PHP won't provide you with any conventional means for catching fatal errors because they really shouldn't be caught. Any techniques for catching them (like string matching an output buffer) are definitely ill-advised.
In general, emailing yourself when errors are thrown could prove to be problematic, at least if it involves calling the mail() function from within an error handler method. If you had a lot of errors, your mail server would be loaded with work, and you'd have a pretty gnarly inbox.
Alternatively, you might consider running a cron to scan error logs periodically and send notifications accordingly. You might also like to look into system monitoring software, such as Nagios.