Page 32 - Photonics Essentials an introduction with experiments

Electrons and Photons

26 Introductory Concepts

Figure 2.9. The relationship between energy and momentum displays bands of energy
that an electron can have. When the electron is in a crystal, the periodic atomic potential
causes gaps to open up in this structure. The gap means that an electron is not allowed to
have these energies.

cation of these different roads, you know that the velocity of an auto-
mobile is limited to a speed of 50 km/h on a residential street, but 100
km/h on the superhighway.
The size of an electron is not well-defined, and so it is not very
meaningful to try to specify its position. A totally free electron be-
haves like a wave. That means it can exist over all space. Since the lo-
cation of such a wave is difficult to specify, it is equally difficult to
specify its velocity.
On the other hand, energy and momentum for an electron can be
specified. Furthermore, the conditions that define the interaction of
electrons in solids with photons, phonons, or other electrons are con-
servation of energy and conservation of momentum. So a “road map”
that summarizes the possible states of electron energy and momen-
tum is particularly useful.
All band structures can be divided into two groups. There are two
bands that form the band gap. If the minimum energy of the upper
band occurs at the same value of momentum as the maximum energy
of the lower band, the corresponding material has a direct band gap.
Such a band structure is shown in Fig. 2.9. For all other situations,
the corresponding material has an indirect band gap.
Whether a material has a direct band gap or an indirect band gap de-
pends entirely on the crystalline potential that splits apart the bands.

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.