Low Frequency Characteristics of TiO2(Rutile)–Glass Thick Films

An analysis is made of the low-frequency characteristics of the permittivity ε′ and of tan δ of a thick-film insulator containing rutile grains bonded with an amorphous glass. The appearance of dielectric relaxation associated with a maximum of tan δ, as well as characteristic Debye dispersions of the electric permittivity is observed. The relaxation time does not depend on the rutile concentration in the dielectric. An equivalent circuit describing the behaviour of a capacitor with such an insulator in the low frequency range is suggested. The experimental results are shown to be consistent with an analysis based on the assumption that a titanium ion relaxation process occurs in the rutile grains. In normal ambient conditions the influence of this kind of polarization disappears at frequencies higher than 102 Hz; ε′ and tan δ then change insignificantly and the value of tan δ is conditioned by the hopping mechanism of conductivity in the glass and in rutile.


INTRODUCTION 2. EXPERIMENTS
Thick-film capacitors, where electrodes are made of a conducting paste Pd-Ag, and an insulating paste containing a mixture of boro-silicon glass and rutile powders have been shown to be usable at frequencies above 102 Hz.
The most promising results were obtained by Borek, Licznerski and Rzasa after the printed and baked capacitors were protected with a silicone varnish. By using an insulator which obtained 90% of TiO2 (rutile) and 10% of glass (by weight) and by choosing the dielectric thickness and the surface area of the electrodes, capacitors of values 15 pF to 600 pF, with tan i < 20.10 -4 and with temperature coefficient of e '' -300 ppmC -1 have been obtained.
The field strength for insulation breakdown was about 20 V/1/am. In difficult working conditions the changes vcere smaller than + 1% for 1000 hours.
Further investigations discussed in this paper showed that the electric properties of these capacitors deteriorate at very low frequencies. Dielectric loss increases and maxima of tan i and dispersions of electric permittivity characterising the Debye relaxation process have been observed. The causes of these phenomena were investigated and results are presented below.
For the experiments presented in this paper, capacitors printed on a substrate of aluminium ceramic were prepared. The area of the electrodes was cm 2 and the dielectric was 100 wn thick. An attempt has been made to evaluate the influence of TiO2 grain concentration in the amorphous glassf and the effect of electrode type on the low frequency characteristics of the capacitor.
In a first group of capacitors used for the experiment the insulator was made of pure glass or contained 60%, 90% and 95% of TiO2 (by weight), and the electrodes were made of a conductive paste Pd-Ag. In a second group of capacitors the electrodes were made from various conductive pastes: Ag, Pd-Ag, Pt-Au, whilst the dielectric contained 90%ofTiO and 10% of glass.
The capacity and tan i of capacitors prepared in this way were measured with a Scheiber bridge in the frequency range of 10 -Hz to 10 2 Hz and with a f The structure of the dielectric films was tested by X-ray diffraction. It was found that crystal indirect phases do not appear in the baking process. The dielectric consists only of an amorphous glass and polycrystalline rutile. The diameters of futile grains did not exceed 6/am. Schering bridge in the higher frequency range. The temperature dependence of capacity and tan 5 have been determined in the range 300 K to 420 K.

Results of Experiments
It has been stated that the maxima of tan 6 and 40 dielectric constant dispersion appear at temperature of 300 K and at a frequency of about 10:2 Hz ( Figure   1) in all the capacitors with the insulator containing rutile grains. The dispersion and the maximum of tan (5 moved with increasing temperature towards higher frequencies ( Figure 2). The fact that maxima of tan (5  The values ro and W m were determined from the plots shown in Figure 4. Further information is also given by the frequency characteristics of the insulator conductivity ( Figure 5) which was calculated and plotted using the results shown in Figure 1. Within the frequency range investigated these characteristics are described by the relation: (.02 7" 6(w) A'w n + B (2) + 6o7" z where: A and B are constants The change in conductivity characteristics at the higher frequencies is consistent with the theory of the hopping mechanism of conductivity, a

Equivalent Orcuit of the Thick-Film Dielectric
An equivalent electric circuit model of a thick-film capacitor with a TiO2 (rutile) + glass insulation, is III //// FIGURE 3 Low-Frequency characteristics of the dielectric constant e' (a) and tan 6 (b) of the insulation 90% TiO + 10% of glass at 333 K (parameter type of electrode).

