I. Introduction
Focused helium ion beam (FHIB) materials modification is an emerging technique with the capability to make high-quality thin-film, high-transition temperature (high-TC) superconducting Josephson junctions [1]. In this method, ion irradiation converts the film from a superconductor to an insulator by disordering the crystalline lattice [2]. In contrast to other techniques to fabricate high-TC superconducting devices based on grain-boundary [3], step-edge [4], or multilayer c-axis sandwich Josephson junctions [5], no material is removed or etched, as a result, nanoscale insulating features are obtainable for both Josephson junctions [6] and superconducting electrodes for devices such as superconducting quantum interference devices (SQUIDs) [7]. Scaling down to smaller junction and SQUID loop dimensions are necessary for higher integration density of superconducting circuits and for improving performance [8]. The smaller dimensions obtainable in circuit geometry afforded by scaling yields more control over circuit parameters such as critical current IC, resistance R and inductance L, the key variables for optimization of SQUIDs.