Fi s -p inciples calcula ions o s uc u al and elec onic p ope ies o monoclinic ha nia su aces
A ashi B. Mukhopadhyay, Ja ie F. Sanz,*and Cha les B. Musg a e
Depa men o Chemical Enginee ing, S an o d Uni e si y, 380 Ro h Way, S an o d, Cali o nia 94305, USA
共Recei ed 10 No embe 2005; e ised manusc ip ecei ed 31 Janua y 2006; published 24 Ma ch 2006兲
We ha e ca ied ou a sys ema ic heo e ical s udy o he su aces o monoclinic ha nia 共H O2兲using plane
wa es and densi y unc ional heo y based on he gene alized g adien app oxima ion. The ully elaxed
s uc u es o he bulk phases o H O2a e ound o be in excellen ag eemen wi h expe imen al da a, he
monoclinic phase being he mos s able. Simula ions o he monoclinic phase su aces indica e a la ge elax-
a ion which educes he o al su ace ene gy o all nine aces conside ed by be ween 23% and 36%, wi h a
s ong co ela ion be ween he un elaxed and elaxed su ace ene gies. Ou calcula ions p edic ha he 共1
¯
11兲
and 共111兲 aces o he monoclinic phase ha e he lowes su ace ene gies and a e hence he mos s able aces.
An analysis o he o al and pa ial elec onic densi y o s a es o bulk monoclinic H O2 e eals ha he ou e
alence band signi ican ly mixes he O 2pand H 5da omic s a es indica ing some co alency o he H -O
bonds. The o al densi y and pa ial densi y o s a es o he monoclinic su aces exhibi a su ace s a e co e-
sponding o he su ace O 2ss a es in he inne alence band egion.
DOI: 10.1103/PhysRe B.73.115330 PACS numbe 共s兲: 68.35.Md, 68.47.Gh, 73.20.A , 81.15.Gh
I. INTRODUCTION
An in ense sea ch o a new high dielec ic cons an ma-
e ial o eplace SiO2ga e dielec ics in me al-oxide-
semiconduc o ield-e ec ansis o s, such as H O2, has
been unde aken o ob ain insula ing ilms wi h highe ca-
paci ance han hin SiO2 ilms and wi h g ea e hicknesses o
esis unneling leakage.1–4 Ha nium dioxide 共H O2兲has
eme ged as an excellen candida e due o i s ela i ely high
dielec ic cons an , wide band gap and s abili y on Si. The
he mal s abili y o high-kma e ials in di ec con ac wi h Si
and SiO2has become a key c i e ion in selec ing sui able
high-kchoices. In addi ion o i s po en ial use as a ga e di-
elec ic, H O2is also used as an op ical coa ing because o i s
high e ac i e index and high ansmission coe icien .5,6
Addi ionally, H O2exhibi s a ela i ely high lase damage
h eshold due o i s high mel ing poin , he mal and chemical
s abili y and wide anspa en ange om he in a ed o
ul a iole .7,8 Fu he mo e, H O2se es as an excellen p o-
ec i e coa ing due o i s he mal s abili y and ha dness.9,10
De e mina ion o s able su ace s uc u es o ma e ials is
equi ed o he ab ini io p edic ion o ma e ial p ope ies as
he ela i e s abili y o he su aces will a ec he o ien a-
ions and sizes o c ys alli es, which in u n a ec ma e ials
p ope ies. This is especially ue o he p edic ion o su -
ace p ope ies such as su ace eac i i y. H O2 hin ilms can
be deposi ed on a a ie y o subs a es using a ious me h-
ods. Techniques being explo ed include a omic laye deposi-
ion 共ALD兲,11 ion beam assis ed deposi ion12 and je apo
deposi ion.13 The s uc u e o as-deposi ed H O2 ilms is no
ye ully esol ed. Fo ins ance, a ious expe imen al s udies
ound ha H O2 ilms deposi ed by ALD a 300 °C using
H Cl4and H2O as p ecu so s a e polyc ys alline, and mainly
consis o he monoclinic phase wi h he 共1
¯
11兲su ace ex-
hibi ed as he main g ow h ace.14,15 Upon annealing he in-
ensi ies o he monoclinic peaks inc ease in he x- ay di -
ac ion 共XRD兲spec a wi h he 共1
¯
11兲and 共111兲monoclinic
su aces p ima ily popula ed.14 On he o he hand, Aa ik e
al. epo ed ha e lec ions om he 共002兲,共200兲, and 共111兲
monoclinic su aces a 300 °C displayed he highes in ensi-
ies a he han he 共1
¯
11兲su ace and ha 共1
¯
11兲 e lec ions
we e weak o absen in he plane in which he XRD pa e n
was eco ded, including a ele a ed empe a u es.16,17 In ye
ano he ALD deposi ed ilm, Kukli e al. epo ha he ilm
g own a low empe a u e shows only aces o c ys allini y
in he XRD pa e n.18 Howe e , e lec ion high-ene gy elec-
on di ac ion o he same ilm e ealed 共002兲and 共1
¯
04兲
o ien a ions o monoclinic phases. Howe e , o ilms g own
a highe empe a u e 共750 °C兲, he 共011兲,共1
¯
11兲, and 共111兲
di ac ion peaks a e s onges . Hence, di ec compa isons o
measu ed su ace p ope ies a e di icul due o a ying ex-
pe imen al condi ions and ilm p epa a ion me hods. These
expe imen al da a hus only p o ide indi ec and incomple e
in o ma ion abou he de ailed su ace a omic s uc u e.
