Page 201 - Electrical Properties of Materials

The tunnel diode 183

minority carriers will not have the time to appear, a mode of operation called
the deep depletion mode.
Inversion and deep depletion are some further representations of the
multifarious phenomena of semiconductor physics. They are certainly interest-
ing, but are they useful? Can a device through which no current flows be of any
use at all in electronics? The secret is that current can flow along the insulator
surface. The emerging devices are very important indeed. Under acronyms
like MOSFETs and CCDs they are the flagbearers of the microelectronics
revolution. I shall talk about them a little later.

9.10 The tunnel diode

So far, we have considered impurity semiconductors with very low impurity
contents, typically less than one part per million. We have characterized the
impurity type and density by working out where the Fermi level is, and have
found that in all cases it is well within the energy gap. This has meant, among
other things, that the sums are much simpler, for we are able to approximate
to the Fermi function. However, when the impurity level becomes very high
24
(typically about 10 m –3 or about 0.01%), the Fermi level moves right up into
the conduction band (or down into the valence band for a p-type impurity). The
semiconductor is then said to be ‘degenerate’. What are degenerate semicon-
ductors good for? One can make diode lasers out of them, as will be discussed
later in Section 12.7. But well before the appearance of diode lasers, Esaki ∗ ∗ Leo Esaki received a Nobel Prize in
realized that they were suitable for producing a revolutionary new device, to 1973. This is another example where the
invention of a new device earned for the
be shown in this section. For a while, they were called Esaki diodes. They are
inventor the Nobel Prize in Physics.
now known as tunnel diodes because their operation is based on tunnelling.
Let us now produce a junction out of two degenerate semiconductors, one
p-type and one n-type. The energy diagram at thermal equilibrium is given in
Fig. 9.24(a), where, for simplicity, we take the difference between the Fermi
level and the band edge as the same on both sides. It is interesting to see
that the ‘built-in’ potential is larger than the energy gap (eU 0 > E g ); thus the
number of electrons crossing over the potential barrier at thermal equilibrium
must be small. Hence, I 0 in the rectifier equation is small, and the rectifying
characteristic is rather elongated, as shown in Fig. 9.25(a).
Looking carefully at the diagram you may realize that another mechanism
of electron flow may also be effective. Remember, tunnel diodes are highly
doped, and high doping means a narrow transition region. Thus, electrons as
well as moving over the potential barrier may also tunnel through the potential
barrier, and if one puts in the figures, it turns out that the tunnelling current is
the larger of the two. Hence, we may imagine thermal equilibrium as the state
in which the tunnelling currents are equal and in opposite directions.
What happens now if we apply a reverse bias? As may be seen in
Fig. 9.24(b), the number of electrons tunnelling from left to right is increased
because the electrons on the p-side face a large number of empty states on the
n-side. We could work out this current by considering a rectangular potential
barrier (the one we so skilfully solved when first confronted with Schrödinger’s
equation) and taking account of the occupancy of states on both sides. It is one
of those fairly lengthy and tedious calculations that are usually left as an exer-
cise for the student. The actual value is of little consequence because this diode