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arXiv:2109.09677 · Physical Review Applied

Radio-Frequency Coulomb-Blockade Thermometry

Florian Blanchet, Yu-Cheng Chang, Bayan Karimi, Joonas T. Peltonen, Jukka P Pekola

Published Jan 26, 2022• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.17.l011003

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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.e.g.e.g. applications in quantum technology.
Coulomb blockade thermometers (CBTs) have attracted more interest in recent years, as the demand for sub-one Kelvin thermometry has increased, especially due to the prevalence of dilution refrigerators in research and applications in quantum technology. CBTs can be operated both as a primary thermometer, requiring no prior calibration, or as a simple resistance thermometer in the secondary mode after calibration. As new scalable fabrication processes for quantum devices and cryogenic electronics are being developed, cryogenic wafer characterization methods must also scale up to provide statistical data on device parameters. Currently, characterization throughput of cryogenic devices is limited by the turnover time and sample capacity of traditional cryostats, where a measurement cycle for only a few devices can take several days. In this work, we demonstrate wafer-scale cryogenic characterization of a recently developed TiW/Al-AlOx/TiW normal-metal tunnel junction technology using CBTs. Measurements performed in a 300 mm cryogenic wafer prober (CWP) show on-chip electron temperatures below 700 mK across a full 150 mm wafer, as determined by primary thermometry. These results establish wafer-level testing below 1 K as a viable approach for large-scale cryogenic characterization of electrical devices, opening a pathway toward high-throughput screening of quantum devices and direct wafer-scale characterization of aluminum-based superconducting circuits.
The performance and accuracy of quantum electronics is substantially degraded when the temperature of the electrons in the devices is too high. The electron temperature can be reduced with appropriate thermal anchoring and by filtering both the low frequency and radio frequency noise. Ultimately, for high performance filters the electron temperature can approach the phonon temperature (as measured by resistive thermometers) in a dilution refrigerator. In this application note, the method for measuring the electron temperature in a typical quantum electronics device using Coulomb blockade thermometry is described. This technique is applied to find the readily achievable electron temperature in the device when using the QFilter provided by QDevil. With our thermometry measurements, using a single GaAs/AlGaAs quantum dot in an optimized experimental setup, we determined an electron temperature of 28 ±\pm± 2 mK for a dilution refrigerator base temperature of 18 mK.
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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.
A cryogenic quantum dot thermometer is calibrated and operated using only a single non-galvanic gate connection. The thermometer is probed with radio-frequency reflectometry and calibrated by fitting a physical model to the phase of the reflected radio-frequency signal taken at temperatures across a small range. Thermometry of the source and drain reservoirs of the dot is then performed by fitting the calibrated physical model to new phase data. The thermometer can operate at the transition between thermally broadened and lifetime broadened regimes, and outside the temperatures used in calibration. Electron thermometry was performed at temperatures between 3.0 K3.0\,\mathrm{K}3.0K and 1.0 K1.0\,\mathrm{K}1.0K, in both a 1 K1\,\mathrm{K}1K cryostat and a dilution refrigerator. The experimental setup allows fast electron temperature readout with a sensitivity of 4.0±0.3 mK/Hz4.0\pm0.3 \, \mathrm{mK}/\sqrt{\mathrm{Hz}}4.0±0.3mK/Hz​, at Kelvin temperatures. The non-galvanic calibration process gives a readout of physical parameters, such as the quantum dot lever arm. The demodulator used for reflectometry readout is readily available and very affordable.
We experimentally demonstrate the high bandwidth readout of a thermometer based on a superconductor–insulator–normal metal (SIN) tunnel junction, embedded in a rf resonant circuit. Our implementation enables basic studies of the thermodynamics of mesoscopic nanostructures. It can also be applied to the development of fast calorimeters, as well as ultrasensitive bolometers for the detection of far-infrared radiation. We discuss the operational details of this device, and estimate the ultimate temperature sensitivity and measurement bandwidth.