Mo eo e , hese di icul ies in in e p e a ing di e en expe i-
men al s udies a e complica ed by ini e-size e ec s because
samples a e o en polyc ys alline, polymo phic, and con ain
impu i ies and dopan s.
Z and H a e ema kably simila elemen s and conse-
quen ly he su ace p ope ies o H O2a e expec ed o be
compa able o hose o Z O2. The su ace p ope ies o Z O2
ha e been ho oughly in es iga ed heo e ically.19 Compa i-
sons be ween ou p edic ed p ope ies o H O2do show
many simila i ies o hose p edic ed o Z O2, al hough we
also ind signi ican quan i a i e di e ences in he calcula ed
p ope ies.
To he bes o ou knowledge, his con ibu ion is he i s
heo e ical in es iga ion o he s uc u al and elec onic p op-
e ies o H O2su aces. In his pape , we ha e in es iga ed
he su ace p ope ies o low-index su aces o he mos
s able 共unde he condi ion o a mosphe ic p essu e and oom
empe a u e兲 o m o H O2, ha is, he monoclinic su aces.
We p esen su ace ene gies and nea su ace ionic elax-
a ions. We ha e also pe o med a de ailed examina ion o he
elec onic s uc u es o he nine inequi alen monoclinic su -
PHYSICAL REVIEW B 73, 115330 共2006兲
1098-0121/2006/73共11兲/115330共7兲/$23.00 ©2006 The Ame ican Physical Socie y115330-1
aces o o e a mo e comple e unde s anding o he s able
H O2phases.
This pape is o ganized as ollows. The nex sec ion de-
sc ibes he compu a ional aspec s o his s udy. In Sec. III we
discuss esul s pe aining o he bulk p ope ies, he su ace
s uc u es and ionic elaxa ion and su ace elec onic p ope -
ies. In he las sec ion we d aw some gene al conclusions.
II. COMPUTATIONAL DETAILS
In o de o model he ex ended na u e o he su aces,
densi y unc ional heo y 共DFT兲calcula ions unde pe iodic
condi ions we e ca ied ou using he Vienna ab ini io simu-
la ion package 共VASP兲.20,21 In hese calcula ions he ene gy
was calcula ed using he PW91 gene alized g adien app oxi-
ma ion 共GGA兲implemen a ion o DFT p oposed by Pe dew
e al.22,23 wi h he elec onic s a es expanded using plane
wa es as basis se . The calcula ions we e pe o med u ilizing
he p ojec ed augmen ed wa e app oach24 implemen ed in
he VASP code. Fo H a oms, he semico e 5pelec ons ha e
also been included in addi ion o he 5d2and 6s2 alence
elec ons because we ound ha explici ly including he 5p
elec ons is equi ed in o de o ob ain co ec la ice pa am-
e e s o bulk H O2. Fo O a oms 2sand 2pelec ons we e
included. The plane-wa e cu o ene gy is 450 eV. The k
poin s we e gene a ed using he Monkho s –Pack me hod
and 4⫻4⫻4 and 4⫻4⫻1 g id sizes we e used o s uc-
u al op imiza ion o he bulk and su aces, espec i ely. Fo
calcula ion o elec onic p ope ies he g id sizes we e in-
c eased o 10⫻10⫻10 and 10⫻10⫻1, o he bulk and
su aces, espec i ely.
