Energy Band Theory

[Swapnil]

In the energy band theory, we are only concerned with two bands - the conduction band and the valance band. Electrons can only be found in one of these bands and they can't have any energy related to the band in the middle - the forbidden bad. My question is that how come there are only two bands, I thought that when you have a bunch of atoms separated by a small distances, then the energy band spilts into many different band?

 

[marcusl]

In the energy band theory, we are only concerned with two bands - the conduction band and the valance band. Electrons can only be found in one of these bands and they can't have any energy related to the band in the middle - the forbidden bad. My question is that how come there are only two bands, I thought that when you have a bunch of atoms separated by a small distances, then the energy band spilts into many different band?

The energy levels split into so many closely-spaced levels that they define a band. There are many bands, but most are completely filled or empty. The two at the boundary between filled and empty, defined by how the atomic shells are filled, determine the behaviors of insulators, metals and semiconductors. At zero temperature the levels are filled by electrons up to the Fermi energy, above which all levels are vacant. If the Fermi level is at the top of a band, the material is an insulator and the filled bands are called valence bands. If the Fermi level is above the bottom of a band, it defines a "conduction band" that's populated by electrons that are free to move. Semiconductors and all the rest build on these...

 

[Swapnil]

OK, I see. So there are many bands and the reason we only talk about conduction band and valance band is because it is the place where all the action really happens i.e the boundry between filled and empty band.

I have one more question though. You talk about fermi energy in the context of insulators, conductors, and semi-conductors. But I always thought that the concept of fermi-enery was only applicable to semi-conductors? Depending on whether the fermi-energy level is more towards the conduction-band minimum or towards the valence-band maximum defined p/n-type semi-conductors.

How does fermi-energy matter in insulators or conductors. I thought that the only thing that separated conductors and insulators was the energy-band gap...

 

[ZapperZ]

You may want to read this thread.

https://www.physicsforums.com/showthread.php?t=133914

Zz.

 

[Swapnil]

In the strictest sense, there really is no "Fermi level" in a semiconductor and band insulators. This is because the term "Fermi level" is defined for the occupied electron states in metals. Many books (and I do this also myself) are sloppy with their notation. In semiconductors and band insultators, what it should really be called is the "chemical potential".

So what is exactly Fermi-level in conductors and semi-conductors?

 

[marcusl]

These concepts don't come easy. Are you working with a text? Books on solid state physics cover this material in detail, those on semiconductors are briefer, but they all cover it. If you need recommendations, here is one of each type:
a) Kittel, Intro to Solid State, is a classic. Older editions seem to be better than new ones, I can recommend the 3rd edition. Start with chapt on Free Electron Fermi Gas and read the next three or so chapters (I don't have the book in front of me...)
b) Here's an ebook that's device oriented
http://ece-www.colorado.edu/~bart/book/book/title.htm" [Broken]
Read at least all of Ch. 2

If that doesn't make it clearer, please back with questions.

 

[Swapnil]

These concepts don't come easy. Are you working with a text? Books on solid state physics cover this material in detail, those on semiconductors are briefer, but they all cover it. If you need recommendations, here is one of each type:
a) Kittel, Intro to Solid State, is a classic. Older editions seem to be better than new ones, I can recommend the 3rd edition. Start with chapt on Free Electron Fermi Gas and read the next three or so chapters (I don't have the book in front of me...)
b) Here's an ebook that's device oriented
http://ece-www.colorado.edu/~bart/book/book/title.htm" [Broken]
Read at least all of Ch. 2

If that doesn't make it clearer, please back with questions.

I see. Thanks for your help. I will check out those books.