Behaviour of semiconductor low temperature sensors in electromagnetic environments

The effect of an electromagnetic field, with frequencies in the 30 – 300 MHz range, on semiconductor cryogenic thermometers, eg silicon diode temperature sensors as well as silicon and germanium resistance thermometers, has been investigated at temperatures from 70 to 300 K.The changes in voltage drop or resistance versus temperature characteristics of the tested thermometers for various fixed frequencies of external electromagnetic field have been found. The frequency dependent electromagnetic field behaviour of the thermometers was studied and a resonance character of the ‘error’ ΔT has been evaluated.It has been shown that the semiconductor low temperature sensors may only be used for accurate recalibration in the presence of a well-known, low-intensity EM field at a constantly held frequency not corresponding with the maximum values of ΔT.     

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.     

Low Temperature Thermometry in High Magnetic Fields

The calibration and reproducibilty of various commercial and homemade thermometers have been investigated over a temperature range from 20 mK to 4.2 K and magnetic field strength from 0 to 16 Tesla. The performance of resistance thermometers made of different materials varies widely as a function of magnetic field. One type (Scientific Instruments RO600) is found to have a relatively small magneto-resistance, which is predictable to better than 1% down to 100 mK, making calibration in a magnetic field unnecessary for many applications. This was not true of homemade ruthenium oxide and Cernox (Lakeshore Cryotronics). A new type of sensor, thin film doped germanium on a GaAs substrate, was also investigated and found to be useful at higher fields and low 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.     

Resistance thermometry in magnetic fields 1. Thermistors and platinum thermometers at 77 K

The effects of static magnetic field up to 16 kG on seven midget disc thermistors and three miniature platinum resistance thermometers were measured at 77 K. Corrections for the magnetoresistance of the electrical leads and solder junctions were made from data taken on a copper wire coil. A virtual temperature rise of the order of millikelvins occurs for both temperature sensors; the lead wire correction is less than a few microkelvins. The thermistors have larger magnetoresistance effects than similar types recommended for use at lower temperatures. A figure of merit comparison suggests that they are slightly less desirable than platinum thermometers in magnetic fields at liquid nitrogen temperatures.     

Propagation model and error analysis of an E-field sensor based on pockels effect and waveguide

Electric field measurement sensors based on the crystal Pockels effect are widely used. Currently, the development aims for electric field sensors are mainly focused on miniaturizing and integrating the sensor structure and improving measurement sensitivity and precision. The goal of this study was to analyse the sources of error in Pockels effect electric field measurement sensors, consider the mutual influence and accumulation effect of the various error factors, and establish a basic mathematical model of the measurement system with error components. Calculation and analysis were used to classify the function and change trend of several main errors, providing reference data for the structure design and error compensation of the sensor. The results show that the polarizing angle and the analyser angle have the same influence on assembly error. The inherent error is positively related to the electric field intensity. The periodic accumulation characteristic error under large electric field is also discussed. In order to avoid this error under an intense electric field, a suitable test electric field range was determined.     

Thermometers in Low Magnetic Fields

In this article the effect of low amplitude DC magnetic fields on different types of thermometers is discussed. By means of a precision water-cooled electromagnet, the effect of a magnetic field on platinum resistance thermometers, thermistors, and type T, J, and K thermocouples was investigated, while thermometers were thermally stabilized in thermostatic baths. Four different baths were used for temperatures from 77 K (?196 °C) to 353 K (80 °C): liquid nitrogen bath (nitrogen boiling point at atmospheric pressure), ice-point bath, room-temperature air bath, and hot-water bath. The generated DC magnetic field of high relative precision (2 × 10^?4 at 1 T, 4 × 10^?5 short-term stability) and high relative uniformity (2 × 10^?5 over 1 cm², 10 mm gap) had a magnetic flux density of 1 T in the center of the gap between the magnet pole caps. The results indicate a magnetic effect of up to 100 mK due to a 1 T magnetic field for the types of thermocouples composed of ferromagnetic materials (Fe, Cr, Ni). For platinum resistance thermometers, thermistors, and non-magnetic type T thermocouples, the detected magnetic effect was weaker, i.e., under 10 mK.     

