Broken phone

Hello,

Try using iCloud to erase the phone. Even if the display is broken then as long as it connect to the Internet it will be erased. See the document below for instructions:

Erase a device in Find Devices on iCloud.com - Apple Support

Remotely erase your device or a family member’s device

1. In Find Devices on iCloud.com, click All Devices, then select the device you want to erase.
2. If
3. you don’t see All Devices, it’s because you’ve already selected a
4. device. Click the name of the current device in the center of the Find
5. Devices toolbar to see the Devices list, then select a new device.
6. Click Erase [device].
7. 
8. Do one of the following, depending on what you want to erase:

• iPhone, iPad, iPod touch, or Apple Watch: Enter
• your Apple ID password or your family member’s Apple ID password. If
• you’re not using a trusted browser, answer your security questions or
• enter the verification code that’s sent to your other devices. If you’re
• using your own computer and want to skip the verification step in the
• future, click Trust. If you’re using a friend’s computer, click Don’t
  • Trust.
• Mac: Enter your Apple ID password or your
• family member’s Apple ID password. If you’re not using a trusted
• browser, answer your security questions or enter the verification code
• that’s sent to your other devices. If you’re using your own computer and
• want to skip the verification step in the future, click Trust. If
• you’re using a friend’s computer, click Don’t Trust. Enter a passcode to
  • lock the Mac (you need to use the passcode to unlock it).

1. If
2. the device is lost and you’re asked to enter a phone number or message,
3. you may want to indicate that the device is lost or how to contact you.
4. The number and message appear on the device’s Lock screen.

If your device is online, the remote erase begins after you follow the onscreen instructions. If your device is offline, the remote erase begins the next time it’s online.

For more information about trusted devices and verification codes, see the Apple Support article Two-factor authentication for Apple ID.