By "broken", do you mean "damaged" or "not working"? If the screen is not working, by no fault of your own, and if you are within one year of the date of purchase, you can get a free replacement. It will most likely be refurbished, but it will be better than what you have now. If you are outside of the one year warranty, but still within two years of the date of purchase, you can still get a refurbished replacement, but it will cost you $50.
If the phone was damaged, or if you are outside the one year warranty, and you have Wireless Phone Protection or Total Equipment Coverage, you can file an insurance claim with Asurion and they will send you a refurbished replacement.