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Journal of Applied Physics

Measurement and calculation of Josephson junction device inductances

Wen‐Hao Chang

Published Mar 1, 1981• 27 citations
Publisher

Abstract

We have measured the inductances of various structures used in Josephson junction devices and circuits by means of a novel differential inductance measurement technique. The structures measured include a single superconductor strip line, multisuperconductor strip lines, a single superconductor strip line crossing a ground plane hole, and two coupled superconductor strip lines crossing a ground plane hole. All measured inductances are compared with inductances calculated from various inductance formulas and two numerical inductance calculation programs. Very good agreements are found between the measured inductances and the calculated results for most cases.

DOI
10.1063/1.329774

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We have measured the inductances of various structures used in Josephson junction devices and circuits by means of a novel differential inductance measurement technique. The structures measured include a single superconductor strip line, multisuperconductor strip lines, a single superconductor strip line crossing a ground plane hole, and two coupled superconductor strip lines crossing a ground plane hole. All measured inductances are compared with inductances calculated from various inductance formulas and two numerical inductance calculation programs. Very good agreements are found between the measured inductances and the calculated results for most cases.
We evaluated mutual inductances between two superconducting striplines coupled through a superconducting intermediate layer in Nb Josephson IC.In order to measure the mutual inductances we designed eight test circuits based on a superconducting quantum interference device (SQUID), which included intermediate layers of two different thicknesses and four different widths. The inductance extraction program FastHenry with superconductor support was used for numerical calculation. The experimental results agreed with the calculated results, both of which confirmed that a thicker and wider intermediate layer reduced the mutual coupling more efficiently.
Several programs exist that calculate inductance in line structures. Some can even handle corners and holes in the ground plane. However, real structures in superconducting electronics are often more complex, and more elaborate techniques are needed to provide a reliable estimate of inductance, especially over very short intra-gate distances. A technique implemented with a modified version of FastHenry is discussed, whereby any inter-junction inductance in RSFQ circuits, in the vicinity of complex three-dimensional structures, junction cover pads and damping resistors, can be estimated. Placement of the reflection plane for the method of images is also discussed, together with the effect of segmentation size, and various results presented.
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.
Mutual inductance between two superconducting strip lines coupled through a grounded shield layer is evaluated by both experiments and numerical calculation. A conventional superconducting quantum interference device (SQUID) method on a Nb Josephson IC chip is employed for experiments, whereas a three-dimensional inductance extraction program "FastHenry" is used in numerical calculation. Five test circuits are designed to investigate the effects of two ground contacts placed parallel to the strip lines with different spacing. Both the experimental and numerical results confirm that the mutual inductance is at its minimum when the contacts are placed close to the Josephson junctions, that is, the edges of the SQUID line under evaluation. In the experiments, the minimum value of the mutual inductance is 26% of the value for the reference circuit with a floating shield layer. A model including the Meissner effect in a superconducting loop is found to provide a quasi-quantitative explanation for the dependence on the spacing between two contacts.
The inductive coupling between a Josephson junction and a superconducting stripline is calculated. In the overlapping region they share a superconducting film, the structure having superconducting (S) and insulating layers (I) sandwiched S—I—S—I—S. The coupling arises from the magnetic field penetration through the common superconductor. An equivalent circuit representation is exhibited which has the same modes and coupling as the original system. Using the circuit analog, the power transfer is calculated for several cases of interest: (a) power is radiated outward in the stripline from a biased junction and (b) power is absorbed by the junction from a source coupled to the stripline. The criterion for matching the tunnel junction to the stripline is discussed.
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.