I am most creative when I sleep. I wake up with ideas. But I'm not productive in the morning. If I can get to the office before it gets too busy or distracting, I find I can jell a lot of ideas in the morning.
I am productive late at night, when I can go into the coding zone with little interruption. But that late night time is generally not creative for me.
I notice that when I get enough sleep I will sometimes spend the last dream of the morning solving (or at least advancing on a solution) to a problem I have been wrestling with. My dead time is after lunch until early evening, I try and schedule phone calls and interaction with other people to renew my energy.
I am productive late at night, when I can go into the coding zone with little interruption. But that late night time is generally not creative for me.