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A differential, membrane-based nanocalorimeter for general specific heatstudies of very small samples, ranging from 0.5 mg to sub-{\mu}g in mass, isdescribed. The calorimeter operates over the temperature range from above roomtemperature down to 0.5 K. It consists of a pair of cells, each of which is astack 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 1K. The device has several distinctive features: i)The resistive thermometer, made of a Ge_{1-x}Au_{x} alloy, displays a highdimensionless sensitivity |dlnR/dlnT | \geq 1 over the entire temperaturerange. ii) The sample is placed in direct contact with the thermometer, whichis allowed to self-heat. The thermometer can thus be operated at high dccurrent to increase the resolution. iii) Data are acquired with a set of eightsynchronized lock-in amplifiers measuring dc, 1st and 2nd harmonic signals ofheaters and thermometer. This gives high resolution and allows continuousoutput adjustments without additional noise. iv) Absolute accuracy is achievedvia a variable-frequency-fixed-phase technique in which the measurementfrequency is automatically adjusted during the measurements to account for thetemperature variation of the sample heat capacity and the device thermalconductance. The performance of the calorimeter is illustrated by studying theheat capacity of a small Au sample and the specific heat of a 2.6 {\mu}g pieceof superconducting Pb in various magnetic fields.

Membrane-based nanocalorimeter for high-resolution measurements of low-temperature specific heat