4.2. Four-point probe resistivity measurements

Specimens were prepared by thermal evaporation onto 18 mm square glass coverslips (Zeiss No. 1.5). Each foil was mounted in the probe instrument, the Faraday cage was enclosed around the device and the measurement taken by applying a fixed current to the outer two probes and simultaneously measuring the voltage between the inner two probes using a calibrated source meter (Kiethley 2450). Each measurement for a particular temperature was made 10–12 times, and the mean taken as the actual value. Temperatures were measured using a calibrated, NIST traceable platinum resistor (Lakeshore Cryotronic) attached to the copper substrate stage. The resistance of the temperature sensor was measured in a four-wire configuration using a commercial source meter (Lakeshore Cryotronic 211). The absolute error in the temperature measurement was estimated to be less than ±24 mK in this range of temperatures. To cool the specimen, the Faraday enclosure was purged with dry, cold nitrogen gas and then the entire apparatus was placed in a stainless steel dewar. Liquid nitrogen was slowly added to the dewar, and the resistivity and temperature measurements were recorded as the instrument cooled to the temperature of liquid nitrogen. After warming back to room temperature, the thickness of the foil was measured by first cleaving it with adhesive tape (3 M Scotch Crystal), and then imaging the cleaved edge by contact mode atomic force microscopy (Asylum Research) as described previously (Russo and Passmore, 2014a). (Note: we neglect the thermal contraction during cooling for these resistivity measurements as it will change the thickness by <0.3%). The thermal expansion coefficients (α in Eq. (2)) are 16.5, 14.2 and 4 μm/(mK) for copper, gold and amorphous carbon respectively (Haynes, 2015). Note: reported values for carbon vary from 2–8 so a value of 4 was taken as a reasonable estimate for the differential contraction calculation.