We report results of measurements of Nb stripline resonators with linewidths ranging from 1.0 to 0.25 μ m, fabricated using an 8-Nb-layer process with planarized SiO2 dielectric developed at MIT Lincoln Laboratory for superconductor single-flux-quantum circuits. The fundamental resonant frequency f 0 was varied from 2.3 to 4.5 GHz. The results show that, at 4 K, the losses for the narrowest lines are dominated by losses in the dielectric. At high power, the nonlinear niobium losses dominate. Spiral inductors have also been used to design and fabricate multipole low-pass filters with three and five poles with cutoff at 1 GHz. The measured and simulated results for the filters agree very well and show almost ideal properties. The precision and high reproducibility of this fabrication process hold the promise of fabricating multipole filters without the need for tuning the individual poles.
We report results of measurements of Nb stripline resonators with linewidths ranging from 1.0 to 0.25 μ m, fabricated using an 8-Nb-layer process with planarized SiO2 dielectric developed at MIT Lincoln Laboratory for superconductor single-flux-quantum circuits. The fundamental resonant frequency f 0 was varied from 2.3 to 4.5 GHz. The results show that, at 4 K, the losses for the narrowest lines are dominated by losses in the dielectric. At high power, the nonlinear niobium losses dominate. Spiral inductors have also been used to design and fabricate multipole low-pass filters with three and five poles with cutoff at 1 GHz. The measured and simulated results for the filters agree very well and show almost ideal properties. The precision and high reproducibility of this fabrication process hold the promise of fabricating multipole filters without the need for tuning the individual poles.
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 understanding of the origins of power loss in superconducting interconnects is essential for the energy efficiency and scalability of superconducting digital logic. At microwave frequencies, power dissipates in both the superconducting wires and the dielectric and these losses can be of comparable magnitude. We describe an approach to accurately disentangle such losses by exploiting their frequency dependence in a multimode transmission-line resonator. This is supported by the concept of a resonator geometric factor extracted from the Ansys High Frequency Structure Simulator (hfss), a commercial three-dimensional finite-element method (FEM) that we adopt for solving a superconductor interior. Using the technique, we have optimized a planarized fabrication process of reciprocal quantum logic (RQL) for the minimum interconnect loss at 4.2 K and gigahertz frequencies. The microstrip interconnects are composed of niobium (Nb) insulated by silicon dioxide (SiO2) made from a tetraethoxysilane (TEOS) precursor. Two process generations use damascene fabrication and the third one uses Cloisonn\'e fabrication. For all three, SiO2 exhibits a dielectric loss tangent $\mathrm{tan}\phantom{\rule{0.1em}{0ex}}\ensuremath{\delta}=0.0012\ifmmode\pm\else\textpm\fi{}0.0001$, independent of the Nb wire width over 0.25--4 $\text{\ensuremath{\mu}}\mathrm{m}$. The intrinsic microwave resistance Rs of Nb varies with both the process and the wire width. For damascene fabrication, scanning transmission electron microscopy (STEM) and energy-dispersive x-ray spectroscopy (EDS) reveal that plasma oxidation and grain-growth orientation increase Rs above the Bardeen-Cooper-Schrieffer (BCS) resistance ${R}_{\mathrm{BCS}}\ensuremath{\approx}17\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{\ensuremath{\Omega}}$ at 10 GHz. For Cloisonn\'e fabrication, we demonstrate ${R}_{s}=13\ifmmode\pm\else\textpm\fi{}1.4\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{\ensuremath{\Omega}}$ down to $0.25\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ wire width, which is below RBCS and arguably the lowest microwave resistance reported for Nb at 4.2 K.
Abstract Data are presented on the inductance of various features used in superconductor digital integrated circuits: microstrip and stripline inductors with linewidths down to 120 nm and different combinations of ground plane layers, effect of perforations of various sizes in the ground planes and their distance to the inductors on inductance, inductance of vias of various sizes between adjacent layers, inductance of composite vias between distant superconducting layers. Test circuits used for the measurements were fabricated in a new 150 nm node of a fully planarized process with eight niobium layers developed at MIT Lincoln Laboratory for superconductor electronics as well as in our standard SFQ5ee and SC1 fabrication processes with 250 nm minimum feature size. The new SC2 process utilizes 193 nm photolithography in combination with plasma etching and chemical mechanical planarization of interlayer dielectrics to define inductors with linewidth down to about 100 nm on critical layers. The standard processes use 248 nm photolithography. The measured data are compared with the results of inductance extraction using software packages InductEx and wxLC. Variations of circuit inductors caused by the fabrication processes are discussed. Magnetic flux trapping in ground plane moats and its coupling to nearby inductors are discussed for circuit cooling in a residual field of several configurations.
