Johnson Noise Thermometry Research Articles

Low-Temperature Thermal Transport Characteristics in Epitaxial Bilayer Graphene Microbridges.

In this paper, we present a study of the thermal transport of epitaxial bilayer graphene microbridges. The thermal conductance of three graphene microbridges with different lengths was measured at different temperatures using Johnson noise thermometry. We find that with the decrease of the temperature, the thermal transport in the graphene microbridges switches from electron-phonon coupling to electron diffusion, and the switching temperature is dependent on the length of the microbridge, which is in good agreement with the simulation based on a distributed hot-spot model. Moreover, the electron-phonon thermal conductance has a temperature power law of T3 as predicted for pristine graphene and the electron-phonon coupling coefficient σep is found to be approximately 0.18 W/(m2 K4), corresponding to a deformation potential D of 55 eV. In addition, the electron diffusion in the graphene microbridges adheres to the Wiedemann-Franz law, requiring no corrections to the Lorentz number.

Infrared photodetection in graphene-based heterostructures: bolometric and thermoelectric effects at the tunneling barrier

Graphene/hBN/graphene tunnel devices offer promise as sensitive mid-infrared photodetectors but the microscopic origin underlying the photoresponse in them remains elusive. In this work, we investigated the photocurrent generation in graphene/hBN/graphene tunnel structures with localized defect states under mid-IR illumination. We demonstrate that the photocurrent in these devices is proportional to the second derivative of the tunnel current with respect to the bias voltage, peaking during tunneling through the hBN impurity level. We revealed that the origin of the photocurrent generation lies in the change of the tunneling probability upon radiation-induced electron heating in graphene layers, in agreement with the theoretical model that we developed. Finally, we show that at a finite bias voltage, the photocurrent is proportional to either of the graphene layers heating under the illumination, while at zero bias, it is proportional to the heating difference. Thus, the photocurrent in such devices can be used for accurate measurements of the electronic temperature, providing a convenient alternative to Johnson noise thermometry.

Probing THz intersubband absorption using Johnson noise thermometry

Abstract We investigate the THz intersubband absorption behavior of a single 40-nm wide GaAs/AlGaAs square quantum well (QW) using Johnson noise thermometry. In our measurements, the Johnson noise associated with intersubband absorption is measured from the in-plane conduction channel of the QW while its intersubband absorption behavior is being tuned through the independent control of the charge density and the perpendicular DC electric field. Our measurements enable the study of intersubband absorption of a small (∼20,000 and potentially fewer) number of electrons in a single mesoscopic device, as well as direct measurement of the electron heating from intersubband absorption. By measuring the Johnson noise response to monochromatic THz radiation at 2.52 THz and 4.25 THz at 20 K as a function of the DC electric field over a wide range of charge density, we show that the observed Johnson noise behavior correlates well with the expected intersubband absorption of the 40-nm QW. To explain the absorption features of the experimental results, we model the data by calculating the THz coupling efficiency based on the impedance model for intersubband absorption, which qualitatively reproduces the observed Johnson noise behavior well. Based on the temperature calibration of the Johnson noise measured at 2.52 THz, we deduce an increase in the electron temperature ΔT e of ∼ 35 ${\sim} 35$ K when the maximum absorption of THz power occurs in the device.

Current Noise of Hydrodynamic Electrons.

A resistor at finite temperature produces white noise fluctuations of the current called Johnson-Nyquist noise. Measuring the amplitude of this noise provides a powerful primary thermometry technique to access the electron temperature. In practical situations, however, one needs to generalize the Johnson-Nyquist theorem to handle spatially inhomogeneous temperature profiles. Recent work provided such a generalization for Ohmic devices obeying the Wiedemann-Franz law, but there is a need to provide a similar generalization for hydrodynamic electron systems, since hydrodynamic electrons provide unusual sensitivity for Johnson noise thermometry but they do not admit a local conductivity nor obey the Wiedemann-Franz law. Here we address this need by considering low-frequency Johnson noise in the hydrodynamic setting for a rectangular geometry. Unlike in the Ohmic setting, we find that the Johnson noise is geometry dependent due to nonlocal viscous gradients. Nonetheless, ignoring the geometric correction only leads to an error of at most 40% as compared to naively using the Ohmic result.

