Full text of DOI:10.1063/1.115138

Relaxation mechanism of Ge islands/Si(001) at low temperature
F. K. LeGoues, J. Tersoff, M. C. Reuter, M. Hammar, and R. Tromp
Citation: Applied Physics Letters 67, 2317 (1995); doi: 10.1063/1.115138
View online: http://dx.doi.org/10.1063/1.115138
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Relaxation mechanism of Ge islands/Si(001) at low temperature
F. K. LeGoues, J. Tersoff, M. C. Reuter, M. Hammar, and R. Tromp
IBM Research Division, Thomas J. Watson Research Center, Yorktown Heights, New York 10598
͑Received 31 March 1995; accepted for publication 14 August 1995͒
Strained layers generally relax by dislocation glide. Here, using UHV-TEM, we study growth of Ge
islands on Si͑001͒ at Շ350 °C. We find that, although conventional relaxation ͑i.e., via glide of 60°
dislocations͒ is suppressed, the islands grow relaxed from the outset, by direct incorporation of
sessile 90° dislocations into the edge of the growing island. Paradoxically, the low-temperature
islands are more fully relaxed than those grown at higher temperature. © 1995 American Institute
of Physics.
Enormous effort has been devoted to understanding the
growth and relaxation of strained epitaxial layers. The SiGe
system has received particular attention in recent years be-
cause of its technological importance. The maximum mis-
match between Si and SiGe alloys is 4% ͑for pure Ge͒, and
in this regime, it is generally agreed that relaxation always
occurs by nucleation and glide of dislocations. However, as
the growth temperature is lowered, glide becomes more slug-
gish, and one may wonder whether, and by which mecha-
nism, relaxation can then occur at all.
Here, we study the growth of Ge on Si͑100͒ at low tem-
perature in situ and in real time. We find that the Ge grows
from the outset as strain-relaxed islands. It does this by di-
rectly incorporating sessile 90° dislocations into the edge of
the growing island. Previously, direct formation of 90° dis-
locations in SiGe was thought so unlikely that, whenever
they were observed, they were attributed to the reaction of
two 60° dislocations.1–4 Paradoxically, islands grown at low
temperature are more fully relaxed than those grown at
higher temperatures, where relaxation should be much easier.
Our ultrahigh vacuum transmission electron microscope
͑UHV-TEM͒ and experimental procedures have been de-
scribed previously.5 A Si͑001͒ wafer is chemically thinned to
electron transparency, and then heated to above 1300 °C in-
side the UHV-TEM. Oxygen is leaked into the TEM to etch
the sample at 950 °C, giving thinner viewing areas. For Ge
deposition, a 10:1 helium/germane mixed is leaked into the
TEM column to a pressure of about 10Ϫ5 Torr. The sample
temperature is measured by pyrometry. The growth is ob-
served in real time, and recorded on video tape. All images
are obtained in weak-beam dark-field conditions using the
͗200͘ reflection.
cated islands is also quite intriguing, and plays an important
role in the relaxation. We speculate that where the corners of
diagonally adjoining huts meets, they can act as pre-existing
dislocations, similar to the ‘‘coreless’’ dislocations discussed
for other systems.7,8 A somewhat related relaxation mecha-
nism, the nucleation of ‘‘V-shaped defects,’’ where two huts
coalesce, has been discussed by Sakai and Tatsumi,9 al-
though in our in situ studies we have never observed such
defects.
Returning to the central question of how the island re-
laxes, we show in Fig. 1͑c͒ the same island as in 1͑b͒ after
further growth. Two additional dislocations are evident.
There are also dislocations in the orthogonal direction, but
they are not visible under our imaging conditions ͑cf. Fig. 2͒.
