VNU. 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: [email protected]. \'H
54
A p p lic a tio n o f I m p e d a n c e T e c h n iq u e fo r S tu d y o f 55 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
56 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 /o1/2 a n d Cs = l/(ơ(01/2) (1) where a is d e t e r m i n e d as follows:
Ơ = R T
[>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 , Cq , Cr- 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 )1 2 ■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:
ZRe = Ro + Ret + ơ© ‘1/2 (5)
z im = CTC0-"2 4- 2ơ2Cd (6)
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 ’
z im = ZRe - R0 - Ret + 2ơ2C d (7)
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:
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 of.. 57
z : = c o C d R c.
i m | + n 2 r 2 R 2 ( )
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:
Í n \ 2 / n
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:
S R a (11)
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
correspo 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.
58 Nguyen N a n g Dinh, Nguyen Thi B a o Ngoe, Le D i n h Trong
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
aro u n d 350 nm. T his may probably ^
be a t t r i b u t e d to t h e films t hi ck nes s o
effect. So that, the choice of N
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),
^ 650 nm (cL2) and 350 nm (d3)
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 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 r e 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
influence of the
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.
60 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
(I) (II) (III)
R1(Q) R2(Q) R3(Q) Cl(nF) C2(|iF) Q
R4(Q) C3(hF)
A(Q) n
794 -2,5 37 1 0 3 0,61 0,2x l0'6 0,52 5,37 0,12
T ak in g the value of R4 = 5.37 Q from t h e table, for the Li012L a088T 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'6
s.
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.
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 iq u e f o r S t u d y of.. 6 1 R e f e r e n c e s
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5. J. M. Amarilla, F. T ed ja r a n d
