10.3 Exciton Recombination
311
(a)
E (meV)
D
b
0
5 0
150
200
Si
5
0
10
15
20
100
In
Ga
Bi
As
P
Sb
B
Al
(b)
Fig. 10.7 Energy Q required to remove an exciton from a neutral impurity (10.24) as a function of the ionization energy
E b
D (open circles) or E b
A (solid circles) of the involved impurity in (a) silicon (experimental data from [965]) and (b)
ZnO (experimental data from [966])
they can be bound to isoelectronic impurities, the most prominent example being N in GaP [954] (cmp.
Sect. 9.7.9) or isoelectronic clusters [955]. The recombination of excitons localized in quantum wells
(Sect. 12.4) and quantum dots (Sect. 14.4.4) is discussed later.
The transition energy of an exciton bound to a neutral impurity is
= E g − E X
b
− Q ,
(10.24)
where Q is the binding (or localization) energy of the exciton to the impurity. The binding energy of
an exciton to an ionized impurity is denoted with Q
∗ . A transition involving an exciton bound to a
neutral donor is denoted (D
0 ,X); correspondingly (D
+ ,X), also denoted as (h,D
0 ), and (A
0 ,X). Values
for donor-bound excitons in various semiconductors are listed in Table 10.2. The (D
0 ,X) complex is
stable for 0 < σ = m
∗
e /m
∗
h < 0.43 according to [956]. The (D
+ ,X) peak can occur on the low- or
high-energy side of the (D
0 ,X) recombination. Whether Q
∗
< Q or Q
∗
> Q depends on σ being
smaller or larger than 0.2, respectively [956], and is fulfilled for many semiconductors, e.g. GaAs,
GaN, CdS, and ZnSe.
Recombination in silicon due to excitons involving phosphorus donors is depicted in Fig. 10.6. The
(D
0 ,X) transition in Si:P is labeled ‘P
0 ’ (Q = 6 meV). Other P-related transitions are discussed in
[950]. In Si, the binding energy to the impurity is about one tenth of the binding energy of the impurity
(Haynes’s rule [951, 965]), i.e. Q/E
b
D and Q/E
b
A ≈ 0.1 (Fig. 10.7a). In GaP the approximate relations
Q = 0.26E
b
D − 7 meV and Q = 0.056E
b
A + 3 meV have been found [954]. For donors in ZnO, the
relation Q = 0.365E
b
D − 3.8 meV holds (Fig. 10.7b) [966]. In Fig. 10.8, the recombination spectrum
of GaAs:C is shown that exhibits recombination from excitons bound to the acceptor (carbon) and
shallow donors. The exciton is more strongly bound to an ionized donor (D
+ ) than to a neutral donor.
Varying the concentration of a specific impurity and observing the corresponding change in the
intensity of the (D
0 ,X) transition allows to identify the chemical species to which the exciton is
bound. This can be achieved via the comparison of different samples or more elegantly by introducing
radioactive isotopes. This is shown in Fig. 10.9 for In in ZnO; the (
111 In
0 ,X) transition disappears with
the characteristic time constant close to that (97 h) of the nuclear decay of
111 In into stable
111 Cd.
However, in such experiments it should be considered that the decay product and accompanying highenergy radiation can create new electronic and structural defects, respectively.
The peak labeled (D
0 ,X) 2s in Fig. 10.8 is called a two-electron satellite (TES) [968]. High-resolution
spectra of the TES in GaAs [581, 969] are shown in Fig. 10.10a. The TES recombination is a (D
0 ,X)
311
(a)
E (meV)
D
b
0
5 0
150
200
Si
5
0
10
15
20
100
In
Ga
Bi
As
P
Sb
B
Al
(b)
Fig. 10.7 Energy Q required to remove an exciton from a neutral impurity (10.24) as a function of the ionization energy
E b
D (open circles) or E b
A (solid circles) of the involved impurity in (a) silicon (experimental data from [965]) and (b)
ZnO (experimental data from [966])
they can be bound to isoelectronic impurities, the most prominent example being N in GaP [954] (cmp.
Sect. 9.7.9) or isoelectronic clusters [955]. The recombination of excitons localized in quantum wells
(Sect. 12.4) and quantum dots (Sect. 14.4.4) is discussed later.
The transition energy of an exciton bound to a neutral impurity is
= E g − E X
b
− Q ,
(10.24)
where Q is the binding (or localization) energy of the exciton to the impurity. The binding energy of
an exciton to an ionized impurity is denoted with Q
∗ . A transition involving an exciton bound to a
neutral donor is denoted (D
0 ,X); correspondingly (D
+ ,X), also denoted as (h,D
0 ), and (A
0 ,X). Values
for donor-bound excitons in various semiconductors are listed in Table 10.2. The (D
0 ,X) complex is
stable for 0 < σ = m
∗
e /m
∗
h < 0.43 according to [956]. The (D
+ ,X) peak can occur on the low- or
high-energy side of the (D
0 ,X) recombination. Whether Q
∗
< Q or Q
∗
> Q depends on σ being
smaller or larger than 0.2, respectively [956], and is fulfilled for many semiconductors, e.g. GaAs,
GaN, CdS, and ZnSe.
Recombination in silicon due to excitons involving phosphorus donors is depicted in Fig. 10.6. The
(D
0 ,X) transition in Si:P is labeled ‘P
0 ’ (Q = 6 meV). Other P-related transitions are discussed in
[950]. In Si, the binding energy to the impurity is about one tenth of the binding energy of the impurity
(Haynes’s rule [951, 965]), i.e. Q/E
b
D and Q/E
b
A ≈ 0.1 (Fig. 10.7a). In GaP the approximate relations
Q = 0.26E
b
D − 7 meV and Q = 0.056E
b
A + 3 meV have been found [954]. For donors in ZnO, the
relation Q = 0.365E
b
D − 3.8 meV holds (Fig. 10.7b) [966]. In Fig. 10.8, the recombination spectrum
of GaAs:C is shown that exhibits recombination from excitons bound to the acceptor (carbon) and
shallow donors. The exciton is more strongly bound to an ionized donor (D
+ ) than to a neutral donor.
Varying the concentration of a specific impurity and observing the corresponding change in the
intensity of the (D
0 ,X) transition allows to identify the chemical species to which the exciton is
bound. This can be achieved via the comparison of different samples or more elegantly by introducing
radioactive isotopes. This is shown in Fig. 10.9 for In in ZnO; the (
111 In
0 ,X) transition disappears with
the characteristic time constant close to that (97 h) of the nuclear decay of
111 In into stable
111 Cd.
However, in such experiments it should be considered that the decay product and accompanying highenergy radiation can create new electronic and structural defects, respectively.
The peak labeled (D
0 ,X) 2s in Fig. 10.8 is called a two-electron satellite (TES) [968]. High-resolution
spectra of the TES in GaAs [581, 969] are shown in Fig. 10.10a. The TES recombination is a (D
0 ,X)