Ge-on-GaAs film resistance thermometers: Low-temperature conduction and magnetoresistance

We investigated and generalized the resistance temperature and magnetic field dependences for various versions of cryogenic resistance thermometers based on Ge films on semi-insulating GaAs substrates. It is shown that, at low temperatures, the conductivity mechanism that is responsible for Ge film heat and magnetic field sensitivity is variable-range hopping (VRH). We found that the exponent x in VRH-type temperature law may take different values (fall between 0.25 and 0.67) for different versions of Ge-on-GaAs film thermometers. The magnetoresistance of Ge films depends strongly on the nature of hopping conductivity. It may be positive and negative as well as high and low. We found that, in the 1.8−4.2 K temperature range studied, the Ge films with x≅0.25x≅0.25 (that corresponds to nonzero constant density of states at the Fermi level) demonstrate high positive magnetoresistance. The films with x > 0.4 (that corresponds to presence of a gap in the density of states at the Fermi level) have negative magnetoresistance component that predominates at magnetic induction up to 3–5 Т. The parameters describing VRH conductivity in the Ge-on-GaAs films thermometers were determined. From practical point of view for thermometry, the possibility to describe the R = f(T) dependence by an analytical equation (VRH-type temperature law) does not require the fitting procedure and makes calibration and thermometry more simple and convenient.

Research highlights
► Exponent x in VRH law is different (0.25–0.67) for different Ge–GaAs thermometers.
► Ge films with exponent x in VRH close to 0.25 have high positive magnetoresistance.
► Ge films with exponent x in VRH more than 0.4 have negative magnetoresistance.