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IEEE Transactions on Applied Superconductivity

Broadband RF Characterization and Modeling of Superconducting Coplanar Waveguides

Corentin Beilvert, Norman Vivien, Candice Thomas, Jean Charbonnier, Edouard Deschaseaux, Franck Badets, Jean-Philippe Michel

Published Dec 13, 2024• 0 citations
Publisher

Abstract

We present the RF characterization of 2-µm-wide superconducting coplanar waveguides made of 100-nm-thick niobium (Nb) or niobium nitride (NbN) films fabricated on 200 mm silicon wafers. Measurements of the two-ports S-parameters up to 25 GHz in a 4.7K–14 K temperature range with an added direct current up to 115 mA were done using a cryogenic probe station. With proper RF calibration and de-embedding procedure, both temperature and dc current dependence of the RF superconducting properties are analyzed. We report a kinetic inductance of 0.15 pH/$\square$, a critical current density of 50 MA/cm$^{2}$, and a critical temperature of 8.9 K for Nb as well as 4.27 pH/$\square$, 3 MA/cm$^{2}$, and 13.8 K for NbN. A telegraphist transmission line model taking into account the BCS theory has been developed and the comparison with the measurements is discussed.

DOI
10.1109/tasc.2024.3516210

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We present the RF characterization of 2-µm-wide superconducting coplanar waveguides made of 100-nm-thick niobium (Nb) or niobium nitride (NbN) films fabricated on 200 mm silicon wafers. Measurements of the two-ports S-parameters up to 25 GHz in a 4.7K–14 K temperature range with an added direct current up to 115 mA were done using a cryogenic probe station. With proper RF calibration and de-embedding procedure, both temperature and dc current dependence of the RF superconducting properties are analyzed. We report a kinetic inductance of 0.15 pH/□\square□, a critical current density of 50 MA/cm2^{2}2, and a critical temperature of 8.9 K for Nb as well as 4.27 pH/□\square□, 3 MA/cm2^{2}2, and 13.8 K for NbN. A telegraphist transmission line model taking into account the BCS theory has been developed and the comparison with the measurements is discussed.
Long superconducting niobium coplanar waveguides (CPW) on silicon wafers have been implemented with inner conductor width, thickness and length of about 50 nm/spl times/250 nm/spl times/3.2 mm, respectively. CPW tapers yield the transition from small to large cross sections for 50 /spl Omega/ coaxial SMA connectors. Microwave properties are measured at 4.2 K via /spl lambda//2-resonators where the inner conductor width w/sub i/ is about half the London penetration depth. Due to the dominant kinetic inductance the measured quality factor is close to an evaluated minimum value for w/sub i/<50 nm. The quality factors of such nanolines with niobium are approximately 150 at 10 GHz, i.e., more than two orders of magnitude larger than with aluminum at the same temperature. An unexpected power dependence of the intermodulation amplitudes and the corresponding dc properties are described.
The high critical magnetic field and relatively high critical temperature of niobium nitride (NbN) make it a promising material for applications in superconducting quantum technology. However, NbN-based superconducting circuits are sensitive to decoherence sources such as two-level system (TLS) defects. Here, we numerically and experimentally investigate NbN superconducting microwave coplanar waveguide resonator arrays with a 100 nm thickness, capacitively coupled to a common coplanar waveguide on a silicon chip. We observe that the resonators' internal quality factor (QiQ_{i}Qi​) decreases fromQi∼1.07×106Q_{i}\sim 1.07\times 10^{6}Qi​∼1.07×106in a high power regime toQi∼1.36×105Q_{i}\sim 1.36\times 10^{5}Qi​∼1.36×105in the single photon regime. Data from this study is consistent with the TLS theory, which describes the TLS interactions in resonator substrates and interfaces. Moreover, we study the temperature (TTT) dependence ofQiQ_{i}Qi​and resonance frequencyfrf_{r}fr​of coplanar waveguide resonators to characterize the quasiparticle density. We observe that the increase in kinetic inductance at higher temperatures is the main reason for the frequency shift. Finally, we measurefrf_{r}fr​andQiQ_{i}Qi​in response to in-plane magnetic fields (B∣∣B_{||}B∣∣​). We verify thatQiQ_{i}Qi​stays well above10410^{4}104up toB∣∣B_{||}B∣∣​= 240 mT in the photon number< ⁣nph ⁣>< \! n_{ph} \! ><nph​>= 1.8 atTTT= 100 mK. Our results could enable the development of robust microwave superconducting circuits for circuit quantum electrodynamics at high magnetic fields required for hybrid superconducting-semiconducting quantum circuits.