DISCUSSION
The low-frequency characteristics of e' and tan 6 obtained for the insulators containing rutile grains that were investigated show that the dielectric relaxation process is of the Debye type. The mean relaxation time, 7", for all investigated compositions is given by the relation: proposed which describes the frequency characteristics of this capacitor in the range 10 -a Hz to 10 -6 Hz. This model is shown in Figure 6. The elements R1, Coo, Cr and Rr represent the properties of rutile, while the elements Rs and Cs represent those of the glass. It has been assumed that a relation process associated with microscopic phenomena in the volume of the rutile grain is responsible for the appearance of maxima of tan 6 of the insulators tested.
In the proposed model, the relaxation time constant is represented by the elements Rr and Cr. The resistances R and Rs represent the losses caused by the conduction mechanism. For frequencies above Ar, As constants The characteristics presented in Figure 5 can be analysed in two frequency ranges. In the lower range (below 10 2 Hz), dielectric relaxation phenomena dominate thus, in the model shown in Figure 6, the elements Rs and R may be neglected.
In the upper range, however (above 10 2 Hz), the influence of relaxation may be ignored and in the model shown in Figure 6 Rr and Cr can be neglected.

Results of Analysis of the Equivalent Circuit
The behaviour of the system in the upper frequency range, i.e. above 10 2 Hz is most easily analysed. In this range (in the model presented in Figure 6)  as small compared to 1. Figure 7 presents the theoretical curve of 6(dr/d2) calculated from Eqs. (6) and (7), assuming that As lOAf, es 8.5; coo = 100; n l; f= kHz. The experimental values obtained from measurements are marked with points.
As Eqs. (6) and (7) give a good fit to plotted values of 6(dr Ida) at fixed o, it may be assumed that a good fit is obtained at other values of o due to the parallel nature of the 6(o) curves on Figure 5.
The values of e' and tan 6 were calculated from the model in Figure 6 with R and Rs neglected.  Table I

Rutile Grains
The low-frequency relaxation mechanism has not been completely explained by other researchers.
The values coo and es used were obtained from measurements of capacitors filled completely with ruffle and glass; and er coo 0,48.  Hansen 4 who explained them by the hopping resonance theory. Kinser s attributed the same effects to the Maxwell-Wagner-Sillars polarization mechanism. These phenomena in rutile are well explained by the model proposed by Kojkov,6 who assumed that a thermally excited titanium ion may pass from a lattice site into an interstitial position. If however the bond between the vacancy and the ion is strong, such that the ion is not able to move freely in the lattice, the potential barrier for the ion has the shape shown in Figure 8a. This situation will change when an electric field is applied. The form of the barriers is shown in Figure   8b. By virtue of this barrier model the relaxation time of dipoles (vacancy-interstitial ion) was calculated and the relations for er' and er" of the rutile grain were given. After the electric field is applied the concentration of ions in positions 2 and 3 will change in time t: dt N:P: + NoP + N3P3 N2P2 3 (11) N3P3 + NoP13 + NzP2 3 + N3P3 dt (12) where'P//-is the probability of ion transition from into j positions.
It is assumed that the increase or decrease in potential barrier (Figure 8b) ebE, e(d-b)E is considerably smaller than kT.
From the analysis presented the following conclusions may be drawn: 1) In rutile grains a Debye relaxation of vacancyinterstitial ion dipoles appears; 2) The activation energy of the relaxation time is equal to Wm (see Figure 8).
According to Kojkov the value of this energy should be in the limits 0.5 eV to eV. The authors obtained a value for Wm in the range 0.6 to 0.7 eV.
In summary the results obtained are consistent with both the assumptions of the authors and as the interpretation of these phenomena proposed by Kojkov.
Rutile glass dielectrics, which have been applied in thick-film techniques are characterized by specific properties in the very low frequency range, namely by an ion-relaxation process, causing a considerable increase of dielectric losses. In the high frequency range tan/5 of this insulation is very small, its value being determined by a hopping conductivity mechanism.