Set of supplementary notes.

Chapter 6
Experimental probes of the band
structure
6.1 Optical transitions
The band structure provides the excitation spectrum of the solid. The ground state of the
system involves filling states up to the fermi energy, but we can also excite the system in
different ways. One of the simplest is the absorption of a photon, which can be visualised as an
excitation of an electron from an occupied state into an empty state, leaving behind a ”hole”
in the valence band. See Fig. 6.1.
Figure 6.1: Direct absorption by light is a nearly vertical transition since the wavevector of a
photon with energy of order a semiconductor gap is much smaller than the typical momentum of
an electron. (a) In a direct gap semiconductor, such as GaAs, the lowest energy available states
for hole and electron are at the same momentum, and the optical threshold is at the vertical
energy gap. (b) IN an indirect gap material (e.g. Si or Ge), the minimum energy excitation
of electron and hole pair connects state of different momenta - and a phonon of momentum q
must be excited concurrently with the photon.
The minimum gap in a semiconductor is the energy difference between the highest occupied
state and the lowest unoccupied state, and this is the threshold for optical absorption (neglecting
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