282
9 Optical Properties
(a)
5
- 1
20
3.380
0
ZnO
3.395
3.375
10
3.390
T
B
5
L
A
5
B
6
T
A
5
L
B
5
A
1,2
E||c
(b)
5
0
1 0
1 5
5
1
-
GaN
Fig. 9.27 a Exciton polariton dispersion (k ⊥ c) of ZnO with experimental data (T = 1.8 K). Solid (dotted) lines are
for polaritons with E c (E ⊥ c). The dashed lines refer to excitons. Adapted from [883]. b Exciton polariton dispersion
(T = 2 K) in GaN (on sapphire) for E ⊥ c. Adapted from [884]
Table 9.7 Index of nitrogen pairs NN n and energy separation of bound-exciton transitions from the free-exciton
line for n = 1 . . . 10 and the ‘A’ line
n
1
2
3
4
5
6
7
8
9
10
∞ (A)
E
(meV)
143
138
64
39
31
25
22
20
18
17
11
In GaP:N excitons are bound to isoelectronic N impurities (substituting P), resulting in the ‘A’ line
at 2.3171 eV (at T = 4.2 K).
9 The absorption due to A excitons is well resolved in the spectrum
of Fig. 9.28b. At sufficiently high nitrogen doping, there exist nitrogen pairs, i.e. a complex where a
nitrogen impurity has a second nitrogen impurity in the vicinity. The pairs are labeled NN n . It was
believed that the second nitrogen atom is in the nth shell around the first one. However, the proper
level asignment is probably different in the view of modern theory [544]. Also clusters with more
than two nitrogen atoms may exist. NN 1 is a prominent level and relates to a N–Ga–N complex
having 12 equivalent sites for the second N atom on the next neighbor anion site. The transitions due
to excitons bound to NN n , as shown in Fig. 9.28a, give a series of lines (see Table 9.7) that fulfill
lim n→∞ NN n = A. Although GaP has an indirect band structure, the absorption coefficient of Nrelated transitions is large, about 10
5 cm
−1 for a nitrogen doping level of 10
19 cm
−3 .
10 This is due to
the fact that the electron spatially localized at the nitrogen isoelectronic trap (Sect. 7.7.9) has a sizeable
k = 0-component of its wave-function (Fig. 7.40), leading to a large transition probability for -point
holes with an oscillator strength of 0.09 [885].
9 The A line is due to excitons with J = 1, resulting of coupling of the electron spin 1/2 with the hole angular momentum
of 3/2. The B-line is a dipole forbidden line due to ‘dark’ excitons with J = 2.
10 Also the recombination (Sect. 10.3.2) is efficient and allows green GaP:N and yellow GaAsP:N light emitting diodes.
9 Optical Properties
(a)
5
- 1
20
3.380
0
ZnO
3.395
3.375
10
3.390
T
B
5
L
A
5
B
6
T
A
5
L
B
5
A
1,2
E||c
(b)
5
0
1 0
1 5
5
1
-
GaN
Fig. 9.27 a Exciton polariton dispersion (k ⊥ c) of ZnO with experimental data (T = 1.8 K). Solid (dotted) lines are
for polaritons with E c (E ⊥ c). The dashed lines refer to excitons. Adapted from [883]. b Exciton polariton dispersion
(T = 2 K) in GaN (on sapphire) for E ⊥ c. Adapted from [884]
Table 9.7 Index of nitrogen pairs NN n and energy separation of bound-exciton transitions from the free-exciton
line for n = 1 . . . 10 and the ‘A’ line
n
1
2
3
4
5
6
7
8
9
10
∞ (A)
E
(meV)
143
138
64
39
31
25
22
20
18
17
11
In GaP:N excitons are bound to isoelectronic N impurities (substituting P), resulting in the ‘A’ line
at 2.3171 eV (at T = 4.2 K).
9 The absorption due to A excitons is well resolved in the spectrum
of Fig. 9.28b. At sufficiently high nitrogen doping, there exist nitrogen pairs, i.e. a complex where a
nitrogen impurity has a second nitrogen impurity in the vicinity. The pairs are labeled NN n . It was
believed that the second nitrogen atom is in the nth shell around the first one. However, the proper
level asignment is probably different in the view of modern theory [544]. Also clusters with more
than two nitrogen atoms may exist. NN 1 is a prominent level and relates to a N–Ga–N complex
having 12 equivalent sites for the second N atom on the next neighbor anion site. The transitions due
to excitons bound to NN n , as shown in Fig. 9.28a, give a series of lines (see Table 9.7) that fulfill
lim n→∞ NN n = A. Although GaP has an indirect band structure, the absorption coefficient of Nrelated transitions is large, about 10
5 cm
−1 for a nitrogen doping level of 10
19 cm
−3 .
10 This is due to
the fact that the electron spatially localized at the nitrogen isoelectronic trap (Sect. 7.7.9) has a sizeable
k = 0-component of its wave-function (Fig. 7.40), leading to a large transition probability for -point
holes with an oscillator strength of 0.09 [885].
9 The A line is due to excitons with J = 1, resulting of coupling of the electron spin 1/2 with the hole angular momentum
of 3/2. The B-line is a dipole forbidden line due to ‘dark’ excitons with J = 2.
10 Also the recombination (Sect. 10.3.2) is efficient and allows green GaP:N and yellow GaAsP:N light emitting diodes.