Modeling Short- and Long-Term NTC Thermistor Resistance Drift

The reliability of negative temperature coefficient (NTC) chip-style thermistors acquired from two suppliers was determined via aging over a broad temperature range, 85°C -200°C, and times, 3000hrs - 8600hrs. Both suppliers advertise their respective thermistors as high stability devices. Stability was determined by periodically pulling the devices from the aging chamber and characterizing the change in resistance (drift) per unit time (<inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>R(t)). In this study, thermistors from both suppliers display decreasing <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>R(t) at shorter time scales and lower temperatures (t<4,000hrs at T <inline-formula> <tex-math notation="LaTeX">$\geq 85^{\circ }$ </tex-math></inline-formula>C) that gradually approaches an inflection point wherein <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>R(t) begins to continuously increase for the remainer of the aging study independent of temperature. This is strikingly unlike other NTC thermistor reliability reports as the short-term decreasing resistance combined with <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>R(t) inflection point is not typically modeled, analyzed and discussed. The change in resistance versus time was mathematically modeled by a piece-wise equation where decreasing resistance was modeled with a stretched exponential function (DeBast-Gillard and Williams-Watts type relaxation) and increasing resistance by a linear function. Both the decrease and increase regions of resistance drift were found to be well represented by Arrhenius expressions indicating both were thermally activated and characterized by Ea=0.43-0.64eV, growth by Ea=0.44-0.57eV, respectively. Further, the time interval that <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>R(t)’s inflection point occurred was also found to be well represented by a thermally activated process with an activation energy of Ea=0.45-0.52eV. Using mathematical fitting functions and activation energies, the implication of decreasing followed by increasing resistance change behavior with respect to device lifetime is described in detail. Finally, a phenomenological defect-chemistry-based model is used to describe the observed <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>R(t) behavior that combines a localized field-induced oxygen vacancy migration mechanism with the classical NTC thermistor degradation mechanism, poisoning, of transition metal oxidation on tetrahedral and octahedral sites that inhibits polaron transport through the ceramic.