312
10 Recombination
Table 10.2 Localization energy Q (Q ∗ ) of excitons on selected impurities (ionized impurities, D + or A − , respectively)
in various semiconductors. σ is the ratio of effective electron and hole (polaron) masses. EMD: effective mass donor
host
donor
Q (meV)
Q ∗ (meV)
Q ∗ /Q
σ
Ref.
GaAs
EMD
Zn
0.88
8.1
1.8
31.1
2.0
3.8
0.28
[957]
GaN
EMD
Mg
6.8
20
11.2
1.6
0.36
[959]
AlN
Si
Mg
16
40
[960]
CdS
EMD
6.6
3.8
0.6
0.17
[961]
Al
4.9
5.4
1.1
ZnSe
Ga
5.1
6.6
1.3
0.27
[962, 963]
In
5.4
7.5
1.4
Al
15.5
3.4
0.21
ZnO
Ga
16.1
4.1
0.25
0.3
[964]
In
19.2
8.5
0.44
1.50
1.51
1.52
1.49
GaAs:C As
(e,A )
0
(D ,A )
0
0
(D ,X)
0
2s
(h,D )
0
(A ,X)
0
(h,D )
2s
0
(D ,X)
0
20
Fig. 10.8 Photoluminescence spectrum (T = 2 K, D = 10 mW cm −2 ) of GaAs:C As (N A = 10 14 cm −3 ) with donorand acceptor-related bound-exciton recombination around 1.512 eV, (e,A 0 ), (h,D 0 ) and (D 0 ,A 0 ) pair and free-exciton
recombination. Adapted from [957]
recombination that leaves the donor in an excited state as schematically shown in Fig. 10.10b. Therefore
a hydrogen-like series with n = 2, 3, . . . is observed with energies
E
n
TES = E (D 0 ,X) − E
b
D
1 −
1
n 2
.
(10.25)
The effect of isotope disorder on the sharpness and splitting of impurity states has been investigated
in [970, 971]. The recombination of excitons bound to Al, Ga and In in natural silicon (92.23%
28 Si,
4.67%
29 Si, 3.10%
30 Si) is split into three lines due to the valley-orbit splitting [972] of electron states
at the band minimum (Fig. 10.11). Each of these (A
0 ,X) lines is split by 0.01 cm
−1 for Si:Al due to a
symmetry reduction of the 4-fold degenerate A
0 ground state, as observed in the presence of applied
axial strain or an electric field. The comparison to spectra from enriched
28 Si shows that the observed
splitting without external perturbation is due to isotope disorder that causes random strains and splits
the A
0 ground state into two doublets [971] (Fig. 10.11). Similarly, the (unsplit) phosphorus-induced
10 Recombination
Table 10.2 Localization energy Q (Q ∗ ) of excitons on selected impurities (ionized impurities, D + or A − , respectively)
in various semiconductors. σ is the ratio of effective electron and hole (polaron) masses. EMD: effective mass donor
host
donor
Q (meV)
Q ∗ (meV)
Q ∗ /Q
σ
Ref.
GaAs
EMD
Zn
0.88
8.1
1.8
31.1
2.0
3.8
0.28
[957]
GaN
EMD
Mg
6.8
20
11.2
1.6
0.36
[959]
AlN
Si
Mg
16
40
[960]
CdS
EMD
6.6
3.8
0.6
0.17
[961]
Al
4.9
5.4
1.1
ZnSe
Ga
5.1
6.6
1.3
0.27
[962, 963]
In
5.4
7.5
1.4
Al
15.5
3.4
0.21
ZnO
Ga
16.1
4.1
0.25
0.3
[964]
In
19.2
8.5
0.44
1.50
1.51
1.52
1.49
GaAs:C As
(e,A )
0
(D ,A )
0
0
(D ,X)
0
2s
(h,D )
0
(A ,X)
0
(h,D )
2s
0
(D ,X)
0
20
Fig. 10.8 Photoluminescence spectrum (T = 2 K, D = 10 mW cm −2 ) of GaAs:C As (N A = 10 14 cm −3 ) with donorand acceptor-related bound-exciton recombination around 1.512 eV, (e,A 0 ), (h,D 0 ) and (D 0 ,A 0 ) pair and free-exciton
recombination. Adapted from [957]
recombination that leaves the donor in an excited state as schematically shown in Fig. 10.10b. Therefore
a hydrogen-like series with n = 2, 3, . . . is observed with energies
E
n
TES = E (D 0 ,X) − E
b
D
1 −
1
n 2
.
(10.25)
The effect of isotope disorder on the sharpness and splitting of impurity states has been investigated
in [970, 971]. The recombination of excitons bound to Al, Ga and In in natural silicon (92.23%
28 Si,
4.67%
29 Si, 3.10%
30 Si) is split into three lines due to the valley-orbit splitting [972] of electron states
at the band minimum (Fig. 10.11). Each of these (A
0 ,X) lines is split by 0.01 cm
−1 for Si:Al due to a
symmetry reduction of the 4-fold degenerate A
0 ground state, as observed in the presence of applied
axial strain or an electric field. The comparison to spectra from enriched
28 Si shows that the observed
splitting without external perturbation is due to isotope disorder that causes random strains and splits
the A
0 ground state into two doublets [971] (Fig. 10.11). Similarly, the (unsplit) phosphorus-induced