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 diagr… - Herbert Kroemer

Whenever I came to him (Fritz Sauter) with a pure physics idea, he would invariably say, with slight sarcasm: "But Mr. Kroemer, you ought to be able to formulate this mathematically! " If I came to him with a math formulation, I would get, in a similar tone: "But Mr. Kroemer, that is just math, what is the physics?" After a few encounters of this kind, you got the idea: You had to be able to go back and forth with ease. Yet, in the last analysis, concepts took priority over formalism, the latter was simply an (indispensable) means to an end.

:: 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,

Ultimately, progress in applications is not deterministic, but opportunistic, exploiting for new applications whatever new science and technology happen to be coming along.