Step-Change Improvements in Traceable Process Control Thermometry

Measurement and control of process temperature is key to maximising product quality, optimising efficiency, reducing waste, safety and minimising carbon dioxide and other harmful emissions. Drift of temperature sensor calibration due to environmental factors such as high temperature, vibration, contamination and ionising radiation results in a progressively worsening temperature measurement error, which in turn results in suboptimal processes. Here we outline some new developments to overcome sensor calibration drift and so provide assured temperature measurement in process, including self-validating thermocouples, embedded temperature reference standards, and practical primary Johnson noise thermometry where the temperature is measured directly without the need for any calibration. These new developments will give measurement assurance by either providing measurements which are inherently stable, or by providing an in situ calibration facility to enable the detection and correction of calibration drift.

Probing the charge and heat transfer channels in optically excited graphene — transition metal dichalcogenide hybrids using Johnson noise thermometry

Graphene (Gr)–transition metal dichalcogenide (TMDC) hybrids are promising platforms for achieving sensitive and ultra-fast photodetection. The process of photo-detection in such van der Waals hybrids is usually dictated by the formation of excitons followed by the transfer of charge and energy from the TMDC layer to graphene, but they have not been explored simultaneously in the same device before. In this work, we have investigated optically excited Gr–WS2 (tungsten disulfide) heterostructures using both standard electrical transport and Johnson noise thermometry. At large negative gate voltages, the experimentally observed photoresponse cannot be explained from conventional photogating but was found to host an increase in electron temperature as large as ∼4 K. Time dependence of the transport and the noise reveals that the change in temperature and photoresistance can originate from distinct microscopic processes. The findings can be exploited for the development of Gr–TMDC based ultra-fast bolometers.

Thermal noise of hot carriers under natural sunlight

The efficiency of hot carrier solar cells strongly depends on the attainable carrier temperature in the absorber material. Measurements of hot carrier temperature under natural concentrated sunlight were performed at thin films of graphite, bismuth and PbTe, cooled through AlN ceramic substrate. The carrier temperature was assessed by magnitude of thermal noise voltage of charge carriers in the frequency range between 300 and 20,000 Hz according to Nyquist formula. Noise measurement equipment was calibrated in a range of sample impedances by using heated metal film resistors. We found that the carrier temperature in graphite films can exceed 600 °C under up to 15,000× suns and is much higher than the estimated lattice temperature in the film under the given cooling conditions. Secondary electron micrographs illustrate a good mechanical contact between the graphite film and the AlN substrate. We found also distinct heating of charge carriers in PbTe up to about 100 °C. Contrary to that, no measurable carrier heating above the lattice temperature was detected in bismuth films. Johnson noise thermometry demonstrates potential in identification of attractive candidate materials for absorbers in hot carrier solar cells.

Dual-mode auto-calibrating resistance thermometer: A novel approach with Johnson noise thermometry.

A dual-mode auto-calibrating resistance thermometer (DART) is presented. The novel DART concept combines in one instrument the fast and accurate resistance thermometry with the primary method of Johnson noise thermometry. Unlike previous approaches, the new thermometer measures the spectral density of the thermal noise in the sensing resistor directly in a sequential measurement procedure without using correlation techniques. A sophisticated data analysis corrects the thermometer output for both the parasitic effects of the sensor wiring and the amplifier current noise. The instrument features a highly linear low-noise DC coupled amplifier with negative feedback as well as an accurate voltage reference and reference resistor to improve the gain stability over time and ambient temperature. Therefore, the system needs only infrequent calibrations with electrical quantum standards and can be operated over long intervals and a wide temperature range without recalibration. A first prototype is designed for the industrially relevant temperature range of the IEC 60751 (-200 °C to +850 °C); a later extension of the measurement range is being considered. A proof-of-principle measurement with a calibrated Pt100 sensor at room temperature yielded an uncertainty of about 100 µK/K. The final device is expected to reach uncertainties of below 10 µK/K, suitable for accurate measurements of the difference between thermodynamic temperatures and temperatures traceable to the International Temperature Scale of 1990 (ITS-90).

