SiC (111) surfaes), Si(or C) +
Si6C4H13andSi(orC)+C6Si4H13(simulatingthe
ad-sorptionoftheCandSiatomsoverSiC(111)surfaes)
lusters. In these alulations the inner atoms were
keptxedattheirSi-C,Si-H,andC-Hbonddistanes,
Thehydrogenatomswereintroduedtoprevent
arti-ialdanglingbondsonthesurfae.
Now, for our slab superell alulations, we have
used both DFT, in the Loal Density
Approxima-tion, and the rystalline EHT methods. The DFT
alulations were done within the Car-Parrinello
ap-proahwithinthefhi96mdode[13℄,withthe
Troullier-Martins pseudopotentials[14℄,andtheCeperley-Alder
exhangetermasparametrizedbyPerdewandZunger
[15℄. In this partiular alulation, we use symmetri
slabsonsistingoffourSiCdoublelayersplustwo
en-tral Si layers(in the ase of Si-terminated surfae) or
twoentralClayers(fortheC-terminatedone),similar
to that proposed by Wenzien et al. [16℄. The lattie
onstantswerexedatthebulktheoretialequilibrium
values, a
0
=4.341
A,onvergedwith60 Rydof uto
energyontheplane-waveexpansion. Weusedvauum
regions withathiknessequivalentto four SiCdouble
layers. Theentrallayersoftheslabwerekeptxedat
thebulkpositionsandtheoutermostlayersofatomson
bothsidesoftheslabwererelaxedto geometriesgiven
bythealulatedtotalenergiesandfores. The
equilib-riumgeometry isidentied whenallfores aresmaller
than 0.01 eV/
A. This orresponds to anumerial
un-ertainty of atomi positions of lessthan 0.01
A. The
summation overfourMonkhorst-Pakspeial k-points
intheirreduiblepartoftheBrillouin-zonewasusedto
replaeBrillouin-zoneintegrations.
TheEHTalulationsweredonewithinthe
Bion-Cedit ode, proposed by Calzaferri et al., whih have
applied suessfully on alulations of the eletroni
propertiesof someCarbonompounds[17℄. This
par-tiular versionof EHT method is basedin anewway
to express the weightedWolfsberg-Helmholtz
parame-ter K, whih is now distane-dependent, having only
two parameters: and Æ. In order to obtain these
parameters for SiC, we have parametrized the lattie
parameter and the Bulk modulus for the ubi
modi-ation, using tenMonkhorst-Pakspeial k-pointsin
the alulations. The obtained values were = 0.87
and Æ = 0.56
A 1
, whih lead to a
0
= 4.19
Aand B
0
= 2.03Mbar, in good agreementwith the
experimen-tal results. Asanalhek,wesimulatetheeletroni
struture of the mostommon polytypes(2H, 4H,3C
and6H),andourresultsforthetotalenergydierenes
betweenthe polytypes agree wellwith other
theoreti-alalulations[4,5℄. Fortheslabalulations,weused
sevenSiCdoublelayersand,forthevauumregion,ve
SiCdoublelayers. Thealulationwereperformedwith
II Results and disussion
IntableI,weshowtheresultsfortherelaxationofthe
C- and Si-terminated SiC(111)(11). Here, only the
surfae atoms, in our luster model alultions, were
left to relax, while in the slab alulations, the
sur-faeandthesub-surfaeatomswerelefttorelax.
Sur-prisingly, the results show that these surfaes relaxes
withsmallstrainsz. Theseresultsareonsistentwith
other alulations[16℄, and with the experimental
re-sults[18℄. Besidesthat,ouralulationsshowthatthe
Si-terminated is the most stable one, when ompared
with the C-terminated in this reonstrution pattern.
Considerationsaboutotherreonstrutionpatternswill
bepublishedsooninanotherpubliation.
To simulate the adsorption of any atom over the
(111) surfae, we must onsider the following
adsorp-tionsites [16℄: T1,T4 andH3,whih areover,
respe-tively,asurfaeatom,asub-surfaeatomandaseond
sub-layeratom. OursimulationsaboutthatforSi and
CatomsadsorbedoverC-terminatedSiCsurfaes,they
preferthe T1 site,whih z =1.85
Aand 1.27
A,
re-spetively. Itisinterestingtonotethat,Si tryto keep
the same interatomi SiC distane, 1.89
A, while the
C-CdistaneislessthantheC-Cinteratomi distane
indiamond,whihis1.54
A.
Table 1: Summary of the alulated surfae strains
z(in
A) fortherelaxationof the3C-SiC(111)(1 1)
surfaes. z
1
isrelated tothe topsurfaeatoms, and
z
2
,to therstsub-layer.
