Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Applied Superconductivity

Calculation of the characteristics of coplanar resonators for kinetic inductance detectors

Adrian Porch, Philip D. Mauskopf, Simon M. Doyle, C. Dunscombe

Published Jun 1, 2005• 19 citations
Publisher

Abstract

Photon detectors based on the change of kinetic inductance of a thin superconducting film have a number of applications, particularly in astronomy, owing to their high sensitivity and ease of integration into large arrays. Here we discuss in detail the analysis of kinetic inductance detectors that use thin film microwave coplanar resonators. Photon absorption decreases the electron pair density, increasing the magnetic penetration depth /spl lambda/, which causes a decrease in the resonant frequency (or phase) of an irradiated resonator. To quantify this effect, we first compute the resonator current distribution, from which the /spl lambda/-dependent parameters (such as kinetic inductance) are calculated. Optimum responsivity for phase measurement is achieved by using the thinnest film with the narrowest center conductor width at the lowest possible temperature. However, the responsivity is compromised by extrinsic microwave losses, in particular due to residual surface resistance, which is likely to be significant in the thinnest films.

DOI
10.1109/tasc.2005.849916

Related papers

Characterization of the kinetic inductance fraction of NbTiN MKIDs

Wei-Tao Lv, Qing Shi, Jing Li +2 more

Microwave Kinetic Inductance Detectors (MKIDs), with high sensitivity and relatively simple frequency multiplexing, are emerging as a kind of large-array detectors in the terahertz (THz) band. An MKID, like a superconducting resonator, is composed of a planar capacitor and inductor that are made from superconducting films. The energy gap of the superconducting film for the planar inductor (at least part of it) is lower than the energy of photons to be detected. The kinetic inductance of the superconducting film irradiated by the photons is increased, shifting the resonance frequency toward a lower frequency. The frequency shift is proportional to the kinetic inductance fraction, i.e., the ratio of the kinetic inductance to the total inductance of the planar superconducting inductor. In this paper, we thoroughly investigate the kinetic inductance fraction for lumped-element and antenna-coupled MKIDs, which are both made from NbTiN. The detailed simulation, calculation, and measurement results will be presented.

Infrared, Millimeter-Wave, and Terahertz Technologies•Oct 8, 2021•0 citations

Inductances and attenuation constant for a thin-film superconducting coplanar waveguide resonator

John R. Clem

The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide resonator consisting of a current-carrying central conductor, adjacent slots, and ground planes that return the current. The analysis focuses on films of thickness d obeying d<2λ (λ is the London penetration depth), for which the material properties are characterized by the two-dimensional screening length Λ=2λ2/d. Introducing a cut-off procedure that guarantees that the magnitudes of the currents in the central conductor and the ground planes are equal, new and simpler results are obtained for the kinetic inductance and the attenuation constant for small Λ. Exact results for arbitrary Λ are presented for the geometric, kinetic, and total inductances in the limit of tiny slot widths, and approximate results are presented for arbitrary slot widths.

arXiv:1210.5929•Journal of Applied Physics•Jan 4, 2013•30 citations

Superconducting Nonlinear Kinetic Inductance Devices

Kher, Aditya Shreyas

We describe a novel class of devices based on the nonlinearity of the kinetic inductance of a superconducting thin film. By placing a current-dependent inductance in a microwave resonator, small currents can be measured through their effect on the resonator’s frequency. By using a high-resistivity material for the film and nanowires as kinetic inductors, we can achieve a large coefficient of nonlinearity to improve device sensitivity. We demonstrate a current sensitivity of 8 pA/√Hz, making this device useful for transition-edge sensor (TES) readout and other cutting-edge applications. An advantage of these devices is their natural ability to be multiplexed in the frequency domain, enabling large detector arrays for TES-based instruments. A traveling-wave version of the device, consisting of a thin-film microwave transmission line, is also sensitive to small currents as they change the phase length of the line due to their effect on its inductance. We demonstrate a current sensitivity of 5 pA/√Hz for this version of the device, making it also suitable for TES readout as well as other current-detection applications. It has the advantage of multi-gigahertz bandwidth and greater dynamic range, offering a different approach to the resonator version of the device. Finally, we also demonstrate a transmission-line resonator version of the device that combines some of the advantages of the nanowire resonator and the traveling-wave device. This version of the device has high dynamic range but can also be easily multiplexed in the frequency domain. A lumped-element resonator similar to the first device can be placed in a loop configuration to make it sensitive to magnetic fields. We demonstrate an example of such a device whose sensitivity could ultimately reach levels similar to those of state-of-the-art DC SQUIDs, making it potentially useful for many magnetometry applications given its ease of multiplexing. Finally, a similar microwave resonator is shown to exhibit parametric gain of up to 29 dB in the presence of a strong pump tone. The noise performance of this parametric amplifier approaches the quantum limit, making it useful for applications in quantum information and metrology.

