Page 30 - Photonics Essentials an introduction with experiments

Electrons and Photons

24 Introductory Concepts

Figure 2.7. Diagram of electron energy as a function of electron momentum for an elec-
tron in a periodic environment. Each period of the structure reflects the same electron be-
havior, just like a mirror.

The diagram of energy and momentum is a picture that shows
which states are allowed to be occupied by electrons. You need extra
information to know which states actually are occupied. In Fig. 2.8,
we show an analogous diagram for cars: a road map. On this road
map we see some lines indicating roads. These lines tell you what
places (or states) can be occupied by automobiles under normal or
equilibrium conditions. However, you need more information in order
to know which states are actually occupied by automobiles. The road
map does not tell you much about the velocity of the cars, either. In
Fig. 2.8a, we see that the shape of the road map with nice straight
lines gives us some information about the terrain of the region: it is
probably rather flat. In Fig. 2.8b, we show another road map. Here
the lines are not so simple, indicating that there are rises and falls in
the terrain of this region. These changes in terrain are changes in po-
tential. They play the same role in a road map as chemistry plays in
the energy–momentum relationship for electrons.
This energy–momentum map is called the band structure. It tells
you what are the allowed (or stable) states of energy and momentum
for electrons in the outermost band (or valence band) of the semicon-
ductor. It is analogous to a road map that tells you the streets and
highways (allowed or stable states for an electron) that your car can
have when it is freed from the garage. Just like the road map, the
band structure does not tell you where the electron is. Rather, the
band structure tells you what the possible states are, and about the
properties that an electron would have if it occupied a particular
state. For example, from a road map you can tell the difference be-
tween a residential street and a superhighway. In addition to the lo-

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