Don't go to sleep, stay up until it's an appropriate time to go to bed (between 7-12). If that doesn't sound appealing then take a
power nap.
When I have to get up early but stayed up too late I set my alarm clock a few hours before I want to get up. When it goes off I get up, set the alarm a half hour ahead and go back to bed. By the time I have to get up I'm wide awake.