In semiconductors electrons in the conduction band are free from bonds and consequently they don't participate in the structural cohesion of material. Considering these electrons are few in percent at working temperatures, it isn't a problem for the cohesion. In metals instead situation is different because generally electrons with greater energy in the valence band become free also at low temperatures and consequently these electrons participate in statistical way whether in the structural cohesion or in the conduction band.

ok.thanks. The initial question may not be correctly enunciated. Sorry. You say that in the all cases, when the electrons become free, they not participates of the structural cohesion of any material. In the case of semiconductors, is clear that, for its small density, the effect of the free electrons is not relevant. But, focusing us in the case of metals, suppose two bands separated for a gap, the valence band and the conduction band, and suppose that, the conduction band is partially occupied. In this case, you say that these electrons not participates to the bonding of the material, no?.

In metals valence band and conduction band aren't separated but they are partially overlapped, consequently electrons in  this common under-band can be bound in the structure of material or be free. In semiconductors the two bands are completely separated and therefore all electrons in the conduction band are free.

Sorry, but the feature of "freedom" of the electrons in the conduction band is due to its ability to acquire energy from an external source such as heat or an electric field, ie, when the band is partially filled, there are levels available that allow electrons to do this. There is no other difference between the valence and conduction bands. If we extract electrons of a given valence band, gradually, the remanent electrons will gain, too gradually, more and more "freedom", until there are not difference whit another conduction band. yes or not?

I think no. Electrons in the conduction band already have acquired energy in order to reach the free state. In semiconductors that energy is greater than in metals.

While more I think this, more I incline to the idea that the electrons of the conduction band effectively participates in the bonding of any material. Look than they are not absolutely free particles. They are in the potential well of the whole material, thereby, in order to extract of it, we have do a work named "work function". In the frame of the quantum mechanics, the electrons of the conduction band are in bonding states with defined energies within a potential well, inclusively when they are excited.

Yes, I agree. Electrons into the conduction band aren't absolutely free, they are free inside the material structure, i.e. they are free to move inside the structure under the action of a force field while bound electrons into the valence band cannot move.

Of course also the electrons in the conduction band still contribute to the total bonding, but in a different way than the (more localized) valence band electrons: At least they guarantee charge neutrality, i.e. they balance the Coulomb interaction.

in semiconductor, there are two types of carrier, free electron in the conduction band and free holes in the valence band during the band structure depends on the concepts of the quantum theory of solids. These free carriers play an important role in the electrical, thermal and magnetic properties of solid. they are not related to the structure of semiconductor or the bond related. 

Ok. but, the picture of "holes" is an interpretation that facilitates the understanding of the processes of conduction. I work with this. But, a "hole" is just the absence of the an electron, and thereby, the "transport of holes" is, actually, a transport of electrons of the valence band. Is to say, the electrons is moves too in the valence band. This can be interpretated too by the other picture, when we extract electrons of the valence band, this becomes a partially fully band, as the conduction band, and then, can conduct. The difference is in the mass and mobility of particles, because these are ubicated in different regions of their respective bands.

I think in this discussion there is a little of confusion that is determined by the fact that semiconductors and metals are considered together. The behaviour of metals and of semiconductors is very different. Firstly they have different chemical bonds. Secondly in metals the mouvement of electric charges is unipolar while in semiconductors is bipolar, like it has been well specified by E. Alshakarchi.  Now nevertheless I would want to understand better the meaning of the question that has been raised: i.e. if electrons of the conduction band contribute to the cohesion of the material structure.

In semiconductors one free electron in conduction band is caused by the breaking of one chemical bond and at the same time one hole is created in the valence band. Consequently whether free electron or hole can participate in the bipolar conduction with different mobility, as C. Figueros specified. It is manifest that electrons in the valence band, that don't have broken the chemical bond, guarantee the cohesion of the structure, but also electrons in the conduction band contribute in a different and weaker way to the cohesion, as J.M. Wagner specified.

In metals, as I specified in a preceding comment, there is partial overlapping of the two bands. Consequently electrons that are in the common sub-band are free for the mouvement and therefore they contribute little to the cohesion. Electrons in the valence band instead are static and don't participate in motion, but guarantee the cohesion of the structure.

It's true. May be the question must be about the metallic bondng, if these electrons participates of the structural cohesion of the materials, or, I think, if the conduction band in the semiconductors are metallic.

  The electrons involved in the cohesion of the material need to belong to a bonding state where they are exchanged between two atoms (hopping). And respect to the electronic transport in a semiconductor there are two possibilities:

  1. One external electric field allows the hopping to a third atom (and so on), which means that the first one needs to take another electron for local conservation of charge. A Hubbard like model could be applied to understand such transport and no relation with the bonding would be done, i.e. the cohesion of the material would be the same.

  2. The inner electric field is so huge that you excite an odd number of electrons are on the conduction band which are almost "free" as a Fermi gas (just an hypothesis). In such a case this material could be considered a "metal" with a shift in the Fermi level and obviously the cohesion of the material has changed. In practice this possibility is almost impossible because the cystalline field would be enormous too and the local electric would change drastically.

  In summary, the bonding states are not changed by the usual electronic transport.

  I hope it helps.

Ok. thanks for all contributions. This exercise was very useful.

Best regards.

Carlos.