Demonstration of a high-sensitivity and wide-dynamic-range terahertz graphene hot-electron bolometer with Johnson noise thermometry

Graphene hot-electron bolometer (HEB) detectors, with weak electron–phonon interaction and a wide working temperature range, are of particular interest for terahertz (THz) applications including astronomy. In this paper, we report on the performance of a zero-biased THz HEB detector using Johnson noise thermometry based on bilayer graphene (BLG) of high charge carrier density. Two BLG HEB devices with respective normal-metal and superconducting electrodes are compared particularly for their thermal conductance and detection sensitivity (noise equivalent power, NEP) in a low-temperature regime (0.3–10 K). With electron out-diffusion largely suppressed by Andreev reflection, the device with superconducting electrodes outperforms the device with normal-metal electrodes, giving an electrical NEP of 15 fW/Hz0.5 and a dynamic range of 47 dB at 0.3 K. Moreover, its optical coupling efficiency is found to be 58% and can reach as high as 92% with the optical losses of the measurement system calibrated out. Graphene detectors of this kind can achieve better detection performance given lower readout noise and decreased electron–phonon thermal conductance.

High-bandwidth, variable-resistance differential noise thermometry.

We have developed Johnson noise thermometry applicable to mesoscopic devices with variable source impedance with high bandwidth for fast data acquisition. By implementing differential noise measurement and two-stage impedance matching, we demonstrate noise measurement in the frequency range of 120 MHz-250MHz with a wide sample resistance range of 30 Ω-100kΩ tuned by gate voltages and temperature. We employed high-frequency, single-ended low noise amplifiers maintained at a constant cryogenic temperature in order to maintain the desired low noise temperature. We have achieved thermometer calibration with temperature precision up to 650 μK measuring a 200 mK temperature modulation on a 10K background with 30s of averaging. Using this differential noise thermometry technique, we measured thermal conductivity on a bilayer graphene sample spanning the metallic and semiconducting regimes in a wide resistance range, and we compared it to the electrical conductivity.

An Integrated Circuit Solution to Johnson Noise Thermometry Using Low-Cost and Fast CMOS Technology

An integrated circuit solution to Johnson noise thermometry (ICJNT) using a low-cost and fast complementary metal–oxide–semiconductor (CMOS) technology is investigated in this paper. Benefits from both noise thermometry and integrated circuits (ICs) can be maintained in ICJNTs, which cost significantly less, work orders of magnitude faster than discrete-device JNTs, and can be applied to various applications. As a first attempt at an ICJNT, this paper presents the relevant analysis and design techniques, demonstrates the potential benefits of ICJNTs, and discusses the challenges unique to integrated circuit solutions. A prototype IC chip is fabricated using the 0.13- $\mu \text{m}$ CMOS technology with fully on-chip circuits, including sensing resistors, a pre-amplifier, and a flash analog-to-digital converter. To demonstrate the efficacy, a test PCB for the ICJNT was developed and measured in a standard industrial thermal chamber with a laboratory grade platinum resistance thermometer as a comparison reference. The test results show that this first ICJNT prototype is able to provide temperature measurement from 0 °C to 70 °C. The maximum deviation with two-point calibration is 1.2 °C at a measurement of 40 °C due to systematic error, and the standard deviation is approximately 2 °C. The measurement time is only 10 ms due to the fast IC technology. These results established the feasibility of the ICJNT concept. Since the ICJNT is a complete solution without discrete devices and the sensing resistors are not limited to specific IC materials, the ICJNT can be applied to various emerging applications, such as electric vehicles and microelectromechanical systems.

Determinations of the Boltzmann constant

Abstract We review measurements of the Boltzmann constant, k, the value of which is soon to be fixed at exactly 1.380 649 × 10 − 23 J⋅K−1 for the future revised Systeme international of units. In addition to a description of the theoretical background and of diverse experimental techniques (acoustic thermometry, Johnson noise thermometry, dielectric constant gas thermometry, and Doppler broadened molecular spectroscopy), the article highlights the decisive role of ab initio calculations of the thermophysical properties of gases, especially helium-4. Perspectives for improvements in thermometry are outlined in the wake of the new definition.

