Computer Fitting of Germanium Thermometer Characteristics

Abstract

Of the various kinds of dopedgermanium investigated for low temperature resistance thermometry, arsenic doping has been found most satisfactory in providing adequate sensitivity over the temperature range from less than 1 to a little over 100 K. Such sensors are highly reproducible as well as sensitive, but for accurate thermometry it has been a disadvantage that the relationship between sensor resistance R and absolute temperature T cannot be expressed accurately in analytic form. However, the relationship can be expressed within close limits over wide temperature ranges by polynomials of the form log 10 R= ∑ i=0 n A j ( log 10 T) i .For an optimum representation, it is necessary to make judicious choices both of the polynomial degree and the temperature range. Insistence on a single polynomial over the entire 1–100 K range produces a solution with spurious oscillations of rms amplitude some 0.3% of the absolute temperature. Such spurious oscillations can be reduced to an amplitude of a few parts in 104 of temperature by using one polynomial for the 1–20 K range and a second polynomial for T≳15 K (thus affording a small overlap region between the two polynomials). The markedly inferior results of using different temperature ranges and a different polynomial regression procedure are illustrated.