Page 272 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Electron-Photon

(D)

(I)

(A)

Figure 7.9. Direct (D) and indi-
rect (I) interband transitions.
Intra-band transitions (A).

Interband transitions show two basic different characters depending on
whether we look at direct or indirect band gap semiconductors. The com-
mon feature is that an electron changes from the valence band edge to the
conduction band edge or vice versa. For direct semiconductors these
band edges lie at the same wavevector. This is indicated with the vertical
line at (D) in Figure 7.9. For indirect semiconductors the band edges lie
at different wavevectors. The band gap energy in semiconductors is of the
order of 1 eV. Thus the photon energy must have the same value and
therefore we obtain —ω = 1eV . With the frequency wavevector relation
for photons ω = ck we immediately may calculate the transferred
⁄
momentum as the one of the absorbed photon to give k = 1eV —c . This
6
⋅
corresponds to a light field wavevector of about 310 m – 1 , which is
roughly 3-4 orders of magnitude smaller than the first brillouin zone
edge. Since we have to respect momentum and energy conservation and
the transferred momentum is rather small, the processes are vertical in
the band structure. Transitions at the band edge in indirect semiconduc-
tors therefore are not possible without the help of a third party system
adding the momentum missing in the balance. It is the phonon system to
allow for these processes indicated as (I) in Figure 7.9. In total there are

Semiconductors for Micro and Nanosystem Technology 269