16.4 Piezoelectricity
463
42
-42
-21
charges
25
(a)
(b)
(c)
(d)
Fig. 16.16 a Piezoelectric charges and b–d resulting Coulomb potential for InAs/GaAs quantum dot with base length b =
12 nm. a Isosurfaces corresponding to volume charges ±0.3 e nm −3 . b Isosurfaces for the Coulomb potential at ±30 meV.
c,d Cross section through the Coulomb potential somewhat above the wetting layer in two different magnifications, d
is a zoom into (c). The InAs/GaAs interface is visible in d due to the image charge effect. Parts a and b reprinted with
permission from [417], ©1995 APS
tric charges are shown for a strained In 0.2 Ga 0.8 As/GaAs quantum wire. In Fig. 16.15c the three-fold
symmetric piezoelectric charge density within the cross-section of a (111)-oriented GaAs wire under
torsion (due to second order piezoelectricity) is depicted.
In Fig. 16.16, the piezoelectric charges and potential are shown for the quantum dot from Fig. 5.34.
The piezoelectric potential has quadrupole character and thus reduces the symmetry of the QD (to C 2v )
[417].
6 Piezoelectric effects are particularly important in wurtzite nanostructures [1515].
6 The strain distribution has C 2v symmetry for a square-based pyramid for zincblende materials. The energy levels and
wavefunctions are more strongly impacted by the piezoelectric effects than by the strain asymmetry [1382, 1383].
463
42
-42
-21
charges
25
(a)
(b)
(c)
(d)
Fig. 16.16 a Piezoelectric charges and b–d resulting Coulomb potential for InAs/GaAs quantum dot with base length b =
12 nm. a Isosurfaces corresponding to volume charges ±0.3 e nm −3 . b Isosurfaces for the Coulomb potential at ±30 meV.
c,d Cross section through the Coulomb potential somewhat above the wetting layer in two different magnifications, d
is a zoom into (c). The InAs/GaAs interface is visible in d due to the image charge effect. Parts a and b reprinted with
permission from [417], ©1995 APS
tric charges are shown for a strained In 0.2 Ga 0.8 As/GaAs quantum wire. In Fig. 16.15c the three-fold
symmetric piezoelectric charge density within the cross-section of a (111)-oriented GaAs wire under
torsion (due to second order piezoelectricity) is depicted.
In Fig. 16.16, the piezoelectric charges and potential are shown for the quantum dot from Fig. 5.34.
The piezoelectric potential has quadrupole character and thus reduces the symmetry of the QD (to C 2v )
[417].
6 Piezoelectric effects are particularly important in wurtzite nanostructures [1515].
6 The strain distribution has C 2v symmetry for a square-based pyramid for zincblende materials. The energy levels and
wavefunctions are more strongly impacted by the piezoelectric effects than by the strain asymmetry [1382, 1383].