Fo ces on he ions we e calcula ed using he Hellmann–
Feynman heo em as he pa ial de i a i es o he ee elec-
onic ene gy wi h espec o he a omic posi ions, and ad-
jus ed using he Ha is–Foulkes25 co ec ion o he o ces.
This app oach o calcula ing he o ces allows a geome y
op imiza ion using he conjuga e-g adien scheme. I e a i e
elaxa ion o a omic posi ions was s opped when he change
in o al ene gy be ween successi e s eps was less han
0.001 eV. Wi h his c i e ion, o ces on he a oms we e gen-
e ally less han 0.1 eV/Å.
To model he monoclinic su aces we employed he well-
known slab app oach consis ing o a supe cell ha includes a
po ion o acuum. A e being eplica ed in he h ee di ec-
ions o space, an a ay o slabs sepa a ed by a acuum is
ob ained. The acuum wid h was wide enough o p e en
laye - o-laye in e ac ions and we ound ha a wid h o 6 Å
was enough o ensu e ha he ene gy was con e ged o
wi hin 0.001 eV/a om. The in luence o slab hickness on he
sui abili y o he su ace models is c ucial and will be ana-
lyzed in he discussion sec ion.
III. RESULTS AND DISCUSSION
A. Bulk p ope ies
To check he eliabili y o he compu a ional app oach we
apply i o calcula e measu ed, well-known p ope ies o he
bulk phases o H O2. A oom empe a u e he equilib ium
phase o H O2is monoclinic which has he lowes ee en-
e gy o o ma ion and he la ges olume.26–28 A app oxi-
ma ely 1300 K monoclinic H O2 ans o ms in o he e ag-
onal s uc u e and ans o ms o he CaF2cubic s uc u e
nea 2700 K.28 He e we ully elax bo h he cell la ice pa-
ame e s as well as he ion posi ions. Table I epo s ou
calcula ed s uc u al pa ame e s o he h ee phases o H O2
we conside along wi h he ene gy o he sys em pe H O2
o mula uni . We also include he da a calcula ed in p e ious
DFT s udies by Zhao and Vande bil 29 using ul aso
pseudopo en ials. We ind ha ou alues a e in excellen
ag eemen wi h he expe imen al esul s. In some cases and,
especially o densi ies, ou GGA esul s ma ch expe imen
be e han ha o p e ious GGA esul s. We also calcula e
ha he hea o o ma ion o he monoclinic c ys al, which is
he mos s able phase, is −1070.5 kJ/mol, in good ag eemen
wi h he expe imen al alue o −1144.7 kJ/mol 共7% e o 兲.30
Ou ene gy pe o mula uni ep oduces he co ec
ene ge ic o de ing o he phases 关EMONOCLINIC共H O2兲
⬍ETETRAGONAL共H O2兲⬍ECUBIC共H O2兲兴.
B. Su ace s uc u e
The abili y o ou app oach o ep oduce he expe imen al
esul s o he bulk p ope ies o H O2indica es ha i should
be capable o accu a ely p edic ing H O2su ace p ope ies.
We emphasize ha he pu pose o his wo k is o de e mine
su ace p ope ies o he pe ec cu c ys al. Tha is, we do
no conside complex o ex ended econs uc ions. The su -
ace models we s udy include an in ege numbe o H O2
o mula uni s and a e hus s oichiome ic. We ollow he gen-
e al ules p o ided by Ch is ensen and Ca e 19 and design
slabs o model su aces wi h maximum su ace compac ness
and minimized coo dina ion loss. We ha e also a oided gen-
e a ing su ace models ha a e signi ican ly pola and hus
a i icially s able due o long- ange elec os a ic o ces.
Because monoclinic su aces a e mo e complex han o he
phases, he choice o a gi en su ace index does no uni o-
cally de ine he su ace s uc u e in an ob ious way. Fo ou
pu pose, a slab co esponding o a gi en Mille ace has an
in ege numbe o planes such ha i is pa allel o he su ace
and has a cen e o symme y a he slab cen e . Conse-
quen ly, i can be mapped on o all pa allel planes below i by
applying symme y ope a o s such as ansla ions, sc ew
axes o glide planes and hus he esul ing slab has no dipole
momen . The un elaxed slabs ha e been cu om he bulk
c ys al, whe e bulk s uc u es ha e been ully elaxed wi h
espec o in acell and uni cell deg ees o eedom. We ha e
pe o med su ace elaxa ions o all nine inequi alen low-
index aces o m-H O2. All a oms in he slab ha e been
allowed o elax, al hough bo h sides o he slab emain
equi alen as hey a e ela ed by an in e sion, o a mi o /
glide plane, loca ed a he cen e o he slab. In hese calcu-
la ions we do no allow he slab uni cell o elax. In Figs. 1
and 2 we only epo he a omic displacemen s o he 共001兲
and 共1
¯
11兲su aces wi h espec o slab hickness as hese
aces we e mos p ominen du ing he g ow h o H O2.14–17
In Figs. 1共a兲and 1共b兲we show he un elaxed and elaxed
共001兲su aces o a ou laye ed slab. As can be seen in Fig.
