Some comments on carbon resistance thermometry below 1 K

Several aspects of carbon thermometry below 1 K are discussed. Some calibrations, performed on home-made carbon resistors, are presented. The lowest reliable calibration temperature was 25 mK. The reproducibility after thermal cycling of these resistors appeared to be good. Comments are given on our measurements, and also on those of others. It is very probable that the thermal resistance between the spin system and the lattice of the cooling salt is in many cases the main obstacle to the attainment of a low resistor temperature.     

Thermometry using 18 W carbon resistors in a temperature region around 10 mK

The resistance-temperature characteristics of $\text{1}\text{8}$ W carbon resistors of grade ERC-18SG, manufactured by Matsushita, with the nominal values of 48, 82, 100, 220, and 330 Ω have been measured in the region 4.2 K-25 mK and their application as thermometers in this region is confirmed. For the 82 Ω resistor, measurements were taken at temperatures below 10 mK. The temperature dependence of the resistance was found to be linear on the log-log plot over a wide range below 50 mK. The sensitivity remains finite even at 6 mK, but below 10 mK rapid measurements were prevented by a considerable increase in the thermal relaxation time. Measurement of the characteristics of several 100 Ω resistors from two different sets showed that resistors from the same set separate into two groups with different characteristics. This becomes appreciable at temperatures below 4.2 K, so it is difficult to predict the behaviour of Matsushita resistors below 4.2 K from the characteristics at higher temperatures.     

Time response and thermal diffusivity of carbon resistance thermometers

The time response of several carbon resistance thermometers has been measured in the liquid helium temperature range. The results are compared to the theoretical analysis of Komatsu and are found to be in fair agreement. The data indicate that carbon resistors have an intrinsic time response of the order of milliseconds. However, this probably would be increased considerably due to contact resistance if the resistor were coupled to a solid surface.     

Transport behavior of commercially available 100-Ω standardresistors

Several types of commercial 100-Ω resistors can be used with the cryogenic current comparator to maintain the resistance unit, derived from the quantized Hall effect (QHE), and to disseminate this unit to laboratory resistance standards. Up until now, the transport behavior of these resistors has not been investigated. Such an investigation is of importance for carrying out comparisons that are close to the level of a direct comparison of two QHE apparatuses. A set of five 100-Ω resistors from three different manufacturers has been sent to 11 participating national metrological institutes. All laboratories but one have measured the resistors based on their laboratory's quantized Hall resistance measurements. A constant drift model has been applied, and the results are evaluated in such a way that the transport properties of these resistors are treated independently for the different types of resistor. Under certain conditions, these resistors allow comparisons with uncertainties better than 1 part in 10 ⁸     

A Direct Current Comparator Bridge for High Resistance Measurements

A dc comparator bridge, which is suitable for measuring resistors from a fraction of an ohm to several megohms with partper-million accuracy or better is described. An analysis of errors which may occur when measuring high-value resistors and methods used for reducing these errors to negligible proportions are included. The bridge can be connected to make either four-terminal or three-terminal measurements. The four-terminal connection is best for measuring low-value resistors. When it was used for measuring high-value resistors, a systematic bridge error was detected, which was found to be primarily due to leakage paths through the insulation, permitting current to bypass one of the measured resistors. This error is avoided by using the three-terminal connection for measuring high-value resistors. The leakage resistance is then in parallel with a low resistance winding rather than one of the measured resistors. The bridge has automatic reversal and a chart recorder output, which continuously indicates the deviation from the set point. The comparator is adjustable in steps of 10-' of full scale, and measurements can be made at ratios up to 11.111/1.     