•Feb 10, 2017•17 citations

Kinetic Inductance of Superconducting Coplanar Waveguides

Koki Watanabe, Keiji Yoshida, Takeshi Aoki Kohjiro

An analytical expression for the kinetic inductance of the superconducting coplanar waveguide is given using the conformal mapping technique. This expression is shown to be in good agreement with experimental results obtained from the temperature dependence of the resonant frequency of the NbN coplanar waveguide resonators, especially in the case of a film thickness smaller than the magnetic penetration depth. It is also shown that the magnetic penetration depth of the superconducting thin films can be evaluated by this method.

Japanese Journal of Applied Physics•Oct 1, 1994•89 citations

Far-infrared kinetic-inductance detectors

Erich N. Grossman, Donald G. McDonald, Joseph E. Sauvageau

Extremely sensitive far-infrared detectors suitable for both direct detection and heterodyne applications, based on mu m-sized thin films with thickness less than a superconducting penetration depth are possible. The penetration depth of such a film, and therefore its inductance, varies with temperature and with quasiparticle population (described by an effective temperature T*), resulting in both bolometric and nonequilibrium photoinductive responses. Incident radiation is coupled into the small-area kinetic inductor by a lithographic antenna, and the resulting inductance changes are amplified and converted to a voltage signal by an integrated microstrip DC SQUID. The device is sensitive because, unlike junction-based devices with large capacitive reactances, the kinetic inductor is naturally well matched to the antenna impedance at the far-IR frequency ( nu >2 Delta /h) and to the preamplifier (SQUID) impedance at microwave or video frequencies ( nu <<2 Delta /h). The best kinetic inductor materials are those with low electronic mean free path, large penetration depth, and high critical current density. Thus, common magnet alloys such as NbTi are the natural choice for liquid-He temperature operation. A detailed analysis predicts a (phonon-limited) NEP of 4*10/sup -17/ W/ square root Hz for a bolometer with an iridium kinetic inductor operated at 0.1 K. A heterodyne noise temperature of 2250 K (single-sideband) at 3 THz, with a 200-MHz bandwidth, is predicted for a Nb-Ti mixer operated at 4 K.

IEEE Transactions on Magnetics•Mar 1, 1991•39 citations

Microwave loss and kinetic inductance of epitaxial TiN films

Yu Wu, Yixin Liu, Wanpeng Gao +7 more

Abstract Low microwave loss and regulatable kinetic inductance are two key characteristics of superconducting films to manufacture high-performance quantum devices. Epitaxial titanium nitride (TiN) thin films have been found to exhibit significant advantages in these two aspects. In this paper, we investigated into the dielectric loss and kinetic inductance of epitaxial TiN films, which were prepared on both silicon and sapphire substrates with different temperatures. Crystal structure, surface morphology, and superconducting properties were characterized systematically. The radio-frequency response of microwave resonators made of TiN films was studied at low temperatures to extract the information of kinetic inductance and quality factor. We obtained the highest internal quality factor up to 1.6 × 10 6 at single photon regime and achieved a regulation of kinetic inductance exceeding 16 times by altering the substrate and the sputtering temperature of the TiN films. This work not only provides an essential foundation for the precise design and preparation of low-loss TiN resonators for superconducting quantum bits, but also demonstrates TiN film as an excellent material platform with both low microwave loss and high kinetic inductance that can be applied in other fields such as microwave kinetic inductance detectors.

