Would it be inappropriate to e-mail my boss concerning a raise?

It is much easier for someone to turn down a request by e-mail than it is in person, and sending an e-mail doesn't seem as sincere as approaching him in person. Find a time when he is not likely to be as busy (such as immediately before or after a break) and approach him and ask to speak with him privately. By speaking with him in person, you appear much more sincere, and it can force him to really think about what you're asking as opposed to just deleting an e-mail.

If need be, send him an e-mail asking when would be a good time to meet with him and discuss something. That way he can set aside the time and he won't feel cornered if he's busy or "in a bad mood". But definitely do not ask for a raise over e-mail; always take up employment issues, good or bad, in person. It shows sincerity and maturity.

I agree with the bassist - don't email asking for the raise. I wouldn't even blindside him with it should you catch him in his office. Either email him asking for a meeting, or stop by his office and ask if he has a few minutes in the next couple days to discuss something with you. You want a chance to state your case, and an email won't allow you to respond to any concerns he may have, and it also makes it easier to turn you down.

email him will be a good option

go for it - it is your right!