how to back up my phone using itunes if the screen is broken

You can't do it to a computer, you have to hope you have set up to do so to iCloud automatically.

In: How to back up your iPhone, iPad, and iPod touch

https://support.apple.com/HT203977

see the section: "Automatically back up with iCloud Backup

To let iCloud automatically back up your device each day, here's what you need to do:

Make sure that iCloud Backup is turned on in Settings > [your name] > iCloud > iCloud Backup.

Connect your device to a power source.

Connect your device to a Wi-Fi network.

Make sure that your device's screen is locked.

Check that you have enough available space in iCloud for the backup."

Related information:

Use iCloud to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch --> https://support.apple.com/HT210217

Some things are not stored in a backup. Click on this link and read "About missing information after you restore your iOS device with iCloud Backup" -->

https://support.apple.com/HT203768