Electrical properties of thulium oxide thin films

Thin Solid Films, 164 (1988) 175 182

175

E L E C T R I C A L P R O P E R T I E S OF T H U L I U M O X I D E T H I N FILMS* T. ZDANOWlCZ

Institute of Electron Technology, Technical University of Wroctaw, ul. Janiszewskiego 11/17, 50-372, Wroc(aw (Poland)

In this work the results of both d.c. and a.c. measurements o f T m 2 0 3 thin films deposited by electron-beam evaporation are presented. For very low frequencies (10- 5-10- ~ Hz) H a m m o n ' s method of time response has been applied for dielectric loss measurement and for higher frequencies (10-1-104 Hz) bridge methods have been used. F r o m d.c. data the resistivity and activation energy were estimated as 1013 f~ cm and 1.02 eV respectively. The current-voltage characteristics suggest that the current is mainly space charge limited. The frequency dependence of the dielectric losses measured over eight decades of frequency clearly shows that T m 2 0 3 reveals the well-known universal dielectric response, i.e. e" ~ ~ " with n = 0.44 or n = 0.52 depending on the frequency range. Possible mechanisms responsible for the dielectric losses and carrier transport in T m 2 0 3 films are discussed and a simple model of the modulated long-range potential created by oxygen vacancies has been adopted.

1. INTRODUCTION

Thulium oxide (Tm203) is a representative of a wide group of rare earth sesquioxides Ln203 (Ln = lanthanides) which are generally characterized by high chemical stability and good insulating and interesting dielectric properties. For this work thin films of T m 2 0 3 were deposited by means of electron-beam evaporation in a simple A 1 - T m 2 0 3 - A I capacitor-like structure. Both the exact deposition procedure and the methods of measurement have been reported earlier 1. 2.

D.C. PROPERTIES

The most frequently observed current-voltage ( I - V ) characteristics for A1-TmzO3-AI structures are shown in Fig. 1. They obey the power law above the ohmic range with a value for the exponent of about 3. This suggests a space-chargelimited current with an exponential distribution of traps (Nt ~ e x p ( E / k T t ) ) in the

* Paper presented at the 7th International Conferenceon Thin Films, New Delhi, India, December7 1I, 1987. 0040-6090/88/$3.50

© ElsevierSequoia/Printed in The Netherlands

176

T. ZDANOWICZ

f o r b i d d e n g a p of an i n s u l a t o r a n d I - V d e p e n d e n c e as follows: u( Tt/ T + I )

I ~ d(2Tt/T_ 1)

(1)

where Ttt is the lattice t e m p e r a t u r e a n d is c h a r a c t e r i s t i c for a given material. T o s u p p o r t eqn. (1) the I = f(d) d e p e n d e n c e was m e a s u r e d for several s a m p l e with oxide thicknesses r a n g i n g from 150 to 370 nm. This is s h o w n in Fig. 2.

10-6

10-7 I

10 a

,~

I

a,so a h,~ 3To

'

10-~

I 10~ti I I

-\

10~ V=SV 1 0 -*

I

10-' 1Ot

\

// ~ 10 °

V[V] 10 t -

, 10"

, 110"

d'~'lm'] 10"

Fig. L / - V p l o t s for AI T m 2 0 3 - A [ structures showing the space-charge-limited current for the case when a continuous trap distribution may exist in the forbidden gap of the insulator,

