It was Michel Eyquem de Montaigne (1533-1592) who invented the essay form. The French word essai means an attempt. It is an attempt to express something entirely new and original, usually an idea, impression, or opinion. To call a biography an essay would be to misuse the word "essay" because in a biography the facts are already available and only need to be written down. Besides that, an essay is usually much shorter than a biography, which usually fills up an entire book. A short biography would probably be called a biographical sketch. To say that you are "attempting" to write a biography would not be very reassuring to a reader. The essay is a wonderful form, a great contribution to world literature. It allows the writer to venture into the unknown, to attempt to say something completely personal and unique, something that may be controversial or quixotic or highly speculative. It is better to reserve the word "essay" for literary works of that nature. There are plenty of other words to apply to other genres.