noun
on the verge of waking; half-awake moment
Refers to the transitional state just before fully waking up, often used in literary or descriptive contexts.
覚め際に夢の内容をはっきり覚えていることがある。
Sometimes I remember the dream clearly just as I'm waking up.
覚め際のぼんやりした意識の中で、誰かの声が聞こえた気がした。
In the hazy consciousness on the verge of waking, I thought I heard someone's voice.
Compound of 覚め (waking, from 覚める) and 際 (moment, verge). The exact historical derivation is straightforward; the word is a transparent combination of its parts.