During a backup, your disk I/O is going to be high. You want to minimize the amount of time this takes so your database can still perform while the backup is running. Therefore, backing up to disk and then from disk to tape is the right approach because hard drives have greater throughput than any tape drive I've ever seen.

You'll need a drive (physical drive, SAN space, etc.) to receive your database backups. You'll want this to be a separate physical disk from your data drive and log drive. Once the database backup is done, you can backup your backup files from there to tape. Because the backup files are on a separate physical drive, it won't impact disk I/O like backing up directly to tape would.

Another related question is about your transaction log backups. Are you taking them throughout the day or just doing the full backup once per day? Taking transaction log backups will keep your log files smaller by marking log entries as backed up and available for use. Smaller files mean less to back up. It'll also be better if you need to recover from a disaster because then you won't loose everything since the last full backup.

Speaking of disaster recovery, please be sure to test your recovery plan before you need it. The whole point of backups is to be able to recover, so you don't want your first time doing it to be the time when time is critical.

HTH