You are right that sleep is necessary in order to increase your productivity and concentration in your work.
Also necessary for good thinking. It is charging to the body for positive energy order.
Having decent and normal sleeping hours do help to become productive. This is a very simple thing but many belittles the power of sleeping, oversleeping is bad as well but lacking of sleep to become productive is almost impossible.
When you lack of sleep, it makes you more irritated for things and you'll be having difficulty to think properly. As a person that always lacks of sleep, I go through with that situation and that lessens my productivity.