Coulomb Blockade Thermometer Research Articles

Thermal Transport in Nanoelectronic Devices Cooled by On-Chip Magnetic Refrigeration.

On-chip demagnetization refrigeration has recently emerged as a powerful tool for reaching microkelvin electron temperatures in nanoscale structures. The relative importance of cooling on-chip and off-chip components and the thermal subsystem dynamics are yet to be analyzed. We study a Coulomb blockade thermometer with on-chip copper refrigerant both experimentally and numerically, showing that dynamics in this device are captured by a first-principles model. Our work shows how to simulate thermal dynamics in devices down to microkelvin temperatures, and outlines a recipe for a low-investment platform for quantum technologies and fundamental nanoscience in this novel temperature range.

Microkelvin electronics on a pulse-tube cryostat with a gate Coulomb-blockade thermometer

Temperatures below 1 mK on-chip hold great potential for quantum physics but present a great challenge due to the lack of suitable thermometry and the detrimental pulse-tube vibrations of cryogen-free refrigerators. Here, we solve the pulse-tube problem using a rigidly wired metallic sample holder, which provides a microkelvin environment with low heat leaks despite the vibrations. Further, we demonstrate an improved type of temperature sensor, the gate Coulomb blockade thermometer (gCBT), employing a gate metallization covering the entire device. This immunizes against nanofabrication imperfections and uncontrollable offset charges, and extends the range to lower temperatures compared to a junction CBT with the same island capacitance, here down to $\ensuremath{\approx}$160 $\ensuremath{\mu}$K for a 10% accuracy. Using on- and off-chip cooling, we demonstrate electronic temperatures as low as 224 $\ifmmode\pm\else\textpm\fi{}$ 7 $\ensuremath{\mu}$K, remaining below 300 $\ensuremath{\mu}$K for 27 hours, thus providing time for experiments. Finally, we give an outlook for cooling below 50 $\ensuremath{\mu}$K for a future generation of microkelvin transport experiments.

Influence of device non-uniformities on the accuracy of Coulomb blockade thermometry

We investigate temperature uncertainty of Coulomb blockade thermometer (CBT) arising from inevitable non-uniformities in tunnel junction arrays. The corrections are proportional to the junction resistance variance in the linear operation regime and this result holds approximately also beyond this originally studied high temperature range. We present both analytical and numerical results, and discuss briefly their implications on achievable uniformity based on state-of-the-art fabrication of sensors.

Radio-Frequency Coulomb-Blockade Thermometry

A Coulomb-blockade thermometer (CBT) provides calibration-free measurement of low temperatures, even in strong magnetic fields---but slowly. A standard conductance measurement with a CBT takes typically minutes, which is useless in applications where relatively fast changes in temperature are monitored. Besides, a slow measurement is prone to drifts, and low-frequency noise. The authors solve this issue by hooking a CBT sensor into a radio-frequency tank circuit, making the measurement about 1000 times faster. Their approach is expected to impact low-temperature thermometry, for $e.g.$ applications in quantum technology.

500 microkelvin nanoelectronics.

Fragile quantum effects such as single electron charging in quantum dots or macroscopic coherent tunneling in superconducting junctions are the basis of modern quantum technologies. These phenomena can only be observed in devices where the characteristic spacing between energy levels exceeds the thermal energy, kBT, demanding effective refrigeration techniques for nanoscale electronic devices. Commercially available dilution refrigerators have enabled typical electron temperatures in the 10 to 100 mK regime, however indirect cooling of nanodevices becomes inefficient due to stray radiofrequency heating and weak thermal coupling of electrons to the device substrate. Here, we report on passing the millikelvin barrier for a nanoelectronic device. Using a combination of on-chip and off-chip nuclear refrigeration, we reach an ultimate electron temperature of Te = 421 ± 35 μK and a hold time exceeding 85 h below 700 μK measured by a self-calibrated Coulomb-blockade thermometer.

On-and-off chip cooling of a Coulomb blockade thermometer down to 2.8 mK

Cooling nanoelectronic devices below 10 mK is a great challenge since thermal conductivities become very small, thus creating a pronounced sensitivity to heat leaks. Here, we overcome these difficulties by using adiabatic demagnetization of both the electronic leads and the large metallic islands of a Coulomb blockade thermometer. This reduces the external heat leak through the leads and also provides on-chip refrigeration, together cooling the thermometer down to 2.8 ± 0.1 mK. We present a thermal model which gives a good qualitative account and suggests that the main limitation is heating due to pulse tube vibrations. With better decoupling, temperatures below 1 mK should be within reach, thus opening the door for μK nanoelectronics.

