TPU black rubber case but don't care for it, it's not as grippy as silicone ones I've used on iPhones, and it shows smudges/grime, you have to wipe it daily so it doesn't get "greasy" feeling. Protects good though, dropped phone a few times and no damage not even scratch to the case.
I just prefer something more grippy. But I got it for like 4 bucks on Ebay with a car charger, nice deal lol. Silicone ones for this phone seem about the same size as the TPU ones, so to answer your question, no they don't really add any noticeable thickness, their fairly thin, not bulky at all (like otterbox etc)