Shape cycle of Ga clusters on GaAs during coalescence growth

Article abstract of DOI:10.1016/j.susc.2007.04.019

GaAs(1 0 0) was heated above its decomposition temperature of 585 °C bringing it into a phase separation regime where the thermodynamic favoured state is liquid Ga clusters on the surface. Varying the annealing times and temperatures provided an overview of the clustering at all stages from transitioning ripening at lower temperatures to coalescence at higher temperatures. We observed a shape cycle between round and rectangular shaped clusters during the growth. This cycle is driven by subcluster etching where pits are formed under clusters during the growth due to preferential loss of As through the liquid Ga cluster. The newly observed shape cycle is compared to a shape cycle observed previously in In on InP illustrating that shape cycles are a common feature of the decomposition of Group III-V semiconductors.

Full text of DOI:10.1016/j.susc.2007.04.019

Surface Science 601 (2007) 2438–2444
www.elsevier.com/locate/susc
Shape cycle of Ga clusters on GaAs during coalescence growth
a,
b
K. Shorlin *, M. Zinke-Allmang
a
Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1B 3X7
b
Department of Medical Biophysics, The University of Western Ontario, London, Ontario, Canada N6A 3K7
Received 15 July 2006; accepted for publication 3 April 2007
Available online 11 April 2007
Abstract
GaAs(100) was heated above its decomposition temperature of 585 °C bringing it into a phase separation regime where the thermo-
dynamic favoured state is liquid Ga clusters on the surface. Varying the annealing times and temperatures provided an overview of the
clustering at all stages from transitioning ripening at lower temperatures to coalescence at higher temperatures. We observed a shape
cycle between round and rectangular shaped clusters during the growth. This cycle is driven by subcluster etching where pits are formed
under clusters during the growth due to preferential loss of As through the liquid Ga cluster. The newly observed shape cycle is compared
to a shape cycle observed previously in In on InP illustrating that shape cycles are a common feature of the decomposition of Group III–
V semiconductors.
Ó 2007 Elsevier B.V. All rights reserved.
Keywords: Surface thermodynamics (including phase transitions); Surface structure, morphology, roughness, and topography; Gallium arsenide; Clusters;
Semiconducting surfaces
1. Introduction
Clustering of Ga on GaAs is observed when GaAs is
heated above temperatures of about 585 °C. This is the
decomposition temperature at which the lattice structure
begins to break down and there is a preferential loss of ar-
senic (As) from the surface. This results in an excess of liquid
Ga and once a sufficiently high surface concentration of Ga
is reached, cluster nucleation begins and phase separation
occurs. The Ga on GaAs(100) growth mechanism is ini-
tially through ripening and then through static coalescence
[5]. As the late stage clustering proceeds there are three pro-
cesses: (i) As diffuses through the substrate lattice and evap-
orates from the surface, (ii) surface Ga diffuses into clusters
and the exposed As desorbs from the surface, and (iii) As
diffuses through the liquid Ga cluster and evaporates. The
thermodynamic data for Ga on GaAs(100) are well known
and an examination of the diffusion coefficients shows a fas-
ter loss of As through a liquid Ga cluster than from the sub-
strate or the surface [1]. The result is subcluster etching
where the cluster etches into the surface during growth.
In this paper, we observe the effect of this subcluster
etching which is to drive a shape cycle from round to rect-
angular based and back to round clusters.
Thin films on gallium arsenide (GaAs) have unique
applications for opto-electronic integration and high fre-
quency devices and therefore is an important system to
study. For such devices, high degrees of flatness are re-
quired which necessitate a large degree of control of the
growth parameters. GaAs is also fundamentally interesting
as subcluster etching, i.e., the formation of depressions un-
der clusters, has been observed after the growth of gallium
(Ga) clusters [1]. With the increasing importance of materi-
als created on the nanoscale, there comes fundamental
interest in self assembled structures and the limits of inher-
ent order in the cluster size and spatial distributions as well
as cluster shape. Prior studies show shape cycles in Ag on
Si(001) [2], Ge on Si(001) [3], and most relevant to the cur-
rent work In on InP(001) [4].
