THE EFFECT OF VARIOUS FACTORS ON THE RESISTANCE AND TCR OF RuOz THICK FILM RESISTORS-- RELATION BETWEEN THE ELECTRICAL PROPERTIES AND PARTICLE SIZE OF CONSTITUENTS , THE PHYSICAL PROPERTIES OF GLASS AND FIRING TEMPERATURE

Thick film resistors were prepared with different variables, they included various 
conductive particle sizes, glass particle sizes, glass softening temperatures, thermal 
expansion coefficients of the glass, mixing ratios of the conductive element and glass, 
firing temperatures, firing cycles, etc. The relation between these factors and electrical 
properties of the thick film resistors was studied. As a result, it was found that when 
a specific glass is chosen, its R-TCR curve, which indicates the relation between 
resistance and TCR of a thick film resistor, is unconditionally fixed regardless of 
various preparation factors, and the R-TCR curve can be moved only by changing the 
thermal expansion coefficient of the glass. In addition, the higher the resistance and 
the larger the thermal expansion coefficient of glass, the larger the resistance change 
against the external force.


INTRODUCTION
Thick film resistors have been widely used as circuit elements in hybrid IC's.Few basic studies have been carried when compared with studies concerning their practical use.Up to now, the important reports concerning the basic studies of thick film resistors include those that deal with the relation between microstructure and elec- trical properties of resistors and particle sizes of the glass and RuO2 , conduction mechanism2'3, temperature characteristics of the resistor4, 68 OSAMU ABE, YOSHIAKI TAKETA AND MIYOSHI HARADOME effects of adding materials5, difference in thermal expansion coef- ficient between resistor and substrate6, etc.However, it seems that there is no study which has investigated the relation between elec- trical properties and factors such as particle size of the conductive material, glass particle size, and preparation condition.In this paper we present the experimental results of our investigation in order to clarify the relation between these factors and the electrical properties of thick film resistors.

SPECIMENS
RuO2 powder, with an average particle size of 0.15 ktm, or 0.35 and glass powder, having various thermal expansion coefficients, as shown in Table I, were used as resistor components.These RuO2 and glass powders were blended with various mixing ratios, ranging from 5/95 to 33/67.The mixtures were uniformly dispersed into the organic vehicles to obtain screen printable pastes.These pastes were printed on a 96% alumina substrate with prefired Pd/Ag conductors.After printing, dried specimens were fired at between 600 and 900C, as shown in Table i, for 10 minutes.In these cases, a differential thermal analysis was conducted for each glass, and the firing temperature at which the glass viscosity, r/, became log r/ 4.0 was selected for the standard value.The geometry of the resistor was 2mm x 2mm x 12ktm.

