14.4 Quantum Dots
421
Fig. 14.33 Quantum dots
of various shapes created
by lithography and etching
techniques. From [1393]
Fig. 14.34 a Schematic
representation of growth on
top of a predefined
template, b cross-sectional
TEM of quantum dot
formation at the apex.
Reprinted with permission
from [1394], ©1992 MRS
(a)
(b)
and can be handled in ensembles and also individually. Such nanocrystals have been synthesized and
investigated in particular for II–VI (Fig. 14.35a) and halide perovskite (Fig. 14.35b) semiconductors.
Mismatched Epitaxy
The self-assembly (or self-organization) relies on strained heterostructures that achieve energy minimization by island growth on a wetting layer (Stranski-Krastanow growth mode, see Sect. 12.2.3 and
[1339]). Additional ordering mechanisms [1397, 1398] lead to ensembles that are homogeneous in
size
2 [1399] and shape [1400] (Fig. 14.36).
When a thin layer of a semiconductor is grown on top of a flat substrate with different lattice constant,
the layer suffers a tetragonal distortion (Sect. 5.3.3). Strain can only relax along the growth direction
(Fig. 14.37). If the strain energy is too large (highly strained layer or large thickness), plastic relaxation
via dislocation formation occurs. If there is island geometry, strain can relax in all three directions and
about 50% more strain energy can relax, thus making this type of relaxation energetically favorable.
When the island is embedded in the host matrix, the strain energy is similar to the 2D case and the
matrix becomes strained (metastable state).
When such QD layers are vertically stacked, the individual quantum dots grow on top of each
other (Fig. 14.38) if the separation is not too large (Fig. 14.40). This effect is due to the effect of the
underlying QD. In the case of InAs/GaAs (compressive strain), the buried QD stretches the surface
above it (tensile surface strain). Thus, atoms impinging in the next QD layer find a smaller strain right
on top of the buried QDs. In STM images of the cross section through (XSTM) such a stack (Fig. 14.39)
individual indium atoms are visible and the shape can be analyzed in detail [1402].
2 The ordering in size is remarkable. Typically Ostwald ripening (due to the Gibbs-Thomson effect; smaller droplets have
larger vapor pressure and dissolve, larger droplets accordingly grow) occurs in an ensemble of droplets or nuclei. In the
case of strained QDs, surface energy terms stabilize a certain QD size.
421
Fig. 14.33 Quantum dots
of various shapes created
by lithography and etching
techniques. From [1393]
Fig. 14.34 a Schematic
representation of growth on
top of a predefined
template, b cross-sectional
TEM of quantum dot
formation at the apex.
Reprinted with permission
from [1394], ©1992 MRS
(a)
(b)
and can be handled in ensembles and also individually. Such nanocrystals have been synthesized and
investigated in particular for II–VI (Fig. 14.35a) and halide perovskite (Fig. 14.35b) semiconductors.
Mismatched Epitaxy
The self-assembly (or self-organization) relies on strained heterostructures that achieve energy minimization by island growth on a wetting layer (Stranski-Krastanow growth mode, see Sect. 12.2.3 and
[1339]). Additional ordering mechanisms [1397, 1398] lead to ensembles that are homogeneous in
size
2 [1399] and shape [1400] (Fig. 14.36).
When a thin layer of a semiconductor is grown on top of a flat substrate with different lattice constant,
the layer suffers a tetragonal distortion (Sect. 5.3.3). Strain can only relax along the growth direction
(Fig. 14.37). If the strain energy is too large (highly strained layer or large thickness), plastic relaxation
via dislocation formation occurs. If there is island geometry, strain can relax in all three directions and
about 50% more strain energy can relax, thus making this type of relaxation energetically favorable.
When the island is embedded in the host matrix, the strain energy is similar to the 2D case and the
matrix becomes strained (metastable state).
When such QD layers are vertically stacked, the individual quantum dots grow on top of each
other (Fig. 14.38) if the separation is not too large (Fig. 14.40). This effect is due to the effect of the
underlying QD. In the case of InAs/GaAs (compressive strain), the buried QD stretches the surface
above it (tensile surface strain). Thus, atoms impinging in the next QD layer find a smaller strain right
on top of the buried QDs. In STM images of the cross section through (XSTM) such a stack (Fig. 14.39)
individual indium atoms are visible and the shape can be analyzed in detail [1402].
2 The ordering in size is remarkable. Typically Ostwald ripening (due to the Gibbs-Thomson effect; smaller droplets have
larger vapor pressure and dissolve, larger droplets accordingly grow) occurs in an ensemble of droplets or nuclei. In the
case of strained QDs, surface energy terms stabilize a certain QD size.