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arXiv:2605.28759

Absolute measurement of penetration depth of superconducting thin films using microwave stripline resonators

Arghya Dutta, Ajeet Salunke, Mahesh Poojary, Vivas C. Bagwe, Sangita Bose, Pratap Raychaudhuri

Published May 27, 2026• 0 citations
arXivHTMLPDF

Abstract

Superconducting microstrip resonators, which leverage kinetic inductance to probe electrodynamics, are sensitive tools for studying superconducting thin films at microwave frequencies. However, extracting the absolute superconducting penetration depth from these measurements remains challenging. In this work, we present a hybrid method to determine the absolute value of penetration depth over a wide temperature range by combining resonator measurements with finite-element electromagnetic simulations in COMSOL Multiphysics. We demonstrate this approach by extracting the penetration depth of NbN films by fabricating resonators from films of various thicknesses. Furthermore, we extend the technique to materials with lower critical temperatures by employing a flip-film geometry. By placing a sample above a NbN resonator, separated by a thin Mylar dielectric, we create a coupled structure where changes in the sample's penetration depth shift the resonant frequency. This non-destructive method provides a reliable, high-sensitivity platform for characterizing the penetration depth of diverse superconducting thin films.

DOI
10.48550/arxiv.2605.28759

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•Mar 1, 2010•1 citation
Superconducting microstrip resonators, which leverage kinetic inductance to probe electrodynamics, are sensitive tools for studying superconducting thin films at microwave frequencies. However, extracting the absolute superconducting penetration depth from these measurements remains challenging. In this work, we present a hybrid method to determine the absolute value of penetration depth over a wide temperature range by combining resonator measurements with finite-element electromagnetic simulations in COMSOL Multiphysics. We demonstrate this approach by extracting the penetration depth of NbN films by fabricating resonators from films of various thicknesses. Furthermore, we extend the technique to materials with lower critical temperatures by employing a flip-film geometry. By placing a sample above a NbN resonator, separated by a thin Mylar dielectric, we create a coupled structure where changes in the sample's penetration depth shift the resonant frequency. This non-destructive method provides a reliable, high-sensitivity platform for characterizing the penetration depth of diverse superconducting thin films.
Abstract In this paper, we report on a systematic study of the inductance and magnetic field penetration depth (λ) of polycrystalline NbN superconducting thin films. By employing a four-metal-layer fabrication process specifically designed for all-NbN single-flux-quantum circuits, we constructed a superconducting quantum interference device loop composed of two parallel NbN SNS junctions, NbN microstrips, and NbN ground planes for precise inductance measurement. At 4.2 K, as the linewidth increases from 1 μm to 30 μm, the inductance per unit length (L u) of NbN microstrips significantly decreases, for example, the L u of 250 nm thick NbN microstrips drops from 0.907 pH/μm to 0.047 pH/μm. Compared to Nb, the L u of polycrystalline NbN microstrips is approximately two to three times that of Nb, offering an advantage for manufacturing smaller superconducting inductors. Furthermore, we conducted simulation analysis using InductEx software to extract the λ of NbN films of varying thicknesses. The results indicate that as the film thickness increased from 45 nm to 600 nm, λ initially decreased sharply and then stabilized, with values ranging from 430 nm to 323 nm. Notably, once the film thickness exceeded 200 nm, λ remained essentially constant, even at a temperature of 10 K, where it showed good stability, albeit with a slight increase (about 50 nm) compared to 4.2 K. This dependence of λ on thickness is reasonably explained by considering the effects of NbN film thickness on the superconducting critical temperature and residual resistivity. These research findings not only deepen our understanding of the characteristics of superconducting films but also lay a solid foundation for the future design and manufacture of more compact superconducting circuits at the higher temperature of 10 K.
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Inductance of superconducting thin-film inductors and structures with linewidth down to 250 nm has been experimentally evaluated. The inductors include various striplines and microstrips, their 90° bends and meanders, interlayer vias, etc., typically used in superconducting digital circuits. The circuits have been fabricated by a fully planarized process with 8 niobium layers, developed at MIT Lincoln Laboratory for very-large-scale superconducting integrated circuits. Excellent run-to-run reproducibility and inductance uniformity of better than 1% across 200-mm wafers have been found. It has been found that the inductance per unit length of stripline and microstrip line inductors continues to grow as the inductor linewidth is reduced deep into the submicron range to the widths comparable to the film thickness and magnetic field penetration depth. It is shown that the linewidth reduction does not lead to widening of the parameter spread due to diminishing sensitivity of the inductance to the linewidth and dielectric thickness. The experimental results were compared with numeric inductance extraction using commercial software and freeware, and a good agreement was found for 3-D inductance extractors. Methods of further miniaturization of circuit inductors for achieving circuit densities> 106Josephson junctions per cm2are discussed.
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.
An on-wafer measurement technique allowing measurement of a superconducting film's penetration depth without post device-fabrication separation of the chips has been investigated. Coplanar waveguide (CPW) probes and a CPW to microstrip transition are utilized, allowing the use of commercially available LakeShore® CPX-1.5K cryogenic CPW probing station capable of microwave measurements to 50 GHz. The use of CPW probes allows for rapid prototyping and is nondestructive to the device wafers, and hence compatible with many device fabrication technologies. Measurement techniques utilizing resonant microwave circuits have been reported (1),(2), but require mounting to custom-made test fixtures and are not performed on-wafer, but instead on individual diced devices. However, such a dicing requirement is incompatible with our ultra-thin Si, Au beam-lead chip architecture (3). In addition to a traditional resonant circuit measurement technique, a technique that uses on-wafer calibration standards is discussed. The on-wafer calibration eliminates possible effects introduced by the testing setup and potentially offers additional advantages such as a size reduction and a direct measurement of RF loss. The designs and results for both measurement techniques are reported for NbTiN films.