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Dielectric properties of electron-beam-evaporated Nd2O3 thin films
Thin Solid Films, 87 (1982) 119-126
119
ELECTRONICS AND OPTICS
DIELECTRIC PROPERTIES OF ELECTRON-BEAM-EVAPORATED Nd20 3 THIN FILMS VINEET S. DHARMADHIKARI * AND A. GOSWAMI
National Chemical Laboratory, Poona 411008 (India) (Received May 26, 1981 ; accepted June 30, 1981)
The dielectric properties of amorphous Nd203 films prepared by vacuum evaporation using an electron beam were investigated as functions of film thickness (700-3000/~), temperature (78-400 K) and frequency (0.040-100 kHz) for various substrate temperatures. A non-linear dependence of the capacitance on inverse film thickness in the thickness region up to 1000/~ was observed. The dielectric constant evaluated (12.64) was independent of film thickness for thicker films (d > 1000/~). The capacitance was dependent on both frequency and temperature, but at low temperatures it became constant for all frequencies. The plot of tan 6 versus frequency showed a pronounced minimum which shifted to a higher frequency region with increasing temperature. The temperature coefficient of capacitance, the percentage variation in capacitance and the breakdown field strength were estimated and the results are discussed.
1. INTRODUCTION The preparation of thin dielectric films has to a great extent been motivated by the need for thin layers in various applications. The required degree of perfection varies according to the specific application. For instance, for small volume capacitors, a high dielectric constant and a low dielectric loss are usually desirable and the variation in these parameters with temperature, frequency, film thickness and applied field are usually important considerations. Thin films of rare earth oxides, owing to their excellent mechanical and chemical stability, are likely candidates for such studies. The dielectric properties of rare earth oxides M203 (M = La, Pr, Nd, Eu, Dy, Er, Yb) ~-7 have been studied by various workers, but comparatively little information is available on the dielectric behaviour of Nd20 3 films. Goswami et al. have studied the dielectric behaviour of La20 3 1, Pr20 3 2 and Dy20 3 5 films. In the present study, we present in detail the dielectric properties of Nd20 3 films prepared by the vacuum evaporation of Nd203 using an electron beam. * Present address: Department of Electrical and Computer Engineering,Universityof New Mexico, Albuquerque,NM 87131,U.S.A. 0040-6090/82/0000-0000/$02.75
© ElsevierSequoia/Printedin The Netherlands
120 2.
v . s . DHARMADHIKARI, A. GOSWAMI
EXPERIMENTAL DETAILS
The electron beam evaporation process was carried out in a 10 in oil diffusion pump system giving a working pressure of around 2 x 10 -6 Torr. A water-cooled 9 kW work-accelerated electron beam gun provided the excitation source. High purity (99.99~o) N d 2 0 3 powder (supplied by Indian Rare Earths Ltd.) was made into a pellet and placed in a graphite boat. Prior to evaporation, each pellet was outgassed for 30 min under the shutter through the application of the electron beam under low power conditions. The films were evaporated onto thoroughly cleaned glass substrates at various substrate temperatures ts up to 180 °C and deposited at a rate of 45 ~ min-~. The source-to-substrate distance was about 23 cm. Thick aluminium (purity, 99.99~o) deposits (2000 ~) were used as base electrode and as counterelectrode to complete the M I M structures. The effective area of a capacitor was 0.16 cm 2. Electrical measurements were carried out on these Nd2Oa capacitor specimens with the aid of a Marconi Universal bridge (model T F 2700) over the frequency range 0.040-100kHz at various temperatures (78-400K). The dielectric film thickness d measured by the multiple-beam interferometry method varied between 700 and 3000/~. All measurements were performed in vacuo (less than 10 -2 Torr) except for the dielectric breakdown study, which was performed in air 8. The results presented here are for completely stabilized thin film capacitors 9. Unannealed samples showed a considerable aging effect and did not attain stability even after 30 days. The capacitance C and the loss factor tan 6 of the stabilized capacitors, however, had not varied much when they were measured a few months later. X-rays and electron diffraction techniques were used for the identification of the material. 3. RESULTS An X-ray study (Fig. 1) of the bulk oxide showed that the material was crystalline with a hexagonal structure (a0 = 3.820/~; bo = 5.952/~; c/a = 1.558) conforming to the N d 2 0 3 structure. In contrast, the vacuum-evaporated films when examined by the electron diffraction method were featureless and amorphous in nature. N o crystallinity was observed even when the films were deposited at a substrate temperature of 180°C. X-ray diffraction studies also confirmed the amorphous nature of these films.
