## Electrical Properties of Materials

The electron conductivity of solid materials gives an almost unambiguous way to classify them. Simply put, on the basis of electrical conductivity, materials are either insulators, semiconductors, conductors, or superconductors. Superconductors are a special class of materials that exhibit zero resistance below a certain temperature. They will not be considered here. The conductivity of all of the more common and widely used materials is shown in Figure 10.1. The range of conductivities is quite large. Where we draw the lines for these materials appears to be somewhat arbitrary, but we can define these three categories fairly precisely in terms of the number of electrons available for conduction. This number can be computed using the energy band structure for the valence electrons, a subject covered in the following section. Insulators and most polymers have a low conductivity because of their strong covalent bonds and the absence of free electrons, but in some polymers a conducting powder is mixed with the polymer to form a conducting composite. In a few others of the so-called conducting polymers, there exist some free electrons within the polymer structure, creating conductivity on the order of that found in crystalline semiconductors, and in some conducting polymers the conductivity approaches that of metals. There is a tremendously large variation in the conductivity of solids, being about a factor of 10

from conductors to insulators. Ohm’s law can be used to express conductivity and its reciprocal, resistivity,

which are not functions of specimen dimensions, and the conductance and resistance, which are functions of specimen dimensions. Resistance is related to resistivity by:

R =

ρ

l

/A

where R = resistance

ρ

= resistivity (usually expressed in

Ω

· m)

l

= specimen length

A

= specimen area

and in terms of conductivity,

σ

,

σ

=

l

/RA units are (

Ω

· m)

For semiconductors it is more desirable and convenient to express the conductivity in terms of the number of charge carriers and their mobility. To accomplish this feat, we state Ohm’s law in a different fashion:

J =

σε

(10.1)

where

J

= current density or flux = Amp/m

σ

= conductivity

ε

= electric field strength = E/

l =

V/m

Now the current density can also be written as

J = nqV

(10.2)

where

n

= number of charge carriers

q

= charge on the carrier, usually that of the electron (1.6

×

C)

V

= average drift velocity of charge carriers

Since the ampere is a rate of flow of 1 coulomb of electric charge per second,

J

is similar to a diffusion flux.