Absolutely Small - Michael D. Fayer [131]
FIGURE 19.5. Schematic of the band structure of an insulator. There is a filled band, with two electrons in each MO. At much higher energy, there is an empty band.
The Band Gap Is Large in Insulators
There are empty atomic orbitals at much higher energy, and these form MOs. However, there are no electrons to put in these MOs. Therefore, the next higher energy band is completely empty. The difference in energy between the top of the filled band and the bottom of the unfilled band is called the band gap. The Fermi level is at the top of the filled band.
As discussed qualitatively above and shown in detail by quantum theory, conductivity requires electrons in MOs with energies above the Fermi level. When an electric field is applied across the material (connected to a battery or other source of voltage), the nature of the delocalized states shifts. In a metal, because the band is only half filled and the energy levels are only separated by an infinitesimal amount, an applied electric field will result in a change such that some electrons are above the zero field Fermi level, and electrons flow through the metal. In an insulator, the next level above the Fermi level is in the empty band. The band gap is large, and the application of an electric field cannot change the system enough to put electrons into the empty band. Therefore, application of an electric field to an insulator is insufficient to produce conductivity, in contrast to a metal.
Another possibility is that thermal energy could excite electrons from the filled band to the empty band. An insulator has the property that the band gap energy is much greater than the thermal energy. As the temperature is increased, the amount of thermal energy increases. But an insulator has a band gap that is so large that the insulating material will be destroyed at temperatures that are still insufficient to thermally excite electrons from the filled band to the empty band. The net result is that application of an electric field cannot modify the states in a way to produce conductivity and thermal excitation of electrons cannot occur. Therefore, insulators do not conduct electricity.
SEMICONDUCTORS
In a Semiconductor the Band Gap Is Small
A semiconductor is like an insulator, but with a small band gap. A schematic of the band structure of a semiconductor is shown in Figure 19.6. In a semiconductor, such as silicon (Si), there are enough electrons to fill the valence band completely. At 0° K, where there is no thermal energy to excite electrons, all of the electrons are paired in the valence band. The Fermi level is at the top of the filled valence band. Therefore, silicon is an insulator at 0° K. However, in silicon and other semiconductors, the band gap is small. At room temperature, there is sufficient thermal energy to excite some electrons above the Fermi level into the next band. The thermal energy is contained in the motions of the atoms in a piece of semiconductor. The thermal excitation of electrons above the Fermi level into the next band is illustrated in Figure 19.6. The electrons that have been excited from filled MOs of the valence band to empty MOs of the conduction band are represented in the figure by arrows above the Fermi level. Because there are electrons above the Fermi level, a piece of semiconductor like silicon can conduct electricity. The electrons in the conduction band are called the conduction electrons.
Semiconductors do not conduct electricity as well as metals because they have far fewer conduction electrons. In a metal, there is no band gap. Large numbers of electrons are easily promoted above the Fermi level. In a semiconductor, there is a band gap, but it is small enough that thermal energy can