Dieletri Properties of thin Film
Al/Sb
2 Pb
1 Se
7
/Al Devies
Shaila Wagle and Vinay Shirodkar
SolidStateEletronisLaboratory, DepartmentofPhysis,
TheInstituteof Siene,15MadamCamaRoad,
Mumhai-400032, India
Reeived20January,2000. Revisedversionreeivedon9May,2000
Metal-glass metal,MGM,thinlmdeviesarepreparedusingvauumdepositionofSb2Pb1Se7
ompound. Theapaitaneand theloss tangent variationasafuntionof temperatureand
fre-quenyisstudied.Theobservedharateristisareexplainedusingsmallsignalairuitanalysis.
Itisshownthatthetheoretialurvegenerated usingtheairuitanalysisgivesexellenttting
withtheexperimentalurve.
I Introdution
Semionduting glasses, partiularly halogenides
have been widely studied owing to their interesting
swithingproperty[1℄. Thesematerialsareusedto
fab-riateavarietyofeletronidevies, whihariseswhen
the material is ast in thin lm form. It is observed
thatmostphysialpropertiesreportedonhalogenides
havebeen investigated using polyrystallinepellets or
eletrodeposits [2,3℄. A good amount of work on d
ondution [4℄, ontatapaitane [5℄, spetral
prop-erties [6℄, a ondution [7℄, strutural and magneti
properties [8℄ has been reported by many researhers.
However,thedieletribehaviour,suhas,variationof
apaitaneanddieletrilossasafuntionof
temper-atureandfrequenyhasbeenoverlookedtoanextent.
In semiondutor thin lm planner integrated
ir-uits,forwhihhighapaityinsmallspaeisrequired,
the apaitorsmaybegrownby using either ev
apora-tionorsputteringtehnique. Tousethematerialinthin
lmiruitsitisneessarythatthe dieletriloss,tan
Æ,shouldbeinaproperrange. Howeverthemajorityof
requirementsdonotneedthelowesttanÆ(1%isquite
suÆient). Butin someases, likeativelters, tanÆ
shouldnotbemorethan0.01%. Theagingand
temper-aturevariationofapaitaneisalsoimportantforthe
material. ThetemperatureoeÆientofaapaitane
is an important pratial parameter for assessing the
expeted behaviour ofathin lm. This malesit
ne-essarytostudytheeetoftemperatureandfrequeny
onthedevie apaitane.
The dieletri behaviour of thin lm devies
de-pendsnotonlyontheirmaterialproperties,butalsoon
metaleletrodes. Fringingeets at theedges of thin
lm dieletris is usually negligiblebeausethe
thik-ness of thedieletri is usually very small ompareto
itslateraldimentions. Themagnitudeofgeometriand
measuredapaitanemaydieriftheeletrield at
the metal insulatorinterfae varies with the insulator
overtheregion. Forthe givenmaterial thelm
thik-nessaloneestablishestheapaitanedensitywhihin
turns an be used to determine the areaneeded for a
partiularapaitanevalue.
Thedieletri loss,whih is thepart ofthe energy
ofaneletrielddissipatedirreoverablyasheatin
di-eletri,isomprisedoftwoparts,therstpart,whih
arisesduetoleadresistaneandeletroderesistaneis
frequenydependentandinuenedathigher
frequen-ies. This an be minimized using the eletrodes of
highlyonduting metal. Theother termisaproperty
ofthematerialitself,whihisfrequenydependent[9℄.
Also,thedieletri strengthisfoundto reduerapidly
belowabout100nm,owingtopinholesand desret
de-fetsinthelm.
To the best of our knowledge no report is
avail-ableonthestudyofdieletripropertiesofSb
2 Pb
1 Se
7
ompound. We attempt to report, in this paper,
some of the dieletri properties of vauum deposited
Al/Sb
2 Pb
1 Se
7
/Al devies. In all the devies used for
the study thethiknessof thedieletri lm waskept
at leastabove100nm tominimizetheinherentdesret
defets and pinholes. Also, aluminiumwas used as an
main-II Experimental
Thehalogenideompound,Sb
2 Pb
1 Se
7
,usedto
fabri-atethemetal-glass -metal,MGM.devies was
pre-paredbymeltquenhing. TheMGMdevieswere
fab-riated on thoroughly leaned mirosope glass slides,
usingEdwardsCo.(UK)Turbomoleularpumping
sta-tion. The working hamber was tted with Maxtek
(USA) lmdeposition ontrollermodelFDC440. The
base platehousedaneightsoureturret,whilethetop
plate was tted with mask hanger assembly, both of
whihouldbemonitoredexternallywithoutrequiring
to break the vauum. The ultimate working pressure
during thedeposition was510 6
mbar.
