Germanium, silicon, and diamond have the same crystal structure, that of diamond

Question

Germanium, silicon, and diamond have the same crystal structure, that of diamond. Bonding in each case involves sp^3 hybridization. The bonding energy decreases as we go from C to Si to Ge, as noted in Table 4.7. a. What would you expect for the band gap of diamond? How does it compare with the experimental value of 5.5 eV? b. Tin has a tetragonal crystal structure, which makes it different than its group members, diamond, silicon, and germanium. 1. Is it a metal or a semiconductor? 2. What experiments do you think would expose its semiconductor properties?

Explanation / Answer

The conductivity mainly depends on molecular orbital overlap. Silicon has a smaller band gap than that of diamond. Hence silicon is an electrical semiconductor; and diamond is an insulator.

As we keep moving down the group, conductivity increases. Germanium is more conductive than silicon and tin and lead are obviously metals. (not semiconductors)

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 be promoted into the conductive band at any temperature.

In a semiconductor, the band gap is finite but small, such that at high 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 access 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
-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 -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).

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