424
14 Nanostructures
Fig. 14.41 Lateral
ordering of QD array. d
Plan-view TEM of QD
array on which the
statistical evaluation is
based. a Two-dimensional
histogram of QDs as a
function of the
nearest-neighbor distance
and direction, (b, c)
projections of part (a).
Solid lines in (b) and (c)
are theory for square array
with σ = 20% deviation
from ideal position.
Adapted from [1339, 1397]
Fig. 14.42 a AFM image
of a Si (001) substrate after
960 min of ion sputtering
(1.2 keV Ar + , normal
incidence). b
Two-dimensional
autocorrelation function
from a 400 × 400 nm 2 area
of image in part (a).
Adapted from [1406] with
permission, ©2001 AIP
The vertical arrangement can lead to further ordering since a homogenization in lateral position
takes place. If two QDs in the first layers are very close, their strain fields overlap and the second layer
‘sees’ only one QD.
The lateral (in-plane) ordering of the QDs with respect to each other occurs in square or hexagonal
patterns and is mediated via strain interaction through the substrate. The interaction energy is fairly
small, leading only to short-range in-plane order [1397] as shown in Fig. 14.41. The in-plane ordering
can be improved up to the point that regular one- or two-dimensional arrays form or individual quantum
dots are placed on designated positions using directed self-assembly [1339]. Among others, dislocation
networks buried under the growth surface of the nanostructure, surface patterning and modification
have been used to direct the QD positioning.
Ion-Beam Erosion
During the erosion of a surface with low-energy ion beam sputtering ordered patterns of dots appear
[1404–1407]. Isotropic [1408] and hexagonal [1404, 1406] (Fig. 14.42) near-range ordering has been
observed. The pattern formation mechanism is based on the morphology-dependent sputter yield and
further mechanisms of mass redistribution [1409]. Also linear patterns have been reported [1410].
14 Nanostructures
Fig. 14.41 Lateral
ordering of QD array. d
Plan-view TEM of QD
array on which the
statistical evaluation is
based. a Two-dimensional
histogram of QDs as a
function of the
nearest-neighbor distance
and direction, (b, c)
projections of part (a).
Solid lines in (b) and (c)
are theory for square array
with σ = 20% deviation
from ideal position.
Adapted from [1339, 1397]
Fig. 14.42 a AFM image
of a Si (001) substrate after
960 min of ion sputtering
(1.2 keV Ar + , normal
incidence). b
Two-dimensional
autocorrelation function
from a 400 × 400 nm 2 area
of image in part (a).
Adapted from [1406] with
permission, ©2001 AIP
The vertical arrangement can lead to further ordering since a homogenization in lateral position
takes place. If two QDs in the first layers are very close, their strain fields overlap and the second layer
‘sees’ only one QD.
The lateral (in-plane) ordering of the QDs with respect to each other occurs in square or hexagonal
patterns and is mediated via strain interaction through the substrate. The interaction energy is fairly
small, leading only to short-range in-plane order [1397] as shown in Fig. 14.41. The in-plane ordering
can be improved up to the point that regular one- or two-dimensional arrays form or individual quantum
dots are placed on designated positions using directed self-assembly [1339]. Among others, dislocation
networks buried under the growth surface of the nanostructure, surface patterning and modification
have been used to direct the QD positioning.
Ion-Beam Erosion
During the erosion of a surface with low-energy ion beam sputtering ordered patterns of dots appear
[1404–1407]. Isotropic [1408] and hexagonal [1404, 1406] (Fig. 14.42) near-range ordering has been
observed. The pattern formation mechanism is based on the morphology-dependent sputter yield and
further mechanisms of mass redistribution [1409]. Also linear patterns have been reported [1410].