*
Corresponding author. Tel.: +1 709 7378877; fax: +1 709 7378739.
E-mail address: kelly@physics.mun.ca (K. Shorlin).
0039-6028/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2007.04.019

K. Shorlin, M. Zinke-Allmang / Surface Science 601 (2007) 2438–2444
2439
2. Experimental
again be kept short enough to not reach too high areal
coverages. With both temperature and annealing time to
be very sensitive parameters, the respective error sources
in their experimental measurement become critical. In
the case of the temperature, calibration errors of the ther-
mocouple and systematic errors of thermocouple/sample/
sample holder thermal contact must be taken into account.
Replacing the thermocouple with a pyrometer does not
significantly improve this situation as calibration steps
are again required. In addition, a wavelength of the
pyrometer has to be chosen for which GaAs is not trans-
parent, which infringes on the precise measurements of
temperatures in the lower range. For the annealing time,
again systematic errors due to heating and particularly
cooling rate variations with the thermal contact to the
sample holder become important. Most critically though,
the fact that both temperature and annealing time are
parameters needed to specify the extent of coalescence
growth prohibits their independent use. Temperature vari-
ations enter the progression of the process through a
Boltzmann term because the chemical decomposition of
GaAs is an activated process; the annealing time is a linear
parameter for the progression of the process. Thus, char-
acterizing the system requires two independent parameter
measurements, each with statistical and systematic errors.
Their combination would further require an error propa-
gation discussion.
Instead, the samples are characterized by a single
parameter measurable after sample preparation. Tempera-
ture and annealing times in this approach are only used as
an estimate of the stage and progression of the final
morphology; the actual result is characterized by w. We
have chosen this parameter as follows: To be a useful
parameter, w must reflect in a steady, continuous fashion
both the time and temperature dependent progression of
the sample. In turn, neither of these dependencies must
be linear, relieving us of the need for a quantitative formula
for the cluster growth rate (which has not yet been devel-
oped for coalescence growth). Thus, we chose w to be the
Ga coverage; this parameter does not only fulfil the
requirements as stated above, but also allows us very di-
rectly to separate late stage coalescence growth from
flow-dominated features and cohesive aggregation which
occur close to 100% coverage. Table 1 is a list of all samples
prepared with the stage of growth and value of w. Fig. 1 is
a phase diagram indicating the stage of cluster formation as
a function of w.
Samples of approximate size 1 cm by 1 cm were cut from
a polished GaAs(100) wafer and heated in the heating
stage of a Group III–V molecular beam epitaxy (MBE)
chamber. The chamber is maintained with a base pressure
less than 10ꢀ8 Pa. The sample was heated by indirect elec-
tron bombardment from a high current filament. The sam-
ples were heated above the decomposition temperatures
with a range of about 585–750 °C with annealing times of
3–8 min. The temperature was measured with a thermocou-
ple placed near the sample surface. The experiments done
are listed in Table 1 with sample number, stage of growth,
and annealing time. The pre-coalescence stage was an-
nealed with temperatures under 600 °C, the coalescence
stage is observed for temperatures in the range of 600–
680 °C, and temperatures above 680 °C result in such a
high fraction of liquid Ga on the surface that a large scale
flowing aggregation forms.
