http://en.wikipedia.org/wiki/Headphones#Technology
"The diaphragm, typically fabricated from lightweight, high stiffness to mass ratio cellulose, polymer, carbon material, or the like..."
This is going to be pretty high tech stuff... the polymers are likely custom molded (high stiffness, but ultra thin). For making your own - I'm not sure what the easiest route is...you're going to need a materials bank and some testing gear. Maybe a custom ultra thin paper - treated with the right starches, or if you can buy some carbon fiber already in sheets - but i doubt it will be thin enough.