Magnetically cooling achieves record low temperatures in Coulomb blockade thermometers

Applying demagnetization cooling in a new way to Coulomb blockade thermometers reduces heat leaks and achieves a record cooling temperature.

New Evaluation of $$T-T_{2000}$$ 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 %.

Nanoelectronic primary thermometry below 4 mK.

Cooling nanoelectronic structures to millikelvin temperatures presents extreme challenges in maintaining thermal contact between the electrons in the device and an external cold bath. It is typically found that when nanoscale devices are cooled to ∼10 mK the electrons are significantly overheated. Here we report the cooling of electrons in nanoelectronic Coulomb blockade thermometers below 4 mK. The low operating temperature is attributed to an optimized design that incorporates cooling fins with a high electron–phonon coupling and on-chip electronic filters, combined with low-noise electronic measurements. By immersing a Coulomb blockade thermometer in the 3He/4He refrigerant of a dilution refrigerator, we measure a lowest electron temperature of 3.7 mK and a trend to a saturated electron temperature approaching 3 mK. This work demonstrates how nanoelectronic samples can be cooled further into the low-millikelvin range.

Silver-epoxy microwave filters and thermalizers for millikelvin experiments

We present silver-epoxy filters combining excellent microwave attenuation with efficient wire thermalization, suitable for low temperature quantum transport experiments. Upon minimizing parasitic capacitances, the attenuation reaches ≥100 dB above ≈150 MHz and—when capacitors are added—already above ≈30 MHz. We measure the device electron temperature with a GaAs quantum dot and demonstrate excellent filter performance. Upon improving the sample holder and adding a second filtering stage, we obtain electron temperatures as low as 7.5 ± 0.2 mK in metallic Coulomb blockade thermometers.

Silicon-based Coulomb blockade thermometer with Schottky barriers

A hybrid Coulomb blockade thermometer (CBT) in form of an array of intermittent aluminum and silicon islands connected in series via tunnel junctions was fabricated on a thin silicon-on-insulator (SOI) film. Tunnel barriers in the micrometer size junctions were formed by metal-semiconductor Schottky contacts between aluminium electrodes and heavily doped silicon. Differential conductance through the array vs. bias voltage was found to exhibit characteristic features of competing thermal and charging effects enabling absolute temperature measurements over the range of ∼65 to ∼500 mK. The CBT performance implying the primary nature of the thermometer demonstrated for rather trivial architecture attempted in this work paves a route for introduction of Coulomb blockade thermometry into well-developed contemporary SOI technology.

Primary Thermometry in the Intermediate Coulomb Blockade Regime

We investigate Coulomb blockade thermometers (CBT) in an intermediate temperature regime, where measurements with enhanced accuracy are possible due to the increased magnitude of the differential conductance dip. Previous theoretical results show that corrections to the half width and to the depth of the measured conductance dip of a sensor are needed, when leaving the regime of weak Coulomb blockade towards lower temperatures. In the present work, we demonstrate experimentally that the temperature range of a CBT sensor can be extended by employing these corrections without compromising the primary nature or the accuracy of the thermometer.

Effect of on-chip filter on Coulomb blockade thermometer

Coulomb Blockade Thermometer (CBT) is a primary thermometer based on electric conductance of normal tunnel junction arrays. One limitation for CBT use at the lowest temperatures has been due to environmental noise heating. To improve on this limitation, we have done measurements on CBT sensors fabricated with different on-chip filtering structures in a dilution refrigerator with a base temperature of 10 mK. The CBT sensors were produced with a wafer scale tunnel junction process. We present how the different on-chip filtering schemes affect the limiting saturation temperatures and show that CBT sensors with proper on-chip filtering work at temperatures below 20 mK and are tolerant to noisy environment.

Metallic Coulomb blockade thermometry down to 10 mK and below

We present an improved nuclear refrigerator reaching 0.3 mK, aimed at microkelvin nanoelectronic experiments, and use it to investigate metallic Coulomb blockade thermometers (CBTs) with various resistances R. The high-R devices cool to slightly lower T, consistent with better isolation from the noise environment, and exhibit electron-phonon cooling [proportional] T(5) and a residual heat-leak of 40 aW. In contrast, the low-R CBTs display cooling with a clearly weaker T-dependence, deviating from the electron-phonon mechanism. The CBTs agree excellently with the refrigerator temperature above 20 mK and reach a minimum-T of 7.5 ± 0.2 mK.

