Mott variable-range hopping based calibration procedure for NTC thermistors in wide cryogenic temperature range

Measurement, vol. 270, pp. 120853

Abstract

In this paper we propose a procedure based on the Mott variable-range hopping model that describes the low-temperature conduction in strongly disordered systems such as negative temperature coefficient (NTC) thermistors. This procedure offers a close approximation to the physical model and provides an accurate R ( T ) fit for the resistance − temperature data over three orders of magnitude temperature range (0.04 K — 40 K) using only 4 fit coefficients. Eventually, the temperature corresponding to any resistance value of the thermistor T ( R ) can be determined with an approximation of an inverted R ( T ) function based on a Puiseux series expansion. This approach has been showed to be applicable to different NTC thermistors, including ruthenium oxide (RuO 2 ) and germanium (Ge) resistors with a range of resistance values. It provides a root mean square of the relative residual of the fit Δ T rel RMS ≤ 1 % and Δ T rel RMS ≤ 1 . 7 % using a n fit ∈ [ 4 , 10 ] and n fit = 4 fit coefficients for RuO 2 and Ge, respectively. Previously reported procedures for the calibration of resistance-temperature data in low-temperature thermistors do not reach this accuracy with a similar number of fit coefficients.

Authors 4

1. E. Taralli corresponding Aachen NWO-I/SRON Space Research Organisation Netherlands

   NWO-I · Space Research Organisation Netherlands

   Affiliation as printed

   NWO-I/SRON Space Research Organisation Netherlands, Niels Bohrweg 4, Leiden, 2333 CA, The Netherlands

2. Sven Visser Aachen NWO-I/SRON Space Research Organisation Netherlands

   NWO-I · Space Research Organisation Netherlands

   Affiliation as printed

   NWO-I/SRON Space Research Organisation Netherlands, Niels Bohrweg 4, Leiden, 2333 CA, The Netherlands

3. R. den Hartog Aachen NWO-I/SRON Space Research Organisation Netherlands

   NWO-I · Space Research Organisation Netherlands

   Affiliation as printed

   NWO-I/SRON Space Research Organisation Netherlands, Niels Bohrweg 4, Leiden, 2333 CA, The Netherlands

4. Paul van der Hulst Aachen NWO-I/SRON Space Research Organisation Netherlands

   NWO-I · Space Research Organisation Netherlands

   Affiliation as printed

   NWO-I/SRON Space Research Organisation Netherlands, Niels Bohrweg 4, Leiden, 2333 CA, The Netherlands