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Design Methodologies for High Density Superconducting Circuits and Systems

Ana Mitrovi

Supervised by Mark Bocko

703 Computer Studies Building

With operating frequencies reaching hundreds of gigahertz and switching energies in the attojoule range, superconducting electronics has become one of the leading candidates among beyond CMOS technologies. The practical implementation of large scale superconducting digital systems is constrained by multiple challenges, including limited power delivery efficiency, restricted scalability and integration density, and the absence of mature electronic design automation tools for large scale circuit design. In this dissertation, modeling, analysis, and design methodologies are presented that address the scalability and integration density challenges of superconducting digital technologies.

A methodology for thermal analysis is introduced to describe heat generation and propagation in rapid single flux quantum (RSFQ) circuits. The modeling approach provides temperature estimates that agree with numerical simulations while maintaining low computational cost, enabling temperature-aware design of RSFQ circuit structures and largescale layouts. By quantifying thermal effects on chip, this method supports reliable operation of digital circuits and guides the scaling of integration density in superconducting systems.

To further improve scalability of superconducting digital circuits, the use of Joseph-son junctions with ferromagnetic barriers is investigated. Replacing the insulating barrier with a ferromagnetic layer modifies the current–phase relationship, enabling π-, 2ϕ-, and ϕ-junction operation. These junctions allow inductorless flux quantum storage, intrinsic bias, and phase logic, offering new approaches for area efficient and energy efficient computing with superconducting devices. An inductorless dynamic logic family based on bistable 2ϕ-junctions is proposed, exhibiting improved scalabil-ity compared with conventional RSFQ circuits. To enable accurate circuit analysis, a compact Verilog-A model of 2ϕ-junctions is developed. The model reproduces exper-imentally observed behavior of junctions with weak ferromagnetic and ferromagnetic insulator barriers, and simulations reveal the influence of harmonic components on switching dynamics, margins, and circuit robustness.

A variation-aware design methodology is introduced for circuits employing su-perconductor–ferromagnet–superconductor π-junctions. Sensitivities of the critical current density to process and temperature variations are quantified, and margins are established for reliable circuit operation. It is shown that magnetic scattering, in particular spin-flip scattering, is the dominant source of parameter sensitivity in junctions with weak ferromagnetic barriers. Material and fabrication choices that enable better control of this parameter are therefore critical for improving reproducibility and reliable device performance. Together, the modeling and design methodologies developed in this dissertation contribute to improving the scalability and reliability of superconducting digital systems, supporting the advancement of high speed, energy efficient computing technologies.