Page 200 - Electrical Properties of Materials

182 Principles of semiconductor devices

shown in Fig. 9.23(b), and we may talk again about the balance of diffusion and
conduction currents. Finally the band-bending picture is shown in Fig. 9.23(c),
from which we can also conclude that the electron density is decreasing to-
wards the insulator. What will happen as we apply higher and higher reverse
bias? The obvious answer is that the depletion region will widen. What else
could one expect? It is difficult to believe at first hearing, but the fact (fortunate
as it happens) is that holes will appear. Can we explain this phenomenon by any
of our models? If we consider only ionized donor atoms and mobile electrons,
as in the model developed in Section 9.2, we have not got the slightest chance
of creating holes. On the other hand if we adopt the notion that the density of a
carrier at any point is determined by the distance in energy from the Fermi level
to the edge of the particular band, then holes have acquired the right to appear.
All we need to do is to apply a sufficiently large reverse bias [Fig. 9.23(d)]
which will bring the Fermi level right down, close to the top of the valence
band. Thus, according to this model, holes may become the majority carri-
ers near to the surface of an n-type semiconductor. Odd, is it not? The problem
still remains, though, that the holes must come from somewhere. The only pro-
cess known to produce holes in an n-type semiconductor is thermal generation
of electron–hole pairs. But are not the rates of generation and recombination
equal? Would not the holes generated thermally immediately disappear by re-
combination? This is true indeed under thermal equilibrium conditions, but our
junction is not necessarily in thermal equilibrium.
Let us look again at the whole process, considering time relationships as
well. At t = 0 we apply a negative voltage to the junction. Most of the elec-
trons clear out by t 1 , leaving a depletion region of the order of 1 μm behind.
What happens now to thermally generated electron–hole pairs? The electrons
move away from the insulator, and the holes move towards the insulator. Not
much recombination will occur because both the electron and hole densities
are small, and they are separated in space. What will happen to the holes?
They will congregate in the vicinity of the insulator, where they can find a nice
comfortable potential minimum.
The conditions of equilibrium are rather complicated. At the end, say by t 2 ,
the hole diffusion current away from the insulator must be equal to the hole
conduction current towards the insulator, and the rates of generation and re-
combination must balance each other. It is then quite reasonable to conclude
that if the applied negative voltage is large enough, that is the potential min-
imum at the insulator surface is deep enough, then a sufficient number of
holes can congregate, and the part of the n-type semiconductor adjacent to
The phenomenon of inversion is the insulator will behave as if it were p-type. This is called inversion.
not restricted of course to n-type Our conclusion so far is that under equilibrium conditions inversion may
semiconductors. Similar inversion occur. Whether equilibrium is reached or not depends on the time constants t 1
occurs in a metal–insulator–p-type and t 2 . How long is t 1 ? As far as we know no one has measured it, but it
semiconductor junction. can not take long for electrons to clear out of a 1 μm part of the material. If
we take a snail moving with a velocity of 1 m h –1 it will need about 3 ms to
cover 1 μm. Thus electrons, which may be reasonably expected to move faster
than snails, would need very little time indeed to rearrange themselves and
create a depletion region. On the other hand, in sufficiently pure materials the
thermal generation time constant might be as long as a few seconds. Thus, if
all the operations we perform in a metal–insulator–semiconductor junction are
short in comparison with the generation time of electron–hole pairs, then the