VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13JULY 1998
Op ical Abso p ion and Non adia i e Decay Mechanism o E000 Cen e in Silica
Gian anco Pacchioni* and Gianluigi Ie anò
Is i u o Nazionale di Fisica della Ma e ia, Dipa imen o di Scienza dei Ma e iali, Uni e si à di Milano,
ia Emanueli 15, 20126 Milano, I aly
An onio M. Má quez
Depa amen o de Quimica Fisica, Facul ad de Quimica, Uni e sidad de Se illa, 41012 Se illa, Spain
(Recei ed 17 Ma ch 1998)
We epo ab ini io con igu a ion in e ac ion calcula ions on he op ical ansi ions o he E0cen e ,
a hole apped a an oxygen acancy, s—Od3Si≤1SisO—d3, in silica. We ound wo compe ing
exci a ion mechanisms: (1) p omo ion o one elec on om an Os2pd alence band o bi al o he singly
occupied Si dangling bond; (2) cha ge ans e (CT) ansi ion om s—Od3Si≤ o 1SisO—d3. The wo
exci a ions occu a simila ene gies, ø5.8 6eV (5.85 eV in he expe imen ), bu only he CT has
a s ong in ensi y. The exci a ion is ollowed by a complex non adia i e decay p ocess which may
explain he absence o luminescence o his cen e . [S0031-9007(98)06572-7]
PACS numbe s: 61.72.Bb, 42.70.Ce, 61.72.Ji, 78.20.–e
Poin de ec s in silica a e o undamen al impo ance
in me al-oxide semiconduc o ield e ec ansis o s and
ibe op ics echnology [1]. One o he mos abundan and
bes cha ac e ized de ec s in SiO2is he E0cen e , a hole
apped a an oxygen acancy, V1
O. The E0cen e is a
undamen al adia ion-induced de ec in amo phous silica,
a-SiO2[1–6], and an impo an sou ce o deg ada ion in
SiySiO2based de ices [4]. Se e al a ian s o he E0cen-
e s exis : E0
1, and H-associa ed E0
2, and E0
4,ina-qua z;
E0
gand E0
dcen e s in a-SiO2.E0
gis he closes analog
o he E0
1in a-qua z [3]. Thanks o he combined use
o op ical abso p ion, OA [1], and elec on pa amagne ic
esonance, EPR [1,6], spec oscopies, and heo e ical cal-
cula ions [7–11], he g ound s a e s uc u e o he E0
1and
E0
gcen e s is now qui e well unde s ood. The E0de i es
om he emo al o a la ice oxygen o o m a neu al oxy-
gen acancy, VO, ollowed by hole apping o gi e V1
O.
Acco ding o he i s model p oposed in 1974 by Feigl,
Fowle , and Yip [7], FFY, he de ec consis s o a sp3hy-
b idized —
—
—Si≤dangling bond and o a nea ly plana —
—
—Si1
uni , —
—
—Si1≤Si—
—
—(—
—
— ep esen s h ee Si-O bonds). The
FFY model, howe e , does no accoun o he la ge hy-
pe ine spli ing, HFS, o ø420 G o he unpai ed elec on
wi h he 29Si nuclide [6]. A e ined model, sugges ed by
Rud a and Fowle in 1985 [8], is based on an asymme ical
elaxa ion o he posi i ely cha ged Si a om in a pucke ed
posi ion whe e i binds o a la ice oxygen which becomes
h ee-coo dina ed. This s uc u e was hen con i med by
o he s udies including accu a e i s p inciple calcula ions
[9–12]. The E0
1g ound s a e s uc u e, as ob ained om
he p esen clus e calcula ions, is illus a ed in Fig. 1(a).
I is gene ally accep ed ha he E0
gin a-SiO2has a e y
simila s uc u e.
Much less is known abou he E0exci ed s a e p ope -
ies. A ypical OA band in bulk silica a 5.85 eV wi h
an oscilla o s eng h o 0.14 60.04 has been assigned o
he E0
gcen e by Weeks and Sonde based on a s ong
co ela ion wi h a cha ac e is ic EPR signal [2]. Two e-
cen s udies u he ein o ced he o iginal assignmen o
he 5.85 eV band o E0
gcen e s [13,14]. The na u e o
he ansi ion, howe e , is s ill unclea . I could in ol e
a cha ge ans e , CT, om —
—
—Si≤ o —
—
—Si1, as en a i ely
sugges ed back in 1980 by G iscom and Fowle [15], o
simply a ansi ion om he alence band o he pa ially
illed Si sp3hyb id o bi al. Fu he mo e, di e en ly om
many o he de ec s in SiO2which exhibi ypical pho o-
luminescence, PL, bands, emission upon exci ing in he
E0
g-abso p ion band has ne e been obse ed. No mecha-
nism has been p oposed so a o elucida e his anomalous
beha io . Ano he aspec which needs cla i ica ion is ha
on he su ace o mechanically ac i a ed silica OA bands
a ound 6.2 eV ha e been a ibu ed o su ace E0
scen e s
[16], consis ing o a —
—
—Si≤dangling bond. In his case he
CT mechanism is no possible since he e is no —
—
—Si1uni
in he icini y o he —
—
—Si≤g oups.