High-dynamic-range magnetometry with a single nuclear spin in diamond

Sensors based on the nitrogen-vacancy defect in diamond are being developed to measure weak magnetic and electric fields at the nanoscale. However, such sensors rely on measurements of a shift in the Lamor frequency of the defect, so an accumulation of quantum phase causes the measurement signal to exhibit a periodic modulation. This means that the measurement time is either restricted to half of one oscillation period, which limits accuracy, or that the magnetic field range must be known in advance. Moreover, the precision increases only slowly (as T(-0.5)) with measurement time T (ref.?3). Here, we implement a quantum phase estimation algorithm on a single nuclear spin in diamond to combine both high sensitivity and high dynamic range. By achieving a scaling of the precision with time to T(-0.85), we improve the sensitivity by a factor of 7.4 for an accessible field range of 16?mT, or, alternatively, we improve the dynamic range by a factor of 130 for a sensitivity of 2.5?μT?Hz(-1/2). Quantum phase estimation algorithms have also recently been implemented using a single electron spin in a nitrogen-vacancy centre. These methods are applicable to a variety of field detection schemes, and do not require quantum entanglement.     

Ge-on-GaAs film resistance thermometers: Low-temperature conduction and magnetoresistance

We investigated and generalized the resistance temperature and magnetic field dependences for various versions of cryogenic resistance thermometers based on Ge films on semi-insulating GaAs substrates. It is shown that, at low temperatures, the conductivity mechanism that is responsible for Ge film heat and magnetic field sensitivity is variable-range hopping (VRH). We found that the exponent x in VRH-type temperature law may take different values (fall between 0.25 and 0.67) for different versions of Ge-on-GaAs film thermometers. The magnetoresistance of Ge films depends strongly on the nature of hopping conductivity. It may be positive and negative as well as high and low. We found that, in the 1.8−4.2 K temperature range studied, the Ge films with x≅0.25 (that corresponds to nonzero constant density of states at the Fermi level) demonstrate high positive magnetoresistance. The films with x > 0.4 (that corresponds to presence of a gap in the density of states at the Fermi level) have negative magnetoresistance component that predominates at magnetic induction up to 3–5 Т. The parameters describing VRH conductivity in the Ge-on-GaAs films thermometers were determined. From practical point of view for thermometry, the possibility to describe the R = f(T) dependence by an analytical equation (VRH-type temperature law) does not require the fitting procedure and makes calibration and thermometry more simple and convenient.     

Operation of the TVO temperature sensors in the range from 4.2 K up to 425 K

The report continues our investigations on cryogenic thermometers. To estimate the influence of warming the well known TVO temperature sensors [Proceedings of the ICEC17 (1998) 699, Cryogenics 41 (2001) 213, Advances in Cryogenic Engineering 45B (2000) 1817, Proceedings of the ICEC18 (2000) 627] up to 425 K on their calibration curve, a series of experiments have been carried out. The number of thermal cycles in the range from 425 K down to 77.3 K was 105. Comparison of readings of the sensors at 293, 77.3 and 4.2 K was performed with initial calibration curves for 100 cycles. Then several sensors were re-calibrated, and a new comparison was done during five additional thermal cycles at the same temperatures. The obtained results are discussed and they seem to be optimistic.     

