Defect Centers in a-SiN
x :
Electronic and Structural Properties
F. de BritoMota,
InstitutodeFsicadaUFBa,CEP40210-340,Salvador,BA,Brazil
J.F. Justo and A. Fazzio
InstitutodeFsicadaUniversidadede S~aoPaulo,CP66318, CEP05315-970, S~aoPaulo,SP,Brazil
Receivedon23April,2001
Bycombiningabinitiomethodsandinteratomicpotentials,weinvestigatedtheelectronicandthe
structuralproperties of amorphous silicon nitride. Ourresults showthe trendsonthe electronic
bandstructureofSiNx(0:5<x<1:8)asthenitrogencontentchanges,andareingoodagreement
withtheexperimental data. Hydrogenationof thesystemswas foundto considerablyreduce the
numberofenergylevelsinthe gap. Theenergylevels whichappearedinthematerials bandgap
werecomparedtotheelectricallyactivecenters,whichhavebeenidentiedbyelectron-paramagnetic
resonanceexperiments.
Amorphous silicon nitride (a-SiN) is a material of
unique electronic properties, such as large electronic
gap, and high dielectric constant. Due to these supe-
riorelectronicproperties,ithasbeenusedinmicroelec-
tronicdevicesasagatedielectricinthinlmtransistors
oras a charge storage medium in non-volatile memo-
ries. Although considerable eort has been spent in
studying silicon nitride, anumber of issues related to
itsmicroscopicpropertiesremainunadressed.
Overthelast decade,SiNhasbeeninvestigatedby
several theoretical methods [2, 3, 4, 5]. Those inves-
tigationsusedparameter-dependentmodels, providing
only a qualitative description of the physical proper-
ties of the systems. Tight-bindingmodels [5], for ex-
ample, introduced unphysical shifts in the electronic
energy levels, in order to reproduce the experimental
electronic band structure. Amorphous silicon nitride
havenotbeeninvestigated by parameter-freeab initio
methods sofar. Here wecombinedinteratomic poten-
tials[2,4]withabinitiomethodstoinvestigatetheelec-
tronicpropertiesofunhydrogenatedandhydrogenated
amorphous silicon nitride in a wide range of nitrogen
contents. The results were compared to available ex-
perimental data.
Atomistic simulations based on ab initio methods
have been a formidable task, specially in the case of
disorderedsystems. Inordertoovercomesuchcompu-
tationaldiÆculties,weusedinteratomicpotentials[2,4]
togeneratetheinitialamorphouscongurations. These
were usedasinputcongurationstotheab initiosim-
ulations,whenfullrelaxation,basedontheHellmann-
Feynman forces, could be performed. This procedure
tional cost in nding the equilibrium congurations
[6,7, 8]. However,thisprocedurewouldonlyspeedup
thesimulationsiftheinteratomic potentialsaretrans-
ferable, i.e., theycanprovide arealisticdescriptionof
the amorphous systems. We have recently developed
aninteratomicpotentialwhichdescribesaccuratelythe
structural properties of silicon nitridein awide range
of nitrogen contents[2, 4]. Theamorphouscongura-
tions were generated using that interatomic potential
combinedwithMonteCarlosimulationsinasimulated
annealingprocedure. Therelaxationofboththeatomic
positionsand thecellvolume were allowedin thesim-
ulatedannealing.
Theabinitiocalculations[9]wereperformedwithin
the local density approximation. The Kohn-Sham
equationsweresolved usingtheCar-Parrinelloscheme
withseparablepseudopotentials[10]. Thebasissetwas
expandedin plane-waves,with kineticenergyupto65
R y. Thenuclearpositions were fullyrelaxedin theab
initio calculations until the Hellmann-Feynman forces
weredownto 10 3
a.u. Thelargeunit cell comprised
66 atomsfor allnitrogen and hydrogencontents. The
Brillouin zone was sampled by the -point. Our in-
vestigations considered only one atomic conguration
for each nitrogen content (a-SiN
x
, x = 0.5, 1.0, 1.33,
1.5, and 1.8). Still we expected to provide a reason-
ably good sampling of an amorphous silicon nitride.
Tocertify that wein fact generated realisticsamples,
wecomputed thepaircorrelation functionand theav-
eragecoordinationnumbers. Forallnitrogencontents,
arst peak appears around1.75
A whichcorresponds
toSi-Nbonds,whileasecondpeakappearsaround2.5
mentwiththeexperimental data[11]. Fortheaverage
coordinationnumberat Si andN sites [2], ourresults
agreeverywellwiththeexperimentaldata[12]forsev-
eralnitrogencontents. Sincethelocalorderdetermines
mostoftheelectronicpropertiesofthematerial,ourab
initiocalculationsshouldprovidearealisticdescription
oftheelectronicband structureofa-SiN.
Generally, the electronic density of states (DOS)
of amorphous semiconductors obtained by theoretical
modeling present a large number of gap levels. Sev-
eral authors have used some artifacts to \clean" the
gap from those spurious levels. Ina-Si,the gap levels
havebeenremovedbyremovingtheatoms which pre-
sented danglingbonds, and passivating the remaining
bonds with H [13]. On the other hand, we removed
the gap levels by introducinghydrogen in the sample,
performed asimulatedannealing with interatomicpo-
tentials,andthenperformedtheab initiocalculations.
Our procedure wasless articial than others [13, 14],
although alsolesseectiveinremovingthegaplevels.
