Why Can Electrons in the Conduction Band Move Around so Easily

[thepolishman]

As my title states, I want to understand why electrons in the conduction band can move around so easily in the material. Is it due to the presence of many closely spaced (blurred out) energy levels which make it easy for the electrons to move around? Or are the electrons undergoing some kind of high probability tunneling? I know from trying to Google search the subject that the electrons become delocalized. Unfortunately, I'm not exactly sure what that means. Any help is appreciated.

P.S. I have an introductory knowledge of QM, in addition to all the physics that comes before that

 

[mfb]

Energy levels in the conduction band correspond to states spread out over the whole metal. The electrons don't have a well-defined (local) position any more. As a pseudo-classical description, this allows to throw them in at one side, and see them at the other side of the conductor afterwards.

 

[thepolishman]

Thanks.

Adding to my question a bit, is there a reason (mathematical or physical) that the conduction band spreads out over the material whereas the valence band remains localized to a single atom (at least that's what I'm assuming)?

 

[mfb]

They are different solutions of the Schroedinger equation. They are closer to individual atoms, therefore their energy is lower.

 

[DrDu]

The levels in the conduction and valence band are not qualtitatively different. What makes the difference is that the valence band is usually full and the conduction band only partly filled. E.g. in semi-conductors you observe also holes in the valence band. These holes move similarly to electrons in the valence band.
There is a further subtlety: The electrons at the top of a band have negative effective mass, which means that they are accelerated in the opposite direction in an electric field as the electrons at the bottom. Thus in a completely filled band the motion of all the electrons in the band exactly cancels.

 

[Dumte]

As the name suggest, conduction band is an area where conduction takes place.
So any electron that had left or escaped from the valence band of a material had the ability to conduct faster.

 

[daveyrocket]

The conduction and valence bands are both delocalized over the whole material. If you take a semi-conductor and remove electrons by doping it, you get conduction in what was once the valence band.

States in a band are identified with their (pseudo-)momentum vector k which gives, imprecisely speaking, the direction and speed that electrons are traveling. In a totally filled band, as many electrons are traveling left as are traveling right and there is no way to change that because every state is occupied. In a partially filled band, you have what's called a Fermi surface. Taking the textbook example of a spherical Fermi surface, this means that there is some Fermi momentum value k_F below which the band is occupied and above which the band is unoccupied. This situation, by itself still represents zero current, since there is symmetry - as many electrons are traveling left as are going right. But because there are unoccupied states just past k_F, you can bias the current in a particular direction by moving electrons from a state near, say, -k_F to a state near k_F. Then you have more electrons traveling right than traveling left. This works in a conduction band because there are unoccupied states you can move electrons into. The bias can be obtained by applying an electric field - this makes states going against the electric field lower in energy and states going in the direction of the E field higher in energy.

 

[hokhani]

You had better compare the situation with that in an atom. In the atom electrons which are near the core are strongly bonded to atom and their wave function don't have great amplitude far from the atom. So the probability of finding them there, is low. The outermost electron's wave function is vice versa delocalized. You can imagine such a situation in solids.

 

[daveyrocket]

You had better compare the situation with that in an atom. In the atom electrons which are near the core are strongly bonded to atom and their wave function don't have great amplitude far from the atom. So the probability of finding them there, is low. The outermost electron's wave function is vice versa delocalized. You can imagine such a situation in solids.

This really isn't relevant. The question is why do electrons in the conduction band conduct but electrons in the valence band don't. Core electrons in a solid are just like core electrons in an atom, but the valence band in a solid is composed of the valence electrons of atoms - they are delocalized. As far as wavefunctions go, the valence and conduction bands are rather similar.

 

[hokhani]

the valence band in a solid is composed of the valence electrons of atoms - they are delocalized.

Ok, you are right. Pardon me for that.

 

[thepolishman]

Wow, I got some great answers to my questions. Thank you for all the replies. I'll definitely be using PF more often from now on.

 

[hokhani]

This really isn't relevant. The question is why do electrons in the conduction band conduct but electrons in the valence band don't. Core electrons in a solid are just like core electrons in an atom, but the valence band in a solid is composed of the valence electrons of atoms - they are delocalized. As far as wavefunctions go, the valence and conduction bands are rather similar.

Excuse me for being late in writing this post. I have still problem understanding the statement "valence electrons in solids are delocalized". Consider as an example the solid Si which is a semiconductor. According to the textbooks, valence electrons are bound between neighbour atoms and radiating photon on them would break some bonds and electrons would become free by going to the conduction band. Could you please help me?

 

[ZapperZ]

Excuse me for being late in writing this post. I have still problem understanding the statement "valence electrons in solids are delocalized". Consider as an example the solid Si which is a semiconductor. According to the textbooks, valence electrons are bound between neighbour atoms and radiating photon on them would break some bonds and electrons would become free by going to the conduction band. Could you please help me?

This is now a different situation because an electron that was localized in the valence band has now been promoted to the conduction band due to a gain in energy. Once in the conduction band, the electron no longer "belongs" to any particular atom. That is what is naively meant as "delocalized".

Zz.

 

[hokhani]

This is now a different situation because an electron that was localized in the valence band has now been promoted to the conduction band due to a gain in energy. Once in the conduction band, the electron no longer "belongs" to any particular atom. That is what is naively meant as "delocalized".

Zz.

Ok, in the conduction band electrons are delocalized, but daveyrocket had told electrons in the valence band are delocalized.

 

[snorkack]

So, when you excite an electron in valence "band" of silicon into "conduction band". Why does the absence of the electron leave a movable, conductive hole rather than a localized, immovable positively charged defect?

 

[hokhani]

So, when you excite an electron in valence "band" of silicon into "conduction band". Why does the absence of the electron leave a movable, conductive hole rather than a localized, immovable positively charged defect?

When the valence band is full, electrons can't move freely and they are bound to their corresponding atoms. When an electron is excited (and so a hole is produced), the adjacent electrons can move towards the produced hole and replace there. So electrons (and hence hole) can move only this way hopping from one atom to another throughout the crystal.