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Primary thermometry

Primary thermometry by means of noise thermometry

 

Primary thermometers are based on well-understood physical systems. Their equation of state, which describes the relation between thermodynamic temperature and other independent quantities, does not contain any unknown or significantly temperature-dependent constants. Depending on how the quantities and parameters occurring in the equation of state have been determined, two variants of primary thermometry are distinguished: For absolute primary thermometry, all parameters must be determined without any reference to other temperatures, whereas this limitation is omitted for relative primary thermometry, which allows reference to one or more temperatures known from previous primary thermometry Opens external link in new window[1].

Noise thermometry, which measures and evaluates the electronic noise in electrical conductors, is an established method for primary thermometry. It reaches from the lowest temperatures below 1 mK to high temperatures above 1000 K. Although different thermometer designs are applied, which are adapted to specific temperature ranges, they are all based on the same effect and evaluate the thermally agitated fluctuations of the charge carriers. This fundamental effect was described already in 1928 by Johnson and Nyquist Opens external link in new window[2]. Compared to typical electrical voltages and currents occurring in everyday life, the thermal noise is – in particular at low temperatures – a tiny effect which can only be registered by sensitive amplifiers or sensors.  In the temperature range below approximately 5 K, Superconducting Quantum Interference Devices (SQUIDs) are applied for this purpose, which feature an extremely low internal noise. Based on this outstanding property, thermometers can be designed to make the residual SQUID noise much lower or even negligible compared to the thermal noise being measured, so that the measured signal is not distorted. For decreasing temperature, however, it becomes increasingly difficult to meet this relation as the signal amplitude of the thermal noise is proportional to the square root of temperature. In a wider consideration, this raises a fundamental question for noise thermometry, whether – and how – it is possible to distinguish the thermal noise from inevitably occurring non-thermal noise components, since the latter must not enter the temperature calculation. One solution to this problem is the cross-correlation method, which is able to distinguish correlated from uncorrelated signal components contained in two signals, and finally to suppress the uncorrelated components. By applying this method, the thermal noise is registered simultaneously as common (correlated) signal using two independent signal channels (SQUID sensors). The inevitable, additional non-thermal noise occurs independently (uncorrelated) in each channel and can be suppressed by the cross-correlation technique.

Magnetic Field Fluctuation Thermometers in the range from 1 mK to approx. 1 K

 

At PTB, noise thermometry at low temperatures is implemented by means of a Magnetic Field Fluctuation Thermometer (MFFT). This thermometer is made from highly pure copper and uses a part of its massive body as actual temperature sensor. The thermally agitated noise currents flowing inside the temperature sensor can be detected indirectly at its surface as fluctuations of the magnetic field. For the sensitive measurement of this temporally fluctuating magnetic field (the component perpendicular to the surface in a distance of 100 µm amounts to ≈ 0.6 nTrms at 1 K, approximately 80,000 times less than the earth’s magnetic field), a Opens internal link in current windowSQUID current sensor connected to a superconducting detection coil is used. In order to apply the cross-correlation technique, every component, including room temperature SQUID electronics, exists twice. The two detection coils are electrically independent of each other, but they cover the same area of the temperature sensor. Figure 1 shows a schematic of the MFFT.

The essential, temperature dependent quantity measured during MFFT operation is the time dependence of the magnetic flux in the detection coil, φD(t). It is advantageous to evaluate these noise data, after a Fourier transform, in the frequency domain in form of a spectral density, SV(f). The evaluation is then based on the simple relation that the spectral density of the thermal fluctuations is proportional to temperature T12. The MFFT is most easily used as relative primary thermometer. A single calibration at a known reference temperature is sufficient to determine all parameters in the equation of state.

Figure 1. Schematic of the MFFT. Components of the signal readout exist twice to apply the cross-correlation technique.

In order to operate the MFFT as an absolute primary thermometer (pMFFT), all relevant aspects of the set-up must be calculable, and all parameters involved in the calculation must be known. The first condition requires, among other things, the calculation of eddy currents in the temperature sensor. If possible, simple and analytically solvable models are used for that Opens external link in new window[3]. To fulfill the second condition, all relevant parameters of the pMFFT must be determined. Besides several geometry parameters such as distances or lengths, the electrical conductivity of the temperature sensors belongs to them, too. If these preconditions are met, the pMFFT can be applied as an absolute primary thermometer. This means that the temperature is directly related to value of the Opens internal link in current windowBoltzmann constant. Figures 2 and 3 depict the construction of the pMFFT with detection coils in planar geometry.

Figure 2. Inside view of the pMFFT. Two planar detection coils are arranged on the inner surface of the Si chip.
Figure 3. Sectional view of the pMFFT with one Si chip and two SQUID boards assembled.

The pMFFT offers some additional advantages in practical application. To cover the whole temperature range from 1 mK to 1 K, which corresponds to three orders of magnitude, a single thermometer set-up is sufficient. Based on the construction of the pMFFT, the thermal coupling between the object, the temperature of which is to be measured and the actual temperature sensor (more precisely: the electron gas in the temperature sensor) is efficiently solved. Independent of the measurement principle of a low-temperature thermometer, a weak thermal coupling is often critical as it causes a relative deviation of the measured temperature from its actual value, which becomes larger for lower temperatures. The reason for this is that even the smallest heat inputs to the temperatures sensor, either due to heat conduction through connected leads or dissipation in the sensor, may cause significantly increased temperatures. In that respect, the current pMFFT design is intrinsically less critical than many other low-temperature thermometers.

Present development activities on the pMFFT are aiming to reduce its measurement uncertainty (2015: 0.6%  Opens external link in new window[4]), which is currently determined by the uncertainty a few geometry parameters. Hence, after the redefinition of the kelvin, a primary noise thermometer is available in the range of the PLTS-2000, allowing the direct measurement of thermodynamic temperature. Moreover, PTB is developing a primary noise thermometer for temperatures above the triple point of water. Several departments belonging to the division 7 Temperature and Synchrotron Radiation and division 2 Electricity are involved in this quite demanding project.

References

[1] Fellmuth B, Fischer J, Machin G, Picard S, Steur PPM, Tamura O, White DR, Yoon H. 2016 The kelvin redefinition and its mise en pratique. Phil. Trans. R. Soc. A 374: 20150037. (Opens external link in new windowhttp://dx.doi.org/10.1098/rsta.2015.0037)

[2] Nyquist H. 1928 Thermal agitation of electric charge in conductors. Phys. Rev. 32, 110-113. (Opens external link in new windowhttp://dx.doi.org/10.1103/PhysRev.32.110)

[3] Kirste A, Regin M, Engert J, Drung D, Schurig T. 2014 A calculable and correlation-based magnetic field fluctuation thermometer. J. Phys.: Conf. Ser. 568, 032012. (Opens external link in new windowhttp://dx.doi.org/10.1088/1742-6596/568/3/032012)

[4] Kirste A, Engert J. 2016 A SQUID-based primary noise thermometer for low- temperature metrology. Phil. Trans. R. Soc. A 374: 20150050. (Opens external link in new windowhttp://dx.doi.org/10.1098/rsta.2015.0050)