322
10 Recombination
Fig. 10.23 Photoluminescence
spectrum (at T = 55 K)
from bulk ZnO excited
homogeneously via
two-photon excitation by a
Q-switched ruby laser
(pulse width 40 ns).
Adapted from [1002]
the scheme D
0 A
0
→ D
+ A
− eh → D
+ A
−
+ γ, where γ is a photon with the energy ω. The energy
of the emitted photon is given by
ω = E g − E
b
D − E
b
A +
1
4ππ 0
e
2
r R
,
(10.37)
where R is the distance between the donor and the acceptor for a specific pair. Since R is discrete, the
DAP recombination spectrum consists of several discrete lines. If the donor and acceptor occupy the
same sublattice, e.g.. O and C both substituting P sites in GaP, the spatial distance of the donor and
acceptor is R(n) = a 0
√
n/2, where a 0 is the lattice constant and n is an integer. However, for certain
‘magic’ numbers n = 14, 30, 46, . . . no lattice points exist and therefore the corresponding lines are
missing (labeled ‘G’ in Fig. 10.24). No such gaps exist in DA spectra where donors and acceptors
occupy different sublattices, e.g. GaP:O,Zn (see also Fig. 10.24). In this case, the spatial separation is
given by R(n) = a 0
√
n/2 − 5/16. If significant broadening is present, the lines are washed out and a
donor–acceptor pair band forms.
10.7 Inner-Impurity Recombination
The transitions of electrons between different states of an impurity level can be nonradiative or radiative.
As an example, the radiative transition of electrons in the Fe
2+ state in InP
5 T 2 →
5 E (Fig. 10.25) and
its fine structure were observed first in [1005] at around 0.35 eV.
Certain defects, also termed ‘color centers’, have been investigated towards their ability to act as
efficient single photon source. If a single defect is optically excited, it can emit a photon. However, it
cannot be excited further. Also, it cannot emit another photon before it has been excited again. This can
be measured through the correlation function for the time difference of emitted photons going to zero
for zero time difference. A popular example of such center is the NV center in diamond, the complex of
a vacancy and a nitrogen impurity [1006, 1007]. The emission rate saturates at about 2 × 10
5 photons/s
(pick up with microscope objective). The sensitivity of the spectrum to magnetic fields makes the NV
center a nanoscopic magnetic field sensor [1008]. Also the spins on the center are fairly isolated and
can be manipulated coherently.
10.8 Auger Recombination
In competition with the radiative, bimolecular recombination is the Auger recombination (Fig. 10.26).
In the Auger process, the energy that is released during the recombination of an electron and hole is
10 Recombination
Fig. 10.23 Photoluminescence
spectrum (at T = 55 K)
from bulk ZnO excited
homogeneously via
two-photon excitation by a
Q-switched ruby laser
(pulse width 40 ns).
Adapted from [1002]
the scheme D
0 A
0
→ D
+ A
− eh → D
+ A
−
+ γ, where γ is a photon with the energy ω. The energy
of the emitted photon is given by
ω = E g − E
b
D − E
b
A +
1
4ππ 0
e
2
r R
,
(10.37)
where R is the distance between the donor and the acceptor for a specific pair. Since R is discrete, the
DAP recombination spectrum consists of several discrete lines. If the donor and acceptor occupy the
same sublattice, e.g.. O and C both substituting P sites in GaP, the spatial distance of the donor and
acceptor is R(n) = a 0
√
n/2, where a 0 is the lattice constant and n is an integer. However, for certain
‘magic’ numbers n = 14, 30, 46, . . . no lattice points exist and therefore the corresponding lines are
missing (labeled ‘G’ in Fig. 10.24). No such gaps exist in DA spectra where donors and acceptors
occupy different sublattices, e.g. GaP:O,Zn (see also Fig. 10.24). In this case, the spatial separation is
given by R(n) = a 0
√
n/2 − 5/16. If significant broadening is present, the lines are washed out and a
donor–acceptor pair band forms.
10.7 Inner-Impurity Recombination
The transitions of electrons between different states of an impurity level can be nonradiative or radiative.
As an example, the radiative transition of electrons in the Fe
2+ state in InP
5 T 2 →
5 E (Fig. 10.25) and
its fine structure were observed first in [1005] at around 0.35 eV.
Certain defects, also termed ‘color centers’, have been investigated towards their ability to act as
efficient single photon source. If a single defect is optically excited, it can emit a photon. However, it
cannot be excited further. Also, it cannot emit another photon before it has been excited again. This can
be measured through the correlation function for the time difference of emitted photons going to zero
for zero time difference. A popular example of such center is the NV center in diamond, the complex of
a vacancy and a nitrogen impurity [1006, 1007]. The emission rate saturates at about 2 × 10
5 photons/s
(pick up with microscope objective). The sensitivity of the spectrum to magnetic fields makes the NV
center a nanoscopic magnetic field sensor [1008]. Also the spins on the center are fairly isolated and
can be manipulated coherently.
10.8 Auger Recombination
In competition with the radiative, bimolecular recombination is the Auger recombination (Fig. 10.26).
In the Auger process, the energy that is released during the recombination of an electron and hole is