Set of supplementary notes.

88 CHAPTER 6. EXPERIMENTAL PROBES OF THE BAND STRUCTURE
excitonic physics, see later). In some semiconductors, the maximum valence band state and the
minimum in the conduction band occur at the same momentum - in such a direct gap system,
direct optical excitation is allowed at the minimum gap, and an important example is GaAs.
Si and Ge are example of indirect gap materials, because the conduction band minimum is
toward the edge of the zone boundary. The minimum energy transition is at large momentum,
and therefore cannot be accomplished by direct absorption of a photon. The lowest energy
transition is instead a phonon-mediated transition where the energy is provided by the photon
and the momentum provided by the phonon. This is much less efficient than direct optical
absorption.
Figure 6.2: The interband absorption spectrum of Si has a threshold at the indirect gap
E g ≈ 1.1 eV which involves a phonon and is very weak. The energies E 1 and E 2 correspond to
critical points where the conduction and valence bands are vertically parallel to one another;
absorption is direct (more efficient) and also enhanced by the enhanced joint density of electron
and hole states. [E.D.Palik, Handbook of the optical constants of solids, AP, 1985]
.
Luminescence is the inverse process of recombination of an electron-hole pair to emit light.
It comes about if electrons and holes are injected into a semiconductor (perhaps electrically,
as in a light-emitting diode). Obviously, this process will not be efficient in an indirect gap
semiconductor but is more so in a direct gap material. This simple fact explains why GaAs and
other III-V compounds are the basis of most practical opto-electronics in use today, whereas
Si is the workhorse of electrical devices.