Superconductor Science and Technology•Sep 18, 2024•4 citations
Photon detectors based on the change of kinetic inductance of a thin superconducting film have a number of applications, particularly in astronomy, owing to their high sensitivity and ease of integration into large arrays. Here we discuss in detail the analysis of kinetic inductance detectors that use thin film microwave coplanar resonators. Photon absorption decreases the electron pair density, increasing the magnetic penetration depth /spl lambda/, which causes a decrease in the resonant frequency (or phase) of an irradiated resonator. To quantify this effect, we first compute the resonator current distribution, from which the /spl lambda/-dependent parameters (such as kinetic inductance) are calculated. Optimum responsivity for phase measurement is achieved by using the thinnest film with the narrowest center conductor width at the lowest possible temperature. However, the responsivity is compromised by extrinsic microwave losses, in particular due to residual surface resistance, which is likely to be significant in the thinnest films.
Microwave Kinetic Inductance Detectors (MKIDs), with high sensitivity and relatively simple frequency multiplexing, are emerging as a kind of large-array detectors in the terahertz (THz) band. An MKID, like a superconducting resonator, is composed of a planar capacitor and inductor that are made from superconducting films. The energy gap of the superconducting film for the planar inductor (at least part of it) is lower than the energy of photons to be detected. The kinetic inductance of the superconducting film irradiated by the photons is increased, shifting the resonance frequency toward a lower frequency. The frequency shift is proportional to the kinetic inductance fraction, i.e., the ratio of the kinetic inductance to the total inductance of the planar superconducting inductor. In this paper, we thoroughly investigate the kinetic inductance fraction for lumped-element and antenna-coupled MKIDs, which are both made from NbTiN. The detailed simulation, calculation, and measurement results will be presented.
The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide resonator consisting of a current-carrying central conductor, adjacent slots, and ground planes that return the current. The analysis focuses on films of thickness d obeying d<2λ (λ is the London penetration depth), for which the material properties are characterized by the two-dimensional screening length Λ=2λ2/d. Introducing a cut-off procedure that guarantees that the magnitudes of the currents in the central conductor and the ground planes are equal, new and simpler results are obtained for the kinetic inductance and the attenuation constant for small Λ. Exact results for arbitrary Λ are presented for the geometric, kinetic, and total inductances in the limit of tiny slot widths, and approximate results are presented for arbitrary slot widths.
We describe a novel class of devices based on the nonlinearity of the kinetic inductance of a superconducting thin film. By placing a current-dependent inductance in a microwave resonator, small currents can be measured through their effect on the resonator’s frequency. By using a high-resistivity material for the film and nanowires as kinetic inductors, we can achieve a large coefficient of nonlinearity to improve device sensitivity. We demonstrate a current sensitivity of 8 pA/√Hz, making this device useful for transition-edge sensor (TES) readout and other cutting-edge applications. An advantage of these devices is their natural ability to be multiplexed in the frequency domain, enabling large detector arrays for TES-based instruments. A traveling-wave version of the device, consisting of a thin-film microwave transmission line, is also sensitive to small currents as they change the phase length of the line due to their effect on its inductance. We demonstrate a current sensitivity of 5 pA/√Hz for this version of the device, making it also suitable for TES readout as well as other current-detection applications. It has the advantage of multi-gigahertz bandwidth and greater dynamic range, offering a different approach to the resonator version of the device. Finally, we also demonstrate a transmission-line resonator version of the device that combines some of the advantages of the nanowire resonator and the traveling-wave device. This version of the device has high dynamic range but can also be easily multiplexed in the frequency domain. A lumped-element resonator similar to the first device can be placed in a loop configuration to make it sensitive to magnetic fields. We demonstrate an example of such a device whose sensitivity could ultimately reach levels similar to those of state-of-the-art DC SQUIDs, making it potentially useful for many magnetometry applications given its ease of multiplexing. Finally, a similar microwave resonator is shown to exhibit parametric gain of up to 29 dB in the presence of a strong pump tone. The noise performance of this parametric amplifier approaches the quantum limit, making it useful for applications in quantum information and metrology.
An analytical expression for the kinetic inductance of the superconducting coplanar waveguide is given using the conformal mapping technique. This expression is shown to be in good agreement with experimental results obtained from the temperature dependence of the resonant frequency of the NbN coplanar waveguide resonators, especially in the case of a film thickness smaller than the magnetic penetration depth. It is also shown that the magnetic penetration depth of the superconducting thin films can be evaluated by this method.
Extremely sensitive far-infrared detectors suitable for both direct detection and heterodyne applications, based on mu m-sized thin films with thickness less than a superconducting penetration depth are possible. The penetration depth of such a film, and therefore its inductance, varies with temperature and with quasiparticle population (described by an effective temperature T*), resulting in both bolometric and nonequilibrium photoinductive responses. Incident radiation is coupled into the small-area kinetic inductor by a lithographic antenna, and the resulting inductance changes are amplified and converted to a voltage signal by an integrated microstrip DC SQUID. The device is sensitive because, unlike junction-based devices with large capacitive reactances, the kinetic inductor is naturally well matched to the antenna impedance at the far-IR frequency ( nu >2 Delta /h) and to the preamplifier (SQUID) impedance at microwave or video frequencies ( nu <<2 Delta /h). The best kinetic inductor materials are those with low electronic mean free path, large penetration depth, and high critical current density. Thus, common magnet alloys such as NbTi are the natural choice for liquid-He temperature operation. A detailed analysis predicts a (phonon-limited) NEP of 4*10/sup -17/ W/ square root Hz for a bolometer with an iridium kinetic inductor operated at 0.1 K. A heterodyne noise temperature of 2250 K (single-sideband) at 3 THz, with a 200-MHz bandwidth, is predicted for a Nb-Ti mixer operated at 4 K.
Abstract Low microwave loss and regulatable kinetic inductance are two key characteristics of superconducting films to manufacture high-performance quantum devices. Epitaxial titanium nitride (TiN) thin films have been found to exhibit significant advantages in these two aspects. In this paper, we investigated into the dielectric loss and kinetic inductance of epitaxial TiN films, which were prepared on both silicon and sapphire substrates with different temperatures. Crystal structure, surface morphology, and superconducting properties were characterized systematically. The radio-frequency response of microwave resonators made of TiN films was studied at low temperatures to extract the information of kinetic inductance and quality factor. We obtained the highest internal quality factor up to 1.6 × 10 6 at single photon regime and achieved a regulation of kinetic inductance exceeding 16 times by altering the substrate and the sputtering temperature of the TiN films. This work not only provides an essential foundation for the precise design and preparation of low-loss TiN resonators for superconducting quantum bits, but also demonstrates TiN film as an excellent material platform with both low microwave loss and high kinetic inductance that can be applied in other fields such as microwave kinetic inductance detectors.