Experimental Investigation of a Johnson Noise Thermometry Using GMR Sensor for Electric Vehicle Applications

A new temperature measurement method using a giant magnetoresistance (GMR) sensor based on Johnson noise thermometry (JNT) is proposed in this paper. This paper presents the principle of this GMR-based JNT and demonstrates its feasibility by measuring power spectral density of noise voltage in the bandwidth from 10 kHz to 22.8 kHz and resistance of GMR sensor and analyzing their relationship with the absolute temperature. The measuring errors throughout the measurement of temperature from −40 °C and 150 °C in the thermal chamber were less than ±1.8 °C with integration time of 58.6 s. Its dynamic sensing performance under both varying temperature and changing external magnetic field was characterized and demonstrated. A practical demonstration of the GMR-based JNT for measurement of surface temperature of a battery pack on an electric-vehicle testbed was also provided. Therefore, it is feasible to implement this new thermometry with a GMR sensor, making spintronic sensor multifunctional in EV applications by being a temperature sensor as well.

A Novel Technique Applying Spectral Estimation to Johnson Noise Thermometry

Johnson noise thermometry is one of many important measurement techniques used to monitor the safety levels and stability in a nuclear reactor. However, this measurement is very dependent on the minimal electromagnetic environment. Properly removing unwanted electromagnetic interference (EMI) is critical for accurate drift-free temperature measurements. The two techniques developed by Oak Ridge National Laboratory (ORNL) to remove transient and periodic EMI are briefly discussed in this paper. Spectral estimation is a key component in the signal processing algorithm used for EMI removal and temperature calculation. The cross-power spectral density is a key component in the Johnson noise temperature computation. Applying either technique requires the simple addition of electronics and signal processing to existing resistive thermometers. With minimal installation changes, the system discussed here can be installed on existing nuclear power plants. The Johnson noise system developed is tested at three locations: ORNL, Sandia National Laboratory, and the Tennessee Valley Authority’s Kingston Fossil Plant. Each of these locations enabled improvement on the EMI removal algorithm. The conclusions made from the results at each of these locations is discussed, as well as possible future work.

The NIST Johnson Noise Thermometry System for the Determination of the Boltzmann Constant.

In preparation for the redefinition of the International System of Units (SI), five different electronic measurements of the Boltzmann constant have been performed using different Johnson noise thermometry (JNT) systems over the past seven years. In this paper, we describe in detail the JNT system and uncertainty components associated with the most recent National Institute of Standards and Technology (NIST) determination of the Boltzmann constant: k = 1.380642 9(69) × 10-23 J/K, with a relative standard uncertainty of 5.0 × 10-6 and relative offset of -4.05 × 10-6 from the Committee on Data for Science and Technology (CODATA) 2014 recommended value. We discuss the input circuits and the approach we used to match the frequency response of two noise sources. We present new measurements of the correlated noise of the 4 K on-chip resistors in the quantum-accurate, pseudorandom, voltage-noise source, which we used to estimate the correlated, frequency-dependent, nonthermal noise in our system. Finally, we contrast our system with those used in other measurements and speculate on future improvements.

Frequency-response mismatch effects in Johnson noise thermometry

Johnson noise thermometry is of considerable interest at present due to the planned redefinition of the kelvin in 2019, and several determinations of the Boltzmann constant have recently been published in support of the redefinition. To determine the Boltzmann constant by noise thermometry, the thermal noise from a sensing resistor at the triple point of water is compared to a pseudo-random noise with a calculable power spectral density traceable to quantum electrical standards. In all the measurements to date, the two dominant sources of measurement uncertainty are strongly influenced by a single factor: the frequency-response mismatch between the sets of leads connecting the thermometer to the two noise sources. In the most recent determination at the National Institute of Metrology, China, substantial changes were made to the connecting leads to reduce the mismatch effects. The aims of this paper are, firstly, to describe and explain the rationale for the changes, and secondly, to better understand the effects of the least-squares fits and the bias-variance compromise in the analysis of measurements affected by the mismatch effects. While significant improvements can be made to the connecting leads to lessen the effects of the frequency-response mismatch, the efforts are unlikely to be rewarded by a significant increase in bandwidth or a significant reduction in uncertainty.

