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Applied Surface Science 244 (2005) 65–70
Surface elemental segregation and the Stranski–Krastanow
epitaxial islanding transition
A.G. Cullis*, D.J. Norris, M.A. Migliorato, M. Hopkinson
Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Received 17 June 2004; accepted 18 October 2004
Available online 13 January 2005
Abstract
It is shown that a new segregation-based mechanism underpins the Stranski–Krastanow (S–K) epitaxial islanding transition
in both the InxGa1�xAs/GaAs and Si1�xGex/Si systems over wide ranges of growth conditions. Quantitative segregation
calculations allow critical ‘wetting’ layer thicknesses to be derived and, for the InxGa1�xAs/GaAs system (x = 0.25–1), such
calculations show good agreement with experimental measurements. The segregation-mediated driving force is considered to be
important, also, for all other epitaxial systems which comprise chemically similar but substantially misfitting materials and
which exhibit the S–K transition.
# 2004 Elsevier B.V. All rights reserved.
Keywords: Epitaxy; Stranski–Krastanow transition; Islanding transition; Quantum dot
1. Introduction
Epitaxial films grow upon crystalline substrates by
one of three mechanisms: (i) 2D layer-by-layer growth
(Frank and Van der Merwe [1]), (ii) 3D island growth
(Volmer and Weber [2]) and (iii) 2D layer growth
followed by 3D islanding, (Stranski and Krastanow
(S–K) [3]). For systems with zero or small lattice
mismatch, 2D layer-by-layer growth typically occurs,
while for systems with highly mismatched and
dissimilar materials 3D island growth usually takes
* Corresponding author.
E-mail address: [email protected] (A.G. Cullis).
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved
doi:10.1016/j.apsusc.2004.10.066
place. For epitaxial systems with similar materials and
high lattice mismatch, the two-stage S–K growth
mode usually occurs. Here, a very thin, flat epitaxial
layer is formed first and a transition to 3D island
growth takes place at a certain critical thickness. This
growth mode has received experimental study across
wide materials areas from metals to semiconductors
(ref. [4] describes early work). For semiconductors,
the transition has assumed importance since the
islands formed can be exploited as quantum dots in
advanced electronic devices. Therefore, many semi-
conductor epitaxial systems exhibiting the S–K
growth mode have been studied in-depth, including
InxGa1�xAs/GaAs [5–11], InP/InxGa1�xP [12,13],
GaSb/GaAs [14] and SiGe/Si [15–20].
.
A.G. Cullis et al. / Applied Surface Science 244 (2005) 65–7066
Fig. 1. Variation in critical thickness of the initial flat layer for the
islanding transition as a function of deposition flux In concentration:
measured values are data points and predicted WCNH values are
presented as continuous curve (after [31]).
2. The basic mechanism of the Stranski–
Krastanow transition
Theoretical models based upon energy calculations
and rate equations [21–28] have been formulated in
order to attempt to explain the features of the 2D–3D
S–K transition. It is generally considered that, when
2D islands exceed a critical size, they should
transform into 3D islands and this has been employed
to model the transition. Nevertheless, the fundamental
driving force for the transition had not been
determined [29] until recent studies of Walther
et al. [30] and Cullis et al. [31] threw new light upon
the mechanism relating to growth of the initial wetting
layer and the critical thickness which it must attain
before the islanding transition occurs. Detailed
measurements [30] of S–K island and ‘wetting’ layer
composition were performed for the InxGa1�xAs/
GaAs system. These measurements led to the proposal
[30,31] that the transition to island growth is
controlled by segregation of elemental In to the
surface of the initial flat crystalline ‘wetting’ layer
(referred to here as the WCNH mechanism). The
segregation-based mechanism is straightforward and
is fundamentally applicable to all materials systems
exhibiting the S–K transition (where the growth
technique does not significantly suppress segregation
– see below). It is considered here with special
reference to the InxGa1�xAs/GaAs system, with some
consideration also of the Si1�xGex/Si system.
