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Why diamond ,as one of the carbon allotropes , is not electrically conductive whereas , tetrahedral silicon is electrically conductive? What is the main difference between carbon and silicon which causes this difference?! Isn't there anything with the "d" orbitals in silicon?
I know it can be explained with MO theory , but not sure what the main reason is!
Can someone please help me figure this out?

[Corribus]

I once had a great figure that showed by conductivity increases going down the carbon group, but I can't seem to find it.  If I do, I'll upload it here.

It does have to do with molecular orbital overlap: Silicon has a smaller bandgap than diamond.  The former is an electrical semiconductor; the latter is an insulator.  If you keep moving down the group, conductivity increases more.  Germanium is more conductive than silicon and tin and lead are obviously metals (not semiconductors).

The basic reason is that the bonding orbitals get larger as you move down the group, and therefore overlap of the orbitals in the bonds gets smaller.  The net effect is to destabilize the bonding orbitals and stabilize the antibonding orbitals.  In solids, these orbitals combine to form what are called bands, and the energy gap between the bands determines electrical conductivity.  Conductivity requires that electrons in the valence band (made of bonding orbitals) have access to the mostly empty conduction band (made of nonbonding orbitals).  In an insulator, this bandgap is large, such that electrons cannot efficiently be promoted into the conductive band at any temperature.  In a semiconductor, the band gap is finite but small, such that at elevated temperatures, there is enough latent energy to promote electrons from the valence band to the conduction band, giving electrical conductivity (at low temperatures, semiconductors are insulators because there is not enough energy to put electrons into the conduction band).  In a conductor, the bandgap is zero, meaning no matter what the temperature is, electrons have free acceses to the conduction band.  That's the basic idea in a nutshell.

Bonding in diamond is strong because orbital overlap is good = large band gap = insulator.
Bonding in silicon is weaker because orbital overlap is less = smaller band gap = semiconductor
Bonding in Germanium is weaker still = much smaller band gap = better semiconductor
Bonding in Tin/Lead is weakest = effectively zero band gap = conductor/metal

Here are the bandgaps and conductivities of the carbon group, for reference.  You'll see a general inverse relationship.  If you looked up the bond lengths for these materials, you'd see they also grow as you go down the group, which is kind of another way of saying the oribtal overlap decreases.

Band gaps (eV):
Carbon (diamond): 5.5
Silicon: 1.11
Germanium: 0.67
α-Tin: < 0.1

Conductivities @ 20 C (S/m):
Carbon (diamond): ~10^-13
Silicon: 1.56x10^-3
Germanium: 2.17   
Tin: 9.17 x 10⁶

The bandgap of tin is so small you'd have to drop the temperature quite a bit to turn it into an insulator.

Of course, the conductivity also depends on the bonding mode.  Diamond is an insulator but graphite, also a carbon allotrope, is a very good conductor (C ~ 1 x 10⁵ S/m) because of its network π-bonds, which give rise to a small band-gap.  On the other hand, the conductivity of graphite is only in two dimensions (along the plates) with poor conductivity across the third (across the grain).

If you are unfamiliar with band theory, you can probably find an article on the subject at Wikipedia.  It's hard to understand conductivity and semiconductivity without some background in this topic.