9.7 Band–Band Transitions
277
(a)
Optical density
Energy (eV)
(b)
2
5
10
20
n
E -E (meV)
n
g
10
1
10
-4
10
-5
10
-6
10
-7
10
-8
Oscillator strength (arb. units)
Fig. 9.21 (One photon) Absorption spectrum of Cu 2 O (thickness 34 µm) at T = 1.2 K with transitions labelled n =
2 . . . 25. Adapted from [863]
The scattering (unbound) states of the exciton [865] for E > E g contribute to absorption above the
band gap. The factor by which the absorption spectrum is changed is called the Sommerfeld factor.
For bulk material it is
S(η) = η
exp(η)
sinh(η)
,
(9.53)
with η = π[E
b
X /(E − E g )]
1/2 . The change of the absorption spectrum due to the Coulomb correlation
is shown in Fig. 9.22. There is a continuous absorption between the bound and unbound states. At the
band gap there is a finite absorption (S(E → E g ) → ∞). The detail to which exciton peaks can be
resolved depends on the spectral broadening.
In Fig. 9.23 the energy separations of the A-, B-, and C-excitons in GaN are shown [540]. Thus, the
ordering of the valence bands depends on the strain state of the semiconductor.
9.7.7 Phonon Broadening
The scattering with phonons and the related dephasing leads to homogeneous broadening hom of
absorption (and recombination) lines. Acoustic and optical phonons contribute to the broadening
according to the dependence [867]
hom (T ) = 0 + γ AC T + γ LO
1
exp(ω LO /kT ) − 1
,
(9.54)
where LO is the optical phonon energy and the last factor is the Bose function (E.24). 0 is a
temperature-independent contribution, 0 = = 0). The increasing broadening with increasing
temperature is obvious, e.g., in absorption spectra (Fig. 9.24a). In Fig. 9.24b experimental data for
GaAs, ZnSe and GaN are assembled. The data have been fitted with (9.54); the resulting phonon
277
(a)
Optical density
Energy (eV)
(b)
2
5
10
20
n
E -E (meV)
n
g
10
1
10
-4
10
-5
10
-6
10
-7
10
-8
Oscillator strength (arb. units)
Fig. 9.21 (One photon) Absorption spectrum of Cu 2 O (thickness 34 µm) at T = 1.2 K with transitions labelled n =
2 . . . 25. Adapted from [863]
The scattering (unbound) states of the exciton [865] for E > E g contribute to absorption above the
band gap. The factor by which the absorption spectrum is changed is called the Sommerfeld factor.
For bulk material it is
S(η) = η
exp(η)
sinh(η)
,
(9.53)
with η = π[E
b
X /(E − E g )]
1/2 . The change of the absorption spectrum due to the Coulomb correlation
is shown in Fig. 9.22. There is a continuous absorption between the bound and unbound states. At the
band gap there is a finite absorption (S(E → E g ) → ∞). The detail to which exciton peaks can be
resolved depends on the spectral broadening.
In Fig. 9.23 the energy separations of the A-, B-, and C-excitons in GaN are shown [540]. Thus, the
ordering of the valence bands depends on the strain state of the semiconductor.
9.7.7 Phonon Broadening
The scattering with phonons and the related dephasing leads to homogeneous broadening hom of
absorption (and recombination) lines. Acoustic and optical phonons contribute to the broadening
according to the dependence [867]
hom (T ) = 0 + γ AC T + γ LO
1
exp(ω LO /kT ) − 1
,
(9.54)
where LO is the optical phonon energy and the last factor is the Bose function (E.24). 0 is a
temperature-independent contribution, 0 = = 0). The increasing broadening with increasing
temperature is obvious, e.g., in absorption spectra (Fig. 9.24a). In Fig. 9.24b experimental data for
GaAs, ZnSe and GaN are assembled. The data have been fitted with (9.54); the resulting phonon