Electrical Conduction by Percolation in Thick Film Resistors

Abstract

Thick film resistors are widely used in microelectronic devices, however the mechanism of electrical conduction in these resistors has not yet been fully understood. In particular the anomalous behaviour of the temperature coefficient of resistance (T.C.R.) vs. temperature for a purely ohmic resistor has not been explained. The anomaly is that the T.C.R. is negative at low temperatures, is zero around room temperature and becomes positive at higher temperatures.This paper demonstrates that the electrical conduction mechanism in thick film resistors can be described by the electron percolation theory already proposed to explain charge transport in amorphous semiconductors. The thick film structure consists of conductive grains with a diameter of 0.1 μm to 0.3 μm separated by dielectric layers. Some of the conductive grains make contact through dielectric layers so thin that electrons are able to tunnel through the layers. The critical percolation path is through these grains. Experimental evidence is given which confirms that the resistance vs. temperature characteristics satisfactorily fit the conduction equation provided by the percolation theory.The T.C.R. anomaly can be explained in the framework of this theory. The decay length of the electron wave-function is shown to be lower than 370 Å for a density of conductive grains in the film in the order of 10¹⁵ cm⁻³. Such a value is consistent with electron tunnelling through layers about 100 Å thick.