Band theory and Semiconductors

[Cehem]

Hello,
I just watched this video, where Dr Brattain talk about semiconductor physics and I thought about what I learned in my solid state physics course, namely band theory. I have several questions :
1)The explanation in terms of chemical bonds given by Dr Brattain (around 10mins) seems a lot more intuitive than the band theory so why did physicists developed a new model (band theory is more recent , right?). I remembered that in the law of mass-action, the constant K' isn't actually constant, it depends on the temperature to 3/2. But was it the only motivation.
2) Is the gap between valence and conduction bands the energy needed to break the chemical bonds ?


I hope it's clear, and that someone will be able to provide answers.

 

[sam_bell]

The chemical bonds in tetrahedral semiconductors (Si, GaN, etc.) are described by forming bonding (and anti-bonding) molecular orbitals from the sp^3 site orbitals. From this point of view you have two electrons in each sigma bond, and there are many, many degenerate sigma bonds in the crystal (2N for N atoms). Promoting an electron in this picture would require taking it directly into an anti-bonding orbital. In reality, there is some overlap between neighboring sigma bonding orbitals, which gives the electrons an opportunity to hop from site to site and therefore have some kinetic energy. Thus the 2N energy levels become split depending on how much kinetic energy the electron has. You could say the band picture accounts for the freedom the electron has to travel through the lattice.

addendum: In semiconductors, the bonding orbitals (read: valence band) is completely filled, so you still have to promote to the anti-bonding orbitals (read: conduction band). You won't get the energy gap correct unless you spread the energy levels out by figuring out how much overlap there is between molecular orbitals and using band theory.

 

[genneth]

Perhaps this attempt at a historical summary will help: http://physics.stackexchange.com/questions/23474/ionic-vs-covalent-bonds-dividing-line/23479#23479