If the database is not mounted then the database has no idea what is the content of the controlfile and thus you can't isue BACKUP CONTROLFILE TO TRACE!

What happens (regarding init, control, log and data files) during each startup phase:

1. NOMOUNT: Instance reads the init.ora (this file also specifies where the instance should look for the control files)

2. MOUNT: Instance opens and locks the controlfiles, specified in the init.ora (controlfile includes all informations regarding redolog and database files)

3. OPEN: Instance reads and locks all redologs and database files and makes the database available for users.

So you must be at lest in the MOUNT mode to get the information contained in controlfile.