Diplomarbeit Diplom-Ingenieur - Institut für Halbleiter

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of this line is due to a slight tilt away from the zone axis to increase the contrast of the
dark field image. The classification of the dots with respect to their size shows a
narrow distribution with a maximum at about 8nm. The upper limit is again sharper
than the lower one, and appears at 11 nm. The smallest dot was 3.5 nm large, but it
was strongly blurred and could also be 5 nm large. The accuracy of this measurement
was about 0.2 nm if the interfaces are sharp for larger dots and get worse for smaller
dots, which can be explained by the shrinking (110) interface down to almost zero, as
can be seen in the cross sectional image of figure 4.8.
The comparison of these two specimens showed that the size of the dots depends
strongly on the original layer thickness. Unfortunately, the cross-sectional specimen
of a 3nm layer was not good enough for statistical evaluation and comparison with the
5nm sample. A rough estimate of the mean volume of the dots from the 3nm layer
resulted in about 6000nm 3 . An accurate estimate of the mean dot volume of the 1nm
samples is 335nm 3 , which corresponds to a dot density of 3 10 11 cm -2 . The largest one
is that from the 5nm layer with a mean volume of about 8000nm 3 , which corresponds
to a dot density of about 6 10 10 cm -2 . Thinner layers break up in dots with smaller
volume. On the other hand, the larger dots of e.g. a 5nm layer, collect much more
material. The volume of the large dots of the 5nm layer is ~25 time larger than for that
ones of the 1nm layer, but the thicker 5nm layer has only 5 times more material per
unit area than a 1nm layer. Thus, one can find 5 times more small dots precipitating
from a 1nm layer than large ones from a 5nm layer.
4.4 Equilibrium shape
As shown in part 4.3, the shape appearance of the dots changes with their size. The
{111} interfaces do not seem to shrink with the same ratio as the others do, when dots
get smaller. As the {111} facets are the interfaces which are hardest to resolve in high
resolution images. The aim of this chapter is to describe the expected shape of the
dots with attention on the {111} interface.
Figure 4.10 shows the length L of the projected (111) interface of dots with
different height H. Only dots with highly symmetric shape of sample series #11 and
#28 were used, which have almost the same height and width. The cross sectional
images of these samples were evaluated. The measurements show that the length of
the {111} interface is almost independent of the size of the dot and varies in a range
of 7 to 10 nm. An exception of this can be found if the interface falls together with a