Samples are classified by a newly introduced parameter
w, which represents the fraction (in %) of the surface cov-
ered by Ga. This parameter is necessary as the traditional
sample characterization by temperature and annealing
time is not suitable for the current study and in situ anal-
ysis was unavailable. The temperature/time window for
coalescence growth is rather narrow, with suitable temper-
atures ranging from 600 °C to less than 700 °C and anneal-
ing times from at least 3 min to about 15 min at the higher
temperatures. The narrow window for these parameters is
generally due to the non-equilibrium behaviour of the sys-
tem. More specifically, the temperature must sufficiently
exceed the decomposition threshold at 585 °C, but must al-
low the coalescence process to evolve without crossing into
the onset of flow-processes or cohesive aggregation, which
occur at areal coverages near 100%. Annealing tempera-
tures must exceed the pre-coalescence range but must
Table 1
List of samples with stage of growth and annealing times
Sample number
Stage
w (%)
G1
G2
G3
G4
G5
G6
G7
G8
Pre-coalescence
Pre-coalescence
Pre-coalescence
Pre-coalescence
Pre-coalescence
Pre-coalescence
Early coalescence
Early coalescence
Early coalescence
Early coalescence
Coalescence
Coalescence
Coalescence
Coalescence
Coalescence
Coalescence
Cohesive aggregation
1.53
1.65
2.10
5.00
7.89
12.7
20.8
25.5
25.8
37.1
41.0
43.3
43.3
50.2
51.7
56.6
75.3
Scanning electron microscopy (SEM) was done on all
samples to obtain surface images and the data analysis
was done using these images. The SEM images were pro-
duced using an Hitachi S-4500 field emission SEM with
EDX system at Surface Science Western of the University
of Western Ontario. The primary electron beam had energy
of 10 KeV and resolutions of 65 nm were obtained. EDX
(energy dispersive X-ray) was used to confirm the clusters
on the surface were Ga and the surrounding surface was
GaAs.
G9
G10
G11
G12
G13
G14
G15
G16
G17

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K. Shorlin, M. Zinke-Allmang / Surface Science 601 (2007) 2438–2444
G1
G2
G3
G4
G7
G8
G9
G11
G12
G13
G17
G14
G15
G16
G10
G5
G6
10 20 30 40 50 60 70 80
ψ(%)
Fig. 1. Phase diagram of clustering stage vs surface coverage. Solid circles
represent samples G1–G6 and are in a pre-coalescence phase, open circles
represent samples G7–G10 and are in early coalescence phase, solid
squares represent samples G11–G15 and are in the coalescence phase, and
open circles represent samples G16 and G17 and are in the cohesive
aggregation phase.
Fig. 3. SEM of Ga on GaAs(100) in pre-coalescence stage growth.
Sample G7, annealing time = 7 min.
3. Results
This section contains images which show, for the first
time, the existence of shape cycles in Ga on GaAs. The
images demonstrate that the clustering process includes a
transition from round to rectangular clusters in growth
where clusters are still comparatively small. The clusters
then go back to a round shape at intermediate sizes and fi-
nally the last stage of cluster formation shows a coexistence
of round clusters with rectangular ones.
The early shape cycle is shown in Figs. 2–5 where clus-
ters are initially small and round as seen in Fig. 2 (sample
G2). In this sample, the areal coverage of Gas is
w = 1.65%. All clusters have round bases where the cluster
contacts the surface. This clustering is a typical pattern of
those observed in other liquid film systems such as Sn/Si
[6,7]. The next two images, Figs. 3 and 4, show the rectan-
gular phase of the early stage shape cycle. These figures
Fig. 4. SEM of Ga on GaAs(100) in pre-coalescence stage growth.
Sample G8, annealing time = 7 min.
Fig. 2. SEM of Ga on GaAs in pre-coalescence stage growth. Sample G2,
annealing time = 5 min.
Fig. 5. SEM of Ga on GaAs in early coalescence stage growth. Sample
G12, annealing time = 3 min.

K. Shorlin, M. Zinke-Allmang / Surface Science 601 (2007) 2438–2444
2441
have clusters have areal coverages of w = 20.8% and
w = 25.5% for runs G7 and G8, respectively, indicating
that the clustering process is further along than in the sam-
ple shown in Fig. 2. In both figures, clusters have a rectan-
gular interface but rounded clusters are stretched over the
rectangular base. That this is the case is particularly evident
in Fig. 4. In this figure, there are several places where two
clusters have touched, merged, and the cluster has retracted
exposing a rectangular shaped pit under the retracting
cluster.
We discuss quantitatively below why the rectangular
shaped pit is responsible for the shape of the cluster as
the liquid cluster clings to the edge of the pit resulting in
a rounded cluster with a rectangular base. We also empha-
size that samples shown in Figs. 2–4 stretch the entire early
stage phase of phase separation in the Ga/GaAs system.