Search for thermometers with low magnetoresistive effects: platinum-cobalt alloy

Measurements performed on thermometers made of dilute ferromagnetic alloys of Pt with 0.45, 0.50, 0.75, 1.06 and 2.15 at% Co, in the temperature range 2–28 K and in magnetic fields up to 6 T showed a large region of negative magnetoresistivity that limits the magnetic error at low temperatures and field values. With 0.5 at% Co or less, the change of the magnetic error with T and B was smooth, while a magnetic transition has been observed with higher cobalt concentrations. Curie temperature has been found to occur at 6.0 K, 14.2 K and, by extrapolation, 32 K for alloys with 0.75, 1.06, and 2.15 at%Co respectively. The transition resulted in a second order discontinuity of the R-T characteristics at B = 0 and B = 3.8 ± 0.2 T with 0.75 at%Co and 8.0 ± 0.5 T with 1.06 at%Co, while for other field values the discontinuity was first-order. Hence, this alloy can be used for thermometry only with very low cobalt concentrations: with 0.3 at%Co it would be possible to limit the magnetic error within ±0.2 K up to 2 T and done to 5 K.     

New Evaluation of $$T-T_{2000}$$ from 0.02 K to 1 K by Independent Thermodynamic Methods

This paper reports on the results achieved within the European Metrology Research Programme project “Implementing the new kelvin—InK” in the low-temperature range below 1 K. One of the main objectives of the InK project was the determination of new thermodynamic temperature data for comparison with the Provisional Low Temperature Scale 2000 (PLTS-2000), to provide reliable \(T-T_{2000}\) values. To this end, we have investigated three different types of primary thermometers: the current sensing noise thermometer, the primary magnetic field fluctuation thermometer and the Coulomb blockade thermometer. Based on a thorough investigation of the thermometers, detailed uncertainty budgets were established for the measurement of thermodynamic temperatures. Direct comparison measurements between all thermometers demonstrate the agreement of temperature measurements within less than 1 %. Our new \(T-T_{2000}\) data confirm the correctness of the PLTS-2000 in the temperature range from 20 mK up to about 700 mK with relative combined standard uncertainties better than 0.62 %.     

Generalized far-infrared magneto-optic ellipsometry for semiconductor layer structures: determination of free-carrier effective-mass,mobility, and concentration parameters in n-type GaAs

We report for the first time on the application of generalized ellipsometry at far-infrared wavelengths (wave numbers from 150 cm(-1) to 600 cm(-1)) for measurement of the anisotropic dielectric response of doped polar semiconductors in layered structures within an external magnetic field. Upon determination of normalized Mueller matrix elements and subsequent derivation of the normalized complex Jones reflection matrix r of an n-type doped GaAs substrate covered by a highly resistive GaAs layer, the spectral dependence of the room-temperature magneto-optic dielectric function tensor of n-type GaAs with free-electron concentration of 1.6 x 10(18) cm(-3) at the magnetic field strength of 2.3 T is obtained on a wavelength-by-wavelength basis. These data are in excellent agreement with values predicted by the Drude model. From the magneto-optic generalized ellipsometry measurements of the layered structure, the free-carrier concentration, their optical mobility, the effective-mass parameters, and the sign of the charge carriers can be determined independently, which will be demonstrated. We propose magneto-optic generalized ellipsometry as a novel approach for exploration of free-carrier parameters in complex organic or inorganic semiconducting material heterostructures, regardless of the anisotropic properties of the individual constituents.     

On the possible use of a commercial Penning gauge as a magnetic field sensor

Penning sensors were originally conceived to extend the measurement range of cold-cathode gauges in the direction of low pressures by introducing an additional constant magnetic field. This paper examines the possibility of using a commercially available sensor to measure magnetic field by keeping pressure constant. For the preliminary tests reported, a commercial Penning gauge was exposed to magnetic fields in the range of a few tens of mT to 1.1 T. Three different regimes were identified. In the first, up to 150 mT, the measured current increases linearly with the applied magnetic field. Following a very irregular transition region of the order of 50 mT, for fields between 200 mT and 1.1 T, the measured current decays relatively smoothly. The results suggest that the principle may be applicable for the measurement of steady-state fields in harsh environments, with high temperature and neutron fluence.     

