1
general::
noun VERB + DOZE have She had a little doze after lunch. | drift into, fall into Sitting in an armchair in front of the fire, I soon fell into a doze., verb ADV. fitfully I dozed fitfully for a few hours.
Oxford Collocations Dictionary
2
general::
doze off
informal
If you doze off, you start to sleep, especially during the day
• The office was so hot I nearly dozed off at my desk.
Cambridge-Phrasal Verbs