298
9 Optical Properties
(a)
9
6
3
0
-3
X
Z
SnO 2
(b)
SnO 2
(10 cm )
-18
2
W
Fig. 9.48 a Band structure of SnO 2 and indirect intra-band absorption process; the transition from the topmost valence
band (dashed arrow) is forbidden. b Calculated free-carrier absorption(σ = α/n) for SnO 2 . The solid and dashed lines
are results including phonon-assisted transitions for two light polarizations. The dotted lines are fits of the Drude model
to the infrared regime. Adapted from [928]
Fig. 9.49 Calculated room
temperature absorption
coefficient Ga 2 O 3 as a
function of energy (for
light polarized along the z
direction) for
undoped/intrinsic material
and three different electron
concentrations as labelled.
Adapted from [930]
of inter-band and intra-band transitions leading to absorption within the band gap transparency regime
has been calculated for Ga 2 O 3 as shown in Fig. 9.49 for various doping levels [930].
9.10 Lattice Absorption
Due to the lack of a dipole moment of the optical phonons, no first order interaction of optical phonons
and (infrared) light exists in the diamond structure for Si and Ge due to crystal structure symmetry
[931]. However, higher order processes contribute to lattice absorption in these materials [932, 933].
E.g., two-photon bands are due to a dipole moment that is of second order in the nuclear displacement.
Strong absorption effects are present for compound semiconductors. A review can be found in [934].
9.10.1 Dielectric Constant
The (relative) dielectric constant (with damping parameter ) in the vicinity of the optical phonon
energies is given by (cf. (9.27))
9 Optical Properties
(a)
9
6
3
0
-3
X
Z
SnO 2
(b)
SnO 2
(10 cm )
-18
2
W
Fig. 9.48 a Band structure of SnO 2 and indirect intra-band absorption process; the transition from the topmost valence
band (dashed arrow) is forbidden. b Calculated free-carrier absorption(σ = α/n) for SnO 2 . The solid and dashed lines
are results including phonon-assisted transitions for two light polarizations. The dotted lines are fits of the Drude model
to the infrared regime. Adapted from [928]
Fig. 9.49 Calculated room
temperature absorption
coefficient Ga 2 O 3 as a
function of energy (for
light polarized along the z
direction) for
undoped/intrinsic material
and three different electron
concentrations as labelled.
Adapted from [930]
of inter-band and intra-band transitions leading to absorption within the band gap transparency regime
has been calculated for Ga 2 O 3 as shown in Fig. 9.49 for various doping levels [930].
9.10 Lattice Absorption
Due to the lack of a dipole moment of the optical phonons, no first order interaction of optical phonons
and (infrared) light exists in the diamond structure for Si and Ge due to crystal structure symmetry
[931]. However, higher order processes contribute to lattice absorption in these materials [932, 933].
E.g., two-photon bands are due to a dipole moment that is of second order in the nuclear displacement.
Strong absorption effects are present for compound semiconductors. A review can be found in [934].
9.10.1 Dielectric Constant
The (relative) dielectric constant (with damping parameter ) in the vicinity of the optical phonon
energies is given by (cf. (9.27))