Texas A&M offers a class that involves working in a small fab. I haven't taken that class, but I know someone who has. It's basically like recreating the day TI invented the IC, although with more modern technology.
Back in high school chemistry class, one of the experiments involved making a photodiode by torching a strip of copper, then putting a drop of salt water on the oxidized end and touching it with a copper wire. When illuminated with a halogen lamp, it outputs a few microamps. I also knew someone who made organic solar cells out of lettuce juice and broken LCDs for a science fair project...