Modelling Magnetic Fields and Shielding Efficiency in Superconductive Integrated Circuits

We present a magnetic field model that shows how single flux quantum (SFQ)-based electronics can be affected by nearby current carrying strip lines and other external magnetic field sources. This work is an enabling step towards the design of SFQ circuits that can operate without the need for ferromagnetic shielding. Firstly, a specific 3-D coil system was optimized to apply external homogeneous magnetic fields during a magneto-quasistatic numerical analysis of a SFQ Delay-Flip-Flop (DFF) circuit. We used magnetic field and current density visualization tools to identify the most affected areas in the circuit layout. Secondly, grid patterned and solid on-chip shielding techniques were verified through simulations to design magnetic field tolerant SFQ circuits. Without any form of shielding, the DFF operated up to maximum external magnetic field of 38 or 46 mu T, whereas with magnetic shields, the DFF failed at 50 or 98 mu T and 50 or 86 mu T for the grid and solid shields, respectively. Both shields have comparable failure points for the DFF. However, the grid-based shield has a lower influence on SFQ circuit inductance, requiring a faster re-optimization without the need to redesign the circuit.