Transient and ac electrical conductivity in evaporated thin rubidium bromide films

Journal of Non-Crystalline Solids 131-133 (1991) 1099-1103 North-Holland

1099

Transient and ac electrical conductivity in evaporated thin rubidium bromide films N i k o l a s I. X a n t h o p o u l o s , S t a v r o u l a N . G e o r g a a n d M i c h a e l N . P i s a n i a s Department of Physics, Universityof Patras, GR-261 10 Patras, Greece

The transient and ac electrical conduction in thin RbBr films has been studied at room temperature as a function of the applied voltage. The results show that the electrical conductivity is due to hopping anions in the ac conductivity and at early times (10-5 to 10-2 s) in the transient conductivity. At times > 10-2 s the transient conductivity is due not only to hopping anions, but to the release of trapped electrons as well, either by overcoming the barrier of the trap (Poole-Frenkel effect) alone or assisted by tunneling through the barrier.

1. Introduction The transient and ac electrical conduction studies on dielectric materials are two powerful tools used in the investigation of the conduction mechanisms to which the polarization of the material is due [1]. These techniques have been employed recently in the investigation of the electrical properties of K I [2-4] and KC1 and KBr thin films [5]. The results can be summarized as follows. (i) Transient conductioity. At early times following the application of a step voltage ( 1 0 - 5 - 1 0 -2 s) the charging current decays in all potassium halides studied, according to I = at", where a and m are constants. This is the power law reported in the literature [1,6-10]. For K I it is also obeyed in the time intervals from 60 ms to 1 s and for times > 10 s, whereas for KC1 and KBr it is not possible to distinguish any region, where the power law is clearly obeyed, beyond 10 -2 s. Most important, it is observed that the current is at any instant not linear with respect to the applied voltage [4,5]. (ii) A C conductioity. Within the frequency range 1 Hz-200 kHz, KC1, KBr and K I show a linear dependence of the ac current with respect to the applied voltage and the power law 0(60)= bw" is obeyed [4,5], where b and n are constants. It is concluded that the ac conductivity is a bulk process and the values of the exponent n obtained

suggest that the ac conductivity is due to hopping charges [1,10]. Taking into consideration the nature of the thin films, it is concluded that the hopping charges are anions [4,5]. By applying the Fourier transform a transient current is determined for each potassium halide in the time interval for which there is correspondence with the transient study. The current, thus determined, decays faster than the current in the transient study. These observations have led Pisanias et al. [4] to suggest that in K I a strong electric field is built up during the application of the step voltage [11], promoting thus the release of the trapped electrons by overcoming the potential barrier through the P o o l e - F r e n k e l effect [12,13]. In KC1 and KBr the strong electric field promotes the release of the trapped electrons through tunneling as well [5]. These ideas were checked in the transient and ac conductivity study of RbBr and the purpose of this paper is to report the results of this investigation.

2. Experimental details RbBr films were prepared by the standard method described previously [2]. The thickness of the films varied from 1000 to 3000 ,~. The linear response of the samples was verified in the ac

0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)

N.I. Xanthopoulos et aL / Conductivity in rubidium bromide films

1100

spectrum analyzer. The ac conductivity was determined with a phase sensitive lock-in amplifier for different applied sinusoidal voltages between 0.8 and 2.4 V peak to peak. The transient charging current was determined in the range 1 0 - 5 - 1 0 4 s for applied voltages f r o m 0.4 to 2.0 V. studies

with a Tektronix

7L13

2.0E-7

........ ! .........

! .........

! .........

o

!.........

°

1.5E-7 < ~ 1.0E-7 tw tw (..)