1共a兲, he e a e wo inequi alen su ace ha nium a oms and
MUKHOPADHYAY, SANZ, AND MUSGRAVE PHYSICAL REVIEW B 73, 115330 共2006兲
115330-2
wo su ace oxygen a oms. These inequi alen a oms a e
placed a di e en zplanes in he un elaxed su ace. How-
e e , upon elaxa ion hese inequi alen a oms displace o
almos align hemsel es in same zplane. Figu e 1共c兲shows
he quan i a i e displacemen s o inequi alen su ace a oms
o each di ec ion. Bo h su ace ha nium a oms mo e ou o
plane, howe e he second H a om 关H 2 in Fig. 1共a兲兴 mo es
abou 0.2 Å mo e in he zdi ec ion han he i s H a om
关H 1 in Fig. 1共a兲兴 in o de o place i sel in he same plane.
The displacemen o O1 along he zdi ec ion is negligible;
howe e , he second oxygen 共O2兲is displaced by ⬃0.5 Å
ou o plane. Hence, he maximum displacemen du ing e-
laxa ion is no necessa ily exhibi ed by he ou e mos a oms.
Fu he mo e, he displacemen o a oms is no es ic ed o
e ical mo emen , bu a oms can also elax la e ally. Fo
example, O1 shi s almos by 0.4 Å in he xdi ec ion. Be-
cause o signi ican subsu ace elaxa ion a slab wi h a leas
ou laye s is necessa y o accu a ely desc ibe he su aces o
p edic hei su ace p ope ies.
Simila ly, in Figs. 2共a兲and 2共b兲we show he un elaxed
and elaxed 共1
¯
11兲su aces, espec i ely. The 共1
¯
11兲 ace is a
mo e complica ed su ace compa ed o he 共001兲su ace.
The 共1
¯
11兲su ace has ou inequi alen su ace H and su -
ace O a oms. The su ace ea u es a e no isibly di e en in
Figs. 2共a兲and 2共b兲. Howe e , in Fig. 2共c兲we quan i y he
displacemen s o he su ace a oms. Like he 共001兲su ace,
mos su ace a oms show ou o plane elaxa ions. The e a e
also signi ican la e al displacemen s o O a oms in he e-
laxed 共001兲s uc u e.
C. Su ace ene gy
The su ace ene gy, Esu 共n兲, o a sys em comp ising n
laye s is de ined as
Esu 共n兲=E o 共n兲−Ebulk共n兲
2A,共1兲
whe e E o 共n兲and Aa e he o al ene gy and o al su ace a ea
pe molecula 共H O2兲uni , espec i ely.31 Ebulk e e s o he
ene gy o he bulk monoclinic sys em con aining he same
numbe o molecula uni s as he slab. Since he slab has wo
su aces, he ene gy di e ence is no malized by wice he
a ea o each su ace in Eq. 共1兲. In Figs. 1共d兲and 2共d兲we
show su ace ene gy as a unc ion o he numbe o laye s. In
Table II we ha e also summa ized ou esul s o all o he
nine inequi alen aces. A use ul ool in he analysis o e-
TABLE I. Calcula ed s uc u al pa ame e s o h ee H O2phases. La ice pa ame e s a,b,ca e Å,
␤
in deg ees and V共 olume pe
o mula兲in Å3. In e nal coo dina es x,y, and za e uni less.
