In phantom of the opera how did the phantoms face become disfigured?

It depends on which version of 'The Phantom of the Opera' you are refering to. In Andrew Lloyd Webber's musical, the Phantom sings about how he was born with a skin infection...which caused a "mother's fear and loathing". So it is most recently said to have been a skin infection, except that his musical version was slightly different from the original novel by Leroux. The most commonly accepted version and theory is that the Phantom was born with a disfigured face (and body). In the 1965 movie, his face was burned by acid, and in 'Phantom of the Paradise', his face is mutilated in a record press accident, just as an example of other theories.