3.1. Dielectric properties 3.1.1. Thickness effect Plots of the dielectric constant e, capacitance C and loss factor tan 6 as functions of the reciprocal thickness lid of films deposited onto substrates at room temperature (26 °C) and at 180 °C are shown in Fig. 2. A non-linear relation between the capacitance of the thin insulating films and the inverse film thickness is observed in the thickness region up to 1000/~, whereas for thicknesses greater than 1000/~ the capacitance decreases linearly with 1/d. The effective dielectric constant evaluated from the measured capacitance, effective area and film thickness increases with
PROPERTIES
DIELECTRIC
OF
Nd203
121
FILMS
>.. n"
] 8~
ra
8
>6O Z
u.I I-
z
70
60
50
40
30
20
tO
- - 2 0
Fig. 1. X-ray powder pattern of Nd203 (Cu K0t radiation). d (A*)
2000
lOOO
750
500
• ~o~
25
24
23
22
~ 21
2o
t-:
Z 19 I0 0 _
18
0
ui 16 0 Z I--
15
0 13 LU .J
(i
012 ~1~ 0
-012 •0 0 8 ~
--~ /
/
I0
.g
^
x
~,x--^
.004
0.5
1~o
~.~
2.0
25
lO+~/d A ° - '
Fig. 2. Variation in the dielectric constant 8, the capacitance C and the dissipation factor tan 6 as functions of inverse film thickness lOa/d at 1 kHz (O, (S), x, t~ = 26 °C; ~, [], (3, ts = 180 °C): O, ~, C; C), FT1,e; x, O, tan 6. increasing thickness towards a constant value (of 12.64) for d > 1000/~. In contrast, tan 6 is low (0.0053) and independent of the film thickness. N d 2 0 3 films formed at the higher substrate temperature (ts = 180 °C) also show similar characteristics. N o significant change in e or tan 6 for these films is observed (Fig. 2). A similar thickness dependence of e has been observed with thin films of other rare earth oxides 2, 4, 5, 7.
3.1.2. Effect of frequency and temperature The variation in capacitance with frequency ( 0 . 0 4 0 - 1 0 0 k H z ) at various temperatures ( 7 8 - 3 7 0 K) for a film thickness d = 1112/~ is s h o w n in Fig. 3. It can be seen that the capacitance is frequency independent at r o o m temperature and below,
122
V . S . DHARMADHIKARI, A. GOSWAMI
whereas at higher temperatures it decreases with frequency. This is well understood when the capacitance is plotted against temperature for various frequencies (Fig. 4). At higher temperatures separate curves characteristic of the frequency are observed, but as the temperature is lowered these curves come closer and finally merge to a single curve at about 200 K. Below this temperature the capacitance varies only slightly with temperature. On plotting it on an enlarged scale (not shown), we observed the variation in capacitance with temperature to be an exponential increase in this region also. We obtained the static dielectric constant es ( ~ 11.64) on extrapolating to 0 K. x,o'
22lO
369
K
21.0 IJ.
n
200 B.O
0 c-
3~] K
180
0
Q.
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Frequency (Hz) Fig. 3. Variation 1112/~).
in capacitance as a function of frequency at different temperatures (film thickness,
2 3x16
40 21
C" lOC
z<
k1K
I0 104
n ........
15
I00
200
500
400
TEMPERATURE, T ( K)
Fig. 4. Variation 1112/~).
in capacitance as a function of temperature at different frequencies (film thickness,
DIELECTRIC PROPERTIES OF N d 2 0 3
123
FILMS
The influences of frequency and temperature on tan 6 are illustrated in Fig. 5. Tan 6 decreases with frequency, attains a minimum (at higher frequencies for higher temperatures) and then slowly increases. This is true for all film thicknesses. Such a behaviour for tan g was first reported by Goswami and Goswami s for ZnS film capacitors. Similar features have also been reported for many other dielectric materials 1, 2, 4, 5, 8-10. Tan 6, however, is higher for higher temperatures. -I
10
~
369 K
16z - zgr
~
:ff...f~j.o
-3'
I0
I
102
103
104 FREQUENCY
....
5 X l O4
(Hz)
Fig. 5. Variation in tan 6 as a function of frequency at different temperatures (film thickness, I 112/~).
