Many of the older phones, (I know Black Berries were this way) had alarms that would work with the "power off". In reality the phone was not actually off, it was in more like a deep sleep, the only way to power them down 100% was to pull the battery.
With the new smart phones when you power them down they are actually off. So you will not be able to find an alarm that works with the phone off.
If your worried about data or battery use, you can switch on airplane mode and put your battery mode on nighttime saver.
Hope this helps.