Fig. 2. Dependence of the current on the thickness ofTm203 films plotted on a logl-d 5 scale proving the existence of a space-charge-limited current with continuous trap distribution. O c c a s i o n a l l y two o t h e r types of I V characteristics were also observed. These were plots which followed the simple square law for a s p a c e - c h a r g e - l i m i t e d current with a single deep t r a p level 3 a n d plots which were linear on a l o g ( l / V ) - V 1/2 scale which is c h a r a c t e r i s t i c for the P o o l e - F r e n k e l field effect 4. This kind of l - V p l o t for T m 2 0 3 films is discussed in detail elsewhere ~. T o d e t e r m i n e an a c t i v a t i o n energy for T m 2 0 a films A r r h e n i u s plots were m e a s u r e d . T h e y are shown in Fig. 3. In the lower t e m p e r a t u r e range they d i s p l a y c h a n g i n g c u r v a t u r e s but s a t u r a t e into c o n s t a n t slope values at higher temperatures. The a c t i v a t i o n energy c a l c u l a t e d from this slope is 1.02 eV a n d does not d e p e n d on the a p p l i e d voltage (on the a s s u m p t i o n that the m e a s u r e m e n t was p e r f o r m e d in the o h m i c range of the I - V characteristic).

E L E C T R I C A L PROPERTIES OF

,[A]

d=330nm S=9mm ~ o V=0.33

TmzO 3

THIN FILMS

177

V

• V=I V V--2V

2~

2.6

za

Fig. 3. A r r h e n i u s plots for a n A I - T m 2 0 a Al s t r u c t u r e m e a s u r e d for three different values of the p o l a r i z a t i o n voltage.

3. A.C. PROPERTIES

The a.c. characteristics in the ultralow frequency ( 1 0 - 5 - 1 0 - 2 Hz) range were measured using H a m m o n ' s "time response" method 6. In the method the charging (absorption) or discharging (resorption) current is measured as a function of time. When the insulator posseses some finite d.c. conductivity then the discharging current rather than the charging current should be used for the frequency response calculation, thereby eliminating the effect of free carrier transport on a pure dielectric response. When the discharging current fulfils the well-known C u r i e - v o n Schweidler law, i.e. (2)

It(t) ~ t "

and 0.3 < n < 1.2, the dielectric losses may be expressed as follows6: e"(¢oi) -

l(t,)

2~oi Co V

(3)

where ~oi is the assumed frequency, ti is the discharging time corresponding to ~ol, Co is the capacity of the measured structure and V is the polarization voltage during the charging period. The quantities ~ and tg are interrelated in a simple way: 0.1 ti = - -

(4)

O) i

Figure 4 shows typical dielectric losses as a function of frequency plots calculated from resorption curves. The loss peak positions marked as com in Fig. 4 (~om is a frequency for which the peak occurs at a given temperature) have been plotted as log(corn) = f(1/T) dependence in Fig. 5. Since the plot obtained is a straight

178

T. ZDANOWICZ

IE"

2o i 10

J :~~--~,~'::~ /u"

,//p/

ko

,' 5.0

\u\

\o

\o, ~"

10! %

o.,,,

"~

A

x~

5~ ,

2.0

1.0

X\

",o \

E"t ~ E = 0 . 3 3 eV i

\~

o

\\

\

\'\ u\

\~.

T[K] O \ \ \u,, 339 ~, \'\

,

3.0

X~\

t,

'~' "~

\

3.2

10 +

3.4

w[Hzl

10 +

10 "Z

10 = :

Fig. 4. Dependence of the dielectric lossese" on the frequency as calculated from the discharging current plots. The well-exposed loss peaks marked by arrows should be noted. The inset shows the dependence of the loss on temperature above the loss peak.

10~w4Hz~

/

AI-Tm~O~-AI * - v a l u e s taken f r o m

/

Fig.4 o - d a t a m e a s u r e d for t w o other samples

/ 10"

/ / //

10'

~/. /

//

o

/

/ AE=O.92eV

/

//

10~/TIK] 2.9

3.0

3.1

3.2

33

3.4

Fig. 5. Dependence of the loss peak frequency on temperature. The data have been taken both for the sample from Fig. 4 and for two other samples. line it follows that the loss peak frequency is thermally activated according to the relation e) m ~ exp - ~ - ~ where AE = 0.92 eV is the activation energy for the process. The curves from Fig. 4 together with the purely exponential response of an ideal D e b y e system have been plotted in Fig. 6 as a n o r m a l i z e d dependence

ELECTRICAL PROPERTIES OF T m 2 0 a THIN FILMS

179

log(g'/e) = f(1og(og/Ogm)), evidencing the "universal" dielectric response above the loss peak 77, i.e. C?' ~ (On - 1

(6)

with a value for the exponent n - 1 = - 0.44.

