How does SOFC work?

The [Solid Oxide Fuel Cell](https://en.wikipedia.org/wiki/Solid_oxide_fuel_cell) is a particular case in which an oxide is used as a conductor. Once i've heard that oxides usually aren't good conductors but it turned out that a lot of oxides are conductors. What i am asking is :


1. How can i know if a oxide is a **conductor or not**?
2. If there isn't any conduction band since it's not a metal, how do the **electrons** move and how does the SOFC work?


Thank you.


