It is actually a bit sad, to be honest, how we got to use the idea of bandgaps to explain conductivity and not to see the deeper side of things. Visualizing the quantum electron unlocks band diagrams as a jewel of quantum mechanics and solid state knowledge. http://lessonpeer.com/drhillteach/Metals%20Semiconductors%20and%20Insulators%20-%20upgrade%20your%20understanding.mp3