Measurement of the Boltzmann constant by Johnson noise thermometry using a superconducting integrated circuit

We report on our measurement of the Boltzmann constant by Johnson noise thermometry (JNT) using an integrated quantum voltage noise source (IQVNS) that is fully implemented with superconducting integrated circuit technology. The IQVNS generates calculable pseudo white noise voltages to calibrate the JNT system. The thermal noise of a sensing resistor placed at the temperature of the triple point of water was measured precisely by the IQVNS-based JNT. We accumulated data of more than 429 200 s in total (over 6 d) and used the Akaike information criterion to estimate the fitting frequency range for the quadratic model to calculate the Boltzmann constant. Upon detailed evaluation of the uncertainty components, the experimentally obtained Boltzmann constant was J K−1 with a relative combined uncertainty of . The value of k is relatively lower than the CODATA 2014 value (Mohr et al 2016 Rev. Mod. Phys. 88 035009).

A Boltzmann constant determination based on Johnson noise thermometry

A value for the Boltzmann constant was measured electronically using an improved version of the Johnson Noise Thermometry (JNT) system at the National Institute of Standards and Technology (NIST), USA. This system is different from prior ones, including those from the 2011 determination at NIST and both 2015 and 2017 determinations at the National Institute of Metrology (NIM), China. As in all three previous determinations, the main contribution to the combined uncertainty is the statistical uncertainty in the noise measurement, which is mitigated by accumulating and integrating many weeks of cross-correlated measured data. The second major uncertainty contribution also still results from variations in the frequency response of the ratio of the measured spectral noise of the two noise sources, the sense resistor at the triple-point of water and the superconducting quantum voltage noise source. In this paper, we briefly describe the major differences between our JNT system and previous systems, in particular the input circuit and approach we used to match the frequency responses of the two noise sources. After analyzing and integrating 50 d of accumulated data, we determined a value: J K−1 with a relative standard uncertainty of and relative offset from the CODATA 2014 recommended value.

An improved electronic determination of the Boltzmann constant by Johnson noise thermometry

Recent measurements using acoustic gas thermometry have determined the value of the Boltzmann constant, k, with a relative uncertainty less than 1 × 10−6. These results have been supported by a measurement with a relative uncertainty of 1.9 × 10−6 made with dielectric-constant gas thermometry. Together, the measurements meet the requirements of the International Committee for Weights and Measures and enable them to proceed with the redefinition of the kelvin in 2018. In further support, we provide a new determination of k using a purely electronic approach, Johnson noise thermometry, in which the thermal noise power generated by a sensing resistor immersed in a triple-point-of-water cell is compared to the noise power of a quantum-accurate pseudo-random noise waveform of nominally equal noise power. The experimental setup differs from that of the 2015 determination in several respects: a 100 Ω resistor is used as the thermal noise source, identical thin coaxial cables made of solid beryllium–copper conductors and foam dielectrics are used to connect the thermal and quantum-accurate noise sources to the correlator so as to minimize the temperature and frequency sensitivity of the impedances in the connecting leads, and no trimming capacitors or inductors are inserted into the connecting leads. The combination of reduced uncertainty due to spectral mismatches in the connecting leads and reduced statistical uncertainty due to a longer integration period of 100 d results in an improved determination of k = 1.380 649 7(37) × 10−23 J K−1 with a relative standard uncertainty of 2.7 × 10−6 and a relative offset of 0.89 × 10−6 from the CODATA 2014 recommended value. The most significant terms in the uncertainty budget, the statistical uncertainty and the spectral-mismatch uncertainty, are uncorrelated with the corresponding uncertainties in the 2015 measurements.

Measuring the Boltzmann’s Constant Using Superconducting Integrated Circuit

We report on our progress in measuring the Boltzmann’s constant by Johnson noise thermometry (JNT) using an integrated quantum voltage noise source (IQVNS) that is fully implemented with superconducting integrated circuit technology. The IQVNS generates calculable pseudo white noise voltages to calibrate the JNT system. Thermal noise of a resistor placed at the temperature of the triple point of water was measured precisely by the IQVNS-based JNT. We accumulated more than 2000 data points to determine the Boltzmann’s constant. The experimentally obtained Boltzmann’s constant was $k_{\mathrm {exp}} = 1.3806493 \times 10^{-23}$ J/K with a relative statistical uncertainty of $8.6 \times 10^{-6}$ , which agreed well with the 2014 Committee on Data for Science and Technology value with a relative offset of $+ 0.6\times 10^{-6}$ .