Band Structure of Charged Insulator

[Rizer]

Dear all, I have been thinking, if insulators have their valence band filled, then which band does the extra electrons go when it is negatively charged?? If it is the conduction band, then it would become a conductor...

Similarly, if it is positively charged, there would be a hold in the valence band and make it become a conduction band...

But obviously this is not the case in real. Can anyone please explain to me how it really works?

 

[DrDu]

The electrons go into the conduction band. This is not as far fetched as you think. E.g. diamond can be turned into quite a good conductor by doping both by introducing holes in the valence band (on boron doping) or by introducing electrons in the conduction band (by doping with phosphorous).

 

[Rizer]

Thank you DrDu. Does this also apply to cases without doping? Like simply charging a plastic ruler with rubbing??

 

[DrDu]

Well, I think the main problem is that as long as the concentration of the charge carriers is that low, they will form so called polarons. The polaron problem has been studied extensively, but is quite involved. There are two limiting cases, the "heavy" and the "light" polaron. The former does not lead to conduction while the latter does. Look for "polaron" in wikipedia as a start.

 

[Rizer]

Thanks you very much, looks like there're some new concepts to learn.

 

[DrDu]

This weekend I found some time to go through my book-shelf. The problem you are interested in is discussed in a very nice booklet by nobel prize winner P W Anderson, Concepts in solids, under the heading "the N+1 electron problem".

 

[shawl]

Dear all, I have been thinking, if insulators have their valence band filled, then which band does the extra electrons go when it is negatively charged?? If it is the conduction band, then it would become a conductor...

Similarly, if it is positively charged, there would be a hold in the valence band and make it become a conduction band...

But obviously this is not the case in real. Can anyone please explain to me how it really works?

Except for the topic of polarons, please note the conception of field effect transistor.

Under a sufficient bias, the concentration of electrons can be enhanced in a very thin layer at the interface between the contact and semiconductor. This layer is called as inversion layer.

Through applied a sufficient bias, an N(P)-type can be achieved in a P(N)-type semiconductor, and even the superconducting behavior can be achieved in an insulator.

Field effect is now a very useful method to study the materials. It was the hottest topic in year 2000~2002.

 

[zhanghe]

Dear all,
I guess it is not so complex, the case you were talking about was so-called "static electrisity" think it over carefully, if you touch the charged insulator with metal or your hands( well it is more dangerous :) ), the charge will go away immediately.
So, i think you are right the electron(hole) will stay in the condunction(valence) band, and the charged insulator indeed performs like a conductor just the moment something conduction touch it, well i guess your question's core is why the charged insulator could not take the place of the conductor and semiconductor in the electric circuit,right? what i want to say is a netural insulator becomes a charged insulator just because it is isolated ( not in the circuit).
speaking of the amount of charge, I don't think it is the real reason.