Influence of Magnetic Flux Trapped in Moats on Superconducting Integrated Circuit Operation

The influence of a trapped flux quantum in a superconducting ground plane hole, called a moat, on superconducting circuit operation was analyzed. We devised a calculation model to estimate the magnetic flux threading a signal line of a superconducting integrated circuit by the trapped flux quantum in a moat placed near the signal line, by using a conventional inductance extraction tool. Assuming one flux quantum trapped in the moat, the dependence of the magnetic flux threading the signal line on the distance between the moat and the signal line were calculated. We measured the flux linkage by measuring the modulation of the I-V characteristic of a dc-SQUID with a moat near the SQUID implemented by using the 2.5 kA/cm
²
Nb standard process. The measured flux linkage agrees well with the analysis results using the devised calculation model. When the distance between the 1 μm × 10 μm moat and the SQUID, the signal line size of which corresponds to the typical inductance of an adiabatic flux quantum parametron (AQFP) is 1 μm and one flux quantum is trapped in the moat, the measured magnetic flux linkage threads the signal line was approximately 1.2% of the flux quantum. This flux linkage induces approximately 4% deterioration of the device margin of the AQFP. The devised calculation model and experimental results provide useful information for designing highly integrated future superconducting integrated circuits.