thought: you can make a diode using a p-n junction or a metal-n (schottky diode) junction. A transistor is two back-to-back diodes with a very thin shared region. Can you make a metal-n-metal "schottky transistor"?
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of course actually manufacturing it would be a _pain_ because you would need to grow a very thin, precise layer of n-type semiconductor on a metal substrate and then apply a second metal terminal to it, as well as making an n+ region in your semiconductor for the base contact, because you need an ohmic contact there but a rectifying contact everywhere else
