  Color centers in diamond are one of the most promising tools for quantum
information science. Of particular interest is the use of single-crystal
diamond membranes with nanoscale-thickness as hosts for color centers. Indeed,
such structures guarantee a better integration with a variety of other quantum
materials or devices, which can aid the development of diamond-based quantum
technologies, from nanophotonics to quantum sensing. A common approach for
membrane production is what is known as "smart-cut", a process where membranes
are exfoliated from a diamond substrate after the creation of a thin
sub-surface amorphous carbon layer by He$^+$ implantation. Due to the high ion
fluence required, this process can be time-consuming. In this work, we
demonstrated the production of thin diamond membranes by neon implantation of
diamond substrates. With the target of obtaining membranes of $\sim$ 200 nm
thickness and finding the critical damage threshold, we implanted different
diamonds with 300 keV Ne$^+$ ions at different fluences. We characterized the
structural properties of the implanted diamonds and the resulting membranes
through SEM, Raman spectroscopy, and photoluminescence spectroscopy. We also
found that a SRIM model based on a two-layer diamond/sp$^2$-carbon target
better describes ion implantation, allowing us to estimate the diamond critical
damage threshold for Ne$^+$ implantation. Compared to He$^+$ smart-cut, the use
of a heavier ion like Ne$^+$ results in a ten-fold decrease in the ion fluence
required to obtain diamond membranes and allows to obtain shallower smart-cuts,
i.e. thinner membranes, at the same ion energy.