Interpolation Errors in Thermistor Calibration Equations

Thermistors are widely used temperature sensors capable of measurement uncertainties approaching those of standard platinum resistance thermometers. However, the extreme nonlinearity of thermistors means that complicated calibration equations are required to minimize the effects of interpolation errors and achieve low uncertainties. This study investigates the magnitude of interpolation errors as a function of temperature range and the number of terms in the calibration equation. Approximation theory is used to derive an expression for the interpolation error and indicates that the temperature range and the number of terms in the calibration equation are the key influence variables. Numerical experiments based on published resistance–temperature data confirm these conclusions and additionally give guidelines on the maximum and minimum interpolation error likely to occur for a given temperature range and number of terms in the calibration equation.     

A weak magnetic field measurement system using micro-fluxgate sensors and delta-sigma interface

This paper presents a weak magnetic field measurement system using micro-fluxgate (FG) sensors and a sensor signal processing technique using the delta-sigma modulation in the negative feedback loop. The feedback of the lowpass filtered bitstream output of a delta-sigma modulator to the magnetic field improves system linearity, hysteresis, and stability. In spite of the fact that the second-order delta-sigma modulator is used, the third-order noise shaping can be obtained in the digital output bit-stream by the use of an integrator in the loop. This improves the SNR of the digital output. The measured noise of the implemented system meets the measured noise of the FG sensing element itself. The weak magnetic field in the range of the Earth's magnetic field is successfully measured. The nonlinearity error is less than 0.4% in the range of /spl plusmn/100 /spl mu/T.     

The use of industrial-grade platinum resistance thermometers between 77 K and 273 K

The stability and interpolation characteristics of some industrial-grade platinum resistance thermometers have been investigated between 77 K and 273 K. Seven sensors were thermally cycled many times between 77 K and 373 K and were found to suffer reversible changes in ice-point resistance. After some tens of cycles between 77 K and 273 K the ice-point resistances of the thermometers stabilised to within a few milliohms, provided that the thermometers were not heated above 300 K. A two-point calibration method for these thermometers is described. Using resistance values at the ice-point and the oxygen boiling point, a measurement accuracy of 35 mK can be obtained over the range 77 K to 273 K. Interpolation data for 27 thermometers are given.     

Behaviour and accurate thermometry of carbon-glass resistance thermometers at low temperatures and in magnetic fields up to 7 T

The behaviour of carbon-glass resistance thermometers over a temperature range of 3.41-20 K and in magnetic fields of up to 7 T are investigated. It is shown that the percentage changes in resistance due to the application of a magnetic field, as a function of both temperature and field strength, can be described by the equation 100ΔR/R_o = [(1/T) − (1/20)] (AH² + BH). Using this equation, the temperature errors due to magneto resistance can be corrected to within 20 mK.     

Calibration of Industrial Platinum Resistance Thermometers up to 700\,^{\circ }\mathrm{C}

Industrial grade platinum resistance thermometers were calibrated in the temperature range from \(200\,^{\circ }\mathrm{C}\) to \(700\,^{\circ }\mathrm{C}\) . Both wire-wound and thin-film sensor-based thermometers were investigated. The purpose of the study was to investigate thermometers which could be used in future coal power plants. The calibrations were performed in a vertical cesium heat-pipe furnace and in a horizontal and vertical sodium heat-pipe furnace. The reference thermometer was a standard platinum resistance thermometer calibrated at fixed points up to the aluminum point. In addition to calibration, various thermal tests including immersion measurements and thermal-cycling tests were performed. The stability of the sensors was determined by monitoring the ice-point resistance. Possible contamination of the sensors was determined by measuring the resistance ratio \(R(30\,^{\circ }\mathrm{C})/R(10\,^{\circ }\mathrm{C})\) several times during the measurement period. The calibration curves were compared with the ICE 60751 standard and International Temperature Scale 1990 (ITS-90) reference functions. Considerable changes were found in all tested thermometers. The wire-wound sensors were more stable than the thin-film sensors.