Membrane-based nanocalorimetry for low temperature studies with high resolution and absolute accuracy

Abstract: A differential, membrane-based nanocalorimeter has been designed and constructed for thermal studies of mesoscopic samples at low temperatures. The calorimeter is intended for sample masses from mg to sub-?g and a broad temperature range from above room temperature down to the sub-K region. It allows concurrent use of ac steady state and relaxation methods. Effort was spent to achieve good absolute accuracy to enable investigations of the electronic contribution to the heat capacity of superconductors. The calorimeter consists of a pair of cells, each of which is a stack of heaters and thermometer in the center of a silicon nitride membrane, in total giving a background heat capacity less than 100 nJ/K at 300 K, decreasing to 10 pJ/K at 1 K. The device has several distinctive features: i) The resistive thermometer, made of a GeAu alloy, displays a high sensitivity, dlnR/dlnT ? ?1 over the entire temperature range. ii) 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. iii) Data are acquired with a set of eight synchronized lock-in amplifiers measuring dc, 1st and 2nd harmonic signals of heaters and thermometer. iv) Absolute accuracy is achieved via a novel variable-frequency fixed-phase technique in which the measurement frequency is automatically adjusted during ac-calorimetry measurements to account for the temperature variation of the sample specific heat and the device thermal conductance. The properties of the empty cell and the effect of the thermal link between sample and cell were analytically studied. Practical expressions for describing the frequency dependence of heat capacity, thermal conductance, and temperature oscillation amplitude of the system were formulated. Comparisons with measurements and numerical simulations show excellent agreement. Calibration procedures are simple, but care should be taken to minimize thermal radiation effects. The experimental setup is operated with self-regulation of heater powers and thermometer bias, including compensation to zero the differential dc signal. As a result its high resolution and compact format, the calorimeter is well suited for studies of phase transitions and phase diagrams as well as electronic specific heat. The performance of the device is demonstrated by a study of the superconducting state of a small lead crystal.