Modeling of thermometric characteristics of thermodiode sensors by using the dimensionless sensitivity

Abstract

Dimensionless sensitivity and slope of its characteristic in the forms α=d(log V)/d(log T) and γ=d(log α)/d(log T) have been proposed as a base for modeling of thermometric characteristics V(T). The differential analysis of V(T) curves within the range from 4.2 up to 400 K by numerical differentiation has allowed obtaining the analytical approximation in the form V(T)=ATαexp[-BTγ1(1+CTγ1)], where A, B and C are the constants depending on physical parameters of thermodiode silicon sensor. This approach is useful both for the analysis of these characteristics as well as for modeling and determining an approximating function by finding out the regions where power-like or exponential dependences are the adequate expressions to describe the thermometric characteristic sections. By contrast to the known methods, one should not know beforehand the function that describes the process or the characteristic. It permits to elucidate fine peculiarities of thermometric characteristics and to achieve high accuracy of modeling by using the analytical expressions. In view of the practical purposes, the thermometric characteristics are approximated within the three temperature ranges. The errors of approximation do not exceed ±0.02%, ±0.2% and ±0.4% within the temperature ranges 4.2…40 K, 40…170 K and 170…400 K, respectively.