In order to produce islands by molecular beam
epitaxy (MBE) in the InxGa1�xAs/GaAs system, either
an alloy or binary material (InAs) is deposited. As the
initial flat epitaxial layer forms, the WCNH mechan-
ism for the S–K transition specifies that the strain
introduced by the vertical segregation of the largest
atomic species (In) in the deposited material provides
the driving force for the transition. This In segregation
results in an increase in surface lattice parameter, as
observed by RHEED [32]. Also, the magnitude of the
strain has been estimated by atomistic simulation [31].
The segregation itself has been simulated using the
Fukatsu/Dehaese model [31,33,34], which considers
exchange of the Group III species between the top two
layers during growth and demonstrates that the surface
layer exhibits a very substantial deviation from the
deposition flux In concentration. If a relatively dilute
(x = 0.25) alloy is deposited, the surface monolayer
attains [31] a saturation value of 80–85% In for initial
layer thicknesses in excess of �2.5 nm. With
increasing deposition flux In concentration, the
surface In concentration increases progressively to
saturation values which, themselves, rise.
Under the WCNH mechanism, a critical surface
concentration of In (and associated strain) must build
up before the S–K islanding transition can take place.
Now, it has been shown [10] that a deposition flux of
25% In is approximately the lowest that will induce
the S–K transition. Therefore, it is possible to identify
the corresponding critical surface In concentration as
the above-mentioned figure, i.e., 80–85% In. It is then
predicted that, for any particular deposition flux, the
S–K transition will take place after the surface In
concentration rises to this critical level so that, using
the segregation model, it is possible to estimate [31]
the critical thickness for the transition of the initial flat
‘wetting’ layer to islanding as a function of deposited
In concentration. This procedure gives the continuous
‘theoretical’ curve in Fig. 1, which extends from
0.3 nm thickness for InAs deposition to �2.5 nm
thickness for a deposition flux of 25% In.
From cross-sectional images of MBE InxGa1�xAs/
GaAs islands it was shown [30] that, for an In
deposition flux concentration of 25%, the ‘wetting’
layer thickness was �3 nm. Similar observations have
been made [31] for growth with In deposition flux
concentrations of 35 and 55%, which have yielded
A.G. Cullis et al. / Applied Surface Science 244 (2005) 65–70 67
Fig. 2. Schematic illustration of variation of adatom number density during progression of S–K islanding transition.
critical ‘wetting’ layer thicknesses of �1.5 and
�1.0 nm, respectively. These experimental thick-
nesses are also plotted in Fig. 1, together with a
critical ‘wetting’ layer thickness of 0.4 nm (1.6
monolayers [11]) for InAs deposition.
It is clearly evident from Fig. 1 that the curves
derived from theory and experiment exhibit exactly
the same form and are displaced from one another by
no more than �0.1–0.5 nm. This small displacement
may result, at least in part, from neglect of any
induction period during island nucleation. Also, the
experimental values should be corrected for the loss of
near-surface In-rich monolayers during initial island
formation. In addition, it is possible that implementa-
tion of an enhanced multilayer segregation model [35]
would give an even closer fit to experiment. However,
the near coincidence of the curves lends strong support
for the importance of segregation in determining the
S–K 2D–3D transition point, as embodied in the
WCNH mechanism [30,31].
Fig. 3. Schematic illustration of free energy variation for surface
atomic clusters and stable islands during progression of S–K island-
ing transition.
