Self- and Mutual Inductance of NbN and Bilayer NbN/Nb Inductors in a Planarized Fabrication Process With Nb Ground Planes

We present measurements of the self- and mutual inductance of NbN and NbN/Nb bilayer inductors (microstrips, striplines, serpentines, etc.) with Nb ground plane(s) fabricated in an advanced process for superconductor electronics developed at MIT Lincoln Laboratory. In this process, the signal traces of logic cell inductors are made either of a 200-nm NbN layer with ${{\bm{T}}}_{\bm{c}} \approx $ 15.5 K or an in-situ deposited NbN/Nb bilayer, replacing a 200-nm Nb layer M6 in the standard SFQ5ee process with nine superconducting layers on 200-mm wafers. Nb ground planes are preserved to maintain a high level of interlayer shielding and low intralayer mutual coupling. A two-step patterning of the top Nb and the bottom NbN layers of the NbN/Nb bilayer allows the creation of inductors with a very wide range of inductances, from low values ∼0.4 pH/μm typical for Nb geometrical inductors to ∼35 pH/μm typical for thin-film kinetic inductors. The mutual inductance of various combinations of NbN, Nb, and NbN/Nb inductors does not depend on superconducting properties of the signal traces in the studied range of linewidths, ${\bm{w}}$ ; it equals the mutual inductance of the Nb inductors with the equivalent geometry and placement between the ground planes. The measured magnetic field penetration depth in NbN films deposited by reactive sputtering at 200 °C is λ_NbN = 491 ± 5 nm. The measured kinetic inductance of the films with thicknesses ${\bm{t}}\ = {\bm{\ }}$ 200 nm and 150 nm, respectively 1.51 pH/sq and 2.06 pH/sq, is larger than that expected for conventional superconductors with short mean free path, corresponding to about 25% lower superfluid density. We also measured kinetic inductance of the right-angle bends of NbN striplines and found it to be negligible at ${\bm{w}} < {\bm{\lambda }}_{{\bm{NbN}}}^2/{\bm{t}}$ , indicating an insignificant effect of current crowding in the presence of superconducting ground plane(s). Implementing NbN and NbN/Nb kinetic inductors enables a significant increase in the integration scale of superconductor digital electronics.