3.1.3. Temperature coefficient of capacitance The temperature coefficient of capacitance 7c of the capacitors was obtained from the equation 1 dC ?c = C dt
(1)
Table I summarizes the measured ?c values for various thicknesses compared with values calculated using Gevers' equation '1 7c = A tan 6 - ~ e
(2)
where A is a constant and for practical purposes is equal to 0.05 + 0.01 K 12 and ae is the linear expansion coefficient. Typical values of the product ~e lie in the range I 0 60 ppm K - 1 12, which may be neglected in comparison with the error in the coefficient A. By plotting ?c(measured) against the loss factor tan 6 and extrapolating to tan 6 ~ 0.45~o (our minimum value), we find ~c(minimum) ~ 350 ppm K - 1. This value is comparable with that for other dielectric materials (e.g. Dy203 s, Yb203 v, Bi203 9, Y203 12 and SiO, SiO2, A1203 and Si3N4 13, which have ?c ~ 100-600 ppm K - 1 for a loss factor greater than 0.1%) that have successfully been used as capacitor elements. The percentage variation in the capacitance at different frequencies normalized to 1 kHz at room temperature is less than + 1~.
3.1.4. Breakdown field strength The dielectric breakdown field strength Fb is of the order of 106 V c m - 1 and decreases from 2.6 x 10 6 t o 1.5 × 10 6 V c m - t with increasing film thickness (7003000/~). In Fig. 6, Fb is represented as a function of film thickness on a log-log scale.
124
v . s . DHARMADHIKARI, A. GOSWAMI
TABLE I COMPARISON
OF MEASURED
d (~)
V A L U E S O F "~C W I T H
tan ~ ~(%)
760 850 970 1010 1149 1250 1748 2847
0.58 0.60 0.57 0.54 0.53 0.52 0.50 0.51
THOSE CALCULATED
USING EQN. (2)
Yc(ppm K - 1) Measured a
Calculated b
430 435 405 380 370 375 360 255
290±58 300±60 285 ± 57 270±57 265 ± 53 260±52 250± 50 255±51
a At 26 °C and 1 kHz. bThe error is due to an uncertainty of 20% in the constant A of eqn. (2). It should also be noted that the product ~e, which lies in the range 10-60 ppm K - 1, was not subtracted from the calculated value of )'c. 107
Eo ,,.p
uJ ,'7"
o ~=,0" .
,
~o~
,
, , , , ,i ,o ~ THICKNESS, d (A °)
. . . . . . . . ,o ~
Fig. 6. Log-log plot of the breakdown field strength vs. film thickness (slope, -0.475). T h e p l o t is a straight line with a negative slope of 0.475, thus following closely the F o r l a n i - M i n n a j a 14 r e l a t i o n F b oc d - 1/2. 4. DISCUSSION T h e results clearly indicate t h a t the films p r e p a r e d in the present s t u d y are a m o r p h o u s in nature, w h e r e a s the b u l k m a t e r i a l is in the A modification. I t is a general o b s e r v a t i o n t h a t m a n y v a c u u m - d e p o s i t e d oxide films are a m o r p h o u s in n a t u r e or h a v e a fine-grained s t r u c t u r e as o b s e r v e d in the case of P r z O 3 2, E u 2 0 3 4, D y 2 0 3 s, S b 2 0 3 lo, YzO3 is, W O 3 16 a n d N b z O 5 17. T h e e ( d ) d e p e n d e n c e of the dielectric c o n s t a n t , the b e h a v i o u r of the c a p a c i t a n c e a n d t a n ~ with frequency a n d t e m p e r a t u r e , a n d o b s e r v a t i o n s of t a n 6ml, are in a c c o r d a n c e with the theoretical m o d e l p r o p o s e d b y G o s w a m i a n d G o s w a m i 8. T h e o b s e r v e d d e p e n d e n c e of the dielectric c o n s t a n t o n the dielectric film thickness for t h i n n e r films (less t h a n 1000 ~ ) is a p p a r e n t l y due to defects such as voids, stresses, i n h o m o g e n e i t y , g r a i n b o u n d a r i e s , discontinuities etc. which are n o r m a l l y present in v a c u u m - d e p o s i t e d films, r a t h e r
DIELECTRIC PROPERTIES OF N d 2 0 3
FILMS
125