P esen GGA P e ious LDAaP e ious GGAaExp .b
Cubic
Ene gy/molecule −30.45 ¯¯¯
V32.11 31.95 36.15 32.77
a5.045 5.248 5.04 5.08
Te agonal
Ene gy/molecule −30.51 ¯¯¯
V32.69 32.77 37.74
a3.565 5.056 5.299
c5.146 5.127 5.373
Monoclinic
Ene gy/molecule −30.69 ¯¯¯
V34.10 34.35 38.01 34.58
a5.079 5.106 5.291 5.117
b5.177 5.165 5.405 5.175
c5.250 5.281 5.366 5.220
␤
99.24 99.35 97.92 99.22
xH 0.277 0.280 0.276 0.276
yH 0.042 0.043 0.039 0.040
zH 0.207 0.209 0.209 0.208
xO1 0.075 0.076 0.089 0.074
yO1 0.343 0.346 0.367 0.332
zO1 0.336 0.337 0.317 0.347
xO2 0.446 0.447 0.447 0.449
yO2 0.759 0.759 0.762 0.758
zO20.481 0.483 0.488 0.480
aRe e ence 29.
bRe e ence 10 o cubic and Re . 32 o monoclinic.
FIRST-PRINCIPLES CALCULATIONS OF STRUCTURAL¼PHYSICAL REVIEW B 73, 115330 共2006兲
115330-3
laxa ion is he oo mean squa ed 共 ms兲ionic displacemen
epo ed in Table II. The ms ionic displacemen is he a e -
age displacemen o all N a oms in each slab ela i e o he
geome ical cen e o mass ⌬ c.m:
⌬ ms =冑兺i=1
N共⌬ i−⌬ c.m.兲2
N.共2兲
This quan i y will end o dec ease wi h inc easing slab
hickness because bulk ions ha e small o anishing dis-
placemen upon elaxa ion. Howe e , compa ison o a omic
displacemen is a meaning ul measu e o elaxa ion as we
ha e chosen all slabs o ha e app oxima ely he same hick-
ness o nea ly 8 Å.
The 共1
¯
11兲and 共111兲su aces a e he mos s able aces o
he monoclinic phase. These aces a e also he ones co e-
sponding o he mos in ense peaks in he XRD o a ious
ALD ilms g own by a ious g oups.14,15,18 Howe e , some
g oups obse ed he peak co esponding o he 共111兲su ace
as he mos in ense peak along wi h ha o he 共001兲 ace.4,16
This can be explained i he 共1
¯
11兲and 共111兲su aces a e
asc ibed as he he modynamically a o ed su aces while
he 共001兲 ace could co espond o he kine ically a o ed
su ace, We p edic a su ace s abili y o de o he su aces
we conside e y simila o ha p edic ed o he Z O2su -
ace.
wi h a ew excep ions.19 The p edic ed o de o s abili y
o Z O2is 共1
¯
11兲⬎共1
¯
01兲⬎共111兲⬎共110兲⬎共011兲⬎共001兲
⬎共100兲⬎共101兲⬎共010兲, whe eas in H O2we p edic he s a-
bili y o de as 共1
¯
11兲⬎共111兲⬎共1
¯
01兲⬎共110兲⬎共001兲⬎共011兲
⬎共101兲⬎共100兲⬎共010兲. Howe e , he magni ude o elax-
a ion ene gy o he H O2su ace is la ge han ha o he
Z O2su ace.19
The su ace ene gies epo ed in Table II indica e ha he
su ace ene gy is highly aniso opic wi h a s ong co ela ion
be ween un elaxed and elaxed su ace ene gies. Conse-
quen ly, he o de ing o he un elaxed su ace s abili ies is
simila o ha o he elaxed su ace ene gies. The elaxa ion
ene gy o he su aces anges om 23% o 36% o he o al
su ace ene gy. We ob ain a sligh co ela ion be ween su -
ace ene gies and he ms ionic elaxa ions.
D. Elec onic s uc u e
In his sec ion we discuss he elec onic p ope ies o he
su aces. In Fig. 3, we epo he bulk o al densi y o s a es
共DOS兲ob ained o he monoclinic c ys al along wi h he
pa ial DOS con ibu ed by he h ee inequi alen a oms o
he uni cell 共one H a om and wo O a oms兲. The con ibu-
ion o he DOS om H comes om he 5pand 5delec-
ons, whe eas o O, he 2sand 2pelec ons con ibu e. The
o al DOS is composed o wo alence bands, a lowe na ow
band lying a abou −16.5 eV composed o mainly O 2s
s a es and an uppe band lying be ween −6.6 and 0.0 eV
mainly a ising om O 2ps a es, wi h a signi ican con ibu-
ion o he H 5do bi als. No e ha he wo inequi alen
a oms ha e no iceably di e en DOS ea u es, as expec ed
om hei di e en en i onmen s. The uppe alence band is
FIG. 1. 共Colo online兲共a兲Un elaxed and 共b兲 elaxed 共001兲s uc-
u e o he ou -laye su ace model o monoclinic H O2. The su -
ace a oms 共H and O a oms兲a e indica ed. 共c兲Calcula ed displace-
men s o su ace H and O a oms as a unc ion o slab hickness. 共d兲
Va ia ion o su ace ene gy as a unc ion o slab hickness.
