If you decide to spawn your tetras, have a separate aquarium just for the spawning. Just about every aquarium fish in the world, including neon tetras, find fish eggs delicious.
Most tetras, especially neon tetras are most comfortable in groups of at least six of their own or a very similar species, like cardinal tetras or black neon tetras.
The neon tetra (Paracheirodon innesi) has been a popular aquarium fish for decades. It's low price, vibrant red and blue coloration, innocuous nature and hardiness contribute to its popularity. Despite its hardiness, it takes intermediate skill as an aquarist to spawn neon tetras. The first step to getting neon tetras to spawn is to identify their gender. This is not difficult, and requires only observation of the fish and a bit of knowledge.
Determine your fishes' gender. Males are slimmer with a straighter neon blue line. The females have a slightly crooked neon blue line with a more full body.
Check and see if the female(s) are gravid. In most egg-laying fish, including neons, the female's abdomen will swell with eggs. A gravid female is a good indicator that your neon tetras are about to spawn.
Lastly, check for courting behavior. Male neon tetras perform a "dance" to attract female attention. The dance consists of swimming in a square motion with jerky movements. The mating dance is punctuated with periods of motionlessness.
If your tetras are showing these signs, there is a good chance they are about to spawn. It would be advisable to research their breeding at this point and attempt to spawn them.