Physical Chemistry , 1st ed.

The very word “defect” has negative connotations, but crystal defects are not

necessarily bad. One area that takes advantage of crystal defects is semiconduc-

tors. For example, many semiconductors are composed mostly of silicon,

whose crystal form is a covalent network solid. Pure silicon is actually non-

conductive, but if a tiny percentage of substitutional defects is present, the

conductivity properties of silicon are changed dramatically. For example, 10 parts

per million of boron substituted in pure silicon increases the conductivity of

the crystalline solid by a factor of 1000! A boron atom does this by substitut-

ing for a Si atom, but in doing so decreases the number of electrons in the solid

by 1; see Figure 21.33a. The unpaired electron on the adjacent silicon atom is

free to conduct electricity (but not very well; hence the semiconductor de-

scription of the doped silicon crystal). An equivalent way of stating this is that

the boron atom “substitutes” a missing electron, called a hole,and it is the hole

that conducts the electricity. (Although the definition of a hole relies on some-

thing that is notthere rather than something that is, it is commonly invoked

to discuss the conductivity of semiconductors. Electricity is conducted as elec-

trons move to fill holes.) Semiconductors that are doped to decrease the num-

ber of electrons are called p-type semiconductors,the pstanding for positive.

That is, having fewer electrons implies a positive charge on a material. This is

somewhat of a misnomer, because the crystal does nothave a positive charge.

Similarly, substituting an atom that has more electrons than a Si atom does

introduces additional electrons, as shown in Figure 21.33b. These excess elec-

trons can also impart some conductivity to the Si crystal. Because of the addi-

tional electrons in the substitutional defect, these semiconductors are called n-

type semiconductors,the nstanding for negativeusing the reverse of the rationale

for the p-type label.

Other substitutions (by different atoms and to different degrees) change the

conductivity of silicon in other ways, and it is this variable conductivity that is

the basis for all solid-state electronics. This intentional introduction of defects

is called doping.In addition to silicon, other materials—properly doped—can

be used as semiconductors. Some of these materials are 11 combinations of

p^3 and p^5 valence shell atoms (Si has a p^4 valence shell, so on average the atoms

have a silicon-like valence shell). GaAs and InAs are common materials that are

also used for semiconductors.

21.10 Summary

In this chapter, we have seen how we can model the solid state of matter,

assuming that the solid is well-ordered and composed of crystals. Not-well-

ordered solids can be polycrystalline, or they may be amorphous. But the reg-

ularity of crystals helps us determine models for describing the solid phase.

Central to modeling the solid state is the understanding that there are only

14 basic crystal arrangements, called Bravais lattices. Crystals are ultimately

composed of repeating units called unit cells, all having the same three-

dimensional arrangement of atoms or molecules, all contributing to the entire

crystal. A unit cell is to a crystal as an atom is to an element: it is the basic

building block of the larger material. Also central is the idea that there is a sim-

ple mathematical model to determine how crystal lattices might interact with

electromagnetic radiation, specifically X rays. The Bragg equation shows how

we can relate the diffraction of X rays by a crystal to that crystal’s structure.

Crystals as simple as NaCl or as complicated as DNA can be studied using X-

ray diffraction, and their structures deduced on the basis of their diffracting

760 CHAPTER 21 The Solid State: Crystals

(a) p-Type semiconductor

Si Si Si

Si Si

Si B

Provides

excess  change

Si

(b) n-Type semiconductor

Si Si Si

Si Si

Si As

Provides

excess  change

Si

Figure 21.33 (a) Substituting a boron atom
for a silicon atom in crystalline Si reduces the
number of electrons in the crystal by 1, making a
positively charged “hole” and a so-called p-type
semiconductor. Electrons can occupy these holes,
allowing for electricity to conduct through the
material. (b) Similarly, substituting an As atom
introduces an extra electron, which is free to
move through the solid. This is an n-type semi-
conductor.