than to the non-stoichiometry of the deposits resulting from an excess of oxygen or metal atoms. Some of these defects are removed by self-annealing or aging processes, but others require more thermal energy such as is provided by an annealing process. Very recently Kornyshev e t al. 18 have theoretically analysed the non-linear dependence of the capacitance on the inverse film thickness in the thickness region up to 1000/~ in terms of spatial dispersion of the dielectric permittivity. On comparison with the experimental results reported for various rare earth oxides, they found that the observed effect was too large to be ascribed solely to the nonlocal nature of the dielectric response and suggested that the presence of voids and other inhomogeneity effects contributed significantly to the observed anomaly, as mentioned in the present case for Nd203 films. Temperature has a complicated influence on the dielectric constant, which in turn depends on electronic and ionic polarization, dipole orientation polarization, space charge polarization etc. The manner in which the dielectric constant varies with frequency gives an indication of which type of contribution is present. The contribution from space charge polarization is mainly noticeable in the low frequency (0.01 Hz) region 19-2l and depends on the purity and perfection of the films. In contrast, dipole orientation polarization can be exhibited by materials even up to 10 l° Hz and is characterized by a Debye-type peak in the dielectric lOSS22, while electronic and ionic polarization always exists below 1013 Hz 23. Since no relaxation effect (i.e. no tan 6max) was observed in the frequency and temperature regions studied, the contribution from orientational polarization and possibly also that from interfacial polarization can be ruled out. The frequency independence of the dielectric constant (12.64) in the audio frequency region at room temperature suggests that only electronic and ionic polarization contributes. The optical dielectric constant (e = n 2 -- 2.10 (ref. 24)) is the electronic contribution; hence the rest is due to ionic polarization. Such a significant contribution could be due to a considerable ionicity of the oxide film. Harrop and Campbell 25 have pointed out that compounds of oxides where the oxygen ion is large and deformable will give rise to an interaction between the electronic and ionic polarization. 5. CONCLUSIONS
We have presented results on the dielectric properties of Nd203 films obtained by electron beam vacuum evaporation of the bulk material. The films possessed the following characteristics: a capacitance density of 0.40-14 ~tF cm -2, a relatively high dielectric constant (12.64), a high breakdown field strength (more than 1.5 x 106 V cm-1), a low dissipation factor (approximately 0.0045) and a low temperature coefficient of capacitance (about 3 5 0 p p m K - 1 ) . Moreover, they had a high resistivity (1012-1013 ~ cm) in a constant electric field at room temperature 9. These characteristics, coupled with the comparative stability of the films, recommend these films for device applications. REFERENCES
1 A. Goswamiand R. R. Varma, unpublished work, 1975. 2 A. Goswamiand A. P. Goswami, Thin Solid Films, 20 (1974)$3. 3 R.A.Kadzhoyan and K. A. Egiyan,lzv. Akad. Nauk Arm. S.S.R., Fiz., 3 (1968)348.
126 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
v . s . DHARMADHIKARI, A. GOSWAMI
H. Nakane, A. Noya, S. Kuriki and G. Matsumoto, Thin Solid Films, 59 (t979) 291. A. Goswami and R. R. Varma, Thin Solid Films, 28 (1975) 157. U. Saxena and O. N. Srivastava, Thin Solid Films, 33 (1976) 185. T. Wiktorczyk and C. Weso|owska, Thin Solid Films, 71 (1980) 15. A. Goswami and A. P. Goswami, Thin Solid Films, 16 (1973) 175. V.S. Dharmadhikari, Ph.D. Thesis, Poona University, India, 1980. S.M. Patel and V. Goerge, Indian J. Phys. A, 52 (1978) 77. M. Gevers, Philips Res. Rep., 11 (1946) 279. C.K. Campbell, Thin Solid Films, 6 (1970) 197. P.J. Harrop and D. S. Campbell, Thin Solid Films, 2 (1968) 273. F. Forlani and N. Minnaja, J. Vac. Sci. Technol., 6 (1969) 518. E. Riemann and L. Young, J. Appl. Phys., 44 (1973) 1044. A. Mansingh, M. Sayer and J. B. Webb, J. Non-Cryst. Solids, 28 (1978) 123. N. Fuschillo, B. Lalevic and N. K. Annamali, Thin Solid Films, 30 (1975) 145. A.A. Kornyshev, M. A. Vorotyntsev and J. Ulstrup, Thin Solid Films, 75 (1981) 105. P.M. Sutton, J. Am. Ceram. Soc., 47(1964) 188. F. Argall and A. K. Jonscher, Thin Solid Films, 2 (1968) 185. H. Birey, J. Appl. Phys., 49 (1978) 2898. P. Debye, Polar Molecules, Dover Publications, New York, 1929. B. Szigeti, Proc. R. Soc. London, Ser. A, 258 (1960) 377. R.M. Douglass, Anal. Chem.,28(1956) 551. P.J. Harrop and D. S. Campbell, in L. I. Maissel and R. Glang (eds.), Handbook of Thin Film Technology, McGraw-Hill, New York, 1970, pp. 16-1636.
