I've noticed the same thing. I've been forced to wake up with an alarm clock at 6am for the past several years, but in the past (and I hope the future) I never used an alarm clock because it doesn't pay attention to my sleep cycle.
Okay..not quite all alarm clocks: http://www.axonlabs.com/products/smart.html
I have found this to be the case. If I wake up alert, I find it much easier to dive into a problem, which then keeps me awake.