Page 145 - Engineering Electromagnetics, 8th Edition

CHAPTER 5 Conductors and Dielectrics 127

Intrinsic semiconductors also satisfy the point form of Ohm’s law; that is, the
conductivity is reasonably constant with current density and with the direction of the
current density.
Thenumberofchargecarriersandtheconductivitymaybothbeincreaseddramat-
ically by adding very small amounts of impurities. Donor materials provide additional
electrons and form n-type semiconductors, whereas acceptors furnish extra holes and
form p-type materials. The process is known as doping, and a donor concentration in
5
7
silicon as low as one part in 10 causes an increase in conductivity by a factor of 10 .
The range of value of the conductivity is extreme as we go from the best insulating
materials to semiconductors and the finest conductors. In siemens per meter, σ ranges
from 10 −17 for fused quartz, 10 −7 for poor plastic insulators, and roughly unity for
8
semiconductors to almost 10 for metallic conductors at room temperature. These
values cover the remarkably large range of some 25 orders of magnitude.

D5.7. Using the values given in this section for the electron and hole mo-
bilities in silicon at 300 K, and assuming hole and electron charge densities
3
3
are 0.0029 C/m and −0.0029 C/m , respectively, find: (a) the component of
the conductivity due to holes; (b) the component of the conductivity due to
electrons; (c) the conductivity.
Ans. 72.5 µS/m; 348 µS/m; 421 µS/m

5.7 THE NATURE OF DIELECTRIC
MATERIALS

A dielectric in an electric field can be viewed as a free-space arrangement of mi-
croscopic electric dipoles, each of which is composed of a positive and a negative
charge whose centers do not quite coincide.These are not free charges, and they cannot
contribute to the conduction process. Rather, they are bound in place by atomic and
molecular forces and can only shift positions slightly in response to external fields.
They are called bound charges, in contrast to the free charges that determine conduc-
tivity. The bound charges can be treated as any other sources of the electrostatic field.
Therefore, we would not need to introduce the dielectric constant as a new parameter
or to deal with permittivities different from the permittivity of free space; however,
the alternative would be to consider every charge within a piece of dielectric material.
This is too great a price to pay for using all our previous equations in an unmodified
form, and we shall therefore spend some time theorizing about dielectrics in a quali-
tative way; introducing polarization P, permittivity , and relative permittivity r ; and
developing some quantitative relationships involving these new parameters.
The characteristic that all dielectric materials have in common, whether they are
solid, liquid, or gas, and whether or not they are crystalline in nature, is their ability
to store electric energy. This storage takes place by means of a shift in the relative
positions of the internal, bound positive and negative charges against the normal
molecular and atomic forces.