Page 243 - Electrical Properties of Materials

Dielectric materials

10

Le flux les apporta, le reflux les emporte.
Corneille Le Cid

10.1 Introduction
In discussing properties of metals and semiconductors we have seen that, with
a little quantum mechanics and a modicum of common sense, a reasonable
account of experiments involving the transport (the word meaning motion in
the official jargon) of electrons emerges. As a dielectric is an insulator, by
definition, no transport occurs. We shall see that we can discuss the effects of
dielectric polarization adequately in terms of electromagnetic theory. Thus, all
we need from band theory is an idea of what sort of energy gap defines an
insulator.
Suppose we consider a material for which the energy gap is 100 times the
thermal energy at 300 K, that is 2.5 eV. Remembering that the Fermi level is
about halfway across the gap in an intrinsic material, it is easily calculated that
the Fermi function is about 10 –22 at the band edges. With reasonable density
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of states, this leads to less than 10 mobile electrons per cubic metre, which is
usually regarded as a value for a good insulator. Thus, because we happen to
live at room temperature, we can draw the boundary between semiconductors
and insulators at an energy gap of about 2.5 eV.
Another possible way of distinguishing between semiconductors and in-
sulators is on the basis of optical properties. Since our eyes can detect
electromagnetic radiation between the wavelengths of 400 nm and 700 nm, we
attribute some special significance to this band, so we may define an insulator
as a material in which electron–hole pairs are not created by visible light. Since
a photon of 400 nm wavelength has an energy of about 3 eV, we may say that
an insulator has an energy gap in excess of that value.

10.2 Macroscopic approach

This is really the subject of electromagnetic theory, which most of you already
know, so I shall briefly summarize the results. In the SI system is the product of
A dielectric is characterized by its dielectric constant , which relates the 0 ( permittivity of free space) and
electric flux density to the electric field by the relationship r (relative dielectric constant).

D = E . (10.1)

The basic experimental evidence (as discovered by Faraday some time ago)
comes from the condenser experiment in which the capacitance increases by
a factor, r , when a dielectric is inserted between the condenser plates. The