I'm trained in Condensed Matter Physics, and I'm trying to learn EE. The concept of band bending always baffled me a bit. Here's why: The band edge bloch states are delocalized over the whole of the crystal, and have fixed given eigenvalues. How can this eigenvalue change over the length of the crystal? I have heard some hand waving arguments, that we must conceptually cut up the crystal into chunks which are the size of the mean free path of the bloch electrons, and at each chunk we can consider the eigenvalue to change slightly according to the applied field. My question is: What is the rigorous theory which describes band bending? I look forward to responses!