We characterize niobium nitride (NbN) λ/2 coplanar waveguide resonators, which were fabricated from a 10-nm-thick film on silicon dioxide grown by sputter deposition. For films grown at 180 °C, we report a superconducting critical temperature of 7.4 K associated with a normal square resistance of 1 kΩ, leading to a kinetic inductance of 192 pH/◻. We fabricated resonators with a characteristic impedance up to 4.1 kΩ and internal quality factors Qi>104 in the single photon regime at zero magnetic field. Moreover, in the many photon regime, the resonators present a high magnetic field resilience with Qi>104 in a 6 T in-plane magnetic field and in a 300 mT out-of-plane magnetic field. These findings make such resonators a compelling choice for circuit quantum electrodynamics experiments involving quantum systems with small electric dipole moments operated in finite magnetic fields.
We characterize inductors fabricated from ultra-thin, approximately 100 nm wide strips of niobium (Nb) and niobium nitride (NbN). These nanowires have a large kinetic inductance in the superconducting state. The kinetic inductance scales linearly with the nanowire length, with a typical value of 1 nH µm(-1) for NbN and 44 pH µm(-1) for Nb at a temperature of 2.5 K. We measure the temperature and current dependence of the kinetic inductance and compare our results to theoretical predictions. We also simulate the self-resonant frequencies of these nanowires in a compact meander geometry. These nanowire inductive elements have applications in a variety of microwave frequency superconducting circuits.
Microwave kinetic inductance detectors (MKIDs) are playing an increasingly role in THz astronomy. Superconducting coplanar waveguide (CPW) lines are commonly adopted in MKIDs for the resonators as well as the readout through line. It is therefore of particular interest to characterize the transmission properities of superconducting CPW lines at low temperatures. A cryogenic through-line method based on two cryogenic RF switches is proposed to characterize Nb and TiN superconducting CPW lines. On-chip calibration has been successfully carried out. Detailed results and analysis will be presented.
The objective of this thesis is to evaluate a generic process for fabrication and characterization of the Superconductive coplanar waveguide (CPW) resonators. Superconductive CPW resonators with various lengths and shapes are designed to investigate their electrical and magnetic properties as well as resonance properties and sensitivities. In the first part of thesis, two different models are introduced in order to estimate the nonlinear kinetic inductance of a superconducting CPW resonator. The first model is based on Bean critical-state model and the second one is based on current dependence of London penetration depth. The existence of a shift in resonant frequency of Superconductive CPW resonator caused by a non-linear kinetic inductance is also shown experimentally. Simulations were carried out to estimate the nonlinear kinetic inductance due to the self- induced magnetic field penetration. The rest of the thesis is concerned with development of very smooth Aluminum (Al) thin films with RMS (Root Mean Square) roughness 1~nm and CAD (Computer Aid Design) of superconductive CPW resonators. Experimental investigation of a generic fabrication technique for superconductive CPW resonator is carried out. Many resonators are fabricated with different design parameters, such as centerline or gap width, film thickness and gap capacitors length. The fabrication process is described in detail. Electron Beam Lithography is used to fabricate Nb and Al CPW resonators which are coupled to outer conductors via gap capacitors. We have fabricated GHz frequency CPW resonators with quality factors, Q up 5X10^5.