MUKHOPADHYAY, SANZ, AND MUSGRAVE PHYSICAL REVIEW B 73, 115330 共2006兲
115330-4
sepa a ed by an ene gy gap o 3.8 eV om a conduc ion
band composed o H 5dcha ac e . This is in ag eemen wi h
p e ious heo e ical s udies33–35 as well as wi h he pho o-
emission and in e se pho oemission da a ob ained om
H O2deposi ed on SiOxNy/pSi, which showed ha he a-
lence band mainly consis s o O 2pnonbonding o bi als o
␲
symme y while he conduc ion band is p ima ily H 5d-like
nonbonding o bi als.35 Howe e , ou calcula ions show ha
he uppe alence band exhibi s mixing o he O 2pand H
5ds a es, indica ing co alency o he H –O bonds.
In Fig. 4 we epo he o al DOS o bo h he un elaxed
and elaxed 共1
¯
11兲su aces as well as ha o he monoclinic
c ys al. Fo he sake o compa ison, he ene gy alues o he
TABLE II. Su ace ene gies o he nine inequi alen low-index aces o monoclinic H O2.
Face
Su ace ene gy 共J/m2兲%Relaxa ion
Ene gy
ms ionic
elaxa ion
ÅRelaxed Un elaxed
共1
¯
11兲0.993 1.460 32 0.026
共111兲1.199 1.562 23 0.023
共1
¯
01兲1.322 1.858 29 0.033
共110兲1.388 2.043 32 0.030
共001兲1.416 2.169 35 0.060
共011兲1.484 2.100 29 0.024
共101兲1.550 2.412 36 0.047
共100兲1.667 2.165 23 0.021
共010兲1.878 2.782 33 0.040
FIG. 2. 共Colo online兲共a兲Un elaxed and 共b兲 elaxed 共1
¯
11兲s uc u e o he h ee-laye su ace model o monoclinic H O2.共c兲Calcula ed
displacemen s o su ace ha nium and oxygen a oms as a unc ion o slab hickness. 共d兲Va ia ion o he su ace ene gy as a unc ion o slab
hickness.
FIRST-PRINCIPLES CALCULATIONS OF STRUCTURAL¼PHYSICAL REVIEW B 73, 115330 共2006兲
115330-5

DOS o he su aces in hese plo s ha e been shi ed in o de
o align hei alence band maxima wi h ha o he bulk.
Hence o h all compa isons will be made based on ene gies
ela i e o he alence band maximum o he monoclinic
bulk c ys al. We do no p esen he calcula ed DOS o he
o he eigh su aces because we ound hem o exhibi simila
ea u es. The e ec o elaxa ion o he slab on he o al DOS
is signi ican . Al hough he p edic ed band gaps may no be
eliable 共acco ding o he well-known DFT unde es ima ion兲,
ends in he p edic ed gap should be meaning ul. As can be
obse ed, he uppe alence band o he bulk and elaxed
共1
¯
11兲su ace look qui e simila o each o he while o he
un elaxed su ace some s a es a e pushed upwa ds in o he
lowe pa o he gap. As he ze o o ene gy is e e enced o
he highes o hese s a es i appea s as hough he en i e
DOS o he un elaxed su ace is shi ed owa ds lowe en-
e gy. The un elaxed su ace has a smalle band gap o 2.1 eV
compa ed o he bulk band gap o 3.8 eV. We p edic wo
su ace s a es nea −15.0 and 0.1 eV o he un elaxed su -
ace co esponding, espec i ely, o he 2sand 2ps a es o
su ace oxygen. Upon elaxa ion o he slab, he la e disap-
pea s, howe e he o me s a e is e ained. The DOS o he
elaxed slab is almos iden ical o he DOS o he bulk excep
o one ea u e a −15.0 eV. A mo e ex ensi e analysis o he
pa ial DOS shows ha hese ex a su ace s a es a ise om
an oxygen 2so bi al co esponding o one o he su ace O
a oms. The band gap o he elaxed su ace is app oxima ely
0.5 eV lowe han ha o he bulk. These ea u es a e e y
simila o hose p edic ed o each o he o he eigh mono-
clinic su aces.
