Temperature dependence of the electrical conduction in RuO2-based thick film resistors

In this paper, the temperature dependence of resistance of two generic RuO₂-based resistors is investigated. The resistor compositions studied are 80 wt.% glass (63 wt.% PbO - 25 wt.% B₂O₃ - 12 wt.% SiO₂, designated as G1) - 20 wt.% RuO₂ and 80 wt.% glass (55.5 wt.% PbO - 22 wt.% B₂O₃ - 10.5 wt.% SiO₂ - 12 wt.% Al₂O₃, designated as G2) - 20 wt.% RuO₂. The sheet resistance of resistor 80 wt.% G1 - 20 wt.% RuO₂ fired at 850° C decreases as the temperature is increased from 100 K to ∼400 K, remains a minimum value at temperatures 400 K ∼690 K, and then increases as the temperature is further raised. A negative temperature coefficient of resistance (TCR) of ∼-480 ppm/°C is obtained from 100 K to 500 K. TheTCR becomes less negative when temperature increases. Three models for conduction mechanism of thick film resistors are employed to explain the experimental results. A modified model, consisting of both tunneling and parallel conduction approaches, is proposed to elucidate the change in slope in the resistance-inverse temperature curve as well as the temperature dependence of the resistance. In addition, an equivalent circuit model is proposed to describe the electrical behavior of the thick film resistors.