Electronic Transport Properties of Speer Carbon Resistors—Experimental Results and Semi-empirical Fits

Speer carbon composition resistors, in particular the 470 and 220 1/2 W grade 1002 resistors, have been used as secondary thermometers at temperatures below 4 K for many years. Their zero field resistances have been measured between 300 K and 4 K using a dip probe. Above 10 K, the resistance behavior can be explained using a simple temperature power law, R(T) R₀/T^0.16. The resistance measurements have been extended to 0.02 K using dilution refrigerators. Between 4 K and 0.3 K, the resistances exhibited activated laws having hopping exponents y 0.5. Below 0.3 K, the 470 resistors exhibit a crossover to a weaker activated law. Crossover resistance expressions suggest that the resistances follow a Mott variable-range hopping (VRH) law below 0.05 K. The low temperature magnetoresistance (MR) data showed changes of less than ±12 % of the zero field resistance values in fields up to 10 T. Fits using the wave function shrinkage and the forward interference models gave only fair agreement with the MR data.     

Thick film resistors in low-temperature resistance thermometry in high magnetic fields

Thick film resistors exhibit a strong dependence on temperature in the cryogenic range below 20 K. In this range the temperature coefficient of resistance is estimated to be comparable to that of commonly used resistance thermometers.The resistance change by the action of the magnetic field is observed to be only small and independent of magnetic field direction. By using these resistors in cryogenic resistance thermometry in intense magnetic field the temperature error due to the magnetoresistance is shown to be only small in comparison with frequently used sensors.According to these results thick film resistors are reported to offer an interesting alternative in cryogenic resistance thermometry within intense magnetic fields.     

Improved thermal contact to unmodified carbon resistors

A technique for making improved thermal contact to unmodified carbon resistors is described. High sensitivity and good reproductibility of Speer resistors are observed down to a minimum temperature of 6 mK. We find that different thermal grounding techniques change the temperature calibration of the same resistor below 0.1 K.     

Study the Performance of the AC/DC Resistors During Their DC and AC Measurements

Some of traceability chains for the AC resistance measurements are based on AC/DC resistors. In this paper, performance of two types of them with different values has been investigated for their optimum utilization. Tinsley and Cambridge AC/DC resistors have been measured as DC resistors using different measurement methods and as AC resistors at various frequencies. DC direct method using digital reference multimeter is more accurate for the resistance values 1, 10, 100 Ω, and 1 kΩ. For the values 10 and 100 kΩ; measurement results are very near by using the DC direct and ratio methods. At 100 kΩ; representation of the resistance as an equivalent series resistance is not suitable at frequencies above 10 kHz, while for 100 mΩ and 1 Ω; the equivalent parallel representation is not suitable above the same frequency. The uncertainty analysis is also studied for all the obtained results.     

Low-temperature characteristics of Matsushita carbon resistors with and without magnetic fields

The resistance versus temperature (RT) characteristics and magnetoresistance (MR) of 1/8 W nominal 68 Ω and 100 Ω Matsushita carbon resistors of grade ERC-18SG have been measured at temperatures between 8 and 0.05 K, in magnetic fields up to 84kOe (84 × 10⁶/4 π Am⁻¹). In both carbon resistors, the RT behaviour is expressed as R(T) = R₂exp{(T₂/T)^1/2} in the high temperature region and as R(T) = R₄exp{(T₄/T)^1/4} in the low temperature region. These relationships are explained as due to variable-range hopping conduction with and without the changing energy between isolated metallic grains, respectively. Negative and positive MR's have been observed in low and high magnetic fields, respectively. The negative MR increases with decreasing temperature at very low temperatures < 0.1 K. These phenomena are discussed in terms of the theory based on the strong Anderson localization.     

The Accuracy of Series and Parallel Connections of Four-Terminal Resistors

The range and accuracy of resistance calibration can be increased by the use of series and parallel connections of four-terminal resistors. Low value resistors can be permanently connected in series and reconnected in parallel by using Hamon's1 technique to change resistance level without materially affecting resistance accuracy. The resistors are connected in parallel by attaching shorting bars to one terminal at each end of each resistor and attaching matched resistors in series with the other terminals. High accuracy can be attained even though lead and connection resistance are relatively high. The purpose of this paper is to provide a theoretical base and an error analysis to justify the use of the series-to-parallel transfer technique at low resistance levels. The analysis uses a four-terminal equivalent circuit suggested by Searle.2 The accuracy of series and parallel connections of groups of like resistors is investigated in terms of the equivalent circuit. Procedures are developed for determining the connection accuracy of a set of resistors in parallel or series.     

Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices

Many ac quantized Hall resistance experiments have measured significant values of ac longitudinal resistances under temperature and magnetic field conditions in which the dc longitudinal resistance values were negligible. We investigate the effect of non-vanishing ac longitudinal resistances on measurements of the quantized Hall resistances by analyzing equivalent circuits of quantized Hall effect resistors. These circuits are based on ones reported previously for dc quantized Hall resistors, but use additional resistors to represent longitudinal resistances. For simplification, no capacitances or inductances are included in the circuits. The analysis is performed for many combinations of multi-series connections to quantum Hall effect devices. The exact algebraic solutions for the quantized Hall resistances under these conditions of finite ac longitudinal resistances provide corrections to the measured quantized Hall resistances, but these corrections do not account for the frequency dependences of the ac quantized Hall resistances reported in the literature.     

Sputtered Ni-Cr-based resistors terminated on sputtered aluminum and screeen-printed Pt-Ag conductors

The standard technology to fabricate thin film resistors is to deposit a layer of resistive material, usually by evaporation or sputtering, followed by thin layers of nickel and gold. Gold plating is then used to augment the thickness of the gold layer, typically to 1 μm. The three-layer structure is then selectively etched to yield resistors with terminations suitable for wire bonding and soldering. We have used a somewhat unconventional approach in which a film 1–2 μm thick of aluminum is first sputtered onto 99.5% Al₂O₃ substrates, then etched to produce the desired conductor pattern. Isotropic (wet) etching is used to produce sloping edges to contact better the Ni-Cr based resistor material which is sputter deposited and patterned using a lift-off technique.We have also combined the thin and thick film technologies by terminating our thin film resistors on Pt-Ag conductors which are screen printed onto the substrate prior to sputter deposition of the resistors.Aluminum terminations can be wire bonded, or, when soldering is required, coated with sputtered or plated nickel. When a layer of suitable adhesion promoter is sputtered between aluminum and nickel, adhesion of aluminum to nickel is greatly improved.The use of a sputtering target made of an Ni-Cr-based alloy has enabled us to obtain resistors in the 50 Ω/□ range which can be mass produced with near-zero temperature coefficient of resistance (TCR). Such resistors show stability within better than 0.02% after 1000 h at 398 K under load. Also reported are resistance spread and shift, due to annealing, as a function of aspect ratio (ratio between length and width of resistor) for both aluminum and Pt-Ag terminations, as well as TCR as a function of annealing temperature.     

On the stability of carbon glass thermometers cycled at low temperatures under high magnetic fields

We report on the reliability of three carbon glass thermometers used in the temperature range 4.2 K – 50 K under high magnetic field conditions.In two of the three sensors we observed a serious lack of reproducibility (1.5 K at 25 K). These results indicate that in experiments requiring precise temperature measurements in the range 20 – 30 K, it is necessary to perform regular calibrations of carbon glass thermometers versus secondary standards such as platinum or germanium resistors.     

Thermal boundary resistance between the end of an individual carbon nanotube and a Au surface

The thermal boundary resistance between an individual carbon nanotube and a Au surface was measured using a microfabricated hot-film sensor. We used both closed and open-ended multi-walled carbon nanotubes and obtained thermal boundary resistance values of 0.947-1.22 × 10(7) K W(-1) and 1.43-1.76 × 10(7) K W(-1), respectively. Considering all uncertainties, including the contact area, the thermal boundary conductances per unit area were calculated to be 8.6 × 10(7)-2.2 × 10(8) W m(-2) K(-1) for c-axis orientation and 4.2 × 10(8)-1.2 × 10(9) W m(-2) K(-1) for the a-axis. The trend in these values agrees with the predicted conductance dependence on the interface orientation of anisotropic carbon-based materials. However, the measured thermal boundary conductances are found to be much larger than the reported results.     

