Metals, Insulators, and Semiconductors

Each crystal has its own energy-band structure. We noted that the splitting of the energy some basic differences in electrical characteristics caused by variations in band structure by considering some simplified energy bands.

There are several possible energy-band conditions to consider. Figure 1.1a shows an allowed energy band that is completely empty of electrons. If an electric field is applied, there are no particles to move, so there will be no current. Figure 1.1b shows another allowed energy band whose energy states are completely full of electrons. We argued in the previous section that a completely full energy band will also not give rise to a current. A material that has energy bands either completely empty or completely full is an insulator. The resistivity of an insulator is very large or, conversely, the conductivity of an insulator is very small. There are essentially no charged panicles that can contribute to a drift current. Figure 1.1c shows a simplified energy band diagram of an insulator. The bandgap energy E_g of an insulator is usually on the order of 3.5 to 6 eV or larger, so that at room temperature, there are essentially no electrons in the conduction band and the valence band remains completely full. There are very few thermally generated electrons and holes in an insulator.

Figure 1.2a shows an energy band with relatively few electrons near the bottom of the band. Now, if an electric field is applied, the electrons can gain energy, move to

Figure 1.1 Allowed energy bands showing (a) an empty band, (b) a completely full band. and (c) the bandgap energy between the two allowed bands.

Figure 1.2 Allowed energy bands showing (a) an almost empty band. (b) an almost full band, and (c) the bandgap energy between the two allowed bands.

Figure 1.3 Two possible energy bands of a metal showing (a) a partially filled band and (b) overlapping allowed energy bands.

higher energy states, and move through the crystal. The net flow of charge is a current. Figure 1.2b shows an allowed energy band that is almost full of electrons., which means that we can consider the holes in this band. If an electric field is applied, the holes can move and give rise to a current. Figure 1.2c shows the simplified energy band diagram for this case. The bandgap energy may be on the order of 1 eV. This energy-band diagram represents a semiconductor for T > 0 K. The resistivity of a semiconductor, as we will see in the next chapter, can be controlled and varied over many orders of magnitude.

The characteristics of a metal include a very low resistivity. The energy-hand diagram for a metal may be in one of two forms. Figure 1.3 a shows the case of a partially full band in which there are many electrons available for conduction, so that the material can exhibit a large electrical conductivity. Figure 1.3b shows another possible energy-band diagram of a metal. The hand splitting into allowed and forbidden energy bands is a complex phenomenon and Figure 1.3b shows a case in which the conduction and valence bands overlap at the equilibrium interatomic distance. As in the case shown in Figure 1.3a, there are large numbers of electrons as well as large numbers of empty energy states into which the electrons can move, so this material can also exhibit a very high electrical conductivity.