119
ELECTRONICS AND OPTICS
DIELECTRIC PROPERTIES OF ELECTRON-BEAM-EVAPORATED Nd20 3 THIN FILMS VINEET S. DHARMADHIKARI * AND A. GOSWAMI
National Chemical Laboratory, Poona 411008 (India) (Received May 26, 1981 ; accepted June 30, 1981)
The dielectric properties of amorphous Nd203 films prepared by vacuum evaporation using an electron beam were investigated as functions of film thickness (700-3000/~), temperature (78-400 K) and frequency (0.040-100 kHz) for various substrate temperatures. A non-linear dependence of the capacitance on inverse film thickness in the thickness region up to 1000/~ was observed. The dielectric constant evaluated (12.64) was independent of film thickness for thicker films (d > 1000/~). The capacitance was dependent on both frequency and temperature, but at low temperatures it became constant for all frequencies. The plot of tan 6 versus frequency showed a pronounced minimum which shifted to a higher frequency region with increasing temperature. The temperature coefficient of capacitance, the percentage variation in capacitance and the breakdown field strength were estimated and the results are discussed.
1. INTRODUCTION The preparation of thin dielectric films has to a great extent been motivated by the need for thin layers in various applications. The required degree of perfection varies according to the specific application. For instance, for small volume capacitors, a high dielectric constant and a low dielectric loss are usually desirable and the variation in these parameters with temperature, frequency, film thickness and applied field are usually important considerations. Thin films of rare earth oxides, owing to their excellent mechanical and chemical stability, are likely candidates for such studies. The dielectric properties of rare earth oxides M203 (M = La, Pr, Nd, Eu, Dy, Er, Yb) ~-7 have been studied by various workers, but comparatively little information is available on the dielectric behaviour of Nd20 3 films. Goswami et al. have studied the dielectric behaviour of La20 3 1, Pr20 3 2 and Dy20 3 5 films. In the present study, we present in detail the dielectric properties of Nd20 3 films prepared by the vacuum evaporation of Nd203 using an electron beam. * Present address: Department of Electrical and Computer Engineering,Universityof New Mexico, Albuquerque,NM 87131,U.S.A. 0040-6090/82/0000-0000/$02.75
© ElsevierSequoia/Printedin The Netherlands
120 2.
v . s . DHARMADHIKARI, A. GOSWAMI
EXPERIMENTAL DETAILS
The electron beam evaporation process was carried out in a 10 in oil diffusion pump system giving a working pressure of around 2 x 10 -6 Torr. A water-cooled 9 kW work-accelerated electron beam gun provided the excitation source. High purity (99.99~o) N d 2 0 3 powder (supplied by Indian Rare Earths Ltd.) was made into a pellet and placed in a graphite boat. Prior to evaporation, each pellet was outgassed for 30 min under the shutter through the application of the electron beam under low power conditions. The films were evaporated onto thoroughly cleaned glass substrates at various substrate temperatures ts up to 180 °C and deposited at a rate of 45 ~ min-~. The source-to-substrate distance was about 23 cm. Thick aluminium (purity, 99.99~o) deposits (2000 ~) were used as base electrode and as counterelectrode to complete the M I M structures. The effective area of a capacitor was 0.16 cm 2. Electrical measurements were carried out on these Nd2Oa capacitor specimens with the aid of a Marconi Universal bridge (model T F 2700) over the frequency range 0.040-100kHz at various temperatures (78-400K). The dielectric film thickness d measured by the multiple-beam interferometry method varied between 700 and 3000/~. All measurements were performed in vacuo (less than 10 -2 Torr) except for the dielectric breakdown study, which was performed in air 8. The results presented here are for completely stabilized thin film capacitors 9. Unannealed samples showed a considerable aging effect and did not attain stability even after 30 days. The capacitance C and the loss factor tan 6 of the stabilized capacitors, however, had not varied much when they were measured a few months later. X-rays and electron diffraction techniques were used for the identification of the material. 3. RESULTS An X-ray study (Fig. 1) of the bulk oxide showed that the material was crystalline with a hexagonal structure (a0 = 3.820/~; bo = 5.952/~; c/a = 1.558) conforming to the N d 2 0 3 structure. In contrast, the vacuum-evaporated films when examined by the electron diffraction method were featureless and amorphous in nature. N o crystallinity was observed even when the films were deposited at a substrate temperature of 180°C. X-ray diffraction studies also confirmed the amorphous nature of these films.