3. Results

S.OE-8

Figure 1 shows the time dependence of the transient current in a log I versus log t presentation with the current scale shifted vertically b y one decade for each applied voltage for clarity. T h e power law is obeyed only in the time interval 1 0 - 5 - 1 0 -2 s, whereas for times > 10 -2 s the power law breaks down. The transient current at different instants in the time interval 1 0 - 5 - 1 0 -3 s increases linearly with increasing voltage, but this linearity is not observed for times > 10 -2 s, as can be seen in fig. 2. O n the other hand, the frequency dependence of the ac conductivity shows two distinct parts, each one of which follows the power law Re o ( w ) = b~0", where b = (2.8 -t- 0.2) x 10 - t ° and n = 0.49 + 0.01 for the frequency range 10-104 H z

0.0

l,,,,, 0.0 l , , , , , , , t ,0.5

'1'.'6 , , , , , , , , i ,1.5 ....... ~.'6 , , , , , , , 2.s APPLIED VOLTAGE( V )

Fig. 2. Voltage dependence of the charging current at different

instants: o, l X l 0 -2 s;[3, 9x10 -2 s.

and b = (1.7 + 0.2) x 10-14 and n = 1.47 + 0.01 for the frequency range 104-106 Hz, respectively. Further, the system behaves linearly with respect to the applied voltage, as can be deduced f r o m the ~ ....... , , ....... , RbBr-2- : d = f

........ ,

........ ,

, , ,~! Ip

2240A

!

10~ -

iI ?

'

!"

,"

~ ,o-'~

~ I 0 -i~'ww~o,..." ~'~h**,qlb,.. ~

"~*,,~

'0'I

-'**o..~..~ 1.2'~

~ ~10

' " -=10 -'

TI M Fig. 1. Time dependence

E

~ 1

10

tic 10 -m~..

I'

f, "

-..

10 - " b " '"''= ' " 10 - = 1 0 ~ 1 0

lib II

......

..... d "P'h"dv""'"~ 1 0 = 1 0 = 1 0 " 10 ='

(see)

of current at different applied voltages.

,

........

,

........

,

,

........

10 = 10 =' 10 " CIRCULAR FREQUENCY ( sec

10 ' -t

)

Fig. 3. F r e q u e n c y dependence of the ac conductivity at different applied voltages (in V): o , 0.4; [3, 0.6; + , 0.8; x , 1.0; * , 1.2.

N.L Xanthopouloset al. / Conductivityin rubidiumbromidefilms I

[

I

IIII1[

1

I

111111

I

I

i

i

i L iii

I

i

i

i

i i i ii

independence of the ac conductivity on the applied voltage (fig. 3). This, in connection with the fact that the ac conductivity increases with increasing thickness (fig. 4), leads to the conclusion that the observed conductivity is a bulk p h e n o m e n o n [1]. T h e values of the exponents, n, for the two parts of the ac conductivity indicate that ac conductivity is due to h o p p i n g charges [1,10]. It is concluded that these charges are anions, following the same a r g u m e n t s presented in detail in ref. [4]. A transient current is determined, as in ref. [4], f r o m the ac conductivity in the time range, 10 - 5 10-2 s, in which there is correspondence with the range from the transient study. This current practically coincides with the experimentally determined transient current, as can be seen from the solid line in fig. 5 in the above range.

10'

.~#~ 1~ _~,.~1~

10 ÷2 Hz

10'

Rbar-2- : d - 2z,0X

oZ v

• eee_ 10" ,, • e 10"~ . . . . . . ." RbBr-,-: d - 108OX " • •Ill • <--- 1 0 " Hz " *

z .<

8 10 Q'--

z < =

~

~.m

10

.. -'~ "'* I

I

I

IIIII1

10103

[

I

I

I I III1

10'

I

I

i

I11111

10 "

I

I

I

1101

I [ II

10e

107

REAL IMPEDANCE ( OHM )

4. D i s c u s s i o n

Fig. 4. The complex impedance diagram for two RbBr thin films: ©, 0.4 V; [3, 0.6 V; + , 0.8 V; × , 1.0 V; *, 1.2 V.

Taking into consideration the blocking nature of the electrodes, a strong internal field is formed [11,14]. This electric field is strong enough to release the t r a p p e d electrons, which are a b u n d a n t in thin alkali halide films f o r m e d b y thermal evaporation [15]. T h e current, which is due to these electrons, should obey the P o o l e - F r e n k e l law, which is expressed b y the relation

10 Rba~-2-: ~- 22.0X ooooo Tronmient Evaluoted +++++ Residual 10

10

.

