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IEEE Transactions on Applied Superconductivity

Anomalous current-dependence of kinetic inductance in ultrathin NbN meander lines

Mark W. Johnson, Alan M. Kadin

Published Jun 1, 1997• 6 citations
Publisher

Abstract

We have measured the rf impedance of 10-nm thick superconducting granular NbN meander lines between 5 /spl mu/m and 20 /spl mu/m wide. The complex reflection coefficient was obtained directly using a vector network analyzer. The impedance (at 10 MHz for a 5 /spl mu/m wide line) is dominated by the large kinetic Inductance of the film, with a sheet inductance of order 1 nH, giving a total inductance of 400 nH for a 5 /spl mu/m/spl times/2 mm line. The kinetic inductance diverges as T/spl rarr/T/sub c/=6.5 K, as expected from Ginzburg-Landau theory (GL). Of particular interest is a substantial decrease of measured inductance with increasing dc current, contrary to the dependence expected from GL. This anomalous current dependence is not well understood, but may be related to vortex dynamics and Josephson effects in these granular films, as supported by preliminary Josephson array simulations. These results have important implications for potential devices such as tunable rf phase shifters and kinetic inductance photodetectors.

DOI
10.1109/77.622146

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We have measured the rf impedance of 10-nm thick superconducting granular NbN meander lines between 5 /spl mu/m and 20 /spl mu/m wide. The complex reflection coefficient was obtained directly using a vector network analyzer. The impedance (at 10 MHz for a 5 /spl mu/m wide line) is dominated by the large kinetic Inductance of the film, with a sheet inductance of order 1 nH, giving a total inductance of 400 nH for a 5 /spl mu/m/spl times/2 mm line. The kinetic inductance diverges as T/spl rarr/T/sub c/=6.5 K, as expected from Ginzburg-Landau theory (GL). Of particular interest is a substantial decrease of measured inductance with increasing dc current, contrary to the dependence expected from GL. This anomalous current dependence is not well understood, but may be related to vortex dynamics and Josephson effects in these granular films, as supported by preliminary Josephson array simulations. These results have important implications for potential devices such as tunable rf phase shifters and kinetic inductance photodetectors.
Experimental studies to enlarge kinetic inductance of NbN thin films using the effects of quality and thickness of the film are made by measuring Fiske current steps in the current-voltage (I-V) characteristics of NbN/Pb-In Josephson junctions. Experiments demonstrate that the specific kinetic inductance L K can be enlarged over a wide range by changing stoichiometry of the film, as well as by making the film thickness thin, and that this enlargement becomes larger by both effects when the film thickness is in an ultra thin regime. This inductance is shown to be well fitted to L K=µ0λ2/d, w h e r e µ_0 i s t h e v a c u u m p e r m e a b i l i t y, d i s t h e t h i c k n e s s, a n d λ i s t h e m a g n e t i c p e n e t r a t i o n d e p t h i n t h e d i r t y l i m i t. I n t h e p r e s e n t e x p e r i m e n t w e a t t a i n e d t h e i n d u c t a n c e a s h i g h a s L_K=130 p H b y t h e c o m b i n e d e f f e c t s o f i m p u r i t y a n d t h i c k n e s s f o r a f i l m w i t h
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.
Disorder is a powerful route to high kinetic inductance in superconducting ultrathin films, enabling compact high-impedance quantum circuits. This functionality, however, comes at the cost of reduced phase rigidity and potentially anomalous electrodynamics. Here, we use NbN microwave resonators with thicknesses down to 2.8 nm and sheet kinetic inductance up to 300 pH per square to probe how this trade-off reshapes the superconducting response. In the thinnest films, transport shows signatures of a Berezinskii-Kosterlitz-Thouless transition, while the microwave response reveals a pronounced low-temperature power-law suppression of the superfluid stiffness, inconsistent with Mattis-Bardeen theory. With increasing thickness, this anomalous regime is progressively suppressed, marking a continuous crossover toward conventional, gap-dominated electrodynamics. Cross-sectional transmission electron microscopy reveals a nanocrystalline twin-domain structure, pointing to oriented microstructural disorder as a crucial factor in the observed response. Overall, the crossover is governed by the ratio of superfluid stiffness to pairing energy, Theta(0)/Tc, identifying this ratio as a parameter governing the boundary between phase-fluctuation-dominated and gap-dominated superconducting electrodynamics in disordered nanofilms.
