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 of states, this leads to less than 10 ⁶ 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 insulators 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...