Comparison of Coulomb Blockade Thermometers with the International Temperature Scale PLTS-2000

The operation of the primary Coulomb blockade thermometer (CBT) is based on a measurement of bias voltage dependent conductance of arrays of tunnel junctions between normal metal electrodes. Here we report on a comparison of a CBT with a high accuracy realization of the PLTS-2000 temperature scale in the range from 0.008 K to 0.65 K. An overall agreement of about 1% was found for temperatures above 0.25 K. For lower temperatures increasing differences are caused by thermalization problems which are accounted for by numerical calculations based on electron-phonon decoupling.

Ex situ tunnel junction process technique characterized by Coulomb blockade thermometry

The authors investigate a wafer scale tunnel junction fabrication method, where a plasma etched via through a dielectric layer covering bottom Al electrode defines the tunnel junction area. The ex situ tunnel barrier is formed by oxidation of the bottom electrode in the junction area. Room temperature resistance mapping over a 150 mm wafer gives local deviation values of the tunnel junction resistance that fall below 7.5% with an average of 1.3%. The deviation is further investigated by sub-1 K measurements of a device, which has one tunnel junction connected to four arrays consisting of N junctions (N=41, junction diameter 700 nm). The differential conductance is measured in single-junction and array Coulomb blockade thermometer operation modes. By fitting the experimental data to the theoretical models, the authors found an upper limit for the local tunnel junction resistance deviation of ∼5% for the array of 2N+1 junctions. This value is of the same order as the minimum detectable deviation defined by the accuracy of the authors’ experimental setup.

Influence of Environment on Tunneling Thermometry

The electromagnetic environment of a tunnel junction can influence significantly the tunneling characteristics. We investigate experimentally a particular environment formed by tunnel junctions and compare the results with a theoretical model. We discuss Single Junction Thermometer and a two junction Coulomb Blockade Thermometer as examples.

EU dissemination of the provisional ultra-low-temperature scale, PLTS-2000

Following the introduction of the provisional low-temperature scale from 0.9 mK to 1K, PLTS-2000, there is a need for primary and secondary thermometers and fixed points, which can disseminate the scale to users. This paper reports on the progress, within the EU collaborative project ‘ULT Dissemination’, in the development and evaluation of several devices with associated instrumentation. Principal among them are a current-sensing noise thermometer, a CMN thermometer adapted for industrial use, a Coulomb blockade thermometer, a second-sound thermometer, a 3 He melting pressure thermometer for a direct realisation of the PLTS-2000. A superconductive reference device has also been developed, as a replacement for the NBS SRM-768 which is no longer available.

3ω method and its applications in nanomaterials and nanodevices

3ω method has been investigated and its applications are analyzed. A wide appli cations in measuring the thermal conducti-vity and specific heat of material s are discussed. Here we discuss the mechanism of this method and introduce some basic applications. With some calculations in the two dimensional tunnel juncti on arrays and applications of 3ω method, a fast, primary Coulomb blockade therm ometer can be realized with a super-high precision in measuring temperatures in the Coulomb blockade regime.

RECENT ADVANCES IN LOW TEMPERATURE THERMOMETRY IN HIGH MAGNETIC FIELDS

The accurate determination of the temperature of an experiment at low temperatures in high magnetic fields is difficult. We present the results of measurements made using a number of new techniques developed over the last few years. In particular we discuss the results of measurements made using a unique capacitor made with Kapton and copper in a cylindrical geometry.1 This capacitance thermometer, dubbed the "Kapacitor", is different from other low temperature thermometers in that the minimum in capacitance vs. temperature can be moved to lower temperatures (to below 20 mK) by changing the construction technique. In addition, we discuss measurements on Coulomb blockade thermometers (CBT's) that offer the possibility of true primary thermomemtry at low temperatures without any magnetic field dependence. Both of these new techniques will be compared to the standard technique of resistance thermometry using RuO chip resistors. The crucial issues of accuracy and precision, usefulness for control, and noise sensitivity will be discussed for each of these technologies. In addition, recent measurements on the magnetic behavior of RuO thermometers at low temperatures and its relationship to anomalous low field peaks in the resistance that develop at temperatures below 50 mK are also presented.