Puzzle about electron affinity in solid-state physics

[qilong]

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.

 

[DrDu]

I still don't see exactly where you see a problem. What do you mean with bending of the conduction band? I think the electron affinity is usually defined for homogeneous bulk materials.

 

[qilong]

I mean the X in the attached picture. This is from Mott's paper of the metal-semiconductor rectifying theory. He just said it varies a little and even did not mention what was its name.

 

[DrDu]

I think what he tries to explain is that the work function is not identical to the electron affinity.
Note that the electron affinity is defined as the difference between the zero level of energy and the lowest state in the conduction band far inside the semiconductor. That means it is a bulk property and by definition does not depend on the band structure near the surface.
You may find something in Ashcroft and Mermin's book.

 

[qilong]

Hi DrDu, I have browsed this book but little was found. Can you be more specific? Thank you very much!

 

[DrDu]

Chapter 18, The Work Function