3. Stranski–Krastanow transition details
3.1. General S–K transition phenomena for
InxGa1�xAs/GaAs
The S–K transition may be described in terms of
near-surface free energy changes. Based upon the
WCNH model, as the transition point is approached the
concentration of In in the surface layer tends towards its
maximum value driven by segregation. The large and
increasing strain in the uppermost crystal layer makes it
increasingly difficult for atoms from the deposition flux
to join this layer, so that the number density of adatoms
increases also, as indicated qualitatively in Fig. 2. The
thermodynamic features of this process are illustrated
in Fig. 3 where the free energy of the initial array of
adatoms and atomic clusters at first rises (A–B) due to
the increasing adatom concentration and the increasing
number density of unstable growth nuclei. However, as
ever larger nuclei are formed, at some point critical
nuclei appear (point C on the curve in Fig. 3), the
expansion of which leads to the formation of stable
islands. The growth of the latter, which are very effec-
tive sinks for adatoms, leads to a rapid decrease in
A.G. Cullis et al. / Applied Surface Science 244 (2005) 65–7068
adatom number density (right-hand side of Fig. 2) and a
corresponding rapid decrease in surface free energy
(right-hand side of Fig. 3) with the production of a
stable state for the system having 3D islands. At the
actual S–K transition point, the overall surface
structure is very strained and, as observed for the
InxGa1�xAs/GaAs system [36], the general disorder
together with the high adatom number density (the peak
in Fig. 2) can lead to the production of a poor RHEED
pattern. It has even been proposed elsewhere that, at the
precise transition point, the surface may actually melt
[37] and/or a ‘floating layer’ of InAs or metallic In may
be produced [38,39]. There is no direct evidence for
such gross surface changes at the present time (indeed,
in the SiGe/Si system, in situ STM work [40] shows
that surface atomic order is retained at the S–K
transition point (see below)) and, in any case, it is not
clear how melt formation would lead to island growth
on an otherwise flat surface. However, a suitably
increased adatom concentration would lead directly to
island nucleation and growth.
The increased surface strain energy, resulting from
the segregation-induced elevated surface In concen-
tration, has a pronounced effect upon layer surface
growth structures in the InxGa1�xAs/GaAs system. For
example, for a low deposition flux In concentration of
15%, the layer-by-layer growth results [10] in the
formation of a very flat surface with evenly spaced
monolayer (ML) surface steps and few, if any, ML
islands. However, an increase in the deposition flux In
concentration to 20% results [10] in a change in
surface step configurations with the formation of
narrow protuberances at step fronts and the production
of many ML islands. The step front distortions would
be expected to yield elastic relaxation by unidirec-
tional expansion across the narrow protuberances. The
ML islands are the expected [22] precursors of 3D
islands produced by the S–K transition when the
deposition flux In concentration is further increased to
25%. Similar ribbon-like wetting layer surface
structures are seen in other systems (e.g., AlSb/GaAs,
GaSb/GaAs and InSb/GaAs) for layers undergoing the
S–K islanding transition [14].
3.2. The S–K transition in other epitaxial systems
Growth in the Si1�xGex/Si epitaxial system has
been studied by many workers [15–20] and it is
important to consider the nature of the islanding
transition. Indeed, it has been shown [17,20,41] that,
for the growth of Ge on Si, the initially deposited
monolayers are flat and exhibit scattered pits or
trenches. At a critical thickness, the S–K transition
occurs by the nucleation of islands (generally ‘hut
clusters’) located at the edges of the pits, while the
layer between the islands remains flat and displays a
regular lattice structure [20,40,41]. This appears to be
an S–K transition with the same characteristics as
that which occurs by the WCNH mechanism for
InxGa1�xAs/GaAs; however, Ge segregation is clearly
involved, while the distribution of the islands pro-
duced is simply determined by preferred nucleation
sites at edges of the pre-existing pits.
It has been indicated that, for Si1�xGex alloy
growth on Si under a restricted range of conditions,
island formation may take place due to an Asaro-
Tiller-Grinfeld (ATG) instability [19,42–44]. There-
fore, it is crucial to confirm the island formation
mechanism for Si1�xGex alloy layer growth. Focusing
first upon MBE, deposition of the alloy on Si has been
carried out [45] for a range of layer thicknesses,
followed by studies of the growth morphology using
the atomic force microscope (AFM). Growth of layers
with x-values of 0.3 and 0.5 has demonstrated that the
islanding mechanism has fundamentally the same S–