Flexible superconducting Nb transmission lines on thin film polyimide for quantum computing applications

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 SiO₂. 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. (paper)