Doubt on Band Theory of Solids: Can It Explain Electron Movement?

[ananthu]

I have a serious doubt about the concept of band theory of solids.

While explaining the behaviour of semi conductors, the following explanation is given.
"The valency bands are completely filled electron-bands, where as the conduction band is usually empty. The conduction takes place when a few electrons leave the valence band due to thermal energy and occupy the conduction band. The place left by the electrons in the valence band act as holes and conduction takes place due to exchange of places of electrons and holes in the valence band. But in the case of conduction band it takes place due to free movement of electrons."

My basic question is this.
This explanation gives a picture of the valence band or co-valent bond as if the electrons remain fixed ie. glued to their seats in the valence band and only if one electron vacates its seat another electron can go and occupy the hole left by it. But in reality no electrons are at rest and all are revolving around the nucleus. Can anybody explain this contradiction?

 

[johng23]

First of all, The picture of electrons orbiting the nucleus is never really right in the first place; there are situations (like the magnetic dipole moment) where it appears that there is a classical orbit, but in reality the probability distribution of orbitals doesn't change with time, so just keep that in mind. If an orbital has two lobes of equal probability of occupancy, you may be tempted to think about the electron oscillating back and forth between them, but it's probably better to think about them as two lobes of constant charge, each with half the charge of the electron.

This picture of hole conduction applies to a covalent semiconductor like Silicon. The electrons don't orbit around a single nucleus, because they are participating in bonding. There will be a molecular orbital formed, and a given electron will have a probability distribution that peaks at some location in the crystal, between the two Si nuclei which are bonding. So the electron distribution has maxima in the places halfway between any two Si atoms, and for the purposes of the semi-classical description used in these sort of valence-band-conduction models, you can imagine that that's where the classical point charge is located. So if one of these is absent, we call that a hole, and the hole can switch positions between these adjacent regions of local high electron density.

Just to break things down even further, if you consider the H2 molecule, each atom contributes one electron to the bond, and the charge distribution really is localized in between the two nuclei. I think there is some small probability of finding an electron on the "outside" of the molecule, but the basic picture is that the electrons really are stuck in between the nuclei.