The Foundations of Chemistry

13-16 Bonding in Solids 519

charged boron atom from the hole, delocalizing the latter. In
this case the charge carriers are the holes, which are positive,
and the crystal is doped p-type.In both p-and n-type dop-
ing, an extremely small concentration of dopants (as little as
one part per billion) is enough to cause a significant increase
in conductivity. For this reason, great pains are taken to purify
the semiconductors used in electronic devices.

Even in a doped semiconductor, mobile electrons and

holes are both present, although one carrier type is predom-

inant. For example, in a sample of silicon doped with arsenic

(n-type doping), the concentrations of mobile electrons are

slightly less than the concentration of arsenic atoms (usually

expressed in terms of atoms/cm^3 ), and the concentrations of

mobile holes are extremely low. Interestingly, the concentra-

tions of electrons and holes always follow an equilibrium

expression that is entirely analogous to that for the autodis-

sociation of water into H
and OHions (Chapter 18); that

is,

[e][h
]Keq

where the equilibrium constant Keqdepends only on the iden-

tity of the semiconductor and the absolute temperature. For

silicon at room temperature, Keq4.9 1019 carriers^2 /cm^6.

Doped semiconductors are extremely important in elec-

tronic applications. A p–njunctionis formed by joining p-

and n-type semiconductors. At the junction, free electrons

and holes combine, annihilating each other and leaving pos-

itively and negatively charged dopant atoms on opposite

sides. The unequal charge distribution on the two sides of

the junction causes an electric field to develop and gives rise

to current rectification (electrons can flow, with a small

applied voltage, only from the nside to the pside of the junc-

tion; holes flow only in the reverse direction). Devices such

as diodesand transistors,which form the bases of most ana-

log and digital electronic circuits, are composed of p–n

junctions.

Professor Thomas A. Mallouk

Pennsylvania State University

Si Si Si Si

Si Si Si Si

Si Si Si

Valence band

Conduction band

Thermal

excitation

Donor

level

Si Si Si Si Si

Si Si Si Si Si

Si Si Si Si Si

Si Si Si Si Si

P

e



The colors of semiconductors are determined by the band gap energy Eg.
Only photons with energy greater than Egcan be absorbed. From the
Planck radiation formula (Ehv) and vc, we calculate that the
wavelength, , of an absorbed photon must be less than hc/ Eg. Gallium
arsenide (GaAs; Eg1.4 eV) absorbs photons of wavelengths shorter
than 890 nm, which is in the near infrared region. Because it absorbs all
wavelengths of visible light, gallium arsenide appears black to the eye.
Iron oxide (Fe 2 O 3 ; Eg2.2 eV) absorbs light of wavelengths shorter
than 570 nm; it absorbs both yellow and blue light, and therefore
appears red. Cadmium sulfide (CdS; Eg2.6 eV), which absorbs blue
light (470 nm), appears yellow. Strontium titanate (SrTiO 3 ; Eg
3.2 eV) absorbs only in the ultraviolet (390 nm). It appears white
to the eye because visible light of all colors is reflected by the fine particles.

(b)n-type doping of silicon by phosphorus. The

extra valence electron from a phosphorus atom

is thermally excited into the conduction band,

leaving a fixed positive charge on the

phosphorus atom.