Impedance spectroscopy IS technique has been analyzed and applied to measure the ionic conductivity of the films.. For a superionic conductor, like a thin-film electrolyte, it is necessa
Trang 1VNU JOURNAL OF SCIENCE, Mathematics - Physics, T.XXII, N01, 2006
A P P L I C A T I O N O F I M P E D A N C E T E C H N I Q U E F O R S T U D Y O F
I O N I C C O N D U C T I N G P R O P E R T I E S O F L i L a ^ T I O g P E R O V S K I T E
T H I N F I L M S
N g u y e n N a n g Dinh*, N g u y e n T h i B a o N g o c
D e fa rtm en t o f E ngineering Physics & Ncinotechnogy, College o f Technology, V N U H
Le D i n h T r o n g
D e fa rtm en t o f Physics, Pedagogical College, Hanoi II, X u a n Hoa, Virth Phuc
A b s t r a c t Impedance spectroscopy (IS) technique has been analyzed and
applied to measure the ionic conductivity of the films For a superionic
conductor, like a thin-film electrolyte, it is necessary to characterize IS by using
a two-electrodes ccll, where the thin film is deposited between two metallic
electrodes In a very thin film, the Helmholtz layer strongly affects to the
conductivity during the measurement So that, an equivalent scheme should be
chosen with a separation of three frequency zones to fit the theoretical curves to
experimental data The best curve fitted with two to three circles is taken and
elaborated to determine all the parameters of the scheme, and R4 — a parameter
of the ionic conductivity - in particular
Electron-beam-deposited LixL a lxTiO:, crystalline thin films were used for IS
measurements Using the fitting method, the experimental data were fitted
with the circles obtained by the chosen equivalent scheme From these circles,
the ionic conductivity at room temperature of a 350-nm thick Li012La088TiO3
film was found to be of Ơ = 6,52 xl 0 ° s.cm \
1 I n t r o d u c t i o n
It is k no wn t h a t for a n al y zi ng an ac c u r r e n t , Y-conductivity h a s been used,
w h e r e Y = l / z If z is z = I z I e'*, Y = 1 / 1 z I e"* T h u s Y is a vector with a value of
1/1 z I a n d a n opposit p h a s e to the phas e of z z is d e p e n d e n t on the frequence of the
ac c u r r e n t T h e common a n d sui ta b le r an g e used for stu d y is of 10 mHz to 10 MHz
In th e electrolytes, in solide s t a te in p a r t i c u l a r the ionic mobility is much small er
t h a n the elect ro n mobility, so t h a t to respond to the ch ang e of the electrical field, it
is n e cce ss ary to m e a s u r e in the r an g e of low frequencies From the e x pe r im a ta l data
ob t a i n e d in th e i m pe d an c e sp ect ra (IS) one can d e te r m i n e the ionic conductivity and
o t h e r p a r a m e t e r s such as the ch arge t r a n s p o r t , diffusion coefficient in solids However, i t is so m e ti m es very difficult to analyze the r es ul ts for t h i n films, because for very t h i n films all above ment ioned p a r a m e t e r s are strongly affected by the
* Corresponding author, email: dinhnn@Yint.edu \'H
54
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thick nes s a nd contacts in the m e a s u r e m e n t cells Thu s, the choice of t h e e q u iv a le n t schemes consisting with subs che m es of resistance, capacity, etc plays a n i m p o r t a n t role to find out real v alu es of the pa ra m e t e r s One of the most i m p o r t a n t principles
to design th e eq u iv a le n t schemes is t h a t the total c u r r e n t value as well a s th e p h a s e shift m u s t have the s a m e values as the m eas ur ed sam ple do
Recently, mu lticom po und superionic conductors with a p e ro v s ki te s t r u c t u r e such as LixLaỊ.xT i 03 have increasingly been studied This is b e c a u s e t hes e
m at er i a ls have a high Li-ion conductivity, even a t not very high t e m p e r a t u r e Especially, the thin-film formed LixL a l xT i 03 can be used in m a n y scopes like all- sold-state ionic b a tte r ie s, electrochromic display, elctrochemical sensors, etc [1]
However, in the e x p er im e n ta l researches, to d e t e r m i n e t h e ionic co ndu ctivity
of the t hi n and/or very t h i n films of LixL a lxT i 03 by t h e IS t e c h n iq u e is a lw ay s to face man y difficulties, t h a t obtain ed r es u lts often h av e a large error So t h a t , the aim of this work is to utilize this technique with a n a l y s i n g a series of e q u i v a l e n t schemes applied to fit with the obtained e x p er im e nt al d a t a from IS m e a s u r e m e n t s
on the t hi n films
b.
