iPhone, half of the screen broken, cannot perform backup
Connect your iPhone with a Mac(that is trusted by your iPhone) using USB cable.
open iTunes.
Select your iPhone.
Select the Backup method to your iCloud account or This Computer.

It will not ask for any passcode, but if it does, you could enter it using a Bluetooth keyboard.


Note: I am not sure if a not trusted Mac or PC connected it will work.
Also See the attached image.