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Superconductor Science and Technology

New microwave components with inductively coupled superconducting striplines

Keiji Yoshida, Mohammad Sajjad Hossain, Keiji Enpuku, K. Yamafuji

Published Nov 1, 1991• 1 citation
Publisher

Abstract

A theoretical study is made of the inductive coupling of two superconducting striplines. The study takes advantage of the kinetic inductance, which is remarkable in superconducting films where the thickness is less than the London penetration depth. In the case of weak coupling where the coupled-mode description is most effective, it has been found that the forward-wave coupling leads to power exchange between two striplines with the efficiency of m= kappa 2 /( kappa 2 + Delta 2 ) at a distance of I= pi /2( kappa 2 + Delta 2 ) 1 2/. Here kappa 2 = beta 1 beta 2 M 2 /4L 1 L 2 is the coupling coefficient and delta =(1/2)(B 1 -B 2 ) is the phase mismatch parameter, where beta i , L i (i=1,2) and M are propagation constants, self-inductances and the mutual inductance of the two striplines, respectively. Numerical studies are also made for new types of kinetic inductance devices for microwave components, i.e. a directional coupler and microwave switch using the scattering coefficients in the general case.

DOI
10.1088/0953-2048/4/11/037

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A theoretical study is made of the inductive coupling of two superconducting striplines. The study takes advantage of the kinetic inductance, which is remarkable in superconducting films where the thickness is less than the London penetration depth. In the case of weak coupling where the coupled-mode description is most effective, it has been found that the forward-wave coupling leads to power exchange between two striplines with the efficiency of m= kappa 2 /( kappa 2 + Delta 2 ) at a distance of I= pi /2( kappa 2 + Delta 2 ) 1 2/. Here kappa 2 = beta 1 beta 2 M 2 /4L 1 L 2 is the coupling coefficient and delta =(1/2)(B 1 -B 2 ) is the phase mismatch parameter, where beta i , L i (i=1,2) and M are propagation constants, self-inductances and the mutual inductance of the two striplines, respectively. Numerical studies are also made for new types of kinetic inductance devices for microwave components, i.e. a directional coupler and microwave switch using the scattering coefficients in the general case.
The properties and applications of the inductive coupling of a superconducting stripline system, which takes advantage of kinetic inductance of thin superconducting films, are studied. The system, composed of two striplines inductively coupled through a common electrode as a four-port circuit, was formulated by obtaining its scattering coefficients in a general form. The system is characterized with the coupled-mode theory. Based on the analysis, it is proposed that a novel type of kinetic inductance devices for microwave analog components, such as directional couplers, microwave switches, variable filters, and efficient coupling elements for striplines. Experiments on stripline coupling with this scheme are also discussed.
We have looked into cobalt disilicide (CoSi2) as a potential building block for superconducting quantum circuits. In order to achieve this, we annealed a thin layer of Co to create microwave cavities with thickness of d = 10–105 nm from CoSi2 embedded in the silicon substrate. The cavity properties were measured as a function of temperature and power. In the films measuring 10 and 25 nm, we find a significant kinetic inductance LK with a non-BCS power-law variation δLK ∝ T4.3±0.2 at low temperatures. The quality factor of the studied microwave resonances varied from 3 × 103 (d = 10 nm) to ∼5 × 104 (d = 105 nm) and increased as d(A − log d) with thickness, with two-level systems having very little effect. The power dependence of kinetic inductance was analyzed in terms of heat flow due to electron–phonon coupling, which was found to be stronger than estimated for heat relaxation by regular quasiparticles.
In order to realize efficient coupling between a flux-flow type Josephson oscillator (FFO) and an external stripline, the authors carried out experiments to investigate the inductive coupling scheme in a strong coupling regime. By adopting NbN films with large penetration depths as electrodes for strong coupling, they were able to realize coupling sections with a coupling coefficient alpha =M/ square root L/sub 1/L/sub 2/ as large as 0.7, with M, L/sub 1/, and L/sub 2/ being mutual inductance, self-inductances of, the FFO, and the stripline, respectively. Using this design for the coupling, the authors succeeded in detecting AC fields at frequencies around 150 GHz, which were emitted from FFO to the stripline via the coupling section.
Aluminum-based platforms have allowed to reach major milestones for superconducting quantum circuits. For the next generation of devices, materials that are able to maintain low microwave losses while providing new functionalities, such as large kinetic inductance or compatibility with CMOS platform, are needed. Here, we report on a combined direct current and microwave investigation of titanium nitride films of different thicknesses grown using CMOS compatible methods. For microwave resonators made of 3 nm thick TiN, we measured large kinetic inductance LK ∼240 pH/sq, high mode impedance of ∼4.2 kΩ while maintaining microwave quality factor ∼105 in the single photon limit. We present an in-depth study of the microwave loss mechanisms in these devices that indicates the importance of quasiparticles and provide insight for further improvement.
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.
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.