<~

÷

Ipf =

~z10

• e e

.%

o ~0-'*

%~ • "%

10-"

"% :

~o ........

~

10 ~

........ J

........ '

10 "~

10-'

........ '

10-'

....... '

TIME (

1

nee

....... '

)

10

.......

' ........' ....

10 t

103

Fig. 5. Time dependence of the current for 1.0 V applied voltage. <3, total transient current; +, electronic transient

current;--,

transient ionic current,

C V

exp

[flPfF]/2] =CVexp{DV1/2}

(1)

2 k T

[12,13], where C and D are parameters. With a non-linear least-squares fitting p r o g r a m the time range within which the experimentally observed current obeys relation (1) was determined. This range extends f r o m 10 -] to 10 s approximately, with increasingly better fitting as time increases in the a b o v e - m e n t i o n e d range. This steadily increasing better fitting suggests that a second mechanism, whose contribution diminishes as time proceeds, c o m p e t e s with the release of electrons. This is attributed to the anions, to which conductivity is due in the range 1 0 - 5 - 1 0 -2 s. By considering the current solely due to the release of trapped electrons at the instant at which the best f i t of relation (1) occurs, a time instant, t 2, is

N.I. Xanthopoulos et aL / Conductivity in rubidium bromidefilms

1102

o b t a i n e d . This t i m e i n s t a n t is equal to 9 × 1 0 - ] s. It is further a s s u m e d that at this i n s t a n t the current that is due to the a n i o n s is a p p r o x i m a t e l y 10% o f the error in the current, resulting f r o m the s t a n d a r d d e v i a t i o n of the p a r a m e t e r s C a n d D in relation (1), whose error is less o r equal t h a n 10% o f the c u r r e n t at the i n s t a n t t 2. Therefore, it m a y be written, that the e v a l u a t e d current, Iev, is equal to Icy(t2) = 0.01 I~x(t2).

100.00

a0.00

--~ -J

60.00

=

40.00

.

.

.

.

.

.

.

.

.

~ ....... --r [] o o%0 0 ° o o o o o ° °% o o o ° ÷÷ +\+ ÷ + + x x x x Xx ~x ×

.

.

.

.

.

.

.

.

.

.

.

.

.

.... ; ~m o o°o o.~J 0 O0 0 °°O # o 0 °0 ° + . . + ,: ÷ ÷+÷... . +÷ ÷ ............ x

xx

x

~

"~

Thus, the solid line is d r a w n c o n n e c t i n g the current at 10 - 2 s a n d l~v at t 2 = 9 x 10 -1 s. F o r times greater t h a n t 2 the fitting o f the e x p e r i m e n t a l l y d e t e r m i n e d c u r r e n t to r e l a t i o n (1) deteriorates. T a k i n g i n t o c o n s i d e r a t i o n the possib i l i t y that the high i n t e r n a l field m a y l e a d to the release of the t r a p p e d electrons n o t o n l y b y overc o m i n g the b a r r i e r b u t also b y tunneling, it was checked with the same curve fitting p r o g r a m ,

20.o0

°°°10

.

.

.

.

. 1 0 .0

.

. . . . . . . . ..

rbME (

sec

.

10100 . .

)

Fig. 7. Time dependence of the percentage of the total current

due to Poole-Frenkel effect for different applied voltages: o, 0.4 v ; n, 1.0 v ; <>, 1.2 v ; + , 1.6 v ; × , 2.0 v.

whether the e x p e r i m e n t a l l y d e t e r m i n e d c u r r e n t o b e y s the r e l a t i o n

t u n n e l i n g c o n t r i b u t i o n to the c u r r e n t [13]. T h e results of this fitting are shown in fig. 6. P h o t o -

