12.4 Recombination in Quantum Wells
377
Fig. 12.39 a Reflectance
spectra at various
temperatures from a 17 nm
thick GaAs/Al 0.3 Ga 0.7 As
quantum well. The inset
shows the temperature
dependence of the
homogeneous linewidth. b
LO phonon broadening
parameter (FWHM) for
various quantum well
widths. Adapted
from [1202]
(a)
(b)
(a)
10
4
10
10
10
10
3
2
1
0
1.50
1.55
1.60
1.65
1.70
GaAs/AlGaAs
(b)
T=4.7K
0.84
0.86
0.88
0.90 0.92
InGaAs/InP
0.82
T=25K
T=80K
E 11
Fig. 12.40 a Photoluminescence spectrum of a 5-nm GaAs/(Al,Ga)As quantum well at T = 300 K. The solid (dashed)
line is fit with (without) excitonic effects. The two peaks are due to transitions involving heavy and light holes. Adapted
from [1199]. b Photoluminescence spectra at three different temperatures as labeled of a 10-nm modulation-doped
(In, Ga)As/InP quantum well with an electron sheet density n s = 9.1 × 10 11 cm −2 . The electron quasi-Fermi level is
F n − (E C + E e1 ) = 44.1 meV from the subband edge. The dashed line in the T = 80 K spectrum is the lineshape from
JDOS and a Fermi–Dirac distribution without enhancement at the Fermi edge. Adapted from [1201]
Inhomogeneous Broadening
Inhomogeneous broadening affects the recombination lineshape. Since the interfaces of the QW are not
ideally flat, the exciton averages over different quantum-well thicknesses within its volume. Also, e.g.,
for the GaAs/(Al,Ga)As system, the wavefunction in the (binary) quantum well tunnels into the barrier,
the amount depending on the QW width, and there ‘sees’ the alloy broadening (see Sect. 10.3.3). The
problem of exciton dynamics in a potential with random fluctuations has been treated in detail [1204,
1205].
A simplified picture is as follows: At low temperatures the excitons populate preferentially the
potential minima. A simple lineshape
5 of the QW absorption or joint density of states is given by a
step function (cf. Table 9.3) at the QW band edge E 0 . The inhomogeneous broadening has a Gaussian
5 neglecting excitonic enhancement.
377
Fig. 12.39 a Reflectance
spectra at various
temperatures from a 17 nm
thick GaAs/Al 0.3 Ga 0.7 As
quantum well. The inset
shows the temperature
dependence of the
homogeneous linewidth. b
LO phonon broadening
parameter (FWHM) for
various quantum well
widths. Adapted
from [1202]
(a)
(b)
(a)
10
4
10
10
10
10
3
2
1
0
1.50
1.55
1.60
1.65
1.70
GaAs/AlGaAs
(b)
T=4.7K
0.84
0.86
0.88
0.90 0.92
InGaAs/InP
0.82
T=25K
T=80K
E 11
Fig. 12.40 a Photoluminescence spectrum of a 5-nm GaAs/(Al,Ga)As quantum well at T = 300 K. The solid (dashed)
line is fit with (without) excitonic effects. The two peaks are due to transitions involving heavy and light holes. Adapted
from [1199]. b Photoluminescence spectra at three different temperatures as labeled of a 10-nm modulation-doped
(In, Ga)As/InP quantum well with an electron sheet density n s = 9.1 × 10 11 cm −2 . The electron quasi-Fermi level is
F n − (E C + E e1 ) = 44.1 meV from the subband edge. The dashed line in the T = 80 K spectrum is the lineshape from
JDOS and a Fermi–Dirac distribution without enhancement at the Fermi edge. Adapted from [1201]
Inhomogeneous Broadening
Inhomogeneous broadening affects the recombination lineshape. Since the interfaces of the QW are not
ideally flat, the exciton averages over different quantum-well thicknesses within its volume. Also, e.g.,
for the GaAs/(Al,Ga)As system, the wavefunction in the (binary) quantum well tunnels into the barrier,
the amount depending on the QW width, and there ‘sees’ the alloy broadening (see Sect. 10.3.3). The
problem of exciton dynamics in a potential with random fluctuations has been treated in detail [1204,
1205].
A simplified picture is as follows: At low temperatures the excitons populate preferentially the
potential minima. A simple lineshape
5 of the QW absorption or joint density of states is given by a
step function (cf. Table 9.3) at the QW band edge E 0 . The inhomogeneous broadening has a Gaussian
5 neglecting excitonic enhancement.