Insulator band gap and applied voltage?

[gaiussheh]

TL;DR Summary

Will an insulator conduct if a voltage greater than the bang gap is applied?

I got confused by the band theory. Does the band gap imply the voltage needed to conduct? This seems to be ridiculous. The band gap of a typical insulator is on the order of a few eV. Hence, if you give electrons 10 eV, they jump to the conduction band. But surely you can't turn an insulator into a conductor by simply applying a 10V voltage? Otherwise, most of the common things in real life will conduct.

 

[Drakkith]

Does the band gap imply the voltage needed to conduct?

No, the band gap is the energy needed to excite an electron from the top of the valence band to the bottom of the conduction band. Notice that band gaps are often given in electronvolts, not volts. An electronvolt is a unit of energy, while the volt is a measure of electric potential, two very different things.

But surely you can't turn an insulator into a conductor by simply applying a 10V voltage? Otherwise, most of the common things in real life will conduct.

Indeed. Applying a voltage does not mean that you are giving energy to electrons to excite them from the valence to the conduction band. Typically it is thermal energy that does this, and the applied voltage is what causes the electrons in the conduction band to move in an electric current. At least until you reach a high enough voltage to cause electrical breakdown of the material.

 

[nasu]

The voltage you apply cannot accelerate the electrons in the valence band, so it does not transfer energy to them. This why they are not conduction electrons.
Strong electric field may alter the band structure itself though and maybe reduce the band gap.