Electron Tunneling and Hopping Possibilites in RuO2 Thick Films

It is proposed in this paper that the temperature coefficient of resistivity (TCR) in thick film resistors arises from (i) the usual particle-to-particle conduction, (ii) electron tunneling, and (iii) the phononassisted hopping. Equations for activation energies are derived for the temperature minimum of the resistance with and without hopping. New equations for TCR are suggested. Some extensive calculations of TCR and activation energy have been made for RuO2 thick film resistors, the results of which agree well with available experimental measurements.