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The Solid State 359

if it is to climb to the conduction band where it can move about freely. With kT 

0.025 eV at room temperature, valence electrons in diamond do not have enough ther-

mal energy to jump the 6 eV gap.

Nor can an energy increment of 6 eV be given to a valence electron in diamond by an

electric field, because such an electron undergoes frequent collisions with crystal imper-

fections during which it loses most of the energy it gains from the field. An electric field

of over 10^8 Vm is needed for an electron to gain 6 eV in a typical mean free path of

5  10 ^8 m. This is billions of times stronger than the field needed for a current to flow

in a metal. Diamond is therefore a very poor conductor and is classed as an insulator.

Semiconductors

Silicon has a crystal structure like that of diamond and, as in diamond, a gap sepa-

rates the top of its filled valence band from an empty conduction band above it (see

Fig. 10.23). The forbidden band in silicon, however, is only about 1 eV wide. At low

temperatures silicon is little better than diamond as a conductor, but at room temper-

ature a small number of its valence electrons have enough thermal energy to jump the

forbidden band and enter the conduction band (Fig. 10.25). These electrons, though

few, are still enough to allow a small amount of current to flow when an electric field

is applied. Thus silicon has a resistivity intermediate between those of conductors and

those of insulators, and it and other solids with similar band structures are classed as

semiconductors.

Impurity Semiconductors

Small amounts of impurity can drastically change the conductivity of a semiconductor.

Suppose we incorporate a few arsenic atoms in a silicon crystal. Arsenic atoms have

five electrons in their outer shells, silicon atoms have four. (These shells have the con-

figurations 4s^24 p^3 and 3s^23 p^2 respectively.) When an arsenic atom replaces a silicon

atom in a silicon crystal, four of its electrons participate in covalent bonds with its

nearest neighbors. The fifth electron needs very little energy—only about 0.05 eV in

silicon, about 0.01 eV in germanium—to be detached and move about freely in the

crystal.

As shown in Fig. 10.26, arsenic as an impurity in silicon provides energy levels just

below the conduction band. Such levels are called donor levels,and the substance is

called an n-typesemiconductor because electric current in it is carried by negative

charges (Fig. 10.27). The presence of donor levels below the conduction band raises

the Fermi energy above the middle of the forbidden band between the valence and

conduction bands.

Conduction band

Valence band

eF

Figure 10.25The valence and conduction bands in a semiconductor are separated by a smaller gap

than in the case of an insulator. Here a small number of electrons near the top of the valence band

can acquire enough thermal energy to jump the gap and enter the conduction band. The Fermi en-

ergy is therefore in the middle of the gap.

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