Dielectric properties of terbium fluoride thin film capacitors

Thin Solid Films, 74 (1980) 189-195 © Elsevier Sequoia S.A., Lausanne--Printed in the Netherlands

189

DIELECTRIC PROPERTIES OF TERBIUM FLUORIDE THIN FILM CAPACITORS K. R. PARAMASIVAM, M. RADHAKRISHNAN AND C. BALASUBRAMANIAN Department of Physics, Madras University Autonomous Postgraduate Centre, Coimbatore 641 041 (India) (Received March 17, 1980; accepted May 19, 1980)

The dielectric properties of thermally evaporated TbF 3 thin film capacitors (AI/TbFa/A1) of various thicknesses were studied in the frequency range 0.5-30 kHz at various temperatures (300-443 K). The dielectric constant was found to increase with increasing film thickness. The large increase in capacitance towards the low frequency region indicates the possibility of an interfacial polarization mechanism prevailing in that region. The frequency-temperature dependence of tan ~ reveals a loss peak which shifts to higher frequencies with increasing temperature. The dielectric relaxation phenomenon in these films was explained on the basis of dipolar reorientation. The activation energy was calculated for the relaxation process. ColeCole diagrams were drawn and used to determine the spreading factor fl and the mean relaxation time za.

1. INTRODUCTION Thin insulating films find innumerable applications in electronic as well as optical devices. The rare earth oxides 1'2 and fluorides3 have received particular attention for device applications owing to their mechanical and chemical stability. A considerable amount of work has been done on the dielectric properties of various rare earth fluoride thin films4-8. However, previous studies of TbF s thin films have been concerned only with their electroluminescence9-11. This paper reports an investigation of the dielectric behaviour of thermally evaporated TbF 3 thin films. 2. EXPERIMENTAL The films were prepared by making use of a conventional 0.30 m vacuum coating unit at a pressure of 33 Pa. Pure aluminium (99.999%) was evaporated from a tungsten filament onto carefully cleaned glass substrates through suitable masks to form the base electrode. Terbium fluoride powder of purity 99.9% (supplied by Indian Rare Earths Ltd.) was air baked at 250 °C for a few hours and was then evaporated from a resistively heated molybdenum boat to form the dielectric layer. Pure aluminium was again evaporated to complete the MIM sandwich structure (A1/TbFa/A1). The dielectric thickness was measured with a multiple-beam interferometer (Fizeau fringes) l 2 An evaporation rate of 12 A s- 1 was maintained to produce thin dielectric films of uniform thickness. Capacitors of fluoride films of

190

K . R . PARAMASIVAM, M. RADHAKRISHNAN, C. BALASUBRAMANIAN

varying thicknesses (300-2600 A) were fabricated. All the capacitors were stabilized by prolonged aging and repeated annealing cycles at about 100 °C. The capacitance C and loss factor tan 6 were measured at 1 V r.m.s, in vacuo in the frequency range 0.5-30 kHz at various temperatures (300-443 K) using a Radart 0.1% universal bridge coupled with an external audio oscillator. The breakdown voltage was measured in vacuo by placing the f i l l capacitor in series in a circuit consisting of a d.c. power supply, a nanoammeter and a limiting resistor. From Xray diffraction studies, deposited films of TbF3 were determined to be amorphous in structure (Fig. 1). 3. RESULTS 3.I. Dielectric constant

The dielectric constant e' was evaluated from a knowledge of capacitance, film thickness and area of the capacitor. Figure 2 shows the variation of the dielectric constant with frequency for films of thicknesses 1530, 1844 and 2100 A at room temperature. The dielectric constants of these films at 1 kHz were estimated to be 7.5, 11 and 13 respectively. The dielectric constant versus frequency curves closely resemble those predicted by the Debye relaxation model for orientational polarization 13. It, 13 ._

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Fig. 1. A typical X-ray diffraction pattern indicating amorphous structure for a film of TbF 3. Fig. 2. Variation of the dielectric constant with frequency for various thicknesses.

