References on Circuit Lower Bounds
What you want is a good reference to understand the exponential lower bounds for $AC^0$ circuits computing the PARITY function.

Now you haven't stated whether you actually want to understand the proof, or just understand things at a high level, the way a survey article would explain things. 

A survey article I recently read and liked is "The complexity of finite functions" by Boppana and Sipser.

If you really want to sit down and understand the proof, then you can either read proofs based on the Switching lemma (which appear in the papers you cited - [FSS], [Y] and [H1]), or the Razborov-Smolensky proof.

For proofs using the Switching Lemma, Håstad's Ph.D. thesis is a good read, if a bit hard to follow if you're new to the area. A better exposition of the proof is in "Introduction to circuit complexity and a guide to Håstad's proof" by Allan Heydon. The only problem with it is that I can't find it online, and I have a hard copy. I really recommend it if you're new to circuit complexity.

For the Razborov-Smolensky approach, just google for it and you'll get a bunch of lecture notes. I understood the lower bound from these three lecture notes: Sanjeev Arora, Madhu Sudan and Kristoﬀer Arnsfelt Hansen.