IV. CONCLUSIONS
In summa y, we ha e p edic ed s uc u al and elec onic
p ope ies o di e en m-H O2su aces. Ou GGA based
DFT esul s a e in excellen ag eemen wi h he exis ing ex-
pe imen al esul s o s uc u al bulk p ope ies. Calcula ed
su ace ene gies demons a e ha he e is a s ong co ela ion
be ween un elaxed and elaxed su ace ene gies. We also
ound a weak co ela ion be ween su ace ene gies and ms
ionic elaxa ions. We p edic ha elaxa ions a e no only
limi ed o he ou e su ace a oms, bu ha subsu ace a oms
unde go signi ican elaxa ion. The calcula ed su ace ene -
gies p edic ha he 共111兲and 共1
¯
11兲su aces a e he mos
s able su aces o he m-H O2sys em in ag eemen wi h he
appea ance o hese su aces in ALD g own H O2 ilms.
Howe e , he su ace ene gy o he 共001兲 ace, which is ob-
se ed in some o he ALD g own ilms, is es ima ed o be
abou 0.7 J/m2la ge han he mos s able su aces sugges -
ing ha such a su ace could be kine ically a o ed unde
gi en expe imen al condi ions. Analysis o he pa ial DOS
o he bulk phase indica es ha he e is a no iceable hyb id-
iza ion o O 2pand H 5ds a es, indica ing a signi ican
co alen con ibu ion o he H –O bond. The elec onic DOS
o he elaxed and un elaxed su aces highligh s he impo -
ance o su ace elaxa ions and desc ibes he na u e o su -
ace dominan s a es. Fo ins ance, we p edic a p ominen
su ace s a e nea −15.0 eV con ibu ed by su ace O 2so -
bi als.
The p esen wo k is in ended as a p elimina y s ep o-
wa ds he unde s anding o H O2su aces and hei eac i i y
which we hope will ul ima ely lead o a be e unde s anding
o he p inciples ha go e n he su ace chemis y espon-
sible o he ALD o H O2 ilms. A subsequen publica ion
will p o ide an in dep h analysis o he su ace eac ions o
ALD p ecu so s on hese elaxed monoclinic su aces.
ACKNOWLEDGMENTS
We g a e ully acknowledge he suppo o he S an o d
Ini ia i e o Nanoscale Ma e ials and P ocessing and he
Ma e ials S uc u es and De ices SRC/DARPA MARCO
Cen e . This wo k was pa ially suppo ed by he Spanish
Minis e io de Educación y Ciencia, and he Eu opean
FEDER, P ojec No. MAT2005-01872. J.F.S. hanks he
Minis e io de Educación y Ciencia, he Uni e sidad de
Se illa and S an o d Uni e si y o suppo ing his sabba ical
s ay a S an o d.
FIG. 3. 共Colo online兲To al and pa ial DOS o bulk monoclinic
H O2.EVBM ep esen s he maximal ene gy o he alence band.
FIG. 4. 共Colo online兲To al DOS o bulk, un elaxed and elaxed
共1
¯
11兲su aces o monoclinic H O2.
MUKHOPADHYAY, SANZ, AND MUSGRAVE PHYSICAL REVIEW B 73, 115330 共2006兲
115330-6
*On lea e om Depa amen o de Química Fisica, Facul ad de
Quimica, E-41012 Se illa, Spain
1P. A. Packan, Science 285, 2079 共1999兲.
2C. T. Kuo, R. Kwo , and K. M. Jones, Thin Solid Films 213, 257
共1992兲.
3M. Ri ala, M. Leskela, L. Niinis o, T. P ohaska, G. F iedbache ,
and M. G asse baue , Thin Solid Films 250,72共1994兲.
4J. Aa ik, A. Aidla, A. A. Kiisle , T. Uus a e, and V. Sammelselg,
Thin Solid Films 340,110共1999兲.
5H. O. Sanku and W. Gunning, Appl. Op . 28, 2806 共1989兲.
6M. Reisse, B. Keipe , S. Weissman el, H. Johansen, R. Scholz,
and T. Ma ini, Thin Solid Films 241,119共1994兲.
7M. Al isi, S. Scaglione, S. Ma elli, A. Rizzo, and L. Vasanelli,
Thin Solid Films 354,19共1999兲.
8M. Gilo and N. C oi o u, Thin Solid Films 350, 203 共1999兲.
