10.8 Auger Recombination
323
0
0.5
1.0
1.5
2.0
2.5
3.0
1.57
1.56
1.55
1.54
1.53
1.52
1.51
1.50
1.49
1.48
1.47
1.46
1.45
1.44
1.43
1.42
1.41
1.40
GaP
C O
Cd O
Zn O
15.5
meV
Fig. 10.24 Transition energies in GaP (T = 1.6 K) of the donor–acceptor recombination involving the deep oxygen
donor and C, Zn, and Cd acceptors, respectively. The lines follow (10.37) for E GaP
g
= 2.339 eV, r = 11.1 and (E b
D ) O =
893 meV, (E b
A ) C = 48.5 meV, (E b
A ) Zn = 64 meV, and (E b
A ) Cd = 96.5 meV. Predicted missing modes for GaP:C,O are
labeled with ‘G’. Adapted from [1003]
(a)
Fe
3+
E V
1.34
Fe
2+
InP:Fe
0.78
1.14
5
T 2
0
5 E
E C
0.25
(b)
0.340
0.345
0.350
InP:Fe
5 T 2
5 E
Fig. 10.25 a Schematic band diagram of InP with levels of Fe impurities in the 3+ and 2+ charge states at low
temperature. All energies are given in eV. The arrow denotes the optical transition from an excited Fe 2+ state to the
Fe 2+ ground state. (b) Photoluminescence spectrum (at T = 4.2 K) of InP:Fe sample with [Fe]=5 × 10 16 cm −3 . Part (b)
adapted from [1004]
not emitted with a photon but, instead, transferred to a third particle. This can be an electron (eeh,
Fig. 10.26a) or a hole (hhe, Fig. 10.26b). The energy is eventually transferred nonradiatively from the
hot third carrier via phonon emission to the lattice. The probability for such process is ∝ n
2 p if two
electrons are involved and ∝ np
2 if two holes are involved. The Auger process is a three-particle
process and becomes likely for high carrier density, either through doping, in the presence of many
excess carriers, or in semiconductors with small band gap. Auger recombination is the inverse of
the impact ionization (cf. Sect. 8.4.4). Phonon-assisted Auger recombination relaxes the momentum
conservation rule for the involved charge carriers at the cost of an additional particle being involved in
the scattering process. It has been pointed out that this process is dominating in bulk material [1010,
1011] and quantum wells [1012].
In thermodynamic equilibrium the rates for Auger recombination and thermal Auger generation
must be equal, thus
323
0
0.5
1.0
1.5
2.0
2.5
3.0
1.57
1.56
1.55
1.54
1.53
1.52
1.51
1.50
1.49
1.48
1.47
1.46
1.45
1.44
1.43
1.42
1.41
1.40
GaP
C O
Cd O
Zn O
15.5
meV
Fig. 10.24 Transition energies in GaP (T = 1.6 K) of the donor–acceptor recombination involving the deep oxygen
donor and C, Zn, and Cd acceptors, respectively. The lines follow (10.37) for E GaP
g
= 2.339 eV, r = 11.1 and (E b
D ) O =
893 meV, (E b
A ) C = 48.5 meV, (E b
A ) Zn = 64 meV, and (E b
A ) Cd = 96.5 meV. Predicted missing modes for GaP:C,O are
labeled with ‘G’. Adapted from [1003]
(a)
Fe
3+
E V
1.34
Fe
2+
InP:Fe
0.78
1.14
5
T 2
0
5 E
E C
0.25
(b)
0.340
0.345
0.350
InP:Fe
5 T 2
5 E
Fig. 10.25 a Schematic band diagram of InP with levels of Fe impurities in the 3+ and 2+ charge states at low
temperature. All energies are given in eV. The arrow denotes the optical transition from an excited Fe 2+ state to the
Fe 2+ ground state. (b) Photoluminescence spectrum (at T = 4.2 K) of InP:Fe sample with [Fe]=5 × 10 16 cm −3 . Part (b)
adapted from [1004]
not emitted with a photon but, instead, transferred to a third particle. This can be an electron (eeh,
Fig. 10.26a) or a hole (hhe, Fig. 10.26b). The energy is eventually transferred nonradiatively from the
hot third carrier via phonon emission to the lattice. The probability for such process is ∝ n
2 p if two
electrons are involved and ∝ np
2 if two holes are involved. The Auger process is a three-particle
process and becomes likely for high carrier density, either through doping, in the presence of many
excess carriers, or in semiconductors with small band gap. Auger recombination is the inverse of
the impact ionization (cf. Sect. 8.4.4). Phonon-assisted Auger recombination relaxes the momentum
conservation rule for the involved charge carriers at the cost of an additional particle being involved in
the scattering process. It has been pointed out that this process is dominating in bulk material [1010,
1011] and quantum wells [1012].
In thermodynamic equilibrium the rates for Auger recombination and thermal Auger generation
must be equal, thus