3.1. Dielectric properties 3.1.1. Thickness effect Plots of the dielectric constant e, capacitance C and loss factor tan 6 as functions of the reciprocal thickness lid of films deposited onto substrates at room temperature (26 °C) and at 180 °C are shown in Fig. 2. A non-linear relation between the capacitance of the thin insulating films and the inverse film thickness is observed in the thickness region up to 1000/~, whereas for thicknesses greater than 1000/~ the capacitance decreases linearly with 1/d. The effective dielectric constant evaluated from the measured capacitance, effective area and film thickness increases with
PROPERTIES
DIELECTRIC
OF
Nd203
121
FILMS
>.. n"
] 8~
ra
8
>6O Z
u.I I-
z
70
60
50
40
30
20
tO
- - 2 0
Fig. 1. X-ray powder pattern of Nd203 (Cu K0t radiation). d (A*)
2000
lOOO
750
500
• ~o~
25
24
23
22
~ 21
2o
t-:
Z 19 I0 0 _
18
0
ui 16 0 Z I--
15
0 13 LU .J
(i
012 ~1~ 0
-012 •0 0 8 ~
--~ /
/
I0
.g
^
x
~,x--^
.004
0.5
1~o
~.~
2.0
25
lO+~/d A ° - '
Fig. 2. Variation in the dielectric constant 8, the capacitance C and the dissipation factor tan 6 as functions of inverse film thickness lOa/d at 1 kHz (O, (S), x, t~ = 26 °C; ~, [], (3, ts = 180 °C): O, ~, C; C), FT1,e; x, O, tan 6. increasing thickness towards a constant value (of 12.64) for d > 1000/~. In contrast, tan 6 is low (0.0053) and independent of the film thickness. N d 2 0 3 films formed at the higher substrate temperature (ts = 180 °C) also show similar characteristics. N o significant change in e or tan 6 for these films is observed (Fig. 2). A similar thickness dependence of e has been observed with thin films of other rare earth oxides 2, 4, 5, 7.
3.1.2. Effect of frequency and temperature The variation in capacitance with frequency ( 0 . 0 4 0 - 1 0 0 k H z ) at various temperatures ( 7 8 - 3 7 0 K) for a film thickness d = 1112/~ is s h o w n in Fig. 3. It can be seen that the capacitance is frequency independent at r o o m temperature and below,
122
V . S . DHARMADHIKARI, A. GOSWAMI
whereas at higher temperatures it decreases with frequency. This is well understood when the capacitance is plotted against temperature for various frequencies (Fig. 4). At higher temperatures separate curves characteristic of the frequency are observed, but as the temperature is lowered these curves come closer and finally merge to a single curve at about 200 K. Below this temperature the capacitance varies only slightly with temperature. On plotting it on an enlarged scale (not shown), we observed the variation in capacitance with temperature to be an exponential increase in this region also. We obtained the static dielectric constant es ( ~ 11.64) on extrapolating to 0 K. x,o'
22lO
369
K
21.0 IJ.
n
200 B.O
0 c-
3~] K
180
0
Q.
333 321
17.0
K K
Ot~ ~6o
2422~r." o
-~....
~5o
,~3 .o ~ g rsK o
.~i : : i
14.0
.
.
.
.
.
.
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8 .
.
.
.
.
.
.
.
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Frequency (Hz) Fig. 3. Variation 1112/~).
in capacitance as a function of frequency at different temperatures (film thickness,
2 3x16
40 21
C" lOC
z<
k1K
I0 104
n ........
15
I00
200
500
400
TEMPERATURE, T ( K)
Fig. 4. Variation 1112/~).
in capacitance as a function of temperature at different frequencies (film thickness,
DIELECTRIC PROPERTIES OF N d 2 0 3
123
FILMS
The influences of frequency and temperature on tan 6 are illustrated in Fig. 5. Tan 6 decreases with frequency, attains a minimum (at higher frequencies for higher temperatures) and then slowly increases. This is true for all film thicknesses. Such a behaviour for tan g was first reported by Goswami and Goswami s for ZnS film capacitors. Similar features have also been reported for many other dielectric materials 1, 2, 4, 5, 8-10. Tan 6, however, is higher for higher temperatures. -I
10
~
369 K
16z - zgr
~
:ff...f~j.o
-3'
I0
I
102
103
104 FREQUENCY
....
5 X l O4
(Hz)
Fig. 5. Variation in tan 6 as a function of frequency at different temperatures (film thickness, I 112/~).