Figure 2 shows weak-beam dark field images of a much
larger island with an extensive network of dislocations. In
Fig. 2͑a͒, only dislocations perpendicular to ͓220͔ are visible
͑thin vertical lines͒. In Fig. 2͑b͒, only dislocations parallel to
͓220͔ appear as thin horizontal lines. The g–b analysis shows
that there are two perpendicular sets of dislocations, whose
¯
Burgers’ vectors are perpendicular to ͓220͔ and ͓220͔, re-
spectively. This is consistent with the dislocation being 90°
Lomer dislocations, bϭ(a/2) 110 . This g–b is not complete
͓
͔
enough to rule out other 90° dislocations. However, the
Lomer dislocation is the only likely possibility, since other
90° dislocations that exist in this system are partials of the
͓112͔ type, which would generate stacking faults. While 90°
dislocations have been seen before in SiGe,1 because they
are immobile and cannot glide to the interface they have
invariably been attributed to the reaction of two 60°
dislocations.1–4 However, we see in the real-time video that
these 90° dislocations are formed directly at the edge of the
island, and not by the reaction of two 60° dislocations. We
suspect this was also the case in previous studies where net-
works of 90° dislocations were seen.1 Direct formation of
90° dislocations has been previously suggested only in sys-
tems with extremely high misfit ͑Շ8%͒.10–12
Figure 1 shows the evolution of the microstructure dur-
ing growth of Ge on Si͑001͒ at a nominal sample tempera-
ture of 350 °C. Initially, Ge forms an array of ‘‘huts’’,6 ͓Fig.
1͑a͔͒. Unlike the larger coherent islands that form at high
temperature,5 we never see these huts form dislocations. In-
stead, once the entire surface is covered with huts, another
kind of island nucleates, Fig. 1͑b͒. This island is quite small,
no larger than a hut, yet it already contains a dislocation
͑arrow͒. Because it is partially relaxed, this island is a pref-
erential site for incorporation of Ge, and subsequent growth
takes place only at such relaxed islands.
The degree of relaxation at low temperature is also quite
surprising. The dislocation spacing is approximately 115 Å,
close enough to relieve about 90% of the strain. This spacing
is much smaller than the hut size, and so is unrelated to the
presence of huts. In contrast, at higher temperature,5 al-
though introduction of dislocations is much easier, the island
remained far more strained, with only 25% relaxation.
As the growth temperature decreases, dislocation glide
While our principal concern here is how the Ge islands
relax as they grow larger, the initial formation of the dislo-
Appl. Phys. Lett. 67 (16), 16 October 1995
0003-6951/95/67(16)/2317/3/$6.00
© 1995 American Institute of Physics
2317
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FIG. 2. Weak-beam dark field g–b analysis of a larger island grown at
350 °C ͑recorded on film͒. Both images show contrast typical of strained
islands, as well as a single array of dislocations, perpendicular to g. ͑a͒ The
left side of the island is bright, while the right side is dark, which is typical
contrast for a strained island, showing that this island is not totally relaxed.
The thin vertical lines ͑more easily visible on the dark side͒ are dislocations.
͑b͒ The strain contrast now appears as a bright half toward the top of the
island, and a darker bottom side. Dislocations are clearly visible on the
bottom part of the island as thin horizontal lines.
However, such a process still requires overcoming an
activation barrier, because the energy cost of the dislocation
core is not compensated by relief of strain until the edge has
moved somewhat beyond the new dislocation. Thus we are
left with two puzzles: how this barrier can be overcome at
low temperature, and why the low-temperature island is so
fully relaxed.
To address these questions, we consider a highly ideal-
ized model of a fully relaxed island. The island and substrate
have isotropic surface energies ␥i and ␥s , respectively. The
island–substrate interface is assumed circular and fully re-
laxed by dislocations, with energy ␥is is per unit area ͑in-
cluding the energy of the dislocations͒. Then in equilibrium
the island is a spherical section, as in Fig. 3͑a͒. The contact
angle ␪ is determined by the condition of zero net force on
the island edge, giving the equilibrium angle ␪e :
FIG. 1. Evolution of the microstructure during growth at 350 °C ͑obtained
by grabbing frames from a video recording of the growth. ͑a͒ Initial forma-
tion of ‘‘huts’’ covering the entire area. ͑b͒ One small island has formed at a
corner between huts. The arrow shows a dislocation present in the island. ͑c͒
Same island after formation of two more dislocations. The arrow indicates
the same dislocations as in ͑b͒.
becomes much slower, and climb is even more difficult.
Thus, an immobile dislocation must be incorporated directly
into the edge of the growing island, without glide or climb.
90° dislocations are then favored over 60°: the respective
Burger’s vectors have equal mangitude, but the 90° Burger’s
vector is better oriented to relive the misfit.
cos ␪ ϭ ␥ Ϫ␥ ͒/␥ .