1.0-

,' " "

o

o ,,ox.°~'~q •

.o . ,,

~" ~

o

0.5

\

&

o

'~

"

o " T~X

t~ i / /

0.2

//////

/

~ ' Y

°//o ~/

,~

\\<,o'~,~oO =I

\

o

o\ \

~

o

°~'

\ \

Debye peak

t

o~ \\\\

o locus of point A from fig.4 o

T[K] 3 3 9 0.1

-1

3,~6 3~le

t3 o ~

3 1~2 3 0o6 2 9 8 . 5

()

.~

o < ~

\

1

2

Fig. 6. Normalized plot of the loss curves from Fig. 4 compared with the pure exponential response of an ideal Debye system. In the 10-1-104 Hz frequency range bridge methods have been used for the dielectric response measurements. The value of the real part of the dielectric complex permittivity g has been calculated from capacity data and the value of the imaginary part e", i.e. the dielectric loss, has been calculated from tan6 data using the simple relation H

tan6 = -:"

(7)

Figure 7 shows the two parts of the complex dielectric permittivity as a function of frequency and Fig. 8 shows the same data as a normalized plot. The universal dielectric response is extremely well visible within about four decades of frequency with a value for the exponent n - 1 of about -0.52. 4. DISCUSSION The physical structure of the evaporated films is usually strongly disordered and the electron diffraction patterns 1'5 showed that this was the case in the present work. Another discrepancy of vacuum processes under a low partial pressure of oxygen is the possibility of a high oxygen vacancy concentration introduced into the oxide film being deposited. When oxygen vacancies ( 0 2- ) enter the system, two metal ions (Tm 2 *) will be formed in the vicinity of the vacancies in order to maintain electrical neutrality. These ions can be considered as electrons bound to T m 3 * sites acting as trapping centres (Tin 3+:e). These centres are characterized by some

180

T.

ZDANOWICZ

kEI 5=10- m d='8Onm

100

A

o 293 ; 313 378

10 0.1

1.0

10

10'

10'

1()'=

=[Hz~

(a)

IE"

"

~

•

46

t,

13

10'

10"

.~

' 10 ~

J 100

' 104

' 102

>~_

, ....... 10 ~

w[Hz] 10'

.

(b) Fig. 7.

Dependenceo f

(a) the r e l a t i v e d i e l e c t r i c c o n s t a n t g a n d (b) the

dielectric loss

~" o n f r e q u e n c y .

Both sets of data were calculated from capacity and tan6 data measured on standard Vince and Schering bridges. localization energy. However, oxygen vacancies form potential wells which may affect the potentials formed by T m 3 + ions within a radius of several lattice spacings. The overall situation is shown in Fig. 9. It is analogous to that assumed by Sayer et al. 8 for explaining the transport properties in MoO3 films. There are at least two reasons for accepting the concept of deep potential wells in T m 2 0 3 films, such as those created by O z- vacancies. The first is a well-defined activation energy of 1.02 eV for d.c. conditions (Fig. 3); the second is the occurrence of a dielectric loss peak at very low frequencies (Fig. 4) with an activation energy for the peak frequency of 0.92 eV which is very close to the value obtained from d.c. measurements. It is most likely that hopping of carriers between adjacent long-range potential wells (Fig.9, process (1)) is the process determining both the relaxation time and the d.c. conductivity at higher temperatures. The other possible mechanism for dielectric losses, especially in the higher frequency range, is hopping between the thulium sites within one defect potential well (Fig. 9, process (2)). The situation, however, is much more complex in this case since the sites differ in energy by the sum of the localization energy for the trapping centres and the energy which depends on the position of the metal ion in the potential well. The trapped carriers may also be ionized from the thulium sites contained within one potential well and captured by

ELECTRICAL

PROPERTIES

OF

Tm203

Eu

THIN

181

FILMS

l o c u s o f p o i n t A f r o m flgs.7a.Tb 4 2 8 401 3 7 8 3 4 6 313 293

10

° o

.

