15.1 Electric Fields
431
Fig. 15.3 a Theoretical
absorption (top panel) with
(solid line) and without
(dash-dotted line) electric
field for a volume
semiconductor (without
Coulomb interaction) and
theoretical change of
absorption (bottom panel).
b Experimental absorption
spectra of (In,Ga)As on InP
at T = 15 K for various
applied voltages as labeled.
Adapted from [1421]
(a)
0.10
0.05
0
0.005
0
-0.005
= (E)- (0)
0.80
0.84
0.88
2
1
3
4
5
(b)
InGaAs
30
25
20
15
10
5
(10 cm )
3
- 1
0.80
0
0.81 0.82 0.83 0.84
e-hh
e-lh
0.3V
0.2V
0V
0.5V
2.0V
A more detailed theory including interband coupling and excitonic effects can be found in [1419]. The
effect is best determined with modulation spectroscopy can measuring the difference of absorption
with and without field [1420] since it exhibits more defined features (Fig. 15.3a, lower panel).
A nonperiodicity can indicate a nonparabolicity of the mass. Also, the contributions of heavy and
light holes merge. For a given mass the electric field strength can be determined. Well-pronounced
oscillations are only present for homogeneous fields.
Experimental spectra show additionally the peaks due to excitonic correlation (Fig. 15.3b) at low
field strength. At higher fields the FKO evolve and the amplitude of the excitonic peaks decreases
because the excitons are ionized in the field.
15.1.2 Quantum Wells
In a quantum well an electric field along the confinement direction (z direction) causes electrons and
holes to shift their mean position to opposite interfaces (Fig. 15.1b). However, excitons are not ionized
due to the electric field. With increasing field (for both field directions) the energy position of the
absorption edge and the recombination energy is reduced. This is the quantum confined Stark effect
(QCSE). Corresponding experimental data are shown in Fig. 15.4i–v. The shift depends quadratically
on the electric field since the exciton has no permanent dipole moment (mirror symmetry of the quantum
well). Thus, only the second-order Stark effect is present (as for the hydrogen atom) in which the field
first induces a dipole p = αE. This dipole interacts with the field with an energy E = −p · E = −αE
2 .
The carrier separation in opposite sides of the quantum well (Fig. 15.4b) leads to a reduced overlap
of the electron and hole wavefunctions and subsequently to an increased recombination lifetime (see
Fig. 12.43).
If the field is within the quantum-well interface plane, the field leads to the ionization of excitons
without shift of the energy position. The loss of the excitonic peak is visualized in the spectra in
Fig. 15.4a–c.
431
Fig. 15.3 a Theoretical
absorption (top panel) with
(solid line) and without
(dash-dotted line) electric
field for a volume
semiconductor (without
Coulomb interaction) and
theoretical change of
absorption (bottom panel).
b Experimental absorption
spectra of (In,Ga)As on InP
at T = 15 K for various
applied voltages as labeled.
Adapted from [1421]
(a)
0.10
0.05
0
0.005
0
-0.005
= (E)- (0)
0.80
0.84
0.88
2
1
3
4
5
(b)
InGaAs
30
25
20
15
10
5
(10 cm )
3
- 1
0.80
0
0.81 0.82 0.83 0.84
e-hh
e-lh
0.3V
0.2V
0V
0.5V
2.0V
A more detailed theory including interband coupling and excitonic effects can be found in [1419]. The
effect is best determined with modulation spectroscopy can measuring the difference of absorption
with and without field [1420] since it exhibits more defined features (Fig. 15.3a, lower panel).
A nonperiodicity can indicate a nonparabolicity of the mass. Also, the contributions of heavy and
light holes merge. For a given mass the electric field strength can be determined. Well-pronounced
oscillations are only present for homogeneous fields.
Experimental spectra show additionally the peaks due to excitonic correlation (Fig. 15.3b) at low
field strength. At higher fields the FKO evolve and the amplitude of the excitonic peaks decreases
because the excitons are ionized in the field.
15.1.2 Quantum Wells
In a quantum well an electric field along the confinement direction (z direction) causes electrons and
holes to shift their mean position to opposite interfaces (Fig. 15.1b). However, excitons are not ionized
due to the electric field. With increasing field (for both field directions) the energy position of the
absorption edge and the recombination energy is reduced. This is the quantum confined Stark effect
(QCSE). Corresponding experimental data are shown in Fig. 15.4i–v. The shift depends quadratically
on the electric field since the exciton has no permanent dipole moment (mirror symmetry of the quantum
well). Thus, only the second-order Stark effect is present (as for the hydrogen atom) in which the field
first induces a dipole p = αE. This dipole interacts with the field with an energy E = −p · E = −αE
2 .
The carrier separation in opposite sides of the quantum well (Fig. 15.4b) leads to a reduced overlap
of the electron and hole wavefunctions and subsequently to an increased recombination lifetime (see
Fig. 12.43).
If the field is within the quantum-well interface plane, the field leads to the ionization of excitons
without shift of the energy position. The loss of the excitonic peak is visualized in the spectra in
Fig. 15.4a–c.