Page 267 - Electrical Properties of Materials

Interaction of optical phonons with drifting electrons 249

were discovered it was the similarity with ferromagnetics that was first noticed.
Ferromagnetics have a B–H loop (which will be tackled in much more detail
in Sections 11.4–11.6), the new materials have a P–E loop. The former is mag-
netic, the latter is electric, so at the baptism ceremony, purely on the basis of
this analogy, they called the new materials ferroelectric—and once you have a
name it is difficult to change it.
Ferroelectrics typically have the perovskite structure, like BaTiO 3 (shown
in Fig. 10.22). The spontaneous polarization comes from the Ti atoms mov-
ing up or down. There are also domains (more about domains in Section 11.4
concerned with ferromagnetic materials) in ferroelectrics which have the same
direction of spontaneous polarization. When we apply an electric field the Ti
atoms respond moving out of their position and thereby change the polariza-
tion. Above the Curie temperature ferroelectrics become ordinary dielectrics
but with the advantage of having very high dielectric constants. That’s a prop-
erty that can find applications in cameras as a way of powering a flash. The
ferroelectric is in a capacitor charged up by a battery. High dielectric con-
stant means high stored energy. When the capacitor is connected to a bulb it
discharges, the high current creating a flash.
Hysteresis, means delay (from the Greek υστερησιζ, meaning delay), and
in this context a delay in the appearance of polarization when the magnitude
of the electric field is varied. Figure 10.24 shows a hysteretic P–E curve. Let p p
us start at a certain point P 1 where there is spontaneous polarization in the 2
absence of an electric field. As the electric field is increased the polarization p 1
increases to P 2 . If we now reduce the electric field the polarization will not
retrace the curve at which it rose. It will now decline at a faster rate. It will
e
reach P = 0 at a value of E c of the electric field, that is (another misnomer) −e c e c
called the coercive force. A further decrease in the electric field causes the
−p
polarization to reverse. When the electric field is zero the polarization is P 3 . 1
Increasing the electric field in the opposite direction will lead to P 4 . A decrease
−p 2
in this electric field will lead to P =0 at E =–E c . A further decrease in the
electric field to zero where P = P 1 will complete the loop.
Fig. 10.24
Ferroelectrics have often been considered for applications in the past (e.g.
Ferroelectric hysteresis loop.
voltage tunable capacitors) but they have never achieved sustained success.
This might change in the future due to improved materials. Their potential
applications as memory elements will be discussed in Appendix VI.

10.14 Interaction of optical phonons with drifting electrons
In the previous section we discussed the acoustic amplifier, in which acoustic
waves could be amplified by interacting with drifting electrons. The remarkable
thing is that there can be transfer of power from the electrons to the acoustic
wave in spite of the presence of collisions. The question naturally arises of
whether we could transfer power from electrons to the optical branch of the
acoustic waves, i.e. produce an amplifier for optical phonons. If we could do
that then it would also be possible to build oscillators. Would it be an advantage
to have such oscillators? The answer is very much so. Remember the range of
the optical phonon resonances. They are all in the THz region—and that is a
region of the electromagnetic spectrum that has hardly been explored. A cheap