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.
A series of NbN thin film SQUIDs with transition temperatures ranging from 5 K to ∼14 K are being characterized by microwave measurements at 9.6 GHz. The data are being used to determine the critical current, resistance, and energy sensitivity of each device, to identify features that may be related particularly to the granular nature of the weak links, and to study systematically the variations of the SQUID response with temperature. The devices are nominally 1 μm long, 10 nm thick and from 1 μm to ∼50 μm wide and are fabricated on 1 mm-diameter quartz rods. All have previously been well characterized as SQUIDs at 23 MHz. Detailed results are presented for the first five devices studied.
We present measurements of the self- and mutual inductance of NbN and NbN/Nb bilayer inductors (microstrips, striplines, serpentines, etc.) with Nb ground plane(s) fabricated in an advanced process for superconductor electronics developed at MIT Lincoln Laboratory. In this process, the signal traces of logic cell inductors are made either of a 200-nm NbN layer with${{\bm{T}}}_{\bm{c}} \approx 15.5Koranin−situdepositedNbN/Nbbilayer,replacinga200−nmNblayerM6inthestandardSFQ5eeprocesswithninesuperconductinglayerson200−mmwafers.Nbgroundplanesarepreservedtomaintainahighlevelofinterlayershieldingandlowintralayermutualcoupling.Atwo−steppatterningofthetopNbandthebottomNbNlayersoftheNbN/Nbbilayerallowsthecreationofinductorswithaverywiderangeofinductances,fromlowvalues∼0.4pH/μmtypicalforNbgeometricalinductorsto∼35pH/μmtypicalforthin−filmkineticinductors.ThemutualinductanceofvariouscombinationsofNbN,Nb,andNbN/Nbinductorsdoesnotdependonsuperconductingpropertiesofthesignaltracesinthestudiedrangeoflinewidths,15.5 K or an in-situ deposited NbN/Nb bilayer, replacing a 200-nm Nb layer M6 in the standard SFQ5ee process with nine superconducting layers on 200-mm wafers. Nb ground planes are preserved to maintain a high level of interlayer shielding and low intralayer mutual coupling. A two-step patterning of the top Nb and the bottom NbN layers of the NbN/Nb bilayer allows the creation of inductors with a very wide range of inductances, from low values ∼0.4 pH/μm typical for Nb geometrical inductors to ∼35 pH/μm typical for thin-film kinetic inductors. The mutual inductance of various combinations of NbN, Nb, and NbN/Nb inductors does not depend on superconducting properties of the signal traces in the studied range of linewidths,15.5Koranin−situdepositedNbN/Nbbilayer,replacinga200−nmNblayerM6inthestandardSFQ5eeprocesswithninesuperconductinglayerson200−mmwafers.Nbgroundplanesarepreservedtomaintainahighlevelofinterlayershieldingandlowintralayermutualcoupling.Atwo−steppatterningofthetopNbandthebottomNbNlayersoftheNbN/Nbbilayerallowsthecreationofinductorswithaverywiderangeofinductances,fromlowvalues∼0.4pH/μmtypicalforNbgeometricalinductorsto∼35pH/μmtypicalforthin−filmkineticinductors.ThemutualinductanceofvariouscombinationsofNbN,Nb,andNbN/Nbinductorsdoesnotdependonsuperconductingpropertiesofthesignaltracesinthestudiedrangeoflinewidths,{\bm{w}};itequalsthemutualinductanceoftheNbinductorswiththeequivalentgeometryandplacementbetweenthegroundplanes.ThemeasuredmagneticfieldpenetrationdepthinNbNfilmsdepositedbyreactivesputteringat200°CisλNbN=491±5nm.Themeasuredkineticinductanceofthefilmswiththicknesses; it equals the mutual inductance of the Nb inductors with the equivalent geometry and placement between the ground planes. The measured magnetic field penetration depth in NbN films deposited by reactive sputtering at 200 °C isλNbN= 491 ± 5 nm. The measured kinetic inductance of the films with thicknesses;itequalsthemutualinductanceoftheNbinductorswiththeequivalentgeometryandplacementbetweenthegroundplanes.ThemeasuredmagneticfieldpenetrationdepthinNbNfilmsdepositedbyreactivesputteringat200°CisλNbN=491±5nm.Themeasuredkineticinductanceofthefilmswiththicknesses{\bm{t}}\ = {\bm{\ }}200nmand150nm,respectively1.51pH/sqand2.06pH/sq,islargerthanthatexpectedforconventionalsuperconductorswithshortmeanfreepath,correspondingtoabout25200 nm and 150 nm, respectively 1.51 pH/sq and 2.06 pH/sq, is larger than that expected for conventional superconductors with short mean free path, corresponding to about 25% lower superfluid density. We also measured kinetic inductance of the right-angle bends of NbN striplines and found it to be negligible at200nmand150nm,respectively1.51pH/sqand2.06pH/sq,islargerthanthatexpectedforconventionalsuperconductorswithshortmeanfreepath,correspondingtoabout25{\bm{w}} < {\bm{\lambda }}_{{\bm{NbN}}}^2/{\bm{t}}$, indicating an insignificant effect of current crowding in the presence of superconducting ground plane(s). Implementing NbN and NbN/Nb kinetic inductors enables a significant increase in the integration scale of superconductor digital electronics.