Cryogenic microwave circuit design is required for the development of future quantum systems. Discrete components can be used to design compact attenuators, matching networks or filters to verify circuit designs for later integration. However, precise passive component characterization is necessary for microwave circuit design, but has not yet been performed in the millikelvin (mK) range. This work presents for the first time a cryogenic model parameter estimation of passive surface-mounted device (SMD) components for microwave circuit design down to 50 mK and up to 8 GHz. The model parameters of an inductor, a capacitor and two resistors have been derived down to 50 mK. Measurement data were de-embedded using coplanar waveguide (CPWG) TRL calibration standards. It is shown that at 50 mK, the characteristic capacitance and inductance of the investigated components change by only 6 % respectively 2.5 % and that the inductor resistance at 50 mK is reduced by 80 % compared to room temperature, proving its suitability for microwave circuit design at mK temperatures. In contrast, the resistance value of the investigated thick film resistors increases by 20 %.
Cryogenic microwave circuit design is required for the development of future quantum systems. Discrete components can be used to design compact attenuators, matching networks or filters to verify circuit designs for later integration. However, precise passive component characterization is necessary for microwave circuit design, but has not yet been performed in the millikelvin (mK) range. This work presents for the first time a cryogenic model parameter estimation of passive surface-mounted device (SMD) components for microwave circuit design down to 50 mK and up to 8 GHz. The model parameters of an inductor, a capacitor and two resistors have been derived down to 50 mK. Measurement data were de-embedded using coplanar waveguide (CPWG) TRL calibration standards. It is shown that at 50 mK, the characteristic capacitance and inductance of the investigated components change by only 6 % respectively 2.5 % and that the inductor resistance at 50 mK is reduced by 80 % compared to room temperature, proving its suitability for microwave circuit design at mK temperatures. In contrast, the resistance value of the investigated thick film resistors increases by 20 %.
Designing large-scale superconducting quantum circuits involves complex microwave engineering to minimize loss, spurious reflections, and signal crosstalk. Essential for engineering more complex circuits is precise knowledge of devices’ microwave performance, which can be characterized by measuring its calibrated scattering parameters (S-parameters) at mK temperatures. In this work, we introduce a full 2-port calibrated S-parameter measurement setup which can characterize superconducting quantum integrated circuits and other RF integrated circuits operating at mK temperatures. The design and architecture of the measurement system consisting of in-house developed microwave calibration unit (MCU) housing the newly designed cryogenic calibration standards and the device under test (DUT) is discussed in detail. The measurement setup is then used to demonstrate the first calibrated S-parameter measurements of an in-house developed superconducting qubit integrated circuit at mK temperature.
In the field of quantum information science, superconducting quantum integrated circuits are operated at millikelvin temperatures inside dilution refrigerators. The microwave performance of such non-connectorised devices can be characterised by measuring their calibrated S-parameters. The design of high-quality microwave standards is essential to achieve accurate calibration. In this work we describe the architecture of a full 2-port S-parameter measurement set-up for use at millikelvin temperatures along with the microwave calibration unit. The design of the standards for use in the calibration unit at millikelvin temperatures is described and verified using electromagnetic simulation and measurements. The suitability of the standards is verified by characterising a commercial attenuator as a test device.
Development of RF and microwave metrology capabilities at cryogenic temperatures is critical for the development of high-performance microwave devices to facilitate commercialization of cryogenic quantum technologies. This article presents a broadband microwave S-parameter calibration scheme suitable for cryogenic environments operating at temperatures down to tens of milli-kelvin (mK). The technique is based on a weighted multi-line thru-reflect-line (TRL) calibration approach and is demonstrated using coaxial air line calibration standards. One-and two-port microwave devices commonly used in cryogenic quantum computing applications, a cryogenic 50Ωmatched load and a cryogenic 6 dB attenuator, were measured. The measured results at mK temperatures indicate that when combined with calibration standards of appropriate electrical length, the weighted multi-line TRL calibration scheme allows broadband frequency coverage compared to conventional TRL calibration schemes utilizing a single line standard. The mechanical and electrical properties of the line standards at mK temperatures were investigated and discussed. These findings establish the feasibility of utilizing multiple off-the-shelf coaxial air lines to enhance the frequency range of calibrations at mK temperatures.