Evaluation of the frequency dependence of the resistance and capacitance standards in the BIPM quadrature bridge

The Bureau International des Poids et Mesures (BIPM) has established a measurement chain allowing calibration of capacitance standards in terms of the quantized Hall resistance (QHR). An important element in the chain is a quadrature bridge linking a pair of ac resistors of values 2R/sub K/ /spl ap/ 51.6 k/spl Omega/ to a pair of capacitance standards. The quadrature bridge can be operated at five different frequencies: 513, 1027, 1541, 3082, and 6164 Hz. For such measurements, we use different ratios (1/1, 4/1 and 1/4) for the main inductive voltage divider in the quadrature bridge and three different pairs of capacitors of values 3000, 2000, and 1000 pF. A calculable coaxial resistance of 1290.6 /spl Omega/ (R/sub K//20) is used as a reference to evaluate the frequency dependence of the 51.6-k/spl Omega/ resistances. This allows the calibration of capacitance standards at the five different frequencies. The measured frequency dependences of 10 and 100 pF capacitance standards are reported.     

Determining the Temperature Coefficient of Reference Resistors

The influence of temperature on electrical resistance of standard resistors is presented within this paper. Electrical resistance is like any other quantity temperature dependent. This dependence is specified with the temperature coefficient, which gives the relative change of resistance with temperature. The level of resistance change is not linear as it changes with temperature, and therefore the coefficient is temperature dependent as well. At a certain temperature, its value is equal to zero—the stationary point. Use of the standard resistor at this exact temperature or in a narrow interval around it greatly reduces the influence of temperature on electrical resistance, even if the thermal conditions are not optimal. Measurements of temperature coefficient were taken on a group of standard resistors of the same type in a wide temperature range, and the temperature of the stationary point was determined. Measurements were taken by placing the resistors in an oil bath and changing its set point temperature from 18 \({^{\circ }}\hbox {C}\) to 38 \({^{\circ }}\hbox {C}\). Electrical resistance of each resistor was measured using a resistance bridge, which had its reference resistor placed in a separate thermal enclosure at a constant temperature.     

Increased Accuracy for Resistance Measurements

The effect of power dissipation on the performance of four-terminal standard resistors has been investigated, using the direct-current-comparator ratio bridge. A theoretical analysis of a typical standard resistor has also been made, which indicates that the average temperature increase of the resistance wire in an oil-filled resistor is approximated by T - T = RI2[6(1-e0.001t)+1] and that the Peltier effect at the copper-manganin junctions may contribute errors of 1 to 10 parts per million of resistance for the lower-valued resistors. Recommendations are made for design and construction changes in standard resistors, which will improve the accuracy with which they may be used.     

Measuring Systems for Thermometer Calibration in Low-Temperature Range

The national temperature standard for the low-temperature range between 13.8033 K and 273.16 K has been established in Poland at the Institute of Low Temperature and Structure Research (INTiBS). The standard consists of sealed cells for realization of six fixed points of the International Temperature Scale of 1990 (ITS-90) in the low-temperature range, an adiabatic cryostat and Isotech water and mercury triple-point baths, capsule standard resistance thermometers (CSPRT), and AC and DC bridges with standard resistors for thermometers resistance measurements. INTiBS calibrates CSPRTs at the low-temperature fixed points with uncertainties less than 1 mK. In lower temperature range??between 2.5 K and about 25 K ?? rhodium?Ciron (RhFe) resistance thermometers are calibrated by comparison with a standard which participated in the EURAMET.T-K1.1 comparison. INTiBS offers a calibration service for industrial platinum resistance thermometers and for digital thermometers between 77 K and 273 K. These types of thermometers may be calibrated at INTiBS also in a higher temperature range up to 550°C. The Laboratory of Temperature Standard at INTiBS acquired an accreditation from the Polish Centre for Accreditation. A management system according to EN ISO/IEC 17025:2005 was established at the Laboratory and presented on EURAMET QSM Forum.     

Linear frequency dependence in AC resistance measurement

The frequency dependence of AC resistors as well as the AC quantum Hall resistance shows sometimes unexpected linear terms of the order of 1/spl middot/10/sup -7/ kHz/sup -1/. Three reasons for measuring linear terms are identified as systematic effects of the coaxial bridge and the compared resistors.