͑1͒
͑
e
s
is
i
Now consider further growth of the island. In the limit of
large misfit, lateral growth is energetically unfavorable, since
2318
Appl. Phys. Lett., Vol. 67, No. 16, 16 October 1995
LeGoues et al.
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be somewhat greater than Lmin, but in general, the thicker the
island, the more complete the relaxation. Furthermore, the
low-temperature islands also benefit from the fact that h0 is
smaller for 90° dislocations than for 60° ones; so for the
same thickness, the low-temperature island will be more
fully relaxed than the high-temperature one, other factors
being equal.
We have sketched a picture of the low-temperature re-
laxation, which consistently explains both how the 90° dis-
locations can be incorporated, and why the relaxation is so
nearly complete. However, the precise nature of the compe-
tition between this mechanism and glide of 60° dislocations
is less clear. The simplest view is that at higher temperatures,
glide can preempt other relaxation mechanisms by allowing
relaxation before the contact angle has grown large enough
to permit incorporation of 90° dislocations. However, the
degree of misfit is apparently as important as the temperature
in controlling the relaxation mechanism. Kvam and
co-workers1 found that increasing misfit favored 90° disloca-
tions even at constant temperature; and 90° dislocations have
been seen at higher temperatures in systems with extremely
large misfit.10–12 Perhaps in these systems, the misfit is so
effective in preventing lateral growth that there is insufficient
strained material at the island edge for a dislocation to glide
into. Thus, for sufficiently large misfit, relaxation by 90°
dislocations would in effect preempt glide.
FIG. 3. ͑a͒ Cross section of idealized island ͑spherical section͒ as it grows,
but before a new dislocation is introduced. Figure corresponds to the strain-
dominated case, where the island does not grow laterally without introduc-
ing additional dislocations. ͑b͒ Schematic of the island energy vs position x
of the advancing edge, illustrating the energy barrier to introduce a disloca-
tion. Dashed and dotted lines correspond to increasing outward tension on
the island edge as the contact angle increases, adding to the energy a term
linear in x, which reduces the barrier.
it results in highly strained material at the island edge. In-
stead, the island will remain fully relaxed by growing verti-
cally. The island remains a spherical section, but with in-
creased contact angle ␪Ͼ␪e , as in Fig. 3͑a͒. The result is a
net tension ͑force per unit length͒ ⌫ pushing the island edge
outward, where
In conclusion, at sufficiently low temperature, islands
cannot readily relax by dislocation glide. However, the is-
lands grow from the outset almost fully relaxed. The
grown-in dislocations are not the usual 60° type, but rather
the unexpected 90° Lomer dislocations. The very difficulty
of incorporating dislocations in this way appears, counterin-
tuitively, to explain why the islands are much more fully
relaxed than those grown at higher temperature.
⌫ϭ␥ cos ␪ Ϫcos ␪͒.
͑2͒
͑
i
e
Now consider the barrier to introduce a dislocation. The
tension ⌫ contributes a term to the energy that decreases
linearly with outward motion of the island edge. This in turn
lowers the activation barrier to introduce the next disloca-
tion, as illustrated in Fig. 3͑b͒. As the relaxed island grows,
the contact angle increases and the barrier is reduced, until
thermally activated nucleation of a new dislocation occurs at
the island edge. While the height and shape of the barrier
depend in a complex way on the shape of the moving edge of
the island, the progressive lowering of the barrier as the is-
land grows vertically should be a rather general phenom-
enon. We have observed this phenomenon using the UHV-
TEM in reflection electron microscopy ͑REM͒ mode, where
islands can be seen almost edge on. The increase in contact
angle preceding the introduction of a dislocation has been
recorded in real time, and has been reported in another
publication.13
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Oddly enough, the very difficulty of introducing disloca-
tions may account for the almost complete relaxation at low
temperature. As seen in Fig. 3, the island must become rela-
tively thick, with a large contact angle, in order to introduce
the next dislocation. The minimum-energy dislocation spac-
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h
L
minϷL0
,
͑3͒
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13 M. Hammar, F. K. LeGoues, J. Tersoff, M. C. Reuter, and R. M. Tromp
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hϪh0
where L0 is the spacing required to completely relieve the
strain, and h0 is the equilibrium critical thickness for intro-
duction of dislocations.14 The actual dislocation spacing may
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Appl. Phys. Lett., Vol. 67, No. 16, 16 October 1995
LeGoues et al.
2319
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