Page 34 - Photonics Essentials an introduction with experiments

Electrons and Photons

28 Introductory Concepts

bonding state, the electron is free to carry electrical current. So this up-
per band, the antibonding state, is also called the conduction band. The
bonding state, or lower band, is also called the valence band.
An electron that occupies a state at the minimum energy of the con-
duction band can make a transition to the top of the valence band,
presuming this state is not already occupied. These two states have a
negligible difference in momentum. Energy is conserved by the emis-
sion of a photon. Since the photon provides very little momentum,
both energy and momentum can be conserved for this transition,
which is called a direct transition.
By comparison, an electron occupying a state at the bottom of the
conduction band in an indirect gap material is in a different situation.
The difference in momentum between these two states is no longer
negligible. The electron can make a transition to a state at the top of
the valence band by the emission of a photon to conserve energy, and
the simultaneous emission of a phonon to conserve momentum. This
is called an indirect transition because two steps are involved.
In the case of Fig. 2.10, there is no difference in momentum be-
tween a state at the top of the valence band and a state at the bottom
of the conduction band. In Fig. 2.11, the situation is different.
In this case, the lowest energy state in the conduction band does not
have the same momentum as the highest energy state in the valence
band. At equilibrium and at T = 0 K, all the valence band states are
occupied and none of the conduction band states are occupied. Now let
us break a bond in Ge. That means that one electron has enough extra
energy to go from a bonding state to an antibonding state. The least
amount of extra energy is the band gap energy. In germanium, this is
0.7 eV. (We use eV to measure energy so you do not have to carry
around mind-boggling powers of 10 in your calculations.) For silicon,
the indirect energy gap is 1.1 eV.
You can see from the energy band structure diagram for germani-
um that the electron needs to get some momentum in addition to en-
ergy to make a transition at this least energy near the band gap. So
the transition to the antibonding state is not direct. There are two
steps required: first, obtain the energy, and second, obtain at the
same time the required momentum from a physical vibration of the
crystal lattice. This is called an indirect transition and germanium is
called an indirect band gap semiconductor.
By referring to the band structure of GaAs, you can see that this
transition can be made in one step with little or no change in momen-
tum required. This happens because the maximum valence band en-
ergy occurs at the same momentum as the minimum conduction band
energy. Since the photon can convey energy with no momentum, the
electron can absorb a single photon and make the transition across

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.