Basic Electronics for Scientists and Engineers

3 Band theory and diode circuits
3.1 The band theory of solids
3.1.1 Introduction
A fundamental result from basic modern physics is that atoms are characterized by
discrete energy levels. Each of these energy levels can accept up to two electrons.
When “building” an atom, we start from the lowest level, fill in two electrons, and
then move up to the next energy level and fill it with electrons. This continues
until we have placed all the atom’s electrons in energy levels. We also know that
if an atom absorbs energy from the outside (for example, by absorbing a photon),
an electron can be promoted to a higher energy level. Conversely, an electron that
falls from a higher to a lower energy level emits a photon.
What happens to this energy level model when we assemble many atoms together
into a solid? As the atoms get closer together, we must start to talk about the energy
levels of the solid as a whole rather than those of the individual atoms. Rather
than doing quantum mechanics for an isolated potential (the atom), we do it for
a periodic array of atoms that exhibits a periodic potential. The net result of this
is that, during the assembly of N atoms, the individual atomic levels split into N
levels. This is shown schematically in Fig. 3.1. Thus when the solid is assembled
and the atoms are at their final equilibrium spacing, the solid is characterized by
aseriesofenergy bands consisting of a large number of closely spaced allowed
energy levels. Just as electrons in individual atoms cannot have energies between
the atomic energy levels, so electrons in a solid are forbidden to have energies
between the allowed bands.
3.1.2 Band theory
Imagine we are constructing a material consisting of N atoms as described above,
but we have not added any electrons yet. We now start to add electrons to the solid,
starting with the lowest energy level. As with atomic energy levels, only certain