The scope o his Le e is o p esen an accu a e
quan um-mechanical s udy o he abso p ion p ope ies o
he E0bulk and su ace cen e s, and o p o ide a mecha-
nism o he dissipa ion o he abso bed ene gy in he bulk
h ough non adia i e decay. The compu a ional app oach
is he same adop ed ecen ly o elucida e he OA and PL
p ope ies o VO[17] and o o he de ec s in silica [18].
We used SiO2clus e s (wi h no symme y) wi h he
b oken bonds sa u a ed by H a oms placed along he O-Si
di ec ions o he c ys al. The posi ion o all he Si
and O a oms, ini ially aken om a-qua z [19], has
been eop imized by compu ing analy ical g adien s o
he o al ene gy [20]. The H a oms we e kep ixed o
p o ide a ep esen a ion o he mechanical embedding
o he solid. A ela i ely la ge clus e Si14O16H26g1
(Fig. 1) was used o de e mine he geome y o g ound and
exci ed s a es o V1
O. All elec on, AE, Ha ee-Fock wa e
0031-9007y98y81(2)y377(4)$15.00 © 1998 The Ame ican Physical Socie y 377
VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13JULY 1998
FIG. 1. Si14O16H26g1model o a E0cen e in a a-qua z.
Whi e sphe es: Si; g ey sphe es, O; small whi e sphe es: H.
(a) G ound s a e minimum, E0
g; (b) exci ed s a e minimum;
(c) me as able E0
d; (d) C !A ansi ion s a e; see Fig. 3.
unc ions ha e been cons uc ed using a 6-31Gbasis se
on Si and O [21]. Smalle clus e s we e used o pe o m
accu a e calcula ions o he ansi ion ene gies, Te.On
hese smalle clus e s we used an e ec i e co e po en ial
[22], ECP, on Si o educe he size o he con igu a ion
in e ac ion (CI) calcula ions and a double-ze a, DZ, basis
[22]. Di use sand p, plus one d, pola iza ion unc ions
ha e been added o Si. Te’s ha e been de e mined by pe -
o ming mul i e e ence CI calcula ions, MRD CI [23,24].
Single and double exci a ions om he 12 highes occupied
le els (24 elec ons) ha e been gene a ed wi h espec o
a se o main (M) con igu a ions; o u he de ails see
Re s. [17] and [18]. Abso p ion in ensi ies ha e been es-
ima ed by means o he oscilla o s eng h, , a dimen-
sionless quan i y, using he dipole-leng h ope a o o mula,
s d
2
3jkC0je jCnlj2sEn2E0d. Typical alues o
o allowed ansi ions a e be ween 0.1 and 1. Radia i e
li e imes, , ha e also been de e mined. Bo h Te’s and in-
ensi ies a e de e mined wi h some unce ain y connec ed
o he clus e and basis se size. These unce ain ies a e
di icul o es ima e: o he Te’s hey a e a leas o he
o de o 60.4 eV.
We s a he discussion om he g ound s a e s uc-
u e o he E0cen e in bulk SiO2as ob ained wi h he
Si14O16H26g1clus e , Fig. 1(a). The de ec is cha ac-
e ized by a a he long Si1-Si2dis ance, 4.06 Å, and by
a sho dis ance, 1.81 Å, be ween he posi i ely cha ged
Si2and he h ee-coo dina ed oxygen. The iso opic HFS
on Si1, 364 G, is in easonable ag eemen wi h he ex-
pe imen al alue, 420 G [6]. These da a a e consis en
wi h hose epo ed in he li e a u e o he E0
gcen e
[7–12]. To s udy he na u e o he lowes exci a ions,
we ha e conside ed wo smalle models, one o he su -
ace and one o he bulk. The model o a su ace E0
s
cen e is sHOd3Si≤, Fig. 2(a). Fo he bulk, we used a
sHOd3Si≤1SisOHd3-sOH2dclus e ; see Fig. 2(b), which in-
cludes also he h ee-coo dina ed oxygen o he E0
gg ound
s a e s uc u e. This la e clus e has been de i ed om
he la ge one, Fig. 1(a), bu i has been ully eop imized
wi h he H a oms ixed. The op imal dis ances a e simila
o hose ob ained wi h he la ge clus e . All he Tea e
compu ed om minimum s uc u es. The E0
ssHOd3Si≤
model allows us o analyze in de ail he dependence o
he Teon he le el o ea men . The lowes double -
o-double ansi ion co esponds o he exci a ion o one
elec on om a nonbonding O 2p alence band o bi al o
FIG. 2. Clus e models o su ace (a) and bulk (b) E0cen e s
used o compu e Te’s.
