Thermometric characteristics approximation of germanium film temperature microsensors by orthonormal polynomials

• Published in: Review of scientific instruments 2005-11, Vol.76 (11), p.116104-116104-4
• Main Authors: Bogdanova, Nina B., Terziyska, B. M., Madge, H.
• Format: Article
• Language: English
• ISSN: 0034-6748; 1089-7623
• DOI: 10.1063/1.2126814

Approximations of thermometric characteristics of germanium film temperature microsensors are presented using a mathematical approach based on their expansion with orthonormal polynomials. A weighted orthonormal polynomial expansion method (OPEM) is applied, involving the experimental errors of calibration test data at every point. The thermometric functions R ( T ) and T ( R ) of resistance and temperature are described in the whole temperature range ( 1.7 - 300 K ) and in three subintervals ( 1.7 - 20 , 20 - 150 , and 150 - 300 K ) . The absolute, relative, and specific sensitivities of the sensor, as well as the main approximation characteristics, are discussed. The OPEM is extended to obtain a mathematical description of R ( T ) and T ( R ) functions by usual polynomial coefficients calculated by orthonormal ones. A comparison between maximal relative deviations of R ( T ) and T ( R ) three-interval approximations, correspondingly, by usual and orthonormal polynomials, is presented. Numerical results of the approximation parameters of these type of temperature sensors are shown in the figures and tables.