9H. Ibegazene, S. Alpe ine, and C. Dio , J. Ma e . Sci. 30, 938
共1995兲.
10J. Wang, H. P. Li, and R. S i ens, J. Ma e . Sci. 27, 5397 共1992兲.
11 M. H. Cho, Y. S. Roh, C. N. Whang, K. Jeong, S. W. Nahm, D. H.
Ko, J. H. Lee, N. I. Lee, and K. Fujiha a, Appl. Phys. Le . 81,
472 共2002兲.
12R. R. Mano y, T. Mo i, I. Shimizu, S. Miyake, and G. Kimmel, J.
Vac. Sci. Technol. A 20, 549 共2002兲.
13W. Zhu, T. P. Ma, T. Tamagawa, Y. Di, J. Kim, R. Ca u he s, M.
Gibson, and T. Fu ukawa, Tech. Dig. - In . Elec on De ices
Mee . 464, 共2001兲.
14M. Y. Ho, H. Gong, G. D. Wilk, B. W. Busch, M. L. G een, P. M.
Voyles, D. A. Mulle , M. Bude, W. H. Lin, A. See., M. E.
Loomans, S. K. Lahi i, and P. T. Räisänen, J. Appl. Phys. 93,
1477 共2003兲.
15D. T iyoso, R. Liu, D. Roan, M. Ramon, N. V. Edwa ds, R. G e-
go y, D. We ho, J. Kulik, G. Tam, E. I win, X. D. Wang, L. B.
La, C. Hobbs, R. Ga cia, J. Bake , B. E. Whi e, and P. Tobin, J.
Elec ochem. Soc. 151, 220 共2004兲.
16J. Aa ik, A. Aidla, H. Mända , V. Sammelselg, and T. Uus a e, J.
C ys . G ow h 220, 105 共2000兲.
17A. Aa ik, H. Mända , M. Ki m, and L. Pung, Thin Solid Films
466,41共2004兲.
18K. Kukli, J. Aa ik, M. Ri ala, T. Uus a e, T. Saja aa a, J. Lu, J.
Sundq is , A. Aidla, L. Pung, A. Ha s a, and M. Lesela, J. Appl.
Phys. 96, 5298 共2004兲.
19A. Ch is ensen and E. A. Ca e , Phys. Re . B 58, 8050 共1998兲.
20G. K esse and J. Ha ne , Phys. Re . B 47, 558 共1993兲.
21G. K esse and J. Fu hmulle , Compu . Ma e . Sci. 6,15共1996兲.
22J. P. Pe dew, J. Che a y, S. Vosko, K. Jackson, M. Pede son, D.
Singh, and C. Fiolhais, Phys. Re . B 46, 6671 共1992兲.
23J. P. Pe dew, in Elec onic S uc u e in Solids, edi ed by P. Zi-
esche and H. Esch ig 共Akademie, Be lin 1991兲.
24P. E. Blöchl, Phys. Re . B 50, 17953 共1994兲.
25J. Ha is, Phys. Re . B 31, 1770 共1985兲.
26S. Desg enie s and K. Laga ec, Phys. Re . B 59, 8467 共1999兲.
27J. E. Low he , J. K. Dewhu s , J. M. Lege , and J. Haines, Phys.
Re . B 60, 14485 共1999兲.
28R. Ru h and V. A. Pa el, J. Am. Ce am. Soc. 56, 606 共1973兲.
29X. Zhao and D. Vande bil , Phys. Re . B 65, 233106 共2002兲.
30Handbook o Chemis y and Physics, 85 h ed. 共CRC, Cle eland,
2004兲.
31S. P. Ba es, G. K esse, and M. J. Gillan, Su . Sci. 385, 368
共1997兲.
32J. Adam and M. D. Rodge s, Ac a C ys allog . 12, 951 共1959兲.
33A. A. Demko , Phys. S a us Solidi B 226,57共2001兲.
34P. K. Boe and R. A. de G oo , J. Phys.: Condens. Ma e 10,
10241 共1998兲.
35S. Sayan, T. Emge, E. Ga unkel, X. Zhao, L. Wielunski, R. A.
Ba ynski, D. Vande bil , J. S. Suehle, S. Suze , and M.
Banaszak-Holl, J. Appl. Phys. 96, 7485 共2004兲.
FIRST-PRINCIPLES CALCULATIONS OF STRUCTURAL¼PHYSICAL REVIEW B 73, 115330 共2006兲
115330-7