This is evident from the w values when compared with
the surface phase diagram, Fig. 1 and is morphologically
evident from the onset of cluster merges in Fig. 4. The sam-
ple in this figure can be seen as in transition to the late
stage, but the late stage has not been reached as clusters
merging does not yet dominate the cluster size distribution
for this sample.
Fig. 7. SEM of Ga on GaAs in cohesive aggregation stage growth. Sample
G16, annealing time = 5 min.
In the late stage, repetitive shape cycles are shown in
Figs. 5–8. These figures show that as the clustering pro-
ceeds, the rectangular features of the clusters diminish so
that while some rectangular nature is present, most clusters
at any given time take on a more rounded shape. This is
shown in Fig. 5 where there are larger clusters and the sur-
face has an areal coverage of w = 43.3% indicating that the
cluster growth is now in late stage and growth is via coales-
cence. This figure shows that while some clusters have par-
tially straight edges, all clusters have rounded corners. The
small clusters present are either round or rectangular or a
combination of both as are freshly exposed subcluster
depressions. This figure shows a transition in the shape
cycle where clusters go from rectangular to round.
Fig. 8. SEM of Ga on GaAs in cohesive aggregation stage growth. Sample
G16, annealing time = 5 min.
The next figure, Fig. 6 is later in the clustering process
with w = 51.7% and the majority of all clusters are
rounded or elliptical as are the pits exposed after a coales-
cence event. This figure shows that the shape cycle repeats
in recently clearly depressions. In the depressions, some of
the larger secondary clusters have rectangular features
while smaller secondary clusters are round. Some of the
smaller recently exposed pits are also rectangular indicating
the new beginning of the early shape cycle in clusters which
have not yet begun to grow via coalescence.
The final three figures, Figs. 7–9 are from the same sam-
ple, G16, which has cluster growth via coalescence with an
areal coverage of w = 56.6%. The scale of each image is
shown in the lower right hand corners. Fig. 7 shows clus-
ters which are all round or elliptical with very few excep-
tions where clusters have a rectangular edge. The next
two figures, Figs. 8 and 9 show examples of the final stage
of the shape cycle where rectangular depressions are
Fig. 6. SEM of Ga on GaAs in coalescence stage growth. Sample G15,
annealing time = 5 min.

2442
K. Shorlin, M. Zinke-Allmang / Surface Science 601 (2007) 2438–2444
of the two cluster shapes. At the point where the stretched,
rectangular based cluster detaches from the edge of the
depression to form a spherical cap shaped cluster, the ener-
gies of the two clusters must be equal, i.e.,
Er ꢀ Es ¼ 0
ð1Þ
where Er is the energy of the rectangular based cluster and
Es is the energy of the spherical cap cluster. The two differ-
ent shaped clusters will have identical volume at the point
of detachment therefore, we may equate the surface ener-
gies of the clusters. The energy of the spherical cap cluster,
with radius r of the contact circle and height h is
Es ¼ csvðA ꢀ pr2Þ þ ccspr2 þ ccvð2pRhÞ
ð2Þ
where A is the area of the substrate, csv is the surface ten-
sion between the surface and vacuum, ccs is the surface ten-
sion between the cluster and the substrate, ccv is the surface
tension between the cluster and the vacuum. The surface
energy of the rectangular based cluster in a depression of
depth d is
Fig. 9. SEM of Ga on GaAs in cohesive aggregation stage growth. Sample
G16, annealing time = 5 min.
exposed after a cluster detached from the edges. These clus-
ter would have had the same rectangular base as the clus-
ters in the early stages of the shape cycle. Fig. 8 is an
image of a cluster which was initially attached to the edges
of the rectangular pit which detached once the energy of
maintaining the rectangular base became too large. After
detaching, the cluster retracted to one corner of the rectan-
gular depression forming a partial spherical shape with two
straight edges. Fig. 9 shows the shape cycle in a different
way: This image shows a coalescence event where two large
clusters touched and the retracting cluster revealed a rect-
angular subcluster depression.