3.2. Frequency and temperature effects

The variation of the capacitance with frequency at various temperatures is presented in Fig. 3 for a f i l l of thickness 1844 A. In general, the capacitance was found to decrease with frequency at all temperatures but this variation is less pronounced as the temperature decreases. The effect of frequency on tan ~ (Fig. 4) shows a striking loss peak which shifts to the higher frequency region with increasing temperature. Similar loss peaks have been reported by earlier investigators during their studies on other insulating films 6'14-17. The variations of 8' and d' with frequency at various temperatures are presented in Fig. 5. 5' decreases with frequency, whereas d' increases initially, attains a maximum and then decreases with

191

DIELECTRIC PROPERTIES OF T b F 3 THIN FILM CAPACITORS

frequency. It is interesting to note that the peak shifts towards the higher frequency region with increasing temperature. Cole-Cole plots 18 of e" versus e' over the audio frequency (a.f.) range for various temperatures are shown in Fig. 6. The points lie on an arc of a circle which tends to become a semicircle with increasing temperature. In the capacitance-temperature plot (Fig. 7) it is observed that the capacitance increases with temperature at all frequencies. The large increase in capacitance beyond 360 K may be attributed to ionic motion in the form of dipolar reorientation. The temperature coeflficient of capacitance (TCC) for a film 1844 A thick was estimated to be 350 ppm °C-1 at room temperature and 1 kHz.

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160 140

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Frequency ( kHz )

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Fig. 3. Variation of the capacitance with frequency at various temperatures (for a film thickness of 1844 A): curve I, 443 K; curve 2, 431 K; curve 3, 418 K; curve 4, 401 K; curve 5, 392 K; curve 6, 375 K; curve 7, 360 K; curve 8, 300 K. Fig. 4. The behaviour of the loss tangent as a function of frequency at various temperatures (for a film thickness of 1844 A) :A, 401 K; I-1,392 K; O, 375 K. 24 80 70

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Fig. 5. Variation ofe' (A, Fq, O) and ~" (&, l , O) with frequency at 418 K (A, &), 401 K ( 0 , m) and 392 K (O, Q) (for a film thickness of 1844 A). Fig. 6. Cole-Cote plots at (a) 392 K and (b) 401 K (for a film thickness of 1844 A).

192

K . R . PARAMASIVAM, M. RADHAKRISHNAN, C. BALASUBRAMANIAN

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Fig. 7. Variation of capacitance with temperature at three different frequencies (for a film thickness of

1844 A). 3.3. Activation energy

Making use of the relation 14,19 f m = foexp(-- E / k T ) a plot was made (Fig. 8) of the logarithm of the frequency fm at which tan 6 is a maximum against the inverse absolute temperature. The slope of this curve yields an activation energy of 1.18 eV. The relaxation frequency here is the frequency at which tan 6 is a maximum. According to Simmons et al. 2°, for any capacitor system with an inherent resistance Ro co = A R o- 1 exp( - E/k T)

where co is the angular frequency ( = 2xf) and A is a constant whose magnitude depends on the particular selected value of constant capacitance. The variation of log co with 1/T for two constant capacitances is presented in Fig. 9. The two plots are found to be linear and parallel; an activation energy of 1.16 eV was calculated from them. 4. DISCUSSION The increase in capacitance towards the low frequency region, which was observed in the present study, may be attributed to an interfacial polarization mechanism in that region. Similar observations have been made by various authors during their studies on different dielectric films15' 21,22. The loss peak observed in the tan ~ versus frequency curve reveals a relaxation effect in these films. The shift in the loss peak towards the higher frequency region with increasing temperature is in accordance with the Debye theory of dipole orientations 13. For a Debye process at high temperatures and for a given frequency, a maximum in tan 6 will occur at a temperature such that 2/tfrelax = l/'r where z is the relaxation time. Accordingly, frcmax will be greater when • is less. The rise in temperature causes a reduction in the mean time of stay of ionic dipoles 2a which in turn causes z to decrease and fr,~axto occur in the higher a.f. range, as observed in the present study. Similar loss peaks reported for insulating filmss' ,s, 19, 24, 2s have also been attributed to a dielectric relaxation phenomenon arising from dipolar reorientation.

