Page 154 - Electrical Properties of Materials

136 Semiconductors

Now we may argue that by adding a small amount of impurity, neither
the rate of creation nor the proportionality constant should change. So for an
extrinsic semiconductor
g extrinsic = aN i 2 (8.49)
is still valid.
The rate of recombination should, however, depend on the actual densities
of electrons and holes, that is
r extrinsic = aN e N h . (8.50)
From the equality of eqns (8.49) and (8.50) we get the required relationship,
2
N = N e N h . (8.51)
i
So we may say that as the density of electrons is increased above the intrinsic
value, the density of holes must decrease below the intrinsic value in order that
the rate of recombination of electron–hole pairs may remain at a constant value
equal to the rate of thermal creation of pairs.
Those of you who have studied chemistry may recognize this relationship as
a particular case of the law of mass action. This can be illustrated by a chemical
reaction between A and B, giving rise to a compound AB,
A+B AB. (8.52)

If we represent the molecular concentration of each component by writing its
symbol in square brackets, the quantity
[A][B][AB] –1 (8.53)

is a constant at a given temperature. Now our ‘reaction’ is
electron + hole bound electron. (8.54)

As the number of bound electrons (cf. [AB]) is constant, this means that
[electron][hole] = N e N h (8.55)
will also be constant.

8.6 III–V and II–VI compounds
In our examples up to now we have referred to germanium and silicon as
typical semiconductors, and indeed they are typical, their technology was cer-
tainly the earliest mastered. They are both tetravalent, so they can be found in
column IVB of our periodic table shown in Fig. 4.5. There are, of course, many
other semiconductors. In this section we shall be concerned with two further
types which are compounds of elements from columns IIIB, VB, IIB, and VIB,
respectively.
Let us talk first about the III–V compounds. Why are they semiconductors?
We can say the same thing about them as about germanium and silicon.
They are insulators at low temperatures because all the electrons parti-
cipate in the bonding process; none of them is available for conduction.
At higher temperatures, however, the electronic bond can be broken by thermal