Absolutely you can use a screw extractor to help you remove a screw that has broken off below the surface and you have no alternative to remove them. Here is a website that walks you through the process. http://www.wikihow.com/Use-a-Screw-Extractor

For a basic outline on how to use a screw extractor, you just basically punch the screw before drilling and make a small hole in the center of the screw. Insert the extract and rotate counter-clockwise until the screw is free. For more detailed information, visit http://www.wikihow.com/Use-a-Screw-Extractor

There are tons of places that you can buy the screw extractor from. Retail stores like Sears and Ace Hardware definitely has them. Amazon.com also have them available online.

Broken screws are incredibly frustrating to remove, especially when it's just the screw head that's broken off. Fortunately, screw extractors make this process as clean and simple as possible. A screw extractor kit should include a number of different bits.

Start with one of the two smallest bits to make a pilot hole, then tap an extractor bit into the pilot hole with a hammer until it's firmly in place. Using a pair of pliers, continue pushing down on the extractor bit but begin to turn it counter-clockwise. The broken screw should, with a little effort, begin to slide out.

Use a screw extractor or easy out.