RESULTS AND DISCUSSION
The change in resistance and TCR as a function of RuO2 concentra- tion was studied.The obtained results are shown in Figure 1.When the RuO2 concentration was less than a few volume percent, the electrical conduction was controlled by the reactive layers created on the surface of the glass particles by the reaction between RuO2 and glass rather than mutual contact of the RuO2 particles7.Therefore, the RuO2 concentration dependence of resistance is large .while the change in TCR is small.On the other hand, when the RuO2 concn, tration was approximately 20 vol % or more the electrical current was conducted by the path which was formed by mutual con:a.tTherefore, the resistance hardly changed even though the RuO2 concentration changed, and the TCR of a resistor have a tendency to move to that of RuO2.In Figure 1 the resistance and TCR depen- dence on the RuO2 diameter is also shown.In the high resistance region, the resistor prepared using larger RuO2 particles shows a tendency to have a higher resistance even in the case with the same RuO2 concentration.Hereafter, we call the curve R-TCR curve, which indicates the relation between resistance and TCR of thick film resistor.) Figure 2 shows the relation between glass particle size and firing temperature and electrical properties.In the case of resistors made by the same mask screen, the larger particle size of glass, the higher the RuO2 concentration distributed along each glass particles, and the lower the resistance.There is almost no difference in resistance and TCR between the specimen whose RuOz/glass composition is 25/75 and firing temperature is 900C and the specimen, 15/85 and THE EFFECT OF VARIOUS FACTORS ON THE RESISTANCE AND TCR   700C; also 7/93, 850C and 4/96, 750C.These specimens seem to differ somewhat in microstructure, especially the RuO2 concentra- tion of the conductive path, and the difference must affect the elec- trical properties.The reason why such a difference is not observed is the focus of our investigation.
When the mixing ratio of RuOz/glass is high, the resistance is small and TCR has a positive value.As the mixing ratio is reduced, the resistance increases and TCR moves to the negative direction.When the mixing ratio is high, the firing temperature affects the TCR change rather than the resistance change, and when the ratio is low, the inverse relation is observed.
According to the decrease in the RuOz/glass ratio or increase in firing temperature, the point which indicates the relation between resistance and TCR shifts in the high resistance direction along the R-TCR curve shown in Figure 1.
The relations between firing temperature and the resistance and the TCR are shown in Figure 3. From the firing temperature of 400C to the softening point of each glass, the resistance decreased and the TCR suddenly increased from a negative value to a positive value   with increasing firing temperature.The resistor that contained lower viscosity glass had a minimum (or maximum) point at lower tem- perature in the firing temperature-resistance (or temperature-TCR) curve.The R-TCR curve obtained by this experiment is shown in Figure 3(c), which is almost the same form as seen in Figure 2. When the glass content is decreased, the heat capacity of the resistor de- creased and the minimum of resistance with a maximum TCR ap- peared at the higher firing temperature.These tendencies became more conspicuous with increasing glass viscosity.However, the maxi- mum or minimum in the curve are all at approximately the same temperature.At each temperature in which a maximum or minimum appeared, glass flow did not occur.Therefore, the glass particles are not joined mutually and the microstructure of the resistors are all of same state independent of the glass viscosity.
From the previously mentioned electrical properties, a glass seems to behave in the resistor as follows: the lower the viscosity of the glass, the tiny glass particles which are smaller than average size soften at a lower temperature.The large glass particles are then joined by the tiny particles.The surface area of the glass particles in the resistor decreased and the RuO2 content distributed on each glass particle increased with the RuO2 particles mutually joining.As a result, the resistance decreased and the TCR shifted to the metallic value of RuO2 (TCR of RuO2 sintered film and single crystal of RuO2 are about 3600 ppm/C and 7000 ppm/C, respectively2).
However, with increasing firing temperature, the resistance in- crease and the TCR moves the negative direction.This change seems to be attributed to the glass opening a gap in the RuO2 particles of the chain path built up by the RuO2 particles.The lower viscosity glass can easily flow into the gap of RuO2 particles and form a glass layer between the RuO2 particles.As a result, the resistor containing lower viscosity glass has a higher resistance at the same firing temperature.
If the glass layer is formed, the resistor should have high resis- tance.However, in our experiment, an extreme increase in resistance could not be detected.This phenomenon occurred due to the crea- tion of a reactive layer7, which shows semiconductive characteristics and was formed by the reaction between the RuO2 and the glass.
As the firing temperature is raised, the glass between the RuO2 particles flowed out of the RuO2 particle drain.The TCR thus showed metallic characteristics because of the mutual re-contact of the RuO2 particles.
Figure 4 shows the relation between resistance and TCR and firing cycle.The resistance was measured at the AD region for the whole resistance, at the AB or CD region for interaction between conductor and resistor and at the BC region to avoid any influence of the con- ductors.Applying a constant current to the AD region, the resistance was calculated by measuring the voltage between the probes.
The relation between resistance or TCR of each region and firing cycle is shown in Figures 4(b) and (c).Since the thermal expansion coefficient of commercially available 96% alumina substrate, asub, is 70 74 10-7/C, the (glass Of glass F is nearly equal to that of the alumina substrate.Since the glass of glass J is larger than that of substrate, the resistor will be under a tensile force from the substrate6.By retiring, the state of force-force free is repeated, and generation of microcracks or destruction of the conductive path occurs, then the resistance and TCR changes.However, in the case of the glass C resistor, whose cfim (Cfim .Cgass) is smaller than sub of substrate, a compression acts on the resistor from the substrate6, resulting in no cracks or destruction of the conductive path.Therefore, the resistance and TCR scarcely change.
The resistance change and TCR change of the AB or CD region, resistor-conductor interface, are smaller than those of the region, in which the conductor has no influence.This result is due to A6 dif- fusion from the conductor to the resistor9.Since the resistance change of the resistor-conductor interface is small, the resistance of the AD region has a smaller value than the BC region, (pure resistor part).The forms in R-TCR curves are not the same as each other due to the difference of the thermal expansion coefficient of each glass.
However, as shown in Figure 4(d), the electrical properties change along the R-TCR curve similarly to that given by other pr.eparation factors.
Figure 5 shows the relation between 0glass of glass and the electrical properties of the resistor.In the case of glass sub (" GglassF), increasing the difference between agss and asub, the TCR moves in a positive direction, and the R-TCR curve saturate quickly.On the other hand, for the case of agss > asub, the reverse phenomena SHEET RESISTANCE (9./rn) R-TCR curve dependence on thermal expansion coefficient of glass.
occurred.As seen in Table I, saturation of the R-TCR curve does not depend on the glass resistivity but the difference in thermal expansion coefficients between substrate and glass.
The electrical resistance of thick film resistors changes by applying an external force.Accordingly, the influence upon the strain characteristics by the preparation condition or physical properties of the glass was examined.The sample was deflected by using the three point bending method shown in Figure 6.When a thick film resistor has an applied external force, the relation between the applied strain F, and resistance change, dR/R, is as followsa: dR/R eF The proportionality constant, e, is called the gauge factor and is a characterization factor for the strain characteristics of thick film resistors.
Figure 7(a) shows the firing temperature dependence of e.As seen in this figure, e has a large value when a high resistive resistor is fired at a high temperature.Figure 7(b) and (c) shows the variation between resistance or TCR and e.The e becomes larger if a glass with a large thermal expansion coefficient is used.
The resistance change by an external force is due to microstructure change in the conductive path formed by RuO2 particles.In a low resistive resistor, in which many conductive particles are contained, COMPRESSED RESISTOR suas'r T FORC FIGURE 6 Three point bending method.conductive RuO2 particles exhibit a buffer effect against external forces, and weaken the tension or compression.As a result, the resistance change is small.However, in the case of a highly resistive resistor, whose conductive path has a low RuO2 concentration, a change of contact state between conductive particles gives rise to an immediate resistance change.

