Disentangling superconductor and dielectric microwave losses in submicrometer $\mathrm{Nb}$/$\mathrm{Si}O$${}_2$ interconnects using a multimode microstrip resonator

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 ($\mathrm{Nb}$) insulated by silicon dioxide ($\mathrm{Si}O$${}_2$) made from a tetraethoxysilane (TEOS) precursor. Two process generations use damascene fabrication and the third one uses Cloisonné fabrication. For all three, $\mathrm{Si}O$${}_2$ exhibits a dielectric loss tangent $\tan \delta =0.0012\pm 0.0001$, independent of the $\mathrm{Nb}$ wire width over 0.25–4 $\text{μ}m$. The intrinsic microwave resistance $R_s$ of $\mathrm{Nb}$ 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 $R_s$ above the Bardeen-Cooper-Schrieffer (BCS) resistance $R_{\mathrm{BCS}}\approx 17\text{μ}\Omega$ at 10 GHz. For Cloisonné fabrication, we demonstrate $R_s=13\pm 1.4\text{μ}\Omega$ down to $0.25\text{μ}m$ wire width, which is below $R_{\mathrm{BCS}}$ and arguably the lowest microwave resistance reported for $\mathrm{Nb}$ at 4.2 K.