  Scanning superconducting quantum interference device microscopy (sSQUID) is
currently one of the most effective methods for direct and sensitive magnetic
flux imaging on the mesoscopic scale. A SQUID-on-chip design allows integration
of field coils for susceptometry in a gradiometer setup which is very desirable
for measuring magnetic responses of quantum matter. However, the spatial
resolution of such a design has largely been limited to micrometers due to the
difficulty in approaching the sample. Here, we used electron beam lithography
technology in the fabrication of the 3D nano-bridge-based SQUID devices to
prepare pick-up coils with diameters down to 150 nm. Furthermore, we integrated
the deep silicon etching process in order to minimize the distance between the
pick-up coil and the wafer edge. Combined with a tuning-fork-based scanning
head, the sharpness of the etched chip edge enables a precision of 5 nm in
height control. By scanning measurements on niobium chessboard samples using
these improved SQUID devices, we demonstrate sub-micron spatial resolutions in
both magnetometry and susceptometry, significantly better than our previous
generations of nano-SQUIDs. Such improvement in spatial resolution of
SQUID-on-chip is a valuable progress for magnetic imaging of quantum materials
and devices in various modes.
