My Samsung Galaxy S3 automaticly block screen after a given numeber of minutes. After this I have to insert secret code to unblock. I can disable this features, checking "Never lock screen". In this way screen will never block (and this is ok) but as side effect it will never turn to black (this isn't ok, this will drain my battery).

I want that screen just to turn to black without blocking, in this way as soon screen is touched phone is immediately active.
If I click the side power button phone will go in blocked mode as usual (secret code is needed to unblock).
 
I've found some application that partially do this. In some case I have to click on the main button to reactivate phone, while I want that entire screen as sensible zone.

What can I do?