Whenever I teach my semiconductor device physics course, one of the central messages I try to get across early is the importance of energy band diagrams. I often put this in the form of "Kroemer's Lemma of Proven Ignorance": If, in discussing a semiconductor problem, you cannot draw an Energy Band Diagram, this shows that you don't know what you are talking about, with the corollary If you can draw one, but don't, then your audience won't know what you are talking about.

in his Nobel Lecture, Quasi-Electric Fields and Band Offsets: Teaching Electrons New Tricks, 8 December 2000, at Aula Magna, Stockholm University.

Herbert Kroemer - Nobel Lecture: Quasi-Electric Fields and Band Offsets: Teaching Electrons New Tricks