Page 186 - Electrical Properties of Materials

168 Principles of semiconductor devices

account recombination and generation of carriers in the depletion region.
A good account is given in the book by J.P. McKelvey cited in the further
reading list.

9.4 Injection

In thermal equilibrium the number of electrons moving towards the left is equal
to the number of electrons moving towards the right. However, when a forward
bias is applied, the number of electrons poised to move left is increased by a
factor, exp eU 1 /k B T. This is quite large; for an applied voltage of 0.1 V the
exponential factor is about 55 at room temperature. Thus the number of elec-
trons appearing at the boundary of the p-region is 55 times higher than the
equilibrium concentration of electrons there.
What happens to these electrons? When they move into the p-region they
become minority carriers, rather like immigrants travelling to a new coun-
try suddenly become foreigners. But, instead of mere political friction, the
electrons’ ultimate fate is annihilation. They are slain by heroic holes, who
∗
∗ I do not think that the pacifist interpret- themselves perish in the battle. Naturally, to annihilate all the immigrants,
ation of the recombination of electrons time and space are needed; so some of them get quite far inside foreign territ-
and holes (they get married, and live hap-
pily ever after) can bear closer scrutiny. ory as shown in Fig. 9.6, where the density of electrons is plotted as a function
When an electron and a hole recombine, of distance in a p–n junction under forward bias. The electron density de-
they disappear from the stage and that’s clines, but not very rapidly. A typical distance is about 1 mm, which is about a
that. I would however, be willing to ac- thousand times larger than the width of the transition region.
cept the above interpretation for excitons Let us go back now to the plight of the holes. They are there in the p-type
which are electron–hole pairs bound to-
gether by Coulomb forces but even then material to neutralize the negative charge of the acceptor atoms. But how will
one cannot claim that they lived hap- space charge neutrality be ensured when electrons are injected? It can be done
pily ever after because the lifetime of in only one way; whenever the electron density is increased, the hole density
excitons is less than a picosecond, even
shorter than the expected duration of must increase as well. And this means that new holes must move in from the
modern marriages. contacts. Thus, as electrons move in from the right, holes must move in from
the left to ensure charge neutrality. Hence the current of electrons and holes
will be made up of six constituents, as shown in Fig. 9.7:

(i) The electron current flowing in the n-type material and providing the
electrons to be injected into the p-type material. It is constant in the
n-region.

Junction

Log N
e
p n

Fig. 9.6
The electron distribution in a
x
forward biased p–n junction.