370
12 Heterostructures
Fig. 12.28 Hole dispersion
in a 68-ML GaAs/71 ML
Al 0.25 Ga 0.75 As superlattice
(numerical calculation).
The double curves
originate from a lifting of
time-reversal symmetry at
k = 0. Reprinted with
permission from [1183],
©1985 APS
0
-10
-20
-30
2
0
.
0
4
0
.
0
0.03
0.01
0 0.01
4
0
.
0
3
0
.
0
2
0
.
0
[100]
[110]
hh1
hh2
lh1
hh3
lh2
hh4
GaAs/
AlGaAs
Fig. 12.29 Observed
electron–hole transitions
(energy difference to the
first e–h transition from
excitation spectroscopy) in
GaAs/(Al,Ga)As quantum
wells of varying thickness.
Symbols are experimental
data, solid lines are
theoretical model. Data
from [1184]
tions and propagation directions are given in Table 12.3. The matrix elements averaged over all in-plane
directions for TE-polarization are 3/2M
2
b (1/2M
2
b ) for the electron to heavy (light) hole transition. For
TM polarization the values are 0 and 2M
2
b , respectively [1185]. The optical selection rules are shown
in Fig. 12.30 (see Fig. 9.12 for bulk material). For propagation along the quantum-well plane, the ratio
between the strength of the TE polarized e–hh and e–lh transitions is 3:1.
The confinement potential squeezes charge carriers bound to impurities closer to the ion. Therefore,
the binding energy increases as shown in Fig. 12.31. This behavior can be modeled theoretically with
good precision. It makes a difference whether the impurity is located at the center or the interface of
the quantum well.
The confinement potential also squeezes electrons and holes in the exciton closer together and thus
increases their Coulomb interaction. The binding energy of the quantum-well exciton is thus larger
than in bulk material and depends on the well width (Fig. 12.32). In the simple hydrogen-like model
with infinite barriers the exciton binding energy is 4 times the bulk binding energy in the limit L z → 0.
12 Heterostructures
Fig. 12.28 Hole dispersion
in a 68-ML GaAs/71 ML
Al 0.25 Ga 0.75 As superlattice
(numerical calculation).
The double curves
originate from a lifting of
time-reversal symmetry at
k = 0. Reprinted with
permission from [1183],
©1985 APS
0
-10
-20
-30
2
0
.
0
4
0
.
0
0.03
0.01
0 0.01
4
0
.
0
3
0
.
0
2
0
.
0
[100]
[110]
hh1
hh2
lh1
hh3
lh2
hh4
GaAs/
AlGaAs
Fig. 12.29 Observed
electron–hole transitions
(energy difference to the
first e–h transition from
excitation spectroscopy) in
GaAs/(Al,Ga)As quantum
wells of varying thickness.
Symbols are experimental
data, solid lines are
theoretical model. Data
from [1184]
tions and propagation directions are given in Table 12.3. The matrix elements averaged over all in-plane
directions for TE-polarization are 3/2M
2
b (1/2M
2
b ) for the electron to heavy (light) hole transition. For
TM polarization the values are 0 and 2M
2
b , respectively [1185]. The optical selection rules are shown
in Fig. 12.30 (see Fig. 9.12 for bulk material). For propagation along the quantum-well plane, the ratio
between the strength of the TE polarized e–hh and e–lh transitions is 3:1.
The confinement potential squeezes charge carriers bound to impurities closer to the ion. Therefore,
the binding energy increases as shown in Fig. 12.31. This behavior can be modeled theoretically with
good precision. It makes a difference whether the impurity is located at the center or the interface of
the quantum well.
The confinement potential also squeezes electrons and holes in the exciton closer together and thus
increases their Coulomb interaction. The binding energy of the quantum-well exciton is thus larger
than in bulk material and depends on the well width (Fig. 12.32). In the simple hydrogen-like model
with infinite barriers the exciton binding energy is 4 times the bulk binding energy in the limit L z → 0.