Er ¼ csvðA ꢀ abÞ þ ccsðab þ 2ad þ 2bdÞ þ ccvS
ð3Þ
where S is the surface area, and a and b are the dimensions
of the rectangle. The surface area of the rectangular based
cluster may be determined, either by measurement or
´
numerical methods [8]. We may also use the Young–Dupre
equation
csv ¼ ccs þ ccv cos h
ð4Þ
to provide another constraint on the surface tension on a
system with angle h between the cluster and the surface.
Combining these equations with a known surface tension
between the cluster and vacuum [9] provides a method of
determining the unknown surface tensions between the
cluster and surface and the surface and vacuum.
4. Discussion
The shape cycle is a result of the subcluster etching
which occurs after clusters form on the substrate. Initial
clusters form once enough material is gathered. Clusters
are initially spherically capped in shape as this is the most
energetically favourable shape. Arsenic loss then continues
faster through the cluster than from the surface so that ini-
tial subcluster depressions are round. As etching continues,
rectangular pits form as certain low Miller index planes
have slower etching rates than high index planes. The bot-
tom plane is a 100 direction (parallel to surface) and has a
very low etching rate. A favourably low interfacial energy
causes the cluster to cling to the edges of the rectangular
pit, stretching out the bottom of the cluster and causing
a change from the spherically capped shape. Because the
cluster has deviated from the spherical shape, it no longer
has minimum surface to volume ratio. Eventually the rect-
angular shape is energetically unfavourable at which point
the cluster will detach and form a partial sphere, typically
in the corner of the pit. Subcluster etching begins under
the reshaped cluster and the shape cycle repeats.
We note that these shape cycles are observed only in a
narrow temperature interval for Ga/GaAs. This indicates
that a full cycle requires a certain ratio of subcluster etch-
ing rates and cluster growth rates. When clusters grow too
fast, etching is subdued and late stage coalescence growth
occurs unaffected by etching-related processes. If clusters
grow too slowly, etching would dominate, but even without
etching, a proper late stage coalescence growth may be
reached only after a period too long for the technical lim-
itations of the experimental study. Concurrent but domi-
nating etching would further disable the occurrence of a
late stage coalescence growth as clusters would not reach
a sufficient areal coverage to touch and merge frequently.
Based on our experimental observations, we note that the
etching and growth length scales in the Ga/GaAs system
are such that full cluster shape cycles are confined to a nar-
row parameter window sensitively depending on both time
and temperature. The experiments show clusters in the
samples with values of w = 20.8, 25.5, and 25.8% have rect-
angular based shapes. The aspect ratio of clusters in these
samples were measured and found to have a constant value
of 1.32 0.13 [8]. Samples with values of w 6 12.7% have
Information about the surface energies of the system
may be determined by consideration of the surface energies

K. Shorlin, M. Zinke-Allmang / Surface Science 601 (2007) 2438–2444
2443
round clusters and samples with w P 37.1% have primarily
round clusters with some associated rectangular features.
As w has a dependence on both temperature and time, it
cannot be used as a sole parameter to determine the per-
centage of clusters with rectangular features.
With the observation of the cycle in Ga/GaAs we can
now connect this shape cycle with observations made in
the In/InP system in which a late stage shape cycle was ob-
served as clusters repeatedly transitioned between round
and rectangular. This connection allows us to demonstrate
that shape cycles are common at least to Group III–V semi-
conductor systems which show cluster growth via coales-
cence during the loss of the Group V element. In on
InP(001) was studied experimentally in our group [4] and
the results pertinent to our case are highlighted below.
