Page 449 - Schaum's Outline of Theory and Problems of Applied Physics

434 THE SOLID STATE [CHAP. 35

SOLVED PROBLEM 35.4
The upper energy band of an insulator is completely filled with electrons and is separated from the next
higher energy band by a forbidden band several electronvolts wide (Fig. 35-4). How does this fact account
for the inability of insulators to conduct electric current?

Fig. 35-4. Energy bands of an insulator.

An electron in an insulator must acquire at least as much energy as the width of the forbidden band if it is to
have the kinetic energy required to move through the crystal. An energy increment of several electronvolts cannot
be readily given to an electron in a solid by an electric field because of the presence of so many other electrons and
nuclei, so insulators are very poor conductors of electric current.

SOLVED PROBLEM 35.5
Why are metals opaque to visible light, whereas insulators are transparent when in the form of regular
crystals?
Photons of visible light have energies of between about 1 and 3 eV. Such amounts of energy are readily absorbed
by a “free electron” in a metal, since its allowed energy band is only partly filled, and metals are accordingly opaque.
The electrons in an insulator, however, need more than 3 eV of energy to jump across the forbidden band to the next
allowed band. Insulators therefore cannot absorb photons of visible light and so are transparent. Of course, most
samples of insulating materials do not appear transparent, but that is because of such other factors as the scattering
of light by irregularities in their structures or an amorphous character.

SOLVED PROBLEM 35.6
What is the energy-band structure of a semiconductor?
In semiconductors, a very narrow forbidden band separates a filled upper energy band from the next empty one
(Fig. 35-5), and some electrons have enough kinetic energy of thermal origin to jump this gap. Such a substance
can conduct electric current to a limited extent. Some semiconductors contain small amounts of impurities which
provide energy levels in the forbidden band, thus reducing the width of the energy gap electrons must overcome in
order to move freely.

Fig. 35-5. Energy bands of a semiconductor.

SOLVED PROBLEM 35.7
What is an n-type semiconductor?

An n-type semiconductor is one in which current is carried by negative charges. These are excess electrons from
impurity atoms whose outermost shells contain too many electrons to fit into the crystal’s electron structure. For