.

.

.

3~ I g ~

'< ~ ' ~ " ~ ~ ~.~o~,~

0~

. . 2.5

/

. . 3.0

3.5

A

10 ~ -4

-3

-2

-1

0

1

2

3

4

Fig. 8. Normalized plots of the two parts of the complex dielectric permittivity (e' and e") showing the universal power law within four decades of frequency. Tm / •

o

o

/

°

•

o

/ /

•

°

/

i/

°

°

°

o

/ ~

•

,

°

o

\j..j 0

\

(a)

(b)

-'1(1)

AE

(c) Fig. 9. (a) Hypothetical model of Tm203 lattice. Tm represents Tm s+ ions and O denotes an oxygen vacancy (OZ-), oxygen ions for simplicity are not shown in the figure• (b) "Modulation" of the local site potential by long-range Coulomb potential of the 0 2 - vacancy. Possible mechanisms for carrier transport are indicated by arrows. (c) Band model for Tm203. the t h u l i u m sites c o n t a i n e d within a n o t h e r well with the a c t i v a t i o n energy needed for the process being m u c h lower t h a n t h a t of the p o t e n t i a l well (Fig. 9, process (3)). This m e c h a n i s m m a y also c o n t r i b u t e to the d.c. c o n d u c t i v i t y as well as to the dielectric losses. M e c h a n i s m s (2) a n d (3) m a y be the basis of the universal dielectric response 6 as p r e s e n t e d in Figs. 6 a n d 8. As a result of the s t r o n g lattice disorder, a high d e n s i t y of t r a p s can be expected in the energy g a p of T m 2 0 3 films. T h e s p a c e - c h a r g e - l i m i t e d current, as s h o w n in Fig. 1, m a y confirm this suggestion, a l t h o u g h the possibility that u n i f o r m l y d i s t r i b u t e d electron t r a p s a n d T m 3 ÷ centres also p l a y a role, thus d e t e r m i n i n g the

182

T. ZDANOWICZ

character of the I - V plots (Fig. 9(c)), cannot be ruled out. The role of the easily activated charge carriers trapped in the shallow traps may be twofold. These carriers may also act as a charge screen during the move of the much slower charged species. The existence of such a screen is the central idea of the Jonscher "screened hopping model ''9 which is the physical basis of the universal law 6. The discussion presented herein is merely an attempt towards a brief explanation of some mechanisms governing both the d.c. conductivity and the a.c. losses in T m 2 0 3 films. The author believes, however, that in spite of its simplicity the concept of long-range potential wells induced by oxygen vacancies is acceptable for most oxide films where oxygen deficiency can be expected. REFERENCES 1 T. Zdanowicz, B. Jankowski and L. Zdanowicz, A cta Phys. Polon, A, 57 (1980) 151. 2 A. Rose, Phys. Rev., 97(1955) 1538. 3 M . A . Lampert and P. Mark, Current Injection in Solids, Academic Press, New York, 1970, p. 18. 4 C . A . Mead, Phys. Rev., 128 (1962) 2088. 5 T. Zdanowicz, Thesis, Wroclaw, 1981. 6 B.Y. H a m m o n , Proc. lEE, 99 (1952) [51. 7 A . K . Jonscher, Nature (London), 267 (1977) 673. 8 M. Sayer, A. Mansingh, J. B. Webb and J. Noad, J. Phys., 11 (1978) 315. 9 A . K . Jonscher, Phys. Status Solidi B, 83 (1977) 585 ; Phys. Status Solidi B, 84 (1977) 159.