William Angerer - Department of Physics and Astronomy - University ...

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5.2.1 Band Gap Physics
GaN is a direct band gap semiconductor with a band gap of 3.4 e V. Because a
medium's response to an incident light field is enhanced when the photon has an
energy nearly equal to an energy state of the system, the properties of the conduction
band minimum and valence band maximum strongly influence the optical characteristics
of GaN in the near band gap region. Therefore. in this section we focus
mainly on the characteristics of the valence band maximum and the conduction band
minimum. This section includes some discussion of group theory, which will be more
thoroughly explained in section 5.4. Fig. 5.2 displays the calculated band structure
of GaN. The band gap sits at the r point of the Brillouin zone (see Fig. 5.3).
The
valence band maximum is built (principally) of the N 2p states. In the absence of
spin orbit splitting, the valence band maximum consists of r 6 and r l bands that are
split by the hexagonal crystal field by ~cr
= 22 meV [78]. \Vhen spin is included.
the r 6 band splits into r 9 and r 7 bands, separated by the spin-orbit energy of ~so =
11 meV [78]. Inclusion of spin also transforms the r l band to r 7 . Because spin orbit
splitting is so small, matrix elements may be calculated from the representation of
the point group without spin.
The conduction band minimum is built (principally) of the Ga and ~ s-states.
Without spin, the state is labeled as r l , and with the inclusion of spin, the band
transforms as r 7. The valence and conduction bands are separated by 3.4 eV at room
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