Development and characterization of a membrane-based nanocalorimeter for low temperatures

Abstract: A differential, membrane-based nanocalorimeter has been constructed for thermal studies of mesoscopic samples at low temperatures. The calorimeter is designed for sample masses from milligram to sub-microgram and a temperature range from room temperature to the sub-Kelvin region. In particular, it finds applications in the study of phase transitions and phase diagrams of superconductors and magnetic systems. Effort was spent to achieve high resolution and good absolute accuracy to be able to investigate the electronic contribution of the heat capacity of superconductors. The device is based on two free-standing silicon nitride membranes that, combined with thin film heaters and temperature sensors, give a background heat capacity < 200 nJ/K at 300 K, decreasing to sub-nJ/K at 10 K. The device has several unique features. i) In differential mode, used for small samples, the background at room temperature is reduced to ~ 2 nJ=K. ii) The resistive thermometer, made of GeAu alloy, has a high sensitivity, dlnR/dlnT ~ 1 over the entire temperature range. iii) The sample is placed in direct contact with the thermometer which is allowed to self-heat. The thermometer can thus be operated at high DC current to increase the resolution. iv) Data are acquired with a set of eight synchronized lock-in ampliers measuring DC, 1st and 2nd harmonic signals of heater powers and temperature oscillations with combined good absolute accuracy and high resolution. The design allows concurrent use of AC steady state and relaxation methods for general studies of specific heat, latent heat and dynamic heat capacity. The properties of the nanocalorimeter were studied both analytically and numerically with excellent agreement with experimental results. The operation of the experimental setup was tested with successful calibration and characterization measurements which suggest promising results.