I just learned that one of the many ways that silicon is purified (for use in microchips and such) is to combine sand (silicon dioxide, a very common form to mine silicon on earth) and hydrochloric acid (HCl, available in your local chemical store and in your stomach). You then get a SiCl compound that decays into pure silicon (and chlorine gas) when heated. Be careful when opening that oven!
So I'm left with the hilarious thought that if civilization ends and you desperately need to make a CPU for some reason, you can dig some sand from the beach, avoid eating for 24 hours, and then barf into the container. Bake in a wood oven, and there's your silicon.
However, if civilization ends, you'll have bigger problems than CPU shortages, and while it still exists, chemical supply stores are assuredly a better source of HCL.
This also reminds me that the northern African countries are probably an excellent source of silicon, since their composition, as I can see it by satellite, are 99% sand. Just bring a bottle of HCl and crank out the ingots by the millions....