Page 132 - Engineering Electromagnetics, 8th Edition

114 ENGINEERING ELECTROMAGNETICS

5.3 METALLIC CONDUCTORS
Physicists describe the behavior of the electrons surrounding the positive atomic
nucleus in terms of the total energy of the electron with respect to a zero reference
level for an electron at an infinite distance from the nucleus. The total energy is the
sum of the kinetic and potential energies, and because energy must be given to an
electron to pull it away from the nucleus, the energy of every electron in the atom is
anegative quantity. Even though this picture has some limitations, it is convenient to
associate these energy values with orbits surrounding the nucleus, the more negative
energies corresponding to orbits of smaller radius. According to the quantum theory,
only certain discrete energy levels, or energy states, are permissible in a given atom,
and an electron must therefore absorb or emit discrete amounts of energy, or quanta,
in passing from one level to another. A normal atom at absolute zero temperature has
an electron occupying every one of the lower energy shells, starting outward from the
nucleus and continuing until the supply of electrons is exhausted.
In a crystalline solid, such as a metal or a diamond, atoms are packed closely
together, many more electrons are present, and many more permissible energy levels
are available because of the interaction forces between adjacent atoms. We find that
the allowed energies of electrons are grouped into broad ranges, or “bands,” each band
consisting of very numerous, closely spaced, discrete levels. At a temperature of abso-
lute zero, the normal solid also has every level occupied, starting with the lowest and
proceeding in order until all the electrons are located. The electrons with the highest
(least negative) energy levels, the valence electrons, are located in the valence band.If
there are permissible higher-energy levels in the valence band, or if the valence band
merges smoothly into a conduction band, then additional kinetic energy may be given
to the valence electrons by an external field, resulting in an electron flow. The solid is
called a metallic conductor. The filled valence band and the unfilled conduction band
foraconductoratabsolutezerotemperaturearesuggestedbythesketchinFigure5.2a.
If, however, the electron with the greatest energy occupies the top level in the
valence band and a gap exists between the valence band and the conduction band, then

Figure 5.2 The energy-band structure in three different types of materials
at 0 K. (a) The conductor exhibits no energy gap between the valence and
conduction bands. (b) The insulator shows a large energy gap. (c) The
semiconductor has only a small energy gap.