Electrical properties and conduction mechanisms of Ru‐based thick‐film (cermet) resistors

This paper presents an experimental study of the electrical conduction mechanisms in thick‐film (cermet) resistor. The resistors were made from one custom and three commercially formulated inks with sheet resistivities ranging from 10² to 10⁶ Ω/⧠ in decade increments. Their microstructure and composition have been examined using optical and scanning electron microscopy, electron microprobe analysis, x‐ray diffraction, and various chemical analyses. This portion of our study shows that the resistors are heterogeneous mixtures of metallic metal oxide particles (∼4×10⁻⁵ cm in diameter) and a lead silicate glass. The metal oxide particles are ruthenium containing pyrochlores, and are joined to form a continuous three‐dimensional network of chain segments. The principal experimental work reported here is an extensive study of the electrical transport properties of the resistors. The temperature dependence of conductance has been measured from 1.2 to 400 K, and two features common to all resistors are found. There is a pronounced decrease in conductance at low temperatures and a shallow maximum at several hundred Kelvin. Within the same range of temperatures the reversible conductance as a function of electric field from 0 to 28 kV/cm has been studied. The resistors are non‐Ohmic at all temperatures, but particularly at cryogenic temperatures for low fields. At higher fields the conductance shows a linear variation with electric field. The thick‐film resistors are found to have a small dielectric constant and a (nearly) frequency‐independent conductance from dc to 50 MHz. The magnetoresistance to 100 kG, the Hall mobility, and the Seebeck coefficient of most of the resistors have been measured and discovered to be quite small. Many of the electrical transport properties have also been determined for the metal oxide particles which were extracted from the fired resistors. These results yielded a quantitative estimate of the metal oxide contribution to the total thick‐film resistance. Using the results of our measurements we examine four broad categories of conduction mechanism models which have been previously suggested in the literature: uniform, uniform channel, nontunneling barrier, and tunneling barrier models. The first three categories are systematically rejected because of disagreements with the data. A tunnel barrier model is then developed which incorporates two features not ordinarily considered in simple tunneling theory. The small metal oxide particle size is shown to cause a small activation energy associated with electrostatic charging of the particles. Also, impurities within the tunnel barriers are presumed to act as resonant centers which increase the barrier transmission coefficient. The model is compared in detail to our experimental results and shown to be in excellent agreement.