Page 185 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Statistics
5.2.4 Quasi Particles and Statistics
The question as to which statistics should be applied to what is answered
by quantum-mechanical considerations. All phenomena occurring in a
semiconductor obey quantum mechanics. Often we are not aware of this
fact, such as when we are dealing with a macroscopically-sized sample.
For special cases, such as on a very small length scale, at very low tem-
peratures, or in a coherent light field from a laser, the quantum nature of
phenomena is directly observable. The lattice vibrational amplitudes
show discrete changes, the light intensity as well, and the electric current
is composed of single charge carriers.

This discrete nature of the phenomena is best described by so called
quasi-particles. These are nothing else than the single quanta by which
the amplitudes of the each observable quantity may increase or decrease
by. It is just by way of talking about quantum phenomena that we intro-
duce the term “phonon” for the quantum of a lattice vibration, “photon”
for the quantum of electromagnetic oscillation, and “electron” or “hole”
for quantum moving charged carrier. The most mechanically intuitive
picture is perhaps that of a phonon, which is the coaction of all the indi-
vidual ions forming a crystal lattice.

In a similar manner as for a photon, we have to imagine an electron in the
conduction band of a semiconductor. The picture we obtain is the net
result of a composed excitation of the bare free-electron, together with
the crystal structure forming the conduction band and the other electrons
in the semi-conductor (and of course strictly-speaking many more
effects.) It is not the electron as a massive particle that makes it different
from a phonon. Rather, it is the kind of interacting subsystems that form
the resulting phenomenon. In this light the “-ons”, the quasi-particle fam-
ily members, lose their mystery and remain simple descriptions of a phe-
nomenon.

182 Semiconductors for Micro and Nanosystem Technology