Influence of the Substrate on the Electrical Properties of Thick-Film Resistors

The thick-film technology is widely used for hybrid circuit manufacturing and there is a definite trend to use it in other applications. However, the understanding of the electrical, mechanical, and chemical characteristics of thick-film materials has been approached essentially on an empirical basis, even if many hypotheses have been formulated on their conduction mechanisms. In fact, thick-film resistors present a temperature coefficient of resistance that is negative at lower temperatures and positive at higher temperatures with a TCR vanishing in the range of the room temperature. Recent papers attribute the conduction mechanism to percolation tunneling of electrons through conductive grains embedded in the glassy matrix of the resistor layer. The model assumes that the resistance of the percolation paths dominates the resistance of a network electrically equivalent to the thick-film resistor. With this model a good fitting of the experimental data is obtained. However only data concerning Ru-based resistors screened and fired on 96 percent alumina substrates were considered. In order to better understand the influence of the ceramic substrates on thc electrical and thermal characteristics of thick-film resistors, zirconia, beryllia, and alumina (with different purity) were employed in the present study. The results indicate that the "substrate effect" plays an important role in ruthenium-based resistors, so that, in order to understand the thick-film conduction mechanisms, it is necessary to take into consideration the "substrate resistor system" and not to limit the analysis to the film in itself. Of particular interest is the fact that the minimum of the resistance-versus-temperature curve varies for different substrate materials, even if the resistors under test are made with the same resistor series and are characterized by the same sheet resistivity. An equation is proposed that correlates the resistor gauge factor to thermal expansion coefficient of the ceramic substrate. By assuming the validity of a recently proposed model of conduction mechanism in thick film, a new set of equations is proposed that fits the experimental results obtained on resistors screened and fired on substrates of different compositions or with a different content of impurities.