Suppose you have a semiconducting wire which has been doped in a gradient, so that one end of the wire is strongly n-type, the other end is strongly p-type, and the middle is neutral. This wire is suspended in air, and is at the same temperature throughout.
Is there a voltage between the ends of the wire?
If not, why not?
If so, what happens if you connect the wire to an electrical load?
Is there a voltage between the ends of the wire?
If not, why not?
If so, what happens if you connect the wire to an electrical load?