High accuracy computational methods for behavioral modeling of thick-film resistors at cryogenic temperatures

The aim of this work was to elaborate two-dimensional behavioral modeling method of thick-film resistors working in low-temperature conditions. The investigated resistors (made from 5 various resistive inks: 10 resistor coupons, each with 36 resistors with various dimensions), were measured automatically in a cryostat system. The low temperature was achieved in a nitrogen-helium continuous-flow cryostat. For nitrogen used as a freezing liquid the minimal temperature possible to achieve was equal to −195.85 °C (77.3 K). Mathematical model in the form of a multiplication of two polynomials was elaborated based on the above mentioned measurements. The first polynomial approximated temperature behavior of the normalized resistance, while the second one described the dependence of resistance on planar resistors dimensions. Special computational procedures for multidimensional approximation purpose were elaborated. It was shown that proper approximation polynomials and sufficiently exact methods of calculations ensure acceptable modeling errors.