3.1.3. Temperature coefficient of capacitance The temperature coefficient of capacitance 7c of the capacitors was obtained from the equation 1 dC ?c = C dt
(1)
Table I summarizes the measured ?c values for various thicknesses compared with values calculated using Gevers' equation '1 7c = A tan 6 - ~ e
(2)
where A is a constant and for practical purposes is equal to 0.05 + 0.01 K 12 and ae is the linear expansion coefficient. Typical values of the product ~e lie in the range I 0 60 ppm K - 1 12, which may be neglected in comparison with the error in the coefficient A. By plotting ?c(measured) against the loss factor tan 6 and extrapolating to tan 6 ~ 0.45~o (our minimum value), we find ~c(minimum) ~ 350 ppm K - 1. This value is comparable with that for other dielectric materials (e.g. Dy203 s, Yb203 v, Bi203 9, Y203 12 and SiO, SiO2, A1203 and Si3N4 13, which have ?c ~ 100-600 ppm K - 1 for a loss factor greater than 0.1%) that have successfully been used as capacitor elements. The percentage variation in the capacitance at different frequencies normalized to 1 kHz at room temperature is less than + 1~.
3.1.4. Breakdown field strength The dielectric breakdown field strength Fb is of the order of 106 V c m - 1 and decreases from 2.6 x 10 6 t o 1.5 × 10 6 V c m - t with increasing film thickness (7003000/~). In Fig. 6, Fb is represented as a function of film thickness on a log-log scale.
124
v . s . DHARMADHIKARI, A. GOSWAMI
TABLE I COMPARISON
OF MEASURED
d (~)
V A L U E S O F "~C W I T H
tan ~ ~(%)
760 850 970 1010 1149 1250 1748 2847
0.58 0.60 0.57 0.54 0.53 0.52 0.50 0.51
THOSE CALCULATED
USING EQN. (2)
Yc(ppm K - 1) Measured a
Calculated b
430 435 405 380 370 375 360 255
290±58 300±60 285 ± 57 270±57 265 ± 53 260±52 250± 50 255±51
a At 26 °C and 1 kHz. bThe error is due to an uncertainty of 20% in the constant A of eqn. (2). It should also be noted that the product ~e, which lies in the range 10-60 ppm K - 1, was not subtracted from the calculated value of )'c. 107
Eo ,,.p
uJ ,'7"
o ~=,0" .
,
~o~
,
, , , , ,i ,o ~ THICKNESS, d (A °)
. . . . . . . . ,o ~
Fig. 6. Log-log plot of the breakdown field strength vs. film thickness (slope, -0.475). T h e p l o t is a straight line with a negative slope of 0.475, thus following closely the F o r l a n i - M i n n a j a 14 r e l a t i o n F b oc d - 1/2. 4. DISCUSSION T h e results clearly indicate t h a t the films p r e p a r e d in the present s t u d y are a m o r p h o u s in nature, w h e r e a s the b u l k m a t e r i a l is in the A modification. I t is a general o b s e r v a t i o n t h a t m a n y v a c u u m - d e p o s i t e d oxide films are a m o r p h o u s in n a t u r e or h a v e a fine-grained s t r u c t u r e as o b s e r v e d in the case of P r z O 3 2, E u 2 0 3 4, D y 2 0 3 s, S b 2 0 3 lo, YzO3 is, W O 3 16 a n d N b z O 5 17. T h e e ( d ) d e p e n d e n c e of the dielectric c o n s t a n t , the b e h a v i o u r of the c a p a c i t a n c e a n d t a n ~ with frequency a n d t e m p e r a t u r e , a n d o b s e r v a t i o n s of t a n 6ml, are in a c c o r d a n c e with the theoretical m o d e l p r o p o s e d b y G o s w a m i a n d G o s w a m i 8. T h e o b s e r v e d d e p e n d e n c e of the dielectric c o n s t a n t o n the dielectric film thickness for t h i n n e r films (less t h a n 1000 ~ ) is a p p a r e n t l y due to defects such as voids, stresses, i n h o m o g e n e i t y , g r a i n b o u n d a r i e s , discontinuities etc. which are n o r m a l l y present in v a c u u m - d e p o s i t e d films, r a t h e r
DIELECTRIC PROPERTIES OF N d 2 0 3
FILMS
125
