  Diamond membrane devices containing optically coherent nitrogen-vacancy (NV)
centers are key to enable novel cryogenic experiments such as optical
ground-state cooling of hybrid spin-mechanical systems and efficient
entanglement distribution in quantum networks. Here, we report on the
fabrication of a (3.4 $\pm$ 0.2) {\mu}m thin, smooth (surface roughness r$_q$ <
0.4 nm over an area of 20 {\mu}m by 30 {\mu}m diamond membrane containing
individually resolvable, narrow linewidth (< 100 MHz) NV centers. We fabricate
this sample via a combination of high energy electron irradiation, high
temperature annealing, and an optimized etching sequence found via a systematic
study of the diamond surface evolution on the microscopic level in different
etch chemistries. While our particular device dimensions are optimized for
cavity-enhanced entanglement generation between distant NV centers in open,
tuneable micro-cavities, our results have implications for a broad range of
quantum experiments that require the combination of narrow optical transitions
and {\mu}m-scale device geometry.
