42 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
The dependence of the dot size and shape as a function of spacer thickness was deduced from
a statistical analysis that also yields the width of the size distributions. Fig. 1.27d –h shows the
height histograms for the samples with spacer thicknesses of 105 to 330 Å. Clearly, for spacer
thicknesses increasing from 85 to 275 Å, the dot height rapidly increases from h 8 5 Å t o
h 149 Å, respectively. For thicker spacers, however, a small left-hand shoulder (A) starts to
emerge at smaller dot heights, and this shoulder becomes even more pronounced for the sam-
ple with 330 Å spacers. Also, the average dot size does not increase anymore but rather slightly
decreases to 138 Å. Both effects are caused by the formation of additional smaller dots on the
surface, which reduces the overall amount of PbSe available for the larger dots.
Figure 1.27j and k summarize the dependence of the average dot height h and dot width b
as a function of spacer thickness. As indicated in Fig. 1.27j , up to d
s
275 Å, the average dot
height increases linearly with increasing spacer thickness, whereas the dot width of about 350
Å remains essentially constant ( Fig. 1.27k ). This translates into a fl attening of the dot shape for
small spacers, indicating that the dot growth is enhanced in the lateral direction. Atomic force
microscopy images recorded with selected sharp atomic force microscopy tips show that these
dots assume a truncated pyramidal shape with triangular base and { 100 } side facets, as shown
schematically in the inset of Fig. 1.27k . For very thin spacer layers, the PbSe dots are rather fl at
with an aspect ratio of only about 1:5, whereas for the thicker spacers the aspect ratio increases
to about 1:3. This is still below the value of 1:2.2 of the pyramidal dots of single dot layers that
do not show any fl attening of the island apex. The modifi cations of dot shape are obviously
induced by the elastic strain fi elds of the buried dots, which are strongest for the thinnest spacer
layers but decay rapidly as the spacer thickness increases. Therefore, for spacer thicknesses larger
than 400 Å, the dots exhibit the same pyramidal shape known for unperturbed single dot layers.
Perhaps the most interesting feature is the pronounced narrowing of the size distribution for the
well-ordered vertically aligned samples. From the dependence of the width of the size distributions
plotted in Fig. 1.27j and k as a function of spacer thickness it is found that the FWHM decreases
from 13% to 8% when d
s
increases from 80 to 160 Å, after which it increases again to above
15% for d
s
330 Å. A similar, but even more pronounced, trend is observed for the variation of
the lateral dot widths ( Fig. 1.27k ), which again shows a pronounced minimum for 160 Å spacers.
Thus, the highest uniformity is obtained for the superlattice with the best hexagonal ordering, dem-
onstrating that the lateral ordering produces a higher uniformity of the dot ensembles.
1.8.2.3 Order parameters derived by X-ray diffraction studies
The vertical and lateral ordering was also characterized by anomalous X-ray diffraction per-
formed at the ESRF synchrotron light source in Grenoble with an X-ray photon energy tuned to
the M shell absorption edge of the Pb atoms. In this way, the structure scattering factor of the
PbEuTe matrix is drastically reduced to about 50 times below that of PbSe and therefore the scat-
tering contrast between the dots and matrix is drastically enhanced. The resulting anomalous
reciprocal space maps are depicted in Fig. 1.28a–d for the superlattices with 105, 165, 215 and
465 Å spacer thicknesses, respectively. Clearly, for all samples a large number of satellite peaks is
observed in the vertical q
z
as well as lateral q
x
direction. However, whereas for the samples with
thin spacers the lateral satellite peaks are aligned parallel to the q
x
direction, for the sample with
thick spacers they are aligned along inclined directions (dashed lines in Fig. 1.28 ). In addition,
reciprocal space maps recorded along different azimuth directions indicate a six-fold symmetry for
the samples with small spacers as compared to a three-fold symmetry for the other sample. This
is additional evidence of the different interlayer dot stackings in the samples, forming a trigonal
fcc -like dot lattice for the latter and a vertically aligned 3D hexagonal dot lattice for the former.
The quality of the dot ordering process was assessed from cross-sectional line scans of the
reciprocal space maps shown in Fig. 1.28 e and f. For the sample with fcc stacking ( Fig. 1.28f ) a
much larger number of lateral satellites can be resolved as compared to those of the vertically
aligned dot samples ( Fig. 1.28e ). In addition, for the latter a signifi cant increase in the peak
widths with increasing q
x
scattering vector occurs. For a quantitative analysis, the widths of the
satellites were derived by fi tting the cross-sectional profi les by Gaussians, with the fi ts represented
as solid lines in Fig. 1.28e and f . The resulting FWHM of the lateral satellite peaks are plotted
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