Fig 1 Equivalent schemes o f samples measured in an electrochemical cell (a)
and the corresponding elements of Zj part
2 A n a ly s is o f t h e im p e d a n c e t h e o r y
2.1 E q u iv a l e n t s c h e m s fo r a three-electrodes cell a n d I S c h a r a c t e r is ti c s
It is well-known t h a t an e q uiv ale nt scheme for the sa m pl e m e a s u r e d in th e three-el ect rode s cell h a s a Ra nd le scheme as p r e s e n t e d in Fig 1 In t h i s s c h em e Cd
is the capa city of t h e double layer, Zf char act eri zes t h e electrochemical proccess For
simplicity, z r is sp li tte d into two p a r t s connected in serial Rs a n d Cs or R ct a n d Zw,
where Rs a n d Cs, respectively is a real an d an image p a r t of th e i m p e d an c e, R ct is
Trang 356 Nguyen N a n g Dinh, Nguyen Thi B a o Ngoe, Le D i n h Trong
the re s i s t a n c e of the c ha r ge t r a n s p o rt , Zw is t h e W a r b u r g i m p e d a n c e c h a r a c t e r i z i n g
a m ass t r a n s p o r t , R0 is th e res ist anc e of the liquid electrolyte.
Am on g t h e s e p a r a m e t e r s , only Cd a n d R0 are n ot d e p e n t onto t h e frequency
By calcu latio n as shown in [2], the expression for the fr e q u e n c y r e l a ti o n s h i p of Rs and C8, res pec tive ly is:
R s = Rct + G /o 1/2 a n d Cs = l/(ơ(01/2) (1) where a is d e t e r m i n e d as follows:
R T
Ơ = [>2F2A n / 2 V ư o ^ o D 1/ 2 C * D 1R *
J
(2)
W h er e R is th e ideal gas cons tan t, T is th e ab so lu te t e m p e r a t u r e , n is th e ion valence, F - F a r a d a y c o ns ta n t, A - electrode a re a, DO, DR - diffusion coefficents,
r e s p e c t i v e l y o f o x i d a t i o n a n d r e d u c t io n r e a c t i o n s , C q , C r - c o r r e s p o n d i n g io n
c o n c e n t r a t i o n s
One c an e xp re ss the frequency dependences of t h e r e a l a n d i m a g e p a r t s of the
e q uiv ale nt sch em as follows:
z im
K 0 +
c o C j 1
( c dơ(0112 + 1
( r cI + ơo>- , / 2 )
)2 +C0 2 C Ỉ ( r ,
+ ơ w"1/2 1
:i + ° “ ‘
1/2
Ơ + 1 j
0C d ơ c o l / 2 + l )
2
1 ■K 0 2 C Ỉ ( R t , + c c o - 1 ' 2 )
2 1
(3)
(4)
At t h e low frequencies, CD—» 0, the e q ua t io n s (1) a n d (2) can be ex pressed as:
By c om bi ni ng two above equations, one can e l i m i n a t e CO a n d o b t a i n ’
T h a t is meaning, the image-vs-real part dependence is a li n n e a r one, when CD-> 0 the image p a r t also approaches to zero, then the real p a rt h a s a value equals to:
(R0 + Rct - 2ơ2Cd)
In t h e r a n g e of high AC frequency, the express ions (3) a n d (4), respectively
t r a n s fo r m into:
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z : = c o C d R c.