−20 −16 −12 −8 −4 0 4 8
E (eV)
(e) (d) (c) (b) (a)
D O S
Figure1. Theoreticaltotaldensityofstatesofa-SiN
x . The
gure shows the DOS for (a) x = 0:5, (b) x = 1:0, (c)
x=1:33,(d)x=1:5,and(e)x=1:8.
Fig. 1shows thecalculatedDOS for thea-SiN
x :H
(0 < x < 1:8) with 18% of hydrogen atomic concen-
tration. For x =1.33, the DOS is equivalent to that
of the crystalline -Si
3 N
4
. Therst region of the va-
lence band (VB), corresponding to the N-2s states,is
between-20.0 eV and -12.5 eV. The second region of
the VB,between-10.5and 1.5 eV,is formedby levels
coming from the hybridization of the N-2p and Si-3p
states. Thetopofvalenceband isformedbytheNp
lonepairs. Thegapis foundtobe2.0eV. Theenergy
gap increases with increasing nitrogen concentration,
in the topof the VB, by Si-Nbonds; and by thedis-
placementof the bottom of the conduction band,due
tothesubstitutionofSi-Sianti-bondingstatesbySi-N
anti-bondingones.
−20 −16 −12 −8 −4 0 4 8 12
E (eV) 0
20 40 60
IPR
(a)
−20 −16 −12 −8 −4 0 4 8 12
E (eV) 0
40 80 120
IPR
(b)
Figure2.Inverseparticipationratio(IPR)forallenergylev-
elsina-SiN
x
:H.Thegureshowsthe IPRfor (a)x=1:33
and(b)x=1:5.
Thegap wasdeterminedbyanalyzingthelocaliza-
tiondegreeofthestatesnear theband edges. Thelo-
calizationofeachelectronicstatewasquantiedbythe
inverseparticipationratio(IPR).TheIPRofanorbital
n (
!
r
i ),I(
n
),is denedby:
I(
n )=N
P
N
i=1 j
n (
!
r
i )j
4
h
P
N
i=1 j
n (
!
r
i )j
2 i
2
; (1)
whereN isthenumber ofvolumeelementsin thecell
andi is theindex of the volume element. TheIPR is
largefor highly localized states and small fordelocal-
izedstates.
The IPR can identify a level as belonging to the
band (delocalized), to the band-tail (partially local-
ized), or to the gap (highly localized). Fig. 2 shows
theIPRforallstatesina-SiN
x
:Hfortwonitrogencon-
tents. ThelargeIPRforthestatesinthebottomofthe
N-2s states. For all nitrogen contents, the closer the
statesare from the gap, thelarger is theIPR. Fig. 3
shows thetheoretical gap asfunction of nitrogen con-
tents obtained by the IPR.The gurealso showsthe
experimental opticalgap [12, 15, 16]. Ourresultsgive
thecorrecttrend: theelectronicgapincreaseswiththe
nitrogen content. Ourresultsalso show that theelec-
tronic gap increases faster with x for x > 1 than for
x < 1, also in agreementwith the experimental nd-
ings. However,ourresultsunderestimatethegapforall
nitrogen contents, which results from the known lim-
itation of the density functional theory in describing
excitedstates.
0 0.5 1 1.5 2 2.5
x 1
2 3 4 5 6
E (eV) g
This work Guraya [11]
Hasegawa [14]
Yin [15]
Figure 3. Electronic energy gap (Eg) versus the nitrogen
content(x).Thegurealsoshowstheexperimentaloptical
gap[12 ,15 ,16 ]. EnergiesareineV.
Electron paramagnetic resonance (EPR) experi-
ments have measured several paramagnetic centers in
siliconnitridewhichhavebeenidentiedtoundercood-
inatedatoms. Acenterwhichgeneratesanenergylevel
inthemiddleofthegaphasbeeninterpretedasdueto
a three-fold coordinated silicon atom (K-center) [17].
A center which generates an energy level in the bot-
tom of the gap hasbeen interpreted asdue to atwo-
fold coordinated nitrogen atom (N
2
-center) [17]. We
investigatedthepropertiesofthegaplevelsina-SiN
1:5
which presented large IPR, and compared their elec-
tronic spatial distribution with the characteristics of
the known EPR centers. We could identify both cen-
ters in ourinvestigation. A level atE
v
+2:48eV(E
v
is thetopof valence band), and thereforeclose tothe
conduction band,clearly showsa danglingbond char-
acteristic,withtheelectronicchargelocalizedarounda
siliconatom. ThislevelisconsistentwiththeK-center
identied byEPR [17]. A levelat E
v
+0:45eV, near
thevalenceband,showsadanglingbondcharacteristic,
with theelectronic chargelocalized aroundanitrogen
atom. ThislevelisconsistentwiththeN
2
-centeriden-
tiedbyEPR[17].
Insummary,wehaveused ab initiocalculationsto
investigate the electronic properties of hydrogenated
trations. Allofourresultswereingoodagreementwith
available experimental data. Theinverseparticipation
ratio allowedto identify thespatial localization of the
all theenergylevels. This showsthat the IPRcanbe
aneectivetooltoinvestigatedeeplevelsinamorphous
materialsevenwhenusingsmallsimulationcells.Addi-
tionally, wehavetheoretically identied theelectronic
active centers which appear in the gap in a realistic
sampleofamorphoussiliconnitride. Thoselevelswere
correlated to theknown EPRresults, namely, the un-
dercoordinatedSiandN atoms.
Acknowledgments
FBM and JFJ acknowledge partial support
from Brazilian agencies PRODOC/CADCT-BA and
FAPESP, respectively. The calculations were per-
formed attheComputerCenter oftheUFBa.
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