Page 184 - Electrical Properties of Materials

166 Principles of semiconductor devices

Equation (9.15) gives nothing new. If we express the electron density in
the p-type material with the aid of the Fermi level, then we could show from
eqn (9.15) that eU 0 should be equal to the difference between the original
Fermi levels, which we already knew. But although eqn (9.15) does not give any
new information, we shall see in a moment that by describing the equilibrium
in terms of currents flowing in opposite directions, the rectifying properties of
the p–n junction can be easily understood.
We could go through the same argument for holes without much difficulty,
provided we can imagine particles rolling uphill, because for holes that is the
way to lower their energy. The equations would look much the same, and I shall
not bother to derive them.

9.3 Rectification

Let us now apply a voltage as shown in Fig. 9.4. Since there are much fewer
carriers in the transition region, we may assume that all the applied voltage
will drop across the transition region. Then, depending only on the polarity,
the potential barrier between the p and n regions will decrease or increase.

(a)

p n

V + –
1

eU
eU 0
1

(b)
p n

– +
V
1

eU
0

eU
1
Fig. 9.4
The energy diagram of a p–n junction
for (a) forward bias and
(b) reverse bias.