Figure 2: CBT behaviour between 80 and 7 mK in two dilution refrigerators.

(a) CBT conductance G versus measured bias voltage V_DC at four temperatures. Symbols show measured values and lines show best fits to the calculated ideal conductance. The warmest measurements (crosses, circles and squares) are fitted simultaneously to calibrate the sensor, giving C_Σ=236.6 fF and R_T=22.42 kΩ. The coldest measurement (triangles) is fitted using this calibration. The minimum electron temperatures are in close agreement with the refrigerator temperature measured by a RuO₂ thermometer: 59.9, 40.1, 20.0 and 7.2 mK respectively. The uncertainties on are calculated from uncertainties in the fitted parameters. (b) CBT electron temperature T_e versus refrigerator temperature T_mxc. Symbols show from fits to conductance dips measured in the cryogen-free refrigerator (circles) and the custom refrigerator (triangles). Error bars are within the symbols. The solid curve shows T_e determined by monitoring the conductance G₀ (at V_DC=0) as the cryo-free fridge cools over 35 min from 52 to 9 mK, showing that the CBT has a stronger thermal link to the refrigerator than the RuO₂ thermometer, leading to the thermal lag (T_mxc≥T_e) during this time. The dashed line shows T_e=T_mxc.