12.4 Recombination in Quantum Wells
375
Fig. 12.37 Progress in the
achievement of high
electron mobility in GaAs,
annotated with the
technical innovation
responsible for the
improvement. Adapted
from [1195], reprinted with
permission, ©2003
Elsevier B.V
12.4 Recombination in Quantum Wells
12.4.1 Thickness Dependence
The energy of exciton recombination in quantum wells is blue-shifted with respect to that in bulk
material due to the quantum-confinement energies of electrons and holes (Fig. 12.38). The electron–
hole recombination lineshape in quantum wells is given by the product of the joint density of states
and the Boltzmann function (when Boltzmann statistics apply). The JDOS is given by a step function
(Heavyside function H (E)).
I (E) ∝ H (E − E 11 ) exp
−
E
kT
,
(12.10)
where E 11 = E g + E e1 + E h1 represents the energy of the E1–H1 subband edge as shown in Fig. 12.38.
An experimental spectrum (Fig. 12.40a) shows that excitonic effects influence the recombination lineshape in a GaAs quantum well even at room temperature [1199].
The recombination decay constant of excitons decreases with decreasing well width, partly due to
the increase of exciton binding energy as discussed in [1200].
12.4.2 Broadening Effects
Many-Body Effects
At high carrier densities when the electron (quasi-) Fermi level is above the electron subband edge,
the spectrum broadens and reflects the Fermi–Dirac distribution (Fig. 12.40b). At low temperatures
375
Fig. 12.37 Progress in the
achievement of high
electron mobility in GaAs,
annotated with the
technical innovation
responsible for the
improvement. Adapted
from [1195], reprinted with
permission, ©2003
Elsevier B.V
12.4 Recombination in Quantum Wells
12.4.1 Thickness Dependence
The energy of exciton recombination in quantum wells is blue-shifted with respect to that in bulk
material due to the quantum-confinement energies of electrons and holes (Fig. 12.38). The electron–
hole recombination lineshape in quantum wells is given by the product of the joint density of states
and the Boltzmann function (when Boltzmann statistics apply). The JDOS is given by a step function
(Heavyside function H (E)).
I (E) ∝ H (E − E 11 ) exp
−
E
kT
,
(12.10)
where E 11 = E g + E e1 + E h1 represents the energy of the E1–H1 subband edge as shown in Fig. 12.38.
An experimental spectrum (Fig. 12.40a) shows that excitonic effects influence the recombination lineshape in a GaAs quantum well even at room temperature [1199].
The recombination decay constant of excitons decreases with decreasing well width, partly due to
the increase of exciton binding energy as discussed in [1200].
12.4.2 Broadening Effects
Many-Body Effects
At high carrier densities when the electron (quasi-) Fermi level is above the electron subband edge,
the spectrum broadens and reflects the Fermi–Dirac distribution (Fig. 12.40b). At low temperatures