274
9 Optical Properties
2.5
3.0
5
15
0
10
k
1/2
3.0
3.1
2.75
3.25
3.05
3.15
5
15
0
10
10
-4
k
2
Fig. 9.16 Absorption of BaTiO 3 at room temperature. Experimental data (circles) from [852] with fits (dashed lines)
∝ E 2 and ∝ E 1/2 , respectively
(a)
10
10
10
10
10
4
3
2
1
0
1.4
1.3
1.5
1.6
1.7
-1
GaAs
(b)
15
10
5
0
500
1000
T
GaAs
Fig. 9.17 a Experimental absorption spectrum (circles) of GaAs at room temperature on a semilogarithmic plot. The
exponential tail below the band gap is called the Urbach tail (the dash-dotted line corresponds to E 0 = 10.3 meV in
(9.48)). The dashed line is the theoretical dependence from (9.45). Adapted from [856]. b Temperature dependence
of Urbach parameter E 0 for two GaAs samples. Experimental data for undoped (solid circles) and Si-doped (n =
2 × 10 18 cm −3 , empty circles) GaAs and theoretical fits (solid lines) with one-phonon model. Adapted from [854]
9.7.5 Amorphous Semiconductors
The sharp features in the dielectric function due to critical points in the band structure of crystalline
semiconductors are washed out in amorphous material. As an example the spectra of the imaginary
part of the dielectric function for crystalline (trigonal) and amorphous selenium are shown in Fig. 9.18.
9.7.6 Excitons
An electron in the conduction band and a hole in the valence band form a hydrogen-like state due to the
mutual Coulomb interaction. Such a state is called an exciton. The center-of-mass motion is separated
and has a dispersion E =
2
2M
K
2 , where M = m e + m h is the total mass and is the center-of-mass
9 Optical Properties
2.5
3.0
5
15
0
10
k
1/2
3.0
3.1
2.75
3.25
3.05
3.15
5
15
0
10
10
-4
k
2
Fig. 9.16 Absorption of BaTiO 3 at room temperature. Experimental data (circles) from [852] with fits (dashed lines)
∝ E 2 and ∝ E 1/2 , respectively
(a)
10
10
10
10
10
4
3
2
1
0
1.4
1.3
1.5
1.6
1.7
-1
GaAs
(b)
15
10
5
0
500
1000
T
GaAs
Fig. 9.17 a Experimental absorption spectrum (circles) of GaAs at room temperature on a semilogarithmic plot. The
exponential tail below the band gap is called the Urbach tail (the dash-dotted line corresponds to E 0 = 10.3 meV in
(9.48)). The dashed line is the theoretical dependence from (9.45). Adapted from [856]. b Temperature dependence
of Urbach parameter E 0 for two GaAs samples. Experimental data for undoped (solid circles) and Si-doped (n =
2 × 10 18 cm −3 , empty circles) GaAs and theoretical fits (solid lines) with one-phonon model. Adapted from [854]
9.7.5 Amorphous Semiconductors
The sharp features in the dielectric function due to critical points in the band structure of crystalline
semiconductors are washed out in amorphous material. As an example the spectra of the imaginary
part of the dielectric function for crystalline (trigonal) and amorphous selenium are shown in Fig. 9.18.
9.7.6 Excitons
An electron in the conduction band and a hole in the valence band form a hydrogen-like state due to the
mutual Coulomb interaction. Such a state is called an exciton. The center-of-mass motion is separated
and has a dispersion E =
2
2M
K
2 , where M = m e + m h is the total mass and is the center-of-mass