Back when i was majoring in ECE at UIUC, we got to play around with Fab labs :). Yeah you'd pretty much need a advanced degree in EE or Physics to be a semi-conductor engineer I'd reckon.
For those you are typically looking at an as or even a bs. They look for strong reliability, precision and attention to detail, and hands on skills. Strong evidence of an ability to learn is also gold.
Plus most of those guys work 3/4 12hr shifts a week...great schedule. No work goes home with you.