AC spectroscopic characterization of the conduction mechanism of tin oxide-glass composite thick film resistor

Tin oxide based thick film resistor (TFR) compositions were studied by immittance spectroscopy (IS) and electron microscopy techniques. Three groups of TFRs, obtained commercially and prepared in the laboratory, were investigated in which the composition was varied by changing the $SnO\sb2$ content in the glass matrix. In addition, samples made from 100% glass were also studied. The main attention was focused on the samples manufactured by Lapp Insulator Company, for which the conduction mechanism, microstructure, and annealing characteristics were studied in detail. From the IS measurements, it was found that these TFRs can be modeled by an equivalent circuit which consists of a resistor $R\sb2$ in series with a parallel $R\sb1C\sb1$ combination. It was found that the temperature dependence of the sheet resistance, $R\sb\square$ and the relaxation time, $\tau$, from 25$\sp\circ$C to about 350$\sp\circ$C can be separated into two regions. Region I (25$\sp\circ$C to $\sim$200$\sp\circ$C) is characterized by a hopping conduction ($T\sp{-1/4}$ dependence) and region II (200$\sp\circ$C to $\sim$350$\sp\circ$C) is characterized by an ionic diffusion process. Multivalent tin ions dissolved in glass during firing is assumed to serve as hopping sites. The hopping parameter, $T\sb0$, in region I, was determined to be,$$\eqalign{T\sb{\rm 0,L70} &= (2.7 \times 10\sp7 \pm 4.8 \times 10\sp5)\ {\rm K},\cr T\sb{\rm 0,L80} &= (3.2 \times 10\sp7 \pm 6.6 \times 10\sp5)\ {\rm K},\cr T\sb{\rm 0,L85} &= (3.9 \times 10\sp7 \pm 6.2 \times 10\sp5)\ {\rm K}.\cr}$$These values of $T\sb0$ are on the same order of magnitude as reported for a host of amorphous semiconducting compounds. The activation energy obtained in region II (0.60 $\pm$ 0.05 eV) is assumed to be the energy of motion of the diffusing $Sn\sp{4+}$ ions in the glass matrix. It was found that annealing the samples for 120+ hours at about 300$\sp\circ$C broadens the region I behavior by about 50$\sp\circ$C, while the hopping parameter, $T\sb0$ decreases slightly. Annealing does not affect the activation energy in region II significantly, but the magnitude of resistance in region II increases considerably. The observed increase in the magnitude of $R\sb\square$ in region II of post-anneal data was assigned to a decrease in the concentration of the diffusing ionic species, namely, $Sn\sp{4+}$. Since in region I the tin ions serve as the hopping sites, the effect of a decrease in the concentration of $Sn\sp{4+}$ also explains the observed lowering of the hopping parameter, $T\sb0$, in region I