In this post Richard Wiseman recommends reducing the use of screens late at night because of the blue light emitted by them as that can keep you awake for longer.
I read books on my phone but I use Screen Filter To bring the brightness way down. Once I start reading a book I generally get sleepy within a dozen words or so! Anyway, I just installed the Twilight app that changes the temperature of the screen at different times of the day. At night it will make the screen go slightly red. I’ll give it a go tonight. Maybe I’ll look at the screen and fall into a deep sleep..
The irony is, I’m typing this at my PC where I should really have something like f.lux installed if I’m that worried about it.