378
VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13JULY 1998
he Si dangling bond. Usinga 6-31GpAE basis se on bo h
O and Si plus di use sand p unc ions on Si, we ob ain a
Teo 6.21 eV, in excellen ag eemen wi h he expe imen
[16]. Using an ECP on Si and a compa able basis, he Teis
sligh ly lowe , 5.94 eV, Table I. The in ensi y o he an-
si ion is p edic ed o be low, s dø1022. The inclusion
o a d unc ion on O, c . 6-31Gand 6-31Gpbasis se s in
Table I, changes Teby only 60.1 eV. In conclusion, an
abso p ion band o weak in ensi y due o a ansi ion om
an Os2pdle el o a Si dangling bond is expec ed a ound
ø6eV o E0
scen e s a he SiO2su ace.
Fo he bulk E0cen e model we sea ched h ee oo s in
he CI secula p oblem: he g ound s a e, he O s2pd!
—
—
—Si≤ ansi ion desc ibed abo e, and he CT ansi ion
whe e one elec on is exci ed om Si1 o Si2. S ic ly
speaking, he Os2pd!—
—
—Si≤is also a CT ansi ion, bu
o cla i y we e e only o he exci a ion om he wo
nonbonded Si a oms as CT. The CI esul s show ha
he wo exci ed s a es ha e e y small mixing and simila
Te,ø5.7 5.8 eV; hey a e sepa a ed by ø0.2 eV, bu
he ela i e o de ing depends also on he de ails o he
calcula ion, Table I. I is no possible o p edic in a i m
way which is he lowes ansi ion in bulk E0based on
he Te’s. Howe e , he wo ansi ions exhibi di e en
in ensi ies: he CT is abou 10 imes s onge han he
Os2pd!—
—
—Si≤ ansi ion. Expe imen ally, i has been
obse ed ha he ansi ion a 5.85 eV associa ed wi h
he E0
gcen e has an oscilla o s eng h o ø0.14 eV [2].
Thus, bo h Teand s da e in ag eemen wi h he CT
ansi ion compu ed he e while he p edic ed in ensi y o
he alence band ansi ion is oo low. Consequen ly,
he CT ansi ion is expec ed o ha e a much sho e
li e ime, ø1029sec, and o occu much mo e apidly
han he Os2pd!—
—
—Si≤ ansi ion, ø1028sec. This
la e ansi ion, howe e , may domina e a he su ace o
he ma e ial.
Ha ing es ablished he na u e o he 5.85 eV band in a-
qua z and a-SiO2, we conside now he decay mechanism.
As we men ioned abo e, no luminescence is s imula ed
by he OA a 5.85 eV. In he bulk, he CT F anck-
Condon exci a ion leads o a s uc u e whe e one elec on
has been ans e ed om Si1 o Si2; see poin A0in
Fig. 3. The neu aliza ion o Si2des abilizes he pucke ed
s uc u e, Fig. 1(a), because o he epulsion wi h he h ee-
coo dina ed oxygen. The Si2-O dis ance inc eases and he
sys em unde goes a s ong geome ical elaxa ion un il i
eaches a minimum; see Fig. 1(b) and poin Bin Fig. 3. In
his minimum he unpai ed elec on is in a Si2sp3dangling
bond, while Si1becomes almos la because o he posi i e
cha ge. No ice ha no pucke ing o Si1occu s in his
case because o he much longe dis ance wi h he la ice
oxygen, Fig. 1(b). S a ing he geome y op imiza ion
om a clus e whe e Si1has been in e ed and pucke ed
inside he ing esul s spon aneously in he s uc u e shown
in Fig. 1(b). In his espec he asymme ic na u e o a-
qua z is e y impo an . F om he exci ed s a e minimum,
see Fig. 1(b) and poin Bin Fig. 3, he sys em could in
p inciple decay adia i ely. Howe e , a ba ie sepa a es
his minimum om ano he impo an econs uc ion. This
can be desc ibed as he in e sion o Si2 h ough he plane
o he h ee O a oms wi h displacemen o he unpai ed
elec on owa d he cen e o he ca i y. I is eminiscen
o he in e sion doubling in a igonal py amidal molecule
like NH3. In an adiaba ic pic u e, i is concei able ha he
s ong elaxa ion ollowing he exci a ion p o ides enough
ib a ional ene gy o he sys em o o e come his ba ie
o ha he elec on can unnel h ough he ba ie and show
up on he o he side o Si2. A mo e de ailed analysis
o he po en ial ene gy su ace a ound his ba ie shows
ha i ac ually o igina es om an a oided c ossing o wo
s a es; see do ed lines in Fig. 3. In a diaba ic pic u e he
e ical CT ansi ion om he E0g ound s a e p omo es
one elec on in a highly exci ed ib a ional le el; see
A!A0in Fig. 3. The elec on can hen decay o lowe
ib a ion le els and, h ough an in e nal con e sion, in o
he minimum o he uppe s a e cu e, Fig. 3, and om
he e can c oss he na ow gap wi h emission o a low-
equency pho on. Wha e e desc ip ion is used, adiaba ic
TABLE I. T ansi ion ene gies, Te, and oscilla o s eng h, s d,o E
0cen e s a he su ace and in he bulk o SiO2.
