Page 409 - Electrical Properties of Materials

The energy gap 391

I

Fig. 14.18
The current as a function of voltage
for a junction between two different
superconductors separated by a thin
V insulator. There is a negative
(Δ - Δ ) /e 2Δ /e resistance region of
2 1 1
( 2 – 1 )/e < U < ( 1 + 2 )/e.

electrons to tunnel across. If the voltage is increased further, the current
decreases because the number of electrons capable of tunnelling is unchanged,
but they now face a lower density of states. When the voltage becomes greater
than ( 2 + 1 )/e the current increases rapidly because electrons below the gap
can begin to flow. The superconducting tunnel diode
Thus, a tunnel junction comprised of two superconductors of different en- was invented by Ivar Giaever. The
ergy gaps may exhibit negative resistance, similarly to the semiconductor fact that it has negative resist-
tunnel diode. Unfortunately, the superconducting tunnel junction is not as ance makes it similar to the diode
useful because it works only at low temperatures. invented by Leo Esaki (see Sec-
The tunnelling we have just described follows the same principles we en- tion 9.10). As it happened, they
countered when discussing semiconductors. There is, however, a tunnelling received the Nobel Prize in 1973.
phenomenon characteristic of superconductors, and of superconductors alone;
it is the so-called superconducting or Josephson tunnelling (discovered theor-
etically by Josephson, a Cambridge graduate student at the time) which takes Brian Josephson was the third re-
place when the insulator is very thin (less than 1.5–2 nm). It displays a number cipient of the Nobel Prize in 1973.
of interesting phenomena, of which we shall briefly describe four.
1. For low enough currents there can be a current across the insulator without
any accompanying voltage; the insulator turns into a superconductor. The
reason is that Cooper pairs (not single electrons) tunnel across.
2. For larger currents there can be finite voltages across the insulator. The
Cooper pairs descending from the higher potential to the lower one may
radiate their energy according to the relationship, U AB is the d.c. voltage between the
two superconductors, and ω is the
angular frequency of the electro-
ω =(2e)U AB . (14.73)
magnetic radiation.
Thus, we have a very simple form of a d.c. tuneable oscillator that could
work up to infrared frequencies. Equation (14.73) gives an extremely simple
relationship between the voltage applied to a Josephson junction and the fre-
quency of the resulting oscillation. All we need is a d.c. source and we have
produced an oscillator. Unfortunately, the power that can be extracted is