hypnopompic

hypnopompic \hip-nuh-POM-pik\, adjective:

Of or pertaining to the semiconscious state prior to complete wakefulness.

He shudders, snaps himself out of it; as one can, with effort, do, to escape from a bad dream, working one's way in stages, toward hypnopompic state until finally, fully awake.
-- Mary Caponegro, The Star Cafe

He woke fitfully, from a dream where his work had gone terribly wrong. He was still hypnopompic.
-- Richard Powers, The Echo Maker

Hypnopompic literally means "sending away sleep" in Greek. It was coined in English in the early 1900s from the roots hypno- meaning "sleep" and pomp meaning "sending away."