To find biographical research, start with a simple encyclopedia like World Book:
The Advanced World Book Web includes Primary source documents, E-books, Encyclopedia articles, Images, as well as links to articles and websites.
You can also search CU Books or OhioLINK for book-length biographies of playwrights:
In both cases, I recommend doing an Advanced Search, specifically a Subject search. Type the playwrights name as Last Name, First Name.
This type of search will provide you with a list of subjects (topics) related to your playwright. Select the first option (which usually includes just your playwright's name):
And you'll find biographies like these:
Arthur Miller: His Life and Works by 
Arthur Miller: 1915-1962 by