Si-terminated C-terminated
z
1
z
2
z
1
z
2
HF -0.06 | -0.01 |
EHT 0.00 0.00 -0.07 0.0
DFT -0.06 0.04 | |
Our simulations for the Si and C adsorption over
Si-terminatedsurfaes show,on theontrary,that the
adsorbatesprefer theT4 site,in goodagreementwith
other alulations [18℄. In this ase z = 1.37
Aand
0.43
Afor the adsorption of Si and C,respetively. A
moredetailedanalysisoftheeletronistatesandtheir
onnetiontotheatomistrutureoftheadsorbed
sur-fae is in progress and will ome up soon in another
publiation.
Finally,wealsohavesimulatethetorsionofthe
ad-sorbedSiovertheC-terminatedSiC(111)surfae,using
themoleular lustermodel. Todothat, weaddmore
three hydrogen atoms on the adsorbed Si in order to
simulate the two possible ongurations for the next
strutures. Our results showedthat the ubi
modi-ation is, at 0 K, the most stable. However, the
en-ergy barrier betweenthe twoongurations isaround
84 meV, whih is extremally smaller. We an infer,
fromthis result,that atthetemperatureonditionsof
theSiCgrowth,weouldnotdistinguishwhatkindof
ongurationan theadsorbedlayersbe,i.e.,ifitisin
a"is"orina"trans"onguration. So,thisouldbe
thereasonforthelargenumberofSiCpolytypesfound
inthenature.
III Final Remarks
In summary, we have presented our preliminary
re-sultsforthe atomiandeletroni struturesof theSi
andCatomsadsorbedoverbothC-terminatedand
Si-terminated SiC (111) surfaes in order to understand
themehanismsofthepolytypeformation. Ourresults
shown that, the relaxations of the (11)
reonstru-tion pattern are small, and the Si-terminated surfae
is more stable than the C-terminated one. We also,
simulatetheadsorptionofSiandCatomsoverthe
re-onstruted surfae. Our results show that, after the
adsorption, the T1 and T4 sites are the most stable
oneforthe,respetively,C-andSi-terminatedsurfaes.
Finally,thetorsionalenergybarrierbetweentheubi
and the hexagonalstrutures is small enoughthat, at
theonditionsofSiCgrowth,itfailitatestheSiC
poly-typeformation.
Aknowledgements
ThisworkwaspartiallysupportedbyCNPqandby
FAPEMIG.
Referenes
1. S.C.Jain,M.Willander,J.Narayan,andR.van
Overstraeten,J.Appl. Phys. 87, 965(2000).
2. R. S. Kern and R. F. Davies, Mater. Si. Eng.
3. G.L.Vignoles,J.Cryst. Growth118,430(1992).
4. P. Kakell, B. Wenzien, and F. Behstedt, Phys.
Rev. B50,17037(1994).
5. S.Limpijumnong andW. R.L.Lambreht,Phys.
Rev. B57,12017(1998).
6. C. -Z. Wang, R. Yu, and H. Krakauer, Phys.
Rev. BB53,5430 (1996);F.Widulle, T.Ruf, O.
Buresh, A. Debernardi, and M. Cardona, Phys.
Rev. Lett. 82,3089(1999).
7. R.S. Kern,S. Tanaka,L.B.Rowland, andR.F.
Davies,J.Cryst. Growth183,581(1998).
8. C.Bittenourt,Semiond. Si. Tehnol. 15,1115
(2000).
9. J.Y. Tsao,Materials Fundamentalsof Moleular
BeamEpitaxy(AademiPress,SanDiego,1993).
10. V.Heine,C.Cheng,andR.J.Needs,Mater. Si.
Eng. B11,55(1992).
11. J.L.A.Alves,H.W. LeiteAlves,C.deOliveira,
R.D. S. C.Valad~ao, andJ.R.Leite,Mater. Si.
Eng. B43,288(1997);Mater. Si. Eng. B50,57
(1997);H.W.LeiteAlves,J.L.A.Alves,J.L.F.
da Silva, J.R. Leiteand R. A. Nogueira, Mater.
SiEng. B59,258(1999);H.W.LeiteAlves,J.L.
A. Alves, R. A. Nogueira, andJ. R. Leite, Braz.
J.Phys. 29,817(1999).
12. Gaussian 94, Revision D.4, M. J. Frish et al.,
GaussianIn.,PittsburghPA,1995.
13. M. Bokstedte, A. Kley, J. Neugebauer, and M.
Sheer, Comput. Phys. Comm. 107, 187
(1997).
14. N. TroullierandJ. L.Martins, Phys. Rev. B43,
1993(1991).
15. J. P. Perdew and A. Zunger, Phys. Rev. B23,
5048(1981).
16. B. Wenzien, P. Kakell and F. Behstedt, Surf.
Si. 331-333,1105(1995).
17. G. CalzaferriandR. Rytz, J.Phys. Chem. 100,
11122(1996);G.Calzaferri,L.Forss,andI.
Kam-ber,J.Phys. Chem. 93,5366(1989).