CONCLUSION
Thick film resistors were prepared with different variables, they in- cluded various conductive particle sizes, glass particle sizes, glass softening temperatures, thermal expansion coefficients of the glass, mixing ratios of the conductive element and glass, firing tempera- tures, firing cycles, etc.The relation between these factors and electrical properties of the thick film resistors was studied.As a result, the following facts have been determined.
(1) When a specific glass is chosen, its R-TCR curve, which indicates the relation between resistance and TCR of a thick film resistor, is unconditionally fixed regardless of the various prepara- tion factors.
(2) The points which indicate the relation between the resistance and TCR shifts to a higher resistance along the R-TCR curve when the firing temperature rises, the RuO2 particle size increases, glass particle size decreases, the softening temperature of glass decreases or the RuOz/glass mixing ratio increases.
(3) As the firing temperature rises, the TCR shifts from a positive to negative value.
(4) When the firing temperature is near the softening temperature of the glass, the resistor has a minimum (maximum) vaIue for re- sistance (TCR).The minimum (maximum) values are equal and independent of glass viscosity if the RuOz/glass ratio is fixed.
(5) The lower the viscosity of the glass, the higher the resistance at a particular firing temperature.
(6) The R-TCR curve can be moved by changing the thermal expansion coefficient of the glass.When the thermal expansion co- efficient is increased, the TCR moves to negative direction.
(7) The higher the resistance and the larger the thermal expansion coefficient of glass, the larger the resistance change against the external force.

FIGURE 4 (
FIGURE 4 (a) Measuring method and points.Applying a constant current to the AD region, the resistance was calculated by measuring voltage of each region.This figure is a case of BC region measurement.(b) Firing cycle versus resistance change.(c) Firing cycle versus TCR. (d) Sheet resistance versus TCR.
FIGURE 5 a) Firing temperature versus gauge factor.(b) Sheet resistance versus gauge factor.(c) TCR versus gauge factor.