(kronig penney) E > Uo still valence energy?

[esdegan]

Hello, I'm trying to understand the kronig penney model which leads to E-k diagram and eventually to conductance energy Ec and valence energy Ev for semiconductor model.

Hmm... I'm having a hard time to describe this, but I'm reading Pierret book now and the solution for kronig penney model shows that the valence bands are the lowest energy bands which would contain the total number of non-core electrons, contributed by the atoms to the crystal.

These valence bands can be at energy larger than the quantum well potential in the kronig penney model. When electron has energy > well potential, doesn't it become a 'free' electron? doesn't that means the electron is a carrier? How to reconcile this with the fact that this energy is still valence energy, not conductance energy?

Isn't this well potential the same as the covalence bond potential energy? If electrons in valence band are those in covalence bonds, doesn't it mean their energy must be less than the well potential?

Thank you in advance for your help.
-andre

 

[Physics Monkey]

In the nearly free electron approximation, the important effect of the potential is to produce a band gap at the zone boundaries where Bragg diffraction makes the electron energies degenerate in the free electron limit. The electrons can have energy greater than the step height in the Kronig-Penny model (I'm not considering the delta function limit) but they still have to sit in the band structure with its band gaps. What makes a band inert from the point of view of conduction is whether it is filled or not. In the simplest model of an undoped semiconductor at zero temperature, the valence band is filled while the conduction band is empty and they are separated by a band gap. Since it is filled, the valence band can still give you zero net contribution to the conductivity regardless of the energies of the electrons in the band.

 

[esdegan]

Ah i misunderstood what that well potential. After reading your answer, I realized i mistaken that potential as valence energy, while it actually is a coulombic attraction energy between 2 neighboring atoms, isn't it? So I should not associate that potential energy with conduction.

Thank you so much for your help, i really appreciate it.