  The development of Si$_3$N$_4$ nanobeam optomechanical crystals is reviewed.
These structures consist of a 350 nm thick, 700 nm wide doubly-clamped
Si$_3$N$_4$ nanobeam that is periodically patterned with an array of air holes
to which a defect region is introduced. The periodic patterning simultaneously
creates a photonic bandgap for 980 nm band photons and a phononic bandgap for 4
GHz phonons, with the defect region serving to co-localize optical and
mechanical modes within their respective bandgaps. These optical and mechanical
modes interact dispersively with a coupling rate $g_{0}/2\pi\approx$100 kHz,
which describes the shift in cavity mode optical frequency due to the
zero-point motion of the mechanical mode. Optical sidebands generated by
interaction with the mechanical mode lie outside of the optical cavity
linewidth, enabling possible use of this system in applications requiring
sideband-resolved operation. Along with a review of the basic device design,
fabrication, and measurement procedures, we present new results on improved
optical quality factors (up to $4\times10^5$) through optimized lithography,
measurements of devices after HF acid surface treatment, and temperature
dependent measurements of mechanical damping between 6~K and 300~K. A
frequency-mechanical quality factor product $\left(f{\times}Q_m\right)$ as high
as $\approx2.6\times10^{13}$ Hz is measured.
