Page 18 - Electrical Properties of Materials

The electron as a particle

1

And I laugh to see them whirl and flee,
Like a swarm of golden bees.
Shelley The Cloud

1.1 Introduction
In the popular mind the electron lives as something very small that has some-
thing to do with electricity. Studying electromagnetism does not change the
picture appreciably. You learn that the electron can be regarded as a negative
point charge and it duly obeys the laws of mechanics and electromagnetism. It
is a particle that can be accelerated or decelerated but cannot be taken to bits.
Is this picture likely to benefit an engineer? Yes, if it helps him to produce a
device. Is it a correct picture? Well, an engineer is not concerned with the truth,
that is left to philosophers and theologians; the prime concern of an engineer
is the utility of the final product. If this physical picture makes possible the
birth of the vacuum tube, we must deem it useful; but if it fails to account for
the properties of the transistor then we must regard its appeal as less alluring.
There is no doubt, however, that we can go quite far by regarding the electron
as a particle even in a solid—the subject of our study.
What does a solid look like? It consists of atoms. This idea originated a few
∗
thousand years ago in Greece, and has had some ups and downs in history, ∗ From ‘ατoμoδ’ = indivisible.
but today its truth is universally accepted. Now if matter consists of atoms, they
must be somehow piled upon each other. The science that is concerned with the
spatial arrangement of atoms is called crystallography. It is a science greatly
revered by crystallographers; engineers are respectful, but lack enthusiasm.
This is because the need to visualize structures in three dimensions adds to
the hard enough task of thinking about what the electron will do next. For this
chapter, let us assume that all materials crystallize in the simple cubic structure
of Fig. 1.1, with the lattice ions fixed (it is a solid) and some electrons are free
to wander between them. This will shortly enable us to explain Ohm’s law,
the Hall effect, and several other important events. But if you are sceptical
about over simplification, look forward to Fig. 5.3 to see how the elemental
semiconductors crystallize in the diamond structure, or get a greater shock
with Fig. 5.4 which shows a form of carbon that was discovered in meteorites
but has only recently been fabricated in laboratories.
Let us specify our model a little more closely. If we postulate the existence
of a certain number of electrons capable of conducting electricity, we must
also say that a corresponding amount of positive charge exists in the solid. It Fig. 1.1
must look electrically neutral to the outside world. Second, in analogy with Atoms crystallizing in a cubical
our picture of gases, we may assume that the electrons bounce around in the lattice.