  Spectroscopic-imaging scanning tunneling microscopy is a powerful technique
to study quantum materials, with the ability to provide information about the
local electronic structure with subatomic resolution. However, as most
spectroscopic measurements are conducted without feedback to the tip, it is
extremely sensitive to vibrations coming from the environment. This requires
the use of laboratories with low-vibration facilities combined with a very
rigid microscope construction. In this article, we report on the design and
fabrication of an ultra-stable STM for spectroscopic-imaging measurements that
operates in ultra high vacuum and at low temperatures (4 K). We perform finite
element analysis calculations for the main components of the microscope in
order to guide design choices towards higher stiffness and we choose sapphire
as the main material of the STM head. By combining these two strategies, we
construct a STM head with measured lowest resonant frequencies above f0=13 kHz
for the coarse approach mechanism, a value three times higher than previously
reported, and in good agreement with the calculations. With this, we achieve an
average vibration level of $\sim$ 6 fm/sqrt(Hz), without a dedicated
low-vibration lab. We demonstrate the microscope's performance with topographic
and spectroscopic measurements on the correlated metal Sr2RhO4, showing the
quasiparticle interference pattern in real and reciprocal space with high
signal-to-noise ratio.