We present the design, fabrication procedure, and measurement results of Nb superconducting microstrip transmission line resonators fabricated using thin-film polyimide HD-4110, including both nonembedded and embedded versions. These resonators were used to characterize the microwave dielectric loss tangent of 20 μm thick polyimide HD-4110 at deep cryogenic temperatures. We observed high-quality factors (Q) up to 21 040 at 1.2 K in the frequency range of 2-21 GHz for nonembedded resonators, indicating that the dielectric loss tangent can be less than 5×10-5. Embedded resonators with an additional 20 μm thick encapsulation layer also exhibited Q values as high as ~19 200. Dielectric and conductor (quasiparticle) loss have been compared between the two types of resonators. This study provides information applicable to the design of future high-density, flexible, multilayer superconducting cables, which are of great interest for potential applications in cryogenic electronics systems, including quantum computers.
We present recent work on design, fabrication, and characterization of thin-film, flexible superconducting stripline cables. Fabrication details, dc, and microwave performance (up to 14 GHz) of cables with Al/Nb/Al conductors and polyimide (PI) dielectric are discussed. Thin Al was used as a barrier layer between Nb and polyimide to protect the Nb superconductivity during subsequent PI curing steps, which were performed at a reduced temperature. The dc performance, including critical transition temperature and critical current, of the stripline transmission lines is presented. We observed Tcvalues of ~8.8 and ~8.6 K for signal traces and ground planes, respectively. Microwave characterization, including cross-talk, was performed on stripline transmission lines and resonators. We observed reasonable impedance match (S11better than -15 dB), low insertion loss (S21better than 0.04 dB/cm) and cross-talk below -60 dB for stripline transmission lines measured up to 10 GHz at 4.2 K. Furthermore, similarly fabricated stripline resonators exhibited quality factors ~7 000 at 10 GHz and 1.2 K for stripline resonators. The results of these experiments provide insight into material stack-ups for robust, multi-layer superconducting flexible cables that can find use in future cryogenic electronics systems.
We describe progress and initial results achieved towards the goal of developing integrated multi-conductor arrays of shielded controlled-impedance flexible superconducting transmission lines with ultra-miniature cross sections and wide bandwidths (dc to >10 GHz) over meter-scale lengths. Intended primarily for use in future scaled-up quantum computing systems, such flexible thin-film niobium/polyimide ribbon cables could provide a physically compact and ultra-low thermal conductance alternative to the rapidly increasing number of discrete coaxial cables that are currently used by quantum computing experimentalists to transmit signals between the several low-temperature stages (from ∼4 K down to ∼20 mK) of a dilution refrigerator. We have concluded that these structures are technically feasible to fabricate, and so far they have exhibited acceptable thermo-mechanical reliability. S -parameter results are presented for individual 2-metal layer Nb microstrip structures having 50 Ω characteristic impedance; lengths ranging from 50 to 550 mm were successfully fabricated. Solderable pads at the end terminations allowed testing using conventional rf connectors. Weakly coupled open-circuit microstrip resonators provided a sensitive measure of the overall transmission line loss as a function of frequency, temperature, and power. Two common microelectronic-grade polyimide dielectrics, one conventional and the other photo-definable (PI-2611 and HD-4100, respectively) were compared. Our most striking result, not previously reported to our knowledge, was that the dielectric loss tangents of both polyimides, over frequencies from 1 to 20 GHz, are remarkably low at deep cryogenic temperatures, typically 100 × smaller than corresponding room temperature values. This enables fairly long-distance (meter-scale) transmission of microwave signals without excessive attenuation, and also permits usefully high rf power levels to be transmitted without creating excessive dielectric heating. We observed loss tangents as low as 2.2 × 10 −5 at 20 mK, although losses increased somewhat at very low rf power levels, similar to the well-known behavior of amorphous inorganic dielectrics such as SiO 2 . Our fabrication techniques could be extended to more complex structures such as multiconductor cables, embedded microstrip, 3-metal layer stripline or rectangular coax, and integrated attenuators and thermalization structures.