Os2pd!—
—
—Si≤—
—
—Si≤!1Si—
—
—
ansi ion CT ansi ion
Clus e O basis Si basis Te(eV) s dTe(eV) s d
sHOd3Si≤, su ace E0
s
6-31G6-31Gp1s1p6.28 0.01 ··· ···
6-31Gp6-31Gp1s1p6.21 0.01 ··· ···
6-31GECP-DZ 1s1d5.81 0.01 ··· ···
6-31GpECP-DZ 1s1d5.94 0.03 ··· ···
Expe imen [16] 6.2 60.1 ··· ···
sHOd3Si≤1SisOHd3-sOH2d, bulk E0
6-31GECP-DZ 1s1d5.7a0.03 5.8a0.30
Expe imen [2] ··· ··· 5.85 0.14 60.04
aA e age alue o di e en CI ea men s.
379
VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13JULY 1998
FIG. 3. Schema ic ene gy p o ile o he exci a ion-
deexci a ion mechanism o he E0cen e in bulk SiO2.
The ene gies a e plo ed e sus he dis ance be ween Si2and
he “ h ee-coo dina ed” O. See Figs. 1(a), 1(b), 1(c), and
1(d) o he s uc u e o he s a iona y poin s A,B,C, and D,
espec i ely.
o diaba ic, he sys em gains enough ib a ional ene gy
h ough he CT exci a ion o escape om he minimum o
he exci ed s a e po en ial, Fig. 3.
Once he ba ie is o e come, he sys em unde goes
ano he impo an elaxa ion which leads o a me as able
a ian o he E0g ound s a e s uc u e. In his local
minimum, poin Cin Fig. 3, he unpai ed elec on is
sha ed among he wo Si a oms o he acancy, Fig. 1(c).
The subs an ial delocaliza ion o he spin is shown by
he exis ence o wo HFS’s o 118 G (Si1) and 62 G
(Si2). The elec on emains apped be ween he wo
Si a oms, a si ua ion eminiscen o F cen e s in alkali
halides; he Si-Si dis ance, 2.67 Å, is no oo a om
ha o he egula la ice, 3.06 Å. This s uc u e is no
unp eceden ed and co esponds o he E0
ddesc ibed by
Snyde and Fowle [10] and by Boe o e al. [11] and
p obably obse ed in Cl-con aining glasses by G iscom
and F iebele [25]. The E0
dis a me as able o m o he
E0g ound s a e. In ou app oach i is 0.64 eV highe
han he global minimum; he ba ie sepa a ing he local,
Fig. 1(c), and he global, Fig. 1(a), minima is 0.32 eV and
co esponds, as shown by a ull ib a ional analysis, o a
ue ansi ion s a e, Fig. 1(d), and poin Din Fig. 3. The
ba ie is small enough ha he la ice ib a ions ollowing
he non adia i e decay will lead o a depopula ion o he
E0
ds uc u e in a o o he asymme ic E0
gg ound s a e,
explaining why he E0
dhas no been clea ly iden i ied in
EPR expe imen s so a . In his way, he sys em e u ns
back o he o iginal s uc u e om which he CT ansi ion
has occu ed and dissipa es comple ely he abso bed
ene gy h ough a non adia i e decay mechanism.
In conclusion, we ha e shown ha E0cen e s a he
su ace and in he bulk o SiO2ha e simila abso p ion
ene gies which, howe e , o igina e om di e en mecha-
nisms. In bulk silica he exci a ion seems o ha e CT
cha ac e ; he absence o luminescence may be explained
as due o a complex non adia i e decay mechanism which
comple ely dissipa es he ene gy o he adso bed pho on.
S imula ing discussions wi h P o esso Beall Fowle a e
g a e ully acknowledged.
*Elec onic add ess: [email p o ec ed]
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