DIELECTRIC PROPERTIES OF

TbF s THIN FILM CAPACITORS

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Fig. 8. A plot of the loss peak frequency against the inverse absolute temperature (for a film thickness of 1844 A). Fig. 9. A plot of log co vs. the inverse absolute temperature for two constant capacitances. The data were taken from Fig. 3.

Normally, vacuum-deposited films of compound insulators are nonstoichiometric because of the preferential evaporation and decomposition of constituents of lower vapour pressure 6' 14. In metal fluoride insulators, the metallic constituent usually has the lower vapour pressure and hence these films may often have a deficit of the non-metallic constituent, namely fluorine. In evaporated rare earth fluoride films, fluorine deficiency has been reported by earlier workers 6' 26 Such fluorine deficiency was also expected in thermally evaporated TbF3 films in the present study and consequently the fluorine deficiency may cause the formation of dipoles in the film structure. According to the simple Debye model 13, for dipoles characterized by a single relaxation time the plot ofe" versus e~ over the entire frequency range will always be a semicircle. In evaporated solid films, the arrangement of nearest neighbour atoms is not exactly the same for all dipoles. Hence the dipoles cannot be characterized by a single relaxation time as in the simple Debye model. They will have a spread of relaxation times. For such materials, Cole and Cole is have modified the Debye theory to obtain the more general expression ~s - - 13oo

d - - j r " = ~oo-t 1 +0co%) 1-p where % is the mean relaxation time and fl is the spreading factor of the actual relaxation times about the mean value za. es and Cooare the static and high frequency dielectric constants respectively. The Cole-Cole plot of e" versus e' (Fig. 6) is a semicircle with its centre below the e' axis. The value offl at 392 K is calculated to be 0.14 and it decreases to 0.11 at 401 K. Thus the spreading factor is found to be

194

K . R . PARAMASIVAM, M. RADHAKRISHNAN, C. BALASUBRAMANIAN

temperature dependent and its value tends to zero at higher temperatures. This is in accordance with the observations made by earlier investigators on insulating films15,19. Knowing fl, ~a can be determined using the relation I s v/u = (co~a) 1-~

where v is the distance on the Cole-Cole diagram between es and the experimental point, u is the distance between that point and ~o and co is the angular frequency. The values of fl and T, obtained for two different temperatures are presented in Table I. The various observations made in this study clearly demonstrate the dielectric relaxation phenomenon arising from the dipolar reorientation in TbF3 films. The large value of the activation energy (1.18 eV) suggests that cor/duction in these films may be due to the motion of fluorine ion vacancies through the film structure. The breakdown field strength for a film 1050 A thick was estimated to be 2.5 x 1 0 6 V cm-1. Capacitors prepared from these films possessed the following interesting characteristics: a capacitance density of 0.03-0.06 I~F cm-z, a high dielectric field strength (exceeding 2.5 x 10 6 V cm- 1), a high dissipation factor (0.03) and a low TCC (about 350 ppm °C- 1). TABLE I EXPERIMENTAL VALUESOF fl AND "~a

Temperature (K)

e~

e,

Spreading factor fl

Mean relaxation time za (s)

392 401

10.25 12.50

78.25 78.50

0.14 0.11

1.8 x 10 -4 4.9 x 10 -s

ACKNOWLEDGMENT

One of the authors (K.R.P.) thanks the Chikkaiah Naicker College, Erode, for deputing him as a Teacher Fellow under the Faculty Improvement Programme of the University Grants Commission, New Delhi. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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DIELECTRIC PROPERTIES OF T b F a THIN FILM CAPACITORS

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