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We know, that conductors, conduct because their valence energy band is "half" full, and k ("wave vector") can increase and therefore the electrons under the influence of a electric field can "move", and similarly insulators wont conduct, because ther valence band is full, and we have a "big" energy gap between the valence and conductivity band.

My question: Why can't under the infulence of a electric field electrons "jump" onto the next energy band (that's the conductivity band) , where their k ("wave vector") can increase "more freely" and therefore conduct electricity?

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    $\begingroup$ It takes energy to make the jump but if the electric field is large enough you can make an insulator conduct. $\endgroup$
    – Farcher
    Mar 4 '16 at 9:09
  • $\begingroup$ So... under a large enough electric field electrons "jump" from the valence band onto the conductivity band? , or is that not the right way to understand this? $\endgroup$
    – Luka8281
    Mar 4 '16 at 9:22
  • $\begingroup$ The strong electric field causes bound electrons to be ejected from atoms and become mobile charge carriers. $\endgroup$
    – Farcher
    Mar 4 '16 at 9:25
  • $\begingroup$ That means those electrons are in the conductivity energy band ? $\endgroup$
    – Luka8281
    Mar 4 '16 at 9:31
  • $\begingroup$ What kind of electric field? From context, I think you mean a static or slowly varying field, not an optical, radio, or x-ray electric field. Can you clarify? $\endgroup$
    – garyp
    Mar 4 '16 at 11:51
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You said it here:

we have a "big" energy gap between the valence and conductivity band.

If you supply enough energy, electrons will jump to the conduction band (become excited). Semiconductors and insulators do not have many differences, it is simply called insulators when the gab is big, and semiconductors when small.

Semiconducting materials may react with sunlight (photovoltaic effect in solar cells), while inductors (like air) has become conducting when you see a lightning flash.

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  • $\begingroup$ "If you supply enough energy, electrons will jump to the conduction band (become excited). " ok.. I get that... but why can't electrons make that jump using the energy they get from the electric field? (their energy is increasing as they "accelerate", <--- their k ("vector") gets larger. $\endgroup$
    – Luka8281
    Mar 4 '16 at 9:26
  • $\begingroup$ Maybe the electric field can't supply enough energy in one "package" for the electron to make that jump? $\endgroup$
    – Luka8281
    Mar 4 '16 at 9:54
  • $\begingroup$ In a big enough field you get tunneling or hopping. $\endgroup$
    – Jon Custer
    Mar 4 '16 at 15:40
  • $\begingroup$ @Lukas8281 The "package" viewpoint is exactly the point. That is the whole origin of quantum mechanics when the quantized behavior of photons was discovered. A photon carrying enough energy can excite electrons, but many smaller-energy photons can't. $\endgroup$
    – Steeven
    Mar 4 '16 at 15:51

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