than to the non-stoichiometry of the deposits resulting from an excess of oxygen or metal atoms. Some of these defects are removed by self-annealing or aging processes, but others require more thermal energy such as is provided by an annealing process. Very recently Kornyshev e t al. 18 have theoretically analysed the non-linear dependence of the capacitance on the inverse film thickness in the thickness region up to 1000/~ in terms of spatial dispersion of the dielectric permittivity. On comparison with the experimental results reported for various rare earth oxides, they found that the observed effect was too large to be ascribed solely to the nonlocal nature of the dielectric response and suggested that the presence of voids and other inhomogeneity effects contributed significantly to the observed anomaly, as mentioned in the present case for Nd203 films. Temperature has a complicated influence on the dielectric constant, which in turn depends on electronic and ionic polarization, dipole orientation polarization, space charge polarization etc. The manner in which the dielectric constant varies with frequency gives an indication of which type of contribution is present. The contribution from space charge polarization is mainly noticeable in the low frequency (0.01 Hz) region 19-2l and depends on the purity and perfection of the films. In contrast, dipole orientation polarization can be exhibited by materials even up to 10 l° Hz and is characterized by a Debye-type peak in the dielectric lOSS22, while electronic and ionic polarization always exists below 1013 Hz 23. Since no relaxation effect (i.e. no tan 6max) was observed in the frequency and temperature regions studied, the contribution from orientational polarization and possibly also that from interfacial polarization can be ruled out. The frequency independence of the dielectric constant (12.64) in the audio frequency region at room temperature suggests that only electronic and ionic polarization contributes. The optical dielectric constant (e = n 2 -- 2.10 (ref. 24)) is the electronic contribution; hence the rest is due to ionic polarization. Such a significant contribution could be due to a considerable ionicity of the oxide film. Harrop and Campbell 25 have pointed out that compounds of oxides where the oxygen ion is large and deformable will give rise to an interaction between the electronic and ionic polarization. 5. CONCLUSIONS
We have presented results on the dielectric properties of Nd203 films obtained by electron beam vacuum evaporation of the bulk material. The films possessed the following characteristics: a capacitance density of 0.40-14 ~tF cm -2, a relatively high dielectric constant (12.64), a high breakdown field strength (more than 1.5 x 106 V cm-1), a low dissipation factor (approximately 0.0045) and a low temperature coefficient of capacitance (about 3 5 0 p p m K - 1 ) . Moreover, they had a high resistivity (1012-1013 ~ cm) in a constant electric field at room temperature 9. These characteristics, coupled with the comparative stability of the films, recommend these films for device applications. REFERENCES
1 A. Goswamiand R. R. Varma, unpublished work, 1975. 2 A. Goswamiand A. P. Goswami, Thin Solid Films, 20 (1974)$3. 3 R.A.Kadzhoyan and K. A. Egiyan,lzv. Akad. Nauk Arm. S.S.R., Fiz., 3 (1968)348.
126 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
v . s . DHARMADHIKARI, A. GOSWAMI
H. Nakane, A. Noya, S. Kuriki and G. Matsumoto, Thin Solid Films, 59 (t979) 291. A. Goswami and R. R. Varma, Thin Solid Films, 28 (1975) 157. U. Saxena and O. N. Srivastava, Thin Solid Films, 33 (1976) 185. T. Wiktorczyk and C. Weso|owska, Thin Solid Films, 71 (1980) 15. A. Goswami and A. P. Goswami, Thin Solid Films, 16 (1973) 175. V.S. Dharmadhikari, Ph.D. Thesis, Poona University, India, 1980. S.M. Patel and V. Goerge, Indian J. Phys. A, 52 (1978) 77. M. Gevers, Philips Res. Rep., 11 (1946) 279. C.K. Campbell, Thin Solid Films, 6 (1970) 197. P.J. Harrop and D. S. Campbell, Thin Solid Films, 2 (1968) 273. F. Forlani and N. Minnaja, J. Vac. Sci. Technol., 6 (1969) 518. E. Riemann and L. Young, J. Appl. Phys., 44 (1973) 1044. A. Mansingh, M. Sayer and J. B. Webb, J. Non-Cryst. Solids, 28 (1978) 123. N. Fuschillo, B. Lalevic and N. K. Annamali, Thin Solid Films, 30 (1975) 145. A.A. Kornyshev, M. A. Vorotyntsev and J. Ulstrup, Thin Solid Films, 75 (1981) 105. P.M. Sutton, J. Am. Ceram. Soc., 47(1964) 188. F. Argall and A. K. Jonscher, Thin Solid Films, 2 (1968) 185. H. Birey, J. Appl. Phys., 49 (1978) 2898. P. Debye, Polar Molecules, Dover Publications, New York, 1929. B. Szigeti, Proc. R. Soc. London, Ser. A, 258 (1960) 377. R.M. Douglass, Anal. Chem.,28(1956) 551. P.J. Harrop and D. S. Campbell, in L. I. Maissel and R. Glang (eds.), Handbook of Thin Film Technology, McGraw-Hill, New York, 1970, pp. 16-1636.