According to Business Insider's "10 Surprising Facts About How Our Brains Work," a sleepy brain is more creative:
If you’re tired, your brain is not as good at filtering out distractions and focusing on a particular task. It’s also a lot less efficient at remembering connections between ideas or concepts. These are both good things when it comes to creative work, since this kind of work requires us to make new connections, be open to new ideas and think in new ways. So a tired, fuzzy brain is much more use to us when working on creative projects.