Sleepiness – noun
Sleep – noun/verb
Sleepily – adverb
Sleepy – adjective
Asleep – adjective

Verb & adjective collocations
Fall asleep
Drift asleep
Lull asleep (lullaby – a song sung to babies to help them fall asleep)

Phrasal verbs
Nod off
Doze off

Adjective – noun collocations
Heavy sleep / heavy sleeper
Light sleep / light sleeper

Adjective – adjective collocations
sound asleep