9.7 Band–Band Transitions
283
Fig. 9.28 a Transmission
spectrum of GaP:N with a
nitrogen concentration of
about 10 19 cm −3 at 1.6 K
(thickness: 1.1 mm). n is
indicated for the first eight
transitions due to excitons
bound to nitrogen pairs.
NN n ’ indicate phonon
replica. The ‘A’ line
denotes the position of the
transition due to excitons
bound to a single nitrogen
atom (observable for
samples with low N
doping). The ‘B’ line is
forbidden and due to the
J = 2 exciton. Adapted
from [694]. b Absorption
spectra of N-doped
(N N = 7 × 10 18 cm −3 ) and
intrinsic GaP (T = 2 K).
Adapted from [690]
(a)
Transmission
n=
4
1 2
6
3
7
BA
5
8
NN 3
NN 1 '
GaP:N
NN 1
NN 2
(b)
9.7.10 Biexcitons
Similar to two hydrogen atoms forming a hydrogen molecule, two excitons can also form a bound
complex, the biexciton involving two electrons and two holes. The biexciton binding energy is defined as
E
b
XX = 2 E X − E XX .
(9.62)
Biexcitons are binding in bulk material. Accordingly, the biexciton recombination or absorption occurs
at lower energy than that of the exciton. Values of the biexciton binding energy are listed in Table 9.4
for various semiconductors. The ratio of biexciton and exciton binding energies is fairly constant
about 0.2. In semiconductors with small exciton binding energy, such as GaAs, biexcitons are hard to
observe in bulk material but show up in heterostructures that provide additional carrier confinement
(see also Sect. 14.4.4). While the exciton density increases linearly with external excitation, the density
of biexcitons increases quadratically.
9.7.11 Trions
The complexes ‘eeh’ and ‘ehh’ are called trions. Also, the notation X
− and X
+ is common. X
−
is typically stable in bulk material but hard to observe. In quantum wells or dots, trions are easier
to observe. In quantum dots excitons with higher charge, e.g. X
2− , have also been observed (see
Fig. 14.45).
283
Fig. 9.28 a Transmission
spectrum of GaP:N with a
nitrogen concentration of
about 10 19 cm −3 at 1.6 K
(thickness: 1.1 mm). n is
indicated for the first eight
transitions due to excitons
bound to nitrogen pairs.
NN n ’ indicate phonon
replica. The ‘A’ line
denotes the position of the
transition due to excitons
bound to a single nitrogen
atom (observable for
samples with low N
doping). The ‘B’ line is
forbidden and due to the
J = 2 exciton. Adapted
from [694]. b Absorption
spectra of N-doped
(N N = 7 × 10 18 cm −3 ) and
intrinsic GaP (T = 2 K).
Adapted from [690]
(a)
Transmission
n=
4
1 2
6
3
7
BA
5
8
NN 3
NN 1 '
GaP:N
NN 1
NN 2
(b)
9.7.10 Biexcitons
Similar to two hydrogen atoms forming a hydrogen molecule, two excitons can also form a bound
complex, the biexciton involving two electrons and two holes. The biexciton binding energy is defined as
E
b
XX = 2 E X − E XX .
(9.62)
Biexcitons are binding in bulk material. Accordingly, the biexciton recombination or absorption occurs
at lower energy than that of the exciton. Values of the biexciton binding energy are listed in Table 9.4
for various semiconductors. The ratio of biexciton and exciton binding energies is fairly constant
about 0.2. In semiconductors with small exciton binding energy, such as GaAs, biexcitons are hard to
observe in bulk material but show up in heterostructures that provide additional carrier confinement
(see also Sect. 14.4.4). While the exciton density increases linearly with external excitation, the density
of biexcitons increases quadratically.
9.7.11 Trions
The complexes ‘eeh’ and ‘ehh’ are called trions. Also, the notation X
− and X
+ is common. X
−
is typically stable in bulk material but hard to observe. In quantum wells or dots, trions are easier
to observe. In quantum dots excitons with higher charge, e.g. X
2− , have also been observed (see
Fig. 14.45).