I = C V e x p ( O V ]/2) + G V 2 e x p ( K / V ) ,

c o n d u c t i v i t y studies o n s u p p o r t the m e c h a n i s m shows the p e r c e n t a g e , t r a n s i e n t current, of

(2)

where G a n d K are constants. T h e s e c o n d t e r m o n the right h a n d side of eq. (2) r e p r e s e n t s the

P o o l e - F r e n k e l effect for different a p p l i e d volt" ages. It c a n b e seen in this figure that the higher the a p p l i e d voltage, the s m a l l e r the c o n t r i b u t i o n of the P o o l e - F r e n k e l effect a n d the higher that of t u n n e l i n g ( ( I t u n / I t r ) = I -- ( I p f / I t r ) ) .

I l l l t t l l ~ l l l l l l l l l l l l l l l l l l ~ l l l t l t t l l l l

,bsr-2- : ~ - 22,0~ ooooo Exl~r. P. rot= -- -- P.F. .... r~,,.,

1.5E-9

r u b i d i u m h a l i d e thin films o f t u n n e l i n g [16]. F i g u r e 7 relative to the o b s e r v e d the c u r r e n t due to the

,'

5. Conclusions
: ,/,f/ 5.0E-10

// / / ,' ,"

/

-" ..-"/ •/ 0.0

0.0

/' ..

... . . . . . . .0.5, . . . . . . . . .1.0 -r.r. . . . . . .1.5 . . . . . . . . . . .2.0 ......... APPLIED VOLTAGE

2.5

( V )

Fig. 6. Voltage dependence of the current and its components at 100 s.

T r a n s i e n t a n d ac electrical c o n d u c t i v i t y studies o n t h e r m a l l y e v a p o r a t e d thin R b B r films suggest that there are c o m m o n features as well as differences. A C c o n d u c t i v i t y is a b u l k process a n d it is d u e to h o p p i n g a n i o n s t h r o u g h o u t the entire f r e q u e n c y r a n g e o f the p r e s e n t study. T r a n s i e n t c o n d u c t i v i t y is also a b u l k process. It is d u e to h o p p i n g a n i o n s at early times following the a p p l i c a t i o n of a step voltage. A s t i m e p r o c e e d s the m e c h a n i s m s of P o o l e - F r e n k e l a n d t u n n e l i n g bec o m e a c t i v e a n d t h e e l e c t r o n s released b y these two m e c h a n i s m s c o n t r i b u t e to the o b s e r v e d t r a n sient m e c h a n i s m s .

N.L Xanthopoulos et al. / Conductivity in rubidium bromide films

References [1] A.K. Jonscher, Dielectric Relaxations in Solids (Chelsea Dielectrics, London, 1983). [2] S.N. Georga and M.N. Pisanias, J. Phys. D 16 (1983) 1521. [3] S.N. Georga and M.N. Pisanias, J. Phys. D 17 (1984) 1233. [4] M.N. Pisanias, S.N. Georga and N.I. Xanthopoulos, J. Phys. D 23 (1990) 903. [5] N.I. Xanthopoulos, PhD thesis, University of Patras (1991). [6] A.K. Jonscher, Nature 267 (1977) 673.

[7] [8] [9] [10] [11] [12] [13] [14]

1103

A.K. Jonscher, Phys. Thin Films 11 (1980) 205. K.L. Ngai and C.T. White, Phys. Rev. B16 (1979) 2475. H. Scher and E.W. Montroll, Phys. Rev. B12 (1975) 2455. M. Pollak and T.H. GebaUe, Phys. Rev. 122 (1961) 1742. J.R. Macdonald, J. Chem. Phys. 30 (1959)806. J. Frenkel, Phys. Rev. 54 (1938) 647. R.M. Hill, Philos. Mag. 23 (1971)59. S.F. Potamianou, K.A.T. Thoma and M.N. Pisanias, J. Phys. A 23 (1990)1313. [15] R.St. Smart, Trans. Faraday Soc. 67 (1971) 1183. [16] M.N. Pisanias, N.I. Xanthopoulos and S.N. Georga, accepted for publication in J. Phys. D.