Your brain tells you when to go to sleep by producing melatonin. Melatonin is what makes you feel tired, and prepares you for sleep.
The brain hormone melatonin is produced later at night for teens than it is for kids and adults. This can make it harder for teens to fall asleep early. – TeensHealth How Much Sleep Do I Need?
This has been noted by many, many reputable sources, here's one more:
Sometime in late puberty, the body secretes the sleep-related hormone melatonin at a different time than it normally does. This changes the circadian rhythms that guide a person's sleep-wake cycle. For instance, if you told your teen to go to bed at 10 p.m., she may end up staring at the ceiling until 1 or 2 a.m. waiting to fall asleep. At about 7:30 p.m. a teen feels wide awake and fully alert, unlike an adult who is starting to "wind down." – Adolescent Sleep (Stanford)
I think controlling your child's bedtime is unhealthy, you should let their body do the healthiest thing that it can, which it will dictate on its own.
Once you start forcing your child into certain circadian rhythms (sleep patterns) you may start detrimentally affecting their health (e.g. as Dan points out), and are definitely decreasing their productivity.
I think the best thing you can do is make a no-screens from 9 PM (her current bedtime) rule. In fact get her to leave her devices somewhere far from her room (try to trust her to do this herself.)
I am 17 years old at the moment and wish my parents had been stricter with this earlier in my adolescence. Now I enforce this rule on myself, and naturally won't feel like sleeping until after 11 o'clock, but when I was staying up glued to a screen earlier in my teens I would be unnaturally (and unhealthily) staying awake until 3 AM, 4 AM in some cases, destroying daily productivity and (hopefully not irreparably) my health.
If you encourage her to read books or do paper-based homework/tests past that time it will be extremely beneficial to her academic life.
We found that memory was superior when sleep occurred shortly after learning rather than following a full day of wakefulness. Lastly, we present evidence that the rate of deterioration across wakefulness was significantly diminished when a night of sleep preceded the wake period compared to when no sleep preceded wake, suggesting that sleep served to stabilize the memories against the deleterious effects of subsequent wakefulness. – Memory for Semantically Related and Unrelated Declarative Information: The Benefit of Sleep, the Cost of Wake. PLoS ONE 7(3): e33079.
Things you read and learn just before going to bed are more likely to be remembered, I wish I'd abused this more often when I was younger.
Also it gives a great opportunity to read books.
The benefits are plenty, which is especially important in a distracted, smartphone age in which one-quarter of American children don’t learn to read. This not only endangers them socially and intellectually, but cognitively handicaps them for life. One 2009 study of 72 children ages eight to ten discovered that reading creates new white matter in the brain, which improves system-wide communication. – How Reading Rewires Your Brain for More Intelligence and Empathy
I hope she'll come to love reading both fiction and non-fiction Since I set myself the no-screens before bed rule I've become happier and more productive in the day, and have fallen in love with reading. Learning about what other people think of the world, comparing theories you read in different books, is so interesting. And immersing yourself in the stories of fabricated worlds is great.
Don't enforce a bed time, just enforce a no-screens time. She will naturally fall asleep whenever her body's ready.