c d R ct From t h e s e e q u a t i o n s one can combine in one expression of t h e o t h e r kind
r e l a ti o n s h i p b e t w e e n th e r eal a n d image pa rts, a s folows:
Z r c - R 0 - ¥
)
R cl
(10)
Th is cle arl y d e m o n s t r a t e s t h a t in the graphic p r e s e n t a ti o n , Zim- ZRe plot is a half of a rou nd T h is r o u n d crosses the horizontal axis a t two points, t h e first one is
a t R„ c o rr e s p o n d i n g to CO > 00 a n d the second one is a t (R0 + Rct) - w h e n to -> 0 The ionic c o n du ct iv it y (ơ) can be found from e x p e r i m e n t a l d a t a o b t a i n e d for Rct, it is
d e t e r m i n e d as follows:
where d a n d s , res p ec t iv e ly is t h e thick nes s and a r e a of the work ing electrode
2.2 E q u iv a l e n t sc h e m f o r a two-electrodes cell a n d its im p e d a n c e sp e c tru m
The t heo ry of th e IS m e a s u r e d on a two-flat-electrodes cell h a s been developed
by MacDonall U s in g this, t h e a u t h o r s of [3,4] have studied ionic co nductance of solid sta te electrolyte (or supe rio nic matGrials) Basing on the MacDonall’s a r g u m e n t in general, the i m p e d a n c e IS a n AC frequency function with threG c h ar ac t er i st i c ranges
of high, midd le a n d low frequencies Depending on both the composition and
s t r u c tu r e of t h e ionic m a t e r i a l s , th e IS may have one, two or three circles in the Z| -ZKp plots (Fig 2) One can a n al y ze the IS ch aracteristics as follows:
- High fr e q u e n c y range : In this range t h e r e is no c har ge t r a n s p o r t a t the interface b o u n d a r i e s b e t w e e n t h e electrodes a nd electrolyte T he e q u i v a l e n t scheme
IS p r e s e n t e d in Fig 2a, w h e r e Cg is the geometrical cap acity of t h e two pa rallel electrodes in t h e solid electrolyte, R b is the re s i s t a n c e of t h e electrolyte T h e IS h a s one circle (Arc3)
- Midd le fr e q u e n c y range : In this range, t h e affect of th e geome tri cal capacity can be neg lected T h e i m p e d a n c e is de te rm in e d m ai n l y by th e capicity of t h e double layer form ed a t t h e c o n ta c t s be tw ee n the solid electrolyte a n d electrodes T h u s the
c har ge t r a n s p o r t a t t h i s i n te r f a c e is d e p en d e n t on th e r ea cti on s a t t h e conta cti ng
b o u nd a ri e s T h e e q u i v a l e n t scheme is p re s e n t e d in Fig 2b, w h e r e R t is the
r e s i s t a n c e of t h e c h a r g e t r a n s p o r t , Cdl is the capicity of the double l ay e r (Helmholtz layer) T h e c o r r e s p o n d i n g IS is Ac r2 circle.
- Low f r e q u e n c y ran g e : in th e first h a lf circle th e action of the AC c u r r e n t on ions e n a b l e s to form a c o n c e n t r a t i o n g ra d ie n t of t h e ions with the i m p e d a n c e Zd The i m p e d a n c e plot h a s l i n e a r form with a slop e q u a l s to unit W h en co-» 0 the AC
c u r r e n t a c t s like a q ua zy- DC one T h u s the ZIm -> 0 a nd ZRp t h e n h a s the
Trang 5correspo nd ing value of Rct in the horizontal axis The i m p c d a n c e s p e c t r u m h a s the
form of A r c l in Fig 2
Fig 2 Equivalent schemes at different friquencies ranges and corresponding impedance spectra of the samples measured by a two- electrodes cell.