Initially, aluminium metal was evaporated to
de-positonthesubstrateintheformoftwoparallelstrips
eahof60mminlength,2mminwidthandseparatedby
5mm from oneanother. These stripsformed thelower
eletrodes. The material wasthen deposited through
appropriate maskto overanareaof 50mm 15mm,
leaving 5mm of the end portions on both the sides
of eah aluminium strip. Six ounter eletrodes, eah
2mm wideand20mmlong,perpendiularto thelower
eletrodesweredeposited onthematerial toobtain12
MGM devies eah of area 4mm 2
(see Figs. 1a and
1b). The entire deposition sequene was ompleted
without breaking the vauum at any stage.
Fabria-tion of twelvedevies onasingle substrateallowedto
repeatedlyarryoutalltheeletrialmeasurementson
alm,ofanypartiularthikness,preparedessentially
under identialdepositiononditions.
Figure1.(a)Shemativiewofmetal-glass-metaldevies.
(b)Crosssetionalviewofthedevies.
The eletrial measurements on the devies were
arried out in vauum using a ryostat, whih ould
be evauated to 10 2
mbar pressure during the
mea-surements. Thesubstratetemperatureinside the
ryo-statouldbevariedfrom150Kto500K.Thedieletri
measurements were arried using `Preision LCR
Me-ter'HPmodel4284Awhihouldmeasureanddisplay
eletrilosset., fordierentfrequeniesrangingfrom
20Hzto 1MHz
III Results
Fig.2showstheapaitane-temperature(C-T)
har-ateristisof atypialrepresentativesamplewith lm
thikness 270nm. The measurements were arried at
1KHzxed applied frequeny. It is seenthat as
tem-peratureinreasestheapaitanealsoinreasesinthe
rangeofthetemperatureusedforthestudy. Duringthe
sampleooling,theC-Turvetraesslightlydierent
pathfor therst heating and oolingyle. However,
duringthesubsequentheatingandoolingyles,theC
-Turveassumesidentialpath. Allthea
harater-istisreportedin thispaperarebasedonthe
measure-mentsarriedoutonthesamples,whihweresubjeted
tothethermalyling asdesribedabove.
Figure2. Capaitane -temperatureharateristisof the
devie with lm thikness 270nm for 1KHz xed applied
frequeny.
Fig. 3showsaapaitaneversusfrequenyplotof
thedevieswithdierentlmthiknessesat295K.Itis
seenthat the apaitane initially falls sharply asthe
frequeny inreases and then saturates to some value
as the frequeny approahes 1MHz. The ratio of low
frequenytohighfrequenyapaitaneobtainedfrom
theurvesis found to be loseto 12:1for allthe lm
devies. Fig. 4 showsthe tanÆ ! harateristis of
queny,attainsaminimum,andagainstartstoinrease
furtherfrequenyisinreased.
Figure3. Capaitaneversusfrequenyplotsofthedevies
withdierentlmthiknessat295K.
Figure4. TanÆversusfrequenyurvesofthedevieswith
dierentlmthiknessesat295K.
Fig.5showstheC-Tharateristisofthedevies
of dierent lmthiknesses at xedapplied frequeny
of 1KHz. Here the temperatures rangehosen forthe
displayofC-Tharateristisis250to 410K.Thisis
beausetheapaitaneisfoundtosaturatenearabout
250Kandtheglasstransitiontemperature,T
g
,isfound
to be419K from theearlierstudies[10℄. Fig. 6shows
theC-Tharateristisofadevie,withlmthikness
270nm,at various onstantfrequenies. It is observed
thattherateatwhihtheapaitaneinitiallyinreases
with temperature redues as the applied frequeny is
marginalhangewithinreaseintemperature. The
sat-urationvalueofapaitaneattainednear250Kis
ap-proximatedasgeometribulkapaitane,C
b
,asthat
obtainedat liquidnitrogentemperature. Hene aplot
of C
b
versus inverse thikness should yield a straight
line. Fig. 7 shows the C
b
versus 1/S plot, whih is
a straightline. The dieletri onstantalulated
us-ing the slope of the urve is found to be 12 whih is
inagreementwiththevaluesreportedforothersimilar
material[11℄.
Figure 5. Capaitane versus temperature harateristis
of the devieswith dierent lm thiknesses and at xed
appliedfrequeny,1KHz.
Figure6. Capaitaneversustemperatureharateristisof
frequen-Figure7. Capaitane versusinverselmthiknessplotat
250K.
Fig. 8showsthetemperaturevariationoftanÆ !
harateristis of a typial representative devie with
lmthikness270nm. It isseenthat thedieletriloss
initially dereases with the inrease in frequeny,
at-tainsaminimum,andthenstartsinreasing
monoton-ially. Thefrequeny,atwhihtanÆattainsminimum,
!
min
; isfoundto inreasewithinreasein devie
tem-perature.
Figure 8. TanÆ versusfrequenyharateristisofthe
de-vie withlmthikness270nmatdierenttemperatures.
IV Disussion
Theaharateristisareusuallyexplainedonthebasis
ofeitherofthethreemodels,namely,Debyerelaxation
model[l2,13℄,Shottkybarriersmodel[14,15℄orgrowth
ofaluminiumoxideatthemetal-insulatorinterfae[16℄.
However,for Debye relaxationproess thelow
fre-queny to the high frequeny apaitane ratio is
ex-petedtypiallyto be3:1[13℄ whiletheobservedratio
in aseof our lmsis 12:1. Further, the Debye
relax-ationmodel isbasedonpolarization ofamaterialand
appliabletoafew polarsolids[17℄. As reported[10℄,
theX-ray diratographofthe evaporatedSb
2 Pb
1 Se
7
lmshowssharppeaksorrespondingonlytoPbSeand
Se
6
. It is known that PbSe is very strong bond [18℄
whileSe
6
ishexagonalin struture. Hene both,PbSe
andSe
6
annotbereadilypolarized. Thisimpliesthat,
inthepresentase,theevaporatedmaterialisnon-polar
innatureandhenetheobserveddieletripropertiesof
thesamplesannotbeexplainedonthebasisofDebye
relaxationmodel.
Inthe aseof Shottky barriers model theratio of
low frequenyto high frequeny apaitane ouldbe
typially 20:1[14℄ while the observed ratiois 12:1. It
has also been observed during the low eld d
mea-surements [19℄,that the dondution is governedby
spaehargelimitedondution mehanism whih
de-mandstheeletrodeontatstobeohmi. Alsoallthe
dharateristiurveswereidentialinnatureevenif
the polarity of the eletrodes wasreversed. Thus the
observedaharateristisannotbeexplainedonthe
basisofShottkybarriersmodelalso.
The third possibilityis the growth of oxide at the
aluminiummaterialinterfaes. Thegrowthofsuh
ox-ide an be made easily evident from the C-T
hara-teristis where the derease in the magnitude of the
apaitaneisobservedineahheatingandooling
y-le [16℄. However, no suh phenomenon wasobserved
andtheC-Turvetraedidentialpathduringheating
andoolingofthesample. Thisisalsotobeexpeted,
asthe entire depositionsequene wasompleted
with-outbraking vauum at any stage. Thus allowing the
interfaestogetexposedtotheoxygenin air.
Thusitis evidentthat theobservedharateristis
annotbeexplained onthebasis ofthese models. An
attempt is therefore, made to interpret the observed
harateristisusingabasismallsignalairuit
anal-ysis[20℄.
As shown in Fig. 9(a), the measured apaitane
anberepresentedasabulkapaitane,C
b
,in
paral-lelwiththebulkresistane,R
b
bothin serieswiththe
leadresistaner=2oneitherside. Theeetiveparallel
andseriesimpedanesofthisiruitanbegivenby,
and
Z
s =R
s +
1
j!C
s
: (2)
With
R
s =r+
R
b
1+! 2
C 2
b R
2
b
(3)
and
C
s =
1+! 2
C 2
b R
2
b
! 2
C
b R
2
b =
1
! 2
C
b R
2
b +C
b
a+b (4)
R
b =R
0 exp
E
kT
(5)
where
R
b
=Bulkresistane
C
h
=Bulkapaitane
r=2=Leadresistane
R
o
=Charateristiresistaneofbulkmaterial
R
s
=Eetiveseriesresistane
C
s
=Eetiveseriesapaitane
T =Temperature
E =Ativation energyofarriers
Figure9. (a)Generalrepresentation;(b)Equivalentseries
iruit.
Thus theequivalentiruitshownin Fig. 9(a)an
berepresented asshown in theFig. 9(b). The above
equationsand theequivalent iruitshown in theFig.
9(b) will be used for the analysis of the results. The
desiredparametersarehoseninthefollowingmanner.
Itisseenfromequation4thatwhentheappliedsignal
frequeny is very high the measured apaitane
ap-frequenyapaitane, i.e., in thepresentase,
apa-itane at 1MHz, anbe approximatedasthe bulk
a-paitaneofthematerialforanygiventhikness. Thus
the bulk apaitaneof the material for thethikness
270nmis10nF.AlsoEishosenas0.09eVandR
0 as
393.
IV.1 Variation of apaitane with
tem-perature
Withthehelpoftheaboveparametersthe
theoreti-alvaluesoftheapaitanewereomputedforvarious
temperature, for the representative sample with lm
thikness 270nm. The theoretial C - T urve
alu-lated for frequeny1KHzis shown byhexagonin Fig.
6. It isseenthat thereis exellent agreementbetween
experimentaland theoretialurves.
Dierentiatingapaitanewithtemperature,
dC
s
dT =
da
dT =
2E
! 2
C
b R
2
b kT
2
>0 (6)
Sine,allthetermsontherighthandsidearepositive;
apaitane is an inreasing funtion of temperature.
Intheaboveequation,righthandsidetermisinversely
proportionalon squareof the applied frequeny. This
impliesthattherateofhangeofapaitane,i.e.,slope
of C - T plot dereasesas thetemperature of the
de-vie inreases(ref. Fig. 6). TemperatureoeÆientof
apaitane(TCC)anbegivenby,
TCC= dC
s
dT
1
C
s
(7)
Sine,all thetermsin theaboveequation are
pos-itive, TCC is an inreasing funtion of temperature.
ThisisshownintheFig. 10.
IV.II Variation of tan Æ with frequeny
Dieletriloss,tanÆ,in general,anbegivenby,
tanÆ=!C
s R
s
(8)
SubstitutingforC
s andR
s
,theequation8maybe
writ-tenas,
tanÆ=! 1+!
2 C 2 b R 2 b ! 2 C b R 2 b r+ R b
1+! 2 C 2 b R 2 b (9)
DierentiatingtanÆ withrespetto!,weget,
d(tanÆ) d! = 1 ! 2 C b R b 1 ! 2 C b R 2 b +rC b (10)
Andseonddierentiationwillbe
d 2 tanÆ) d! 2 = 2 ! 3 C b R b + 2r ! 3 C b R 2 b
>0 (11)
Sine allthetermsin theaboveequation arepositive,
tan Æ must go througha minimum value at a ritial
frequeny, !
min
. Hene equation 10 must be zero at
ritialfrequeny,!
min . Thus, 1 ! 2 min C b R b r ! 2 min C b R 2 b +rC b
=0 (12)
Sineleadresistane,r=2,isverysmallomparedtothe
bulkresistane,R
b
,ofthematerial,theseondtermin
the aboveequation approaheszero. Hene negleting
this term,theaboveequationmaybewritten as,
! min = 1 rC 2 b R b 1=2 (13)
Equation13showsthattheritialfrequeny!
min
de-pends on the bulk resistane, whih is temperature
dependent suh that R
b
dereases as temperature
in-reases (refer equation5). Hene, !
min
should depend
ontemperaturesuhthat!
min
shouldinreaseas
tem-perature inrease, whih is preisely what is observed
(refer Fig. 8).
V Conlusion TheSb 2 Pb 1 Se 7
7lmsarepreparedbyvauum
deposi-tion of the ompound. The observedapaitaneand
dieletri lossasafuntion of frequenyand
tempera-tureanbesatisfatorilyexplainedonthebasisofsmall
signala iruitanalysis. Thetheoretial urve
gener-atedusingtheanalysisshowexellentttingwith
or-respondingexperimentalurve.
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