One has to remember that necessary (crystal structure) is not also sufficient ( for having conductivity) . For conductivity the specific atoms have to have a small energy interval to the conduction band, the band shared with the whole crystal lattice.

It takes very little energy to raise an electron from a valence state to the conduction band of the crystal , in conductors. Energy which is provided by the voltage imposed.

So the crystal lattice is necessary in order to model the bands, but conduction happens when the conduction band has a small energy difference from the valence band.

This is a very successful model in describing the behavior of solids to electric fields.

One has to remember that necessary (crystal structure) is not also sufficient ( for having conductivity) . For conductivity the specific atoms have to have a small energy interval to the conduction band, the band shared with the whole crystal lattice.

It takes very little energy to raise an electron from a valence state to the conduction band of the crystal , in conductors. Energy which is provided by the voltage imposed.

So the crystal lattice is necessary in order to model the bands, but conduction happens when the conduction band has a small energy difference from the valence band.

This is a very successful model in describing the behavior of solids to electric fields.