The system studied was In on InP(001) at 500 15 °C
and at this temperature, the cluster growth is via coales-
cence. Cluster formation and growth proceed via the same
mechanism as outlined above: Above the decomposition
temperature there is a continuous loss of P resulting in a
supersaturation of In at the surface. The system then enters
the phase separating regime where clusters grow through
coalescence. Fig. 10 is an SEM micrograph of an In on
InP surface after annealing at 500 °C for 10 min. Present
in this figure are both large and small clusters and the mea-
sured cluster size distribution [4] indicates the bimodal nat-
ure of the cluster size distribution predicted by the theory
[10] and indicate that the cluster size distribution follows
a self similar growth like that observed in Ga on GaAs
[7]. Also observed in this system was a distinct deviation
from rounded cluster shapes and this is seen in Fig. 10
where a minority of the clusters have a rectangular nature
either having a rectangular shape or one or more rectangu-
lar edges in the contact between the surface and cluster.
The clusters with rectangular features were observed to
contribute an estimated 10% of the clusters present on the
surface. By consideration of the cluster size relative to
annealing time, it was seen that cluster size increases mono-
tonically with time. This increase of cluster size with time,
together with observations of multiple rectangular pits asso-
ciated with a single round cluster as seen in the centre panel
of Fig. 10 indicates that there is an oscillating shape cycle be-
tween round and rectangular based clusters in In on
InP(001) which occurs during the sample annealing period.
A quantitative analysis of the cluster shape cycle was
also provided with consideration of the etching rates as
the subcluster depressions form during cluster growth.
Depressions under clusters occur commonly in Group
III–V compound semiconductors and this is illustrated in
Fig. 11. In the top panel of this figure, it is seen that the
subcluster depression is shallow compared to both the
other dimensions of the depression and the cluster itself.
The bottom panel, showing the surface after the Indium
clusters have been chemically removed, indicates the coex-
istence of round and rectangular depressions. Further seen
in this image from the contrast at the edges, is that the rect-
angular depressions appear deeper than the round ones.
Fig. 10. SEM of In on InP(001) after annealing at 500 °C for 10 min [4].
The three images show two features of the cyclic shape changes. The first
feature is that approximately 90% of the clusters are partially spherical
with diameters of up to 10 lm. The second feature is that approximately
10% of clusters are associated with rectangular features either in the
cluster itself as indicated by the arrows or in the underlying depression as
indicated with the R.
Round depressions have been observed in other III–V
compound semiconductors and the origin of the depres-
sions in the Ga on GaAs has been discussed [1]. The same
reasoning applies to depressions in In on InP and clustering
phenomena on other decomposing III–V compound semi-
conductors. As the annealing proceeds there is a competi-
tion between the loss of the Group V element (P or As)
via two processes (i) through bulk diffusion through the
semiconductor and subsequent desorption from the surface
and (ii) dissolution of the compound semiconductor into
the growing group III cluster, followed by diffusion of
the group V element to the cluster surface and desorption
from that surface. Consideration of the thermodynamic
data available for InP shows that the P loss is faster from
areas beneath clusters [4].

2444
K. Shorlin, M. Zinke-Allmang / Surface Science 601 (2007) 2438–2444
This cycle was seen for certain large clusters at least to have
been traversed twice during the time of the experiment
(10 min).
This observation is fundamentally important in that a
similar cycle has been observed in another Group III–V
semiconductor system and thus the shape cycle is seen to
occur not as an isolated phenomenon but as part of a non-
linear nonequilibrium thermodynamic physical process.
5. Conclusion
We have presented an experimental study of cluster
growth of Ga on GaAs(100). A shape cycle has been ob-
served and is a result of subcluster etching where faster loss
of material through a cluster results in an underlying
depression. The subcluster etching further introduces an-
other length scale in the system which causes the break-
down in self similarity on the cluster size and spatial
distributions.
Acknowledgement
Fig. 11. SEM of In on InP(001) after annealing at 500 °C for 10 min [4].
(a) is a cross sectional image of an In cluster in a subcluster depression.
The image shows that the depression has rectangular features (as seen in
Fig. 10) with a rounded cluster in one corner of the depression. (b) is the
InP surface after the In clusters have been removed chemically. This image
illustrates the evolution of the shape as after the cluster retracts from the
rectangular base the etching begins again under the new round cluster.
The authors gratefully acknowledge the support of
NSERC.
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