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Superconductor Science and Technology

Inductance and penetration depth measurements of polycrystalline NbN films for all-NbN single flux quantum circuits

Yulong Zhong, Lu Zhang, Junjie Xie, Zengxu Zheng, Mingjun Lu, Hua Jin, Lingnan Wu, Weifeng Shi, Huiwu Wang, Wei Peng, Lei Chen, Zhen Wang

Published Nov 18, 2024• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6668/ad941a

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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.
In recent years, rapid single flux quantum (RSFQ) circuits, which are promising for the development of high-speed digital electronics, have attracted widespread interest. Niobium nitride (NbN) films have also attracted significant attention for high-frequency applications in superconducting electronics because of their superior material parameters, including their high critical temperature Tc and large gap voltage Vg. To enable the development of all-NbN SFQ circuits, we have developed a fabrication process based on NbN junctions and inductors made of NbN strip lines. It is important to evaluate the inductance because it can affect the performance of an RSFQ circuit and is essential for the RSFQ design. We measured the inductance properties of both epitaxial and polycrystalline NbN strip lines using a superconducting quantum interference device modulation technique at 4.2 K and obtained the width dependence on the inductance of the NbN films. The penetration depth was then calculated from these measurements. The NbN inductance values were calculated numerically with respect to the penetration depth and were then compared with the measured values from the experiments. It was demonstrated that the differences between these values were within 5%. The results reported here will be useful for the design and fabrication of all-NbN RSFQ circuits.
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.
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.
Abstract Superconducting quantum interference devices (SQUIDs) with 3D nano-bridge junctions can be miniaturized into nano-SQUIDs that are able to sense a few spins in a large magnetic field. Among all device parameters, the inductance is key to the performance of SQUIDs with 3D nano-bridge junctions. Here, we measured the critical-current magnetic flux modulation curves of 12 devices with three design types using a current strip-line directly coupled to the SQUID loop. A best flux modulation depth of 71% was achieved for our 3D Nb SQUID. From the modulation curves, we extracted the inductance values of the current stripe-line in each design and compared them with the corresponding simulation results of InductEX. In this way, London penetration depths of 110 and 420 nm were determined for our Nb (niobium) and NbN (niobium nitride) films, respectively. Furthermore, we showed that inductances of 11 and 119 pH for Nb and NbN 3D nano-bridge junctions, respectively, dominated the total inductance of our SQUID loops which are 23 pH for Nb and 255 pH for NbN. A screening parameter being equal to one suggests optimal critical currents of 89.6 and 8.1 μ A for Nb and NbN SQUIDs, respectively. Additionally, intrinsic flux noise of 110 ± 40 n Φ 0 /(Hz) 1/2 is calculated for the Nb SQUIDs with 3D nano-bridge junctions by Langevin simulation.
Data are presented on mutual and self-inductance of various inductors used in multilayered superconductor integrated circuits: microstrips and striplines with widths from 250 nm to a few micrometers, located on the same layer at various distances from each other, from 250 nm to a few micrometers, and/or on different layers spaced vertically; effect of long slits in the ground plane(s) along the inductors on their mutual inductance; inductance of right-angled bends; and inductance of meanders. Measurements were done using circuits fabricated in the SFQ5ee and the SC1 fully planarized fabrication processes with eight niobium layers and Nb/Al-AlOx/Nb Josephson junctions, developed at MIT Lincoln Laboratory for superconductor electronics. Simple analytical expressions for mutual and self-inductance of the basic inductors are given, describing experimental data with accuracy better than 2% over a very wide range of parameters. Mutual coupling between microstrips is long-ranged and decreases as a second power of distance between them, making microstrips unsuitable for very large scale integrated circuits. Mutual inductance of striplines decreases exponentially with distance between them on a scale of(H+2λ)/π({\boldsymbol{H}} + 2{\boldsymbol{\lambda }})/{\boldsymbol{\pi }}(H+2λ)/π∼ 0.3 μm, whereH{\boldsymbol{H}}Handλ{\boldsymbol{\lambda }}λare, respectively, the distance between and magnetic field penetration depth in superconducting ground planes, whereas superconducting properties of the signal traces are practically irrelevant. This decay distance determines the scale of integration above which adjacent inductors in a circuit become strongly coupled. Dependence of mutual inductance on the linewidth of wires is weak. As a result, the area of flux transformers—an essential component of all superconductor digital circuits using ac power, qubits, and sensor arrays—scales poorly with the linewidth, potentially restricting scalability of the circuits.
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.