Is a capital letter or a small letter used after a semicolon?
Usually a lowercase letter, since there is no need for a capital letter unless the succeeding word requires one.
Bob ran to the nurse; his hand was bleeding.
Semicolons are conjunctions. They take the place in between two different pieces of sentences. There is no need for a capital letter except for the existing reasons (name, place, etc.).
There were a lot of articles about Greece in the newspaper; Greece's economy was in a bad state.
This sentence used a capital letter, but not because of the semicolon.
Just a review of conjunctions:
FANBOYS to help you remember. Don't forget the semicolon, it's a conjunction as well.