I wrote specifications for architects for about 60 years. I have some advice.
Do not put a vapor barrier material on top of a slab unless you know that there is a very effective vapor barrier or waterproofing below the slab. Water vapor is always present even in desert climates. It wants to move upward and evaporate; if blocked it will condense. The moisture movement will bring salts with it that damage the slab surface.
I strongly recommend loose laid carpet tile for your application.
Otherwise, I've found that "rebond" rubber padding is most popular for stretch-in carpet installations. It's effective, inexpensive, and breathable.
Do not put a vapor barrier material on top of a slab unless you know that there is a very effective vapor barrier or waterproofing below the slab. Water vapor is always present even in desert climates. It wants to move upward and evaporate; if blocked it will condense. The moisture movement will bring salts with it that damage the slab surface.
I strongly recommend loose laid carpet tile for your application.
Otherwise, I've found that "rebond" rubber padding is most popular for stretch-in carpet installations. It's effective, inexpensive, and breathable.