bei48482_FM

with the 2Nelectrons the 3sband can hold, the 3s 3 pband in magnesium can hold

8 Nelectrons in all. With only 2Nelectrons in the band, it is only one-quarter filled

and so magnesium is a conductor.

Insulators

In a carbon atom the 2pshell contains only two electrons. Because a pshell can hold

six electrons, we might think that carbon is a conductor, just as sodium is. What ac-

tually happens is that, although the 2sand 2pbands that form when carbon atoms

come together overlap at first (as the 3sand 3pbands in sodium do), at smaller sep-

arations the combined band splits into two bands (Fig. 10.23), each able to contain

4 Nelectrons. Because a carbon atom has two 2sand two 2pelectrons, in diamond

there are 4Nvalence electrons that completely fill the lower (or valence) band, as in

Fig. 10.24. The empty conduction bandabove the valence band is separated from it

by a forbidden band 6 eV wide. Here the Fermi energy Fis at the top of the valence

band. At least 6 eV of additional energy must be provided to an electron in diamond

358 Chapter Ten

4 N levels

Conduction

band

8 N levels

6 N levels

2 N levels

44 NN levels levels

Valence band

Carbon Silicon

Energy

6 eV

1 eV

2 p (carbon)

3 p (silicon)

2 s (carbon)

3 s (silicon)

Internuclear distance

Figure 10.23Origin of the energy bands of carbon and silicon. The 2sand 2plevels of carbon atoms

and the 3sand 3plevels of silicon atoms spread into bands that first overlap with decreasing atomic

separation and then split into two diverging bands. The lower band is occupied by valence electrons

and the upper conduction band is empty. The energy gap between the bands depends on the inter-

nuclear separation and is greater for carbon than for silicon.

Conduction band

Forbidden band

Valence band

6 eV

eF

Figure 10.24Energy bands in diamond. The Fermi energy is at the top of the filled lower band. Be-

cause an electron in the valence band needs at least 6 eV to reach the empty conduction band, dia-

mond is an insulator.

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