Hi everyone, I am a student studying semiconductors and solid-state physics. I have a question which is haunting for several years. That is about the definition of electron affinity in solid-state physics. Its definition in solid state physics may be quite different from that in chemistry. Almost in every textbook it is said to be fixed, no matter if the conduction band is bent or not. But nobody gives a rigid proof or a quantitative analysis of this. They just throw out the definition:a value between the vacuum energy and the bottom of the conduction band, and then say it is fixed by nature. I even doubt how those great physicists like Shockley or Sze.M dared to use it without a thorough understanding. Can anybody offer a quantitative explanation to this? Both some derivations related to QM are some papers are welcomed.