Cryogenic systems are essential to many modern scientific and technological applications, including MRI superconducting magnets, particle accelerators, astrophysical detectors and quantum computing platforms, all of which operate at temperatures well below 120 K. In this framework, accurate temperature monitoring is, therefore, critical. However, conventional Resistance Temperature Detectors (RTDs) suffer from significant limitations in cryogenic environments, such as wiring complexity, power dissipation, limited low-temperature operation and large footprint, which restrict their integration in increasingly complex cryogenic infrastructures. Superconducting devices offer a promising alternative due to their high sensitivity at low temperatures, low power dissipation and compatibility with integrated quantum technologies. Inspired by Microwave Kinetic Inductance Detectors (MKIDs), this work investigates superconducting microwave resonators as minimally invasive, frequency-multiplexed cryogenic thermometers operating below 12 K. In particular, strategies to tune and enhance temperature sensitivity are explored by studying the effects of the superconducting thin-film thickness and surface nanostructuring. The first part of the study examines NbTi(N) planar resonators with thicknesses ranging from 20 nm to 150 nm, where temperature sensing is based on the temperature dependence of the kinetic inductance. S-shaped split-ring resonators resonating near 1.1 GHz are inductively coupled to a coplanar transmission line and characterized under cryogenic conditions. A clear trade-off between temperature sensitivity and quality factor is observed: thinner films achieve higher sensitivity, up to approximately 19 MHz/K for 20 nm thick devices, while the quality factor, typically exceeding 10^4, is found to degrade when the thickness is reduced. This trade-off leads to an optimal temperature resolution, with sub-microkelvin noise-equivalent temperature (NET) values. In particular, a minimum NET of (0.53±0.09) µK/Hz^(1/2) at 4.2 K is achieved for a 100 nm thick resonator, which is also exploited to study low-frequency temperature fluctuations in liquid helium. In the second part, a possible approach to enhance the temperature sensitivity, through surface nanostructuring, is investigated. Arrays of nanogaps are patterned in high-current regions of a 1.3 GHz resonator, in order to locally suppress superconductivity, reduce the critical temperature of the film and, therefore, accentuate the slope of the temperature-sensitive curve. These weak-links are realized by partially etching a 100 nm NbTi film, to leave 20-30 nm thick remaining nanogaps. Measurements reveal a significant increase in temperature sensitivity, reaching values as high as up to (62±1) MHz/K, which correspond to one order-of-magnitude improvement over non-nanostructured devices. Although this enhancement comes with increased noise-equivalent temperature, the results demonstrate the feasibility of engineering superconducting weak links to improve RF cryogenic thermometry and provide a solid foundation for future optimization. In reason of the achieved results, such an approach could find successful applications for a sub-µK high-resolution cryogenic temperature monitoring, specifically for integrated quantum architectures, further benefiting from the frequency-multiplexing that naturally arises from the multiple allocation of different superconducting microwave resonators.
Thousands to millions of sensitive signals will need to be conveyed through all the temperature stages of a dilution fridge to operate future large-scale quantum processors made of many quantum bits. The exploding number of heat-conductive coaxial cables will overwhelm the fridge cooling capabilities, detrimental to the quantum core. Moving the control electronics down to cryogenic temperatures allows the use of already-available superconducting cables, alleviating heat conduction between low-temperature stages, and appears as a clear path towards scalability in the number of operating qubits.This Ph.D. work aimed to explore the use of the industrial CMOS 28nm Fully-Depleted Silicon-On-Insulator (FD-SOI) technology at cryogenic temperatures for quantum computing applications. Our first objective is to extend the sparse existing knowledge about the FD-SOI 28nm transistors at cryogenic temperatures for practical aspects of circuit design and later for developments of compact models.To speed-up the characterization of single devices with the inherent hour-long cooling cycles, we designed an integrated circuit multiplexing a thousand of transistors for different geometries and gate-stack flavors for low-frequency measurement of the current-voltage characteristics and pair-matching analysis from 300 down to 0.1K. We discuss and analyze the evolution trends with varying geometry at different temperatures for important quantities in circuit design, such as the transconductance, the conductance, and the transconductance over drain current ratio of individual transistors.Secondly, we explore the low-temperature co-integration and the full on-chip integration of semiconductor quantum devices with classical electronics aimed at specific measurements down to the millikelvin range.We first focus on the sub-nanoampere current measurement of quantum dot devices by designing and characterizing a low-power transimpedance amplifier (TIA). The high-gain amplifier is successfully applied to measure the current across single- and double quantum-dot devices, respectively wire-bonded a few mm away or on-chip integrated a few micrometers-away. To further leverage the integration into the same substrate, we connected GHz-range voltage-controlled oscillators to one of the gates of the double dot in an attempt to observe discrete charge pumping in a fully-integrated device.Lastly, we tackled the measurement of the gate capacitance of single quantum devices by proposing a new measurement scheme making use of the cryogenic electronics capabilities as an alternative to the well-known reflectometry. By integrating a voltage-controlled current excitation and a voltage-sensing amplifier in the 200 MHz range, both in close proximity to the quantum device connected to an LC tank, the read-out circuitry of a variation in the device capacitance becomes a purely lumped-element system with impedance measurement of the resonant circuit without any wave propagation like in reflectometry. This approach increases simplicity and compactness of the measurement set-up. We even replace the bulky passive inductor used in reflectometry by an active inductor made of transistors and capacitors, offering improved scalability with a 3-orders of magnitude lower area for the same inductance. The resulting circuit successfully measured aF-capacitance variations of nanometric transistors at 4.2K revealing oscillatory quantum effects in the gate capacitance as a function of the gate and back-gate voltages.At the end of this dissertation, a picture is given with the challenges laying ahead related to circuit architecture and design for the ultimate goal of entering into the era of large-scale quantum processing.
Abstract Superconducting circuit testing and materials loss characterization requires robust and reliable methods for the extraction of internal and coupling quality factors of microwave resonators. A common method, imposed by limitations on the device design or experimental configuration, is the single-port reflection geometry, i.e. reflection-mode. However, impedance mismatches in cryogenic systems must be accounted for through calibration of the measurement chain while it is at low temperatures. In this paper, we demonstrate a data-based, single-port calibration using commercial microwave standards and a vector network analyzer with samples at millikelvin temperature in a dilution refrigerator, making this method useful for measurements of quantum phenomena. Finally, we cross reference our data-based, single-port calibration and reflection measurement with over-coupled 2D- and 3D-resonators against well established two-port techniques corroborating the validity of our method.