3 T he im p e d a n c e s p e c t r a o f LixLaj.xT i 0 3 th in film s
3 ,1 E x p e r i m e n t a l e v i d e n c e The t h i n films of Li xL a lxT i 03 with X “ 0.12 ha s been p r e p a r e d by electron beam deposition T he e x p e r i m e n t a l im p e d a n c e spectra obtained for two-electrodes cells vs the film t h ick nes s a r e s h ow n in Fig 3 For the films th ic k e r 350 nm, t h e IS becomes n a r r o w e r with t h e d e c r e a se of t h e film thickness This is c o n si st e n t with the Ma cDonall’s t h e o r y for t h e two-electrodes cells From the t h i c k n e s s of 350 nm down, in ste a d, the con du cti vi ty is increased, the
IS is not only con den sed b u t also expand ed into 2 tim e s of t h e circle r a d i u s (see d3 plot) T h is shows t h a t the
Ma cDonall’s t heo ry can be applied
onlv for the films with some critical
thickness In p r e s e n t sa m p le s it is
be a t t r i b u t e d to t h e films t hi ck nes s o
e q u iv a le n t schem es s i m il a r to the
schemes from Fig 1 is not suitable
more for such a t h i n film It is
ne cessary to t a k e th e influence of
both the capacity of H e lm ho lt z layer
a n d t h e c h a r g e of t h e c o n c e n t r a t i o n Fig 3 Im p ed a n ce spectra o f L ixL a J^ r iU 3 tn in
g r a d i e n t into t h e eq u iv a le n t films with different thickness: d = 900 nm (dl),
Trang 6A p p l i c a t i o n o f I m p e d a n c e T e c h n i q u e f o r S t u d y of 59
3.2 A n a l y s i s a n d e s t i m a t i o n o f io n ic c o n d u c t i v i t y Fi g u re 4 p r e s e n t s the
IS d a ta (d ark points) of a 350 nm - thick LixL a l xT i 03 film In the frequ en cy range
from 10 mHz to 10 MHz, the
IS splits on two c lea r circles
Moreover, t h e second circle
s t a r t s at t h e f r eq u e nc y w h e n
th e first circle is not finis hed
yet This sho w s t h a t all th e
processes occuring in the
middle a n d low f re qu en cie s
have stron gly affected to the
samples In dee d, t h e
a p p e a r a n c e of large circle
con ce rn ni ng to t h e low
frequency r a n g e pro ves a
much c o n si de r a b ly larg e
electrochem ical p ro ce sses in P ig 4 Im p ed a n ce spectra d a ta (dark p o in ts ) o f a 350-
the in te rf ac e b e t w e e n th e nm thick LiJLdj.xTiOfr measured in frequency range from
solid ele ctro lyte * a n d 10 mHz to 10 MHz The solid circles are the fitted IS
electrodes T h u s , for f i tt i n g obtained from the equivalent scheme o f Fig 5
the t he o re tic al IS wi th the
e x p e r i m e n t a l d a t a it is n e cc es s ar y to design a series of e q u iv a le n t sc h em e s where
above m e n t i o n e d p ro ce ss es m u s t be t a k e n in considering Us ing so ft w a re available
in the A u t o L a b - P o te n ti o s t a t- P G S -3 0 , one can choose different p ara lle l a n d serial
p a r t s of th e s c h e m e s to des ign a n e qu iv a le nt sc h em e t h a t is most fi tte d with
e x p e r i m e n t a l circles By t h i s meth od we have o b ta in ed a scheme as p r e s e n t e d in
fi g 5 The r e s u l t of th is fi tt i n g is shown by the solid circles in Fig 4
1 he e q u i v a l e n t s c h em e in Fig 5 consists of t h r e e p a r t s c o r r e sp o nd i ng to thr ee
r a n g e s of AC freq ue n ci e s, a s follows:
- The p a r t I h a s only R l , the res istance of co nta ct a n d lead wires does not
depen d on th e freq ue ncy So t h e impedance h a s only real part
The p a r t II c h a r a c t e r i z e s the contribution of th e electrochemical processes in
the in te rf ac e b e t w e e n t h e t h i n film an d electrodes Her e R2 is t h e r e s i s t a n c e of
metal/solid e le ct ro ly te co ntact; C l a n d R3, respectively a re t h e cap aci ty a nd the
re s ista n c e c a u s e d by th e con cen tration of ions in th e electrolyte; C2 is th e capacity
of the H e l m h o l t z l a y e r ( t h a t strongly affect to th e sa m pl e w h e n t h e l a s t is thin
enough) Besides, Q c h a r a c t e r i z e s the gr ain a n d b o u n d a r i e s size effect Its
c o r re sp on d i ng i m p e d a n c e is Z(Q) = A*(jco)'n, w he re n = 0, Q is in tr i ns i c re s i st a n c e , n
= 0.55, Q is t h e W a r b u r g i m p e d an c e, a n d n = 1, Q is the capacity
- T h e p a r t III c h a r a c t e r i z e s ionic conductivity of t h e t h i n films in t h e low
fr equency ra ng e H e r e C3 is th e capacity formed b etw een th e two pa ral lel electrodes
a nd R4 is t h e r e s i s t a n c e of t h e ionic conductance
Trang 760 Nguyen N a n g Dinh, Nguyen Thi Bao Ngoe, Le Dinh T ro ng
T a b l e 1 P r e s e n t e d all the va lue s of the p a r a m e t e r s obtained from the calculation by this eq u iv a le n t scheme
F ig 5 Equivalent schemes for a 350 nm - thick film o f LixL a l xT i 0 3
Table 1 Physical parameters determined from the equivalent scheme in Fig 5 for the
Lio 12^"^0 thin film
R4(Q) C3(hF)
T ak in g the value of R4 = 5.37 Q from t h e table, for the Li0 12L a0 88T i 03 sam ple with a thickne ss of 350 nm a n d a n electrode a r e a of 1 c m 2, us in g formula (11), one can d e t e r m i n e th e Li-ion conductivity, it e q u a l s to Ơ = 6,52 x i o 6 s.cm'1 t h a t is much h i g h e r t h a n t h a t of th e t h i c k e r sa m ple T hi s va lu e is q u ite close to the
re s u l t t h a t was r e p o r t e d in [5]
4 C o n c lu sio n
The ionic conducting pro per ti es of thin fimls of perovskite s t r u c t u r e s h a s been studied by a n a l y si n g a n d application of t h e imp ed anc e te c h n iq u e for the two- electrodes cells The r e s u l t h a s shown how to fit the theo re tical IS with the
ex p er im e nt al d a t a for very t h i n film samples The ionic conductivity of the LixLaj
xT i 03 thin films deposited by electron beam was d e t e r m i n e d with a high accuracy due to the application of th e fitting method For a 35C nm -thick film of
Li012L a088TiO 3, the Li-ion conductivity was found to be Ơ % 6,52 xlO'6s.cm '1
A c k n o w l e d g e m e n t s T his work is fulfilled due to th e financial sup po rt of the Vietnam Na tional U ni ve rs i ty Hanoi by a Special project for re s ea r ch e s in 2006- 2007
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c h em ist ry , v 7 3 ( 1 9 8 8 ) , pp 127 - 139.
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di ssolutin kinetics of t u n g s t e n in hydr ogen peroxide, J Phys Chem B
V.102(1998), pp 9501 - 9507
4 S P a p a e t h im i o u s, G leftheriotis, p Yianoulis, St u d y of electrochromic cell
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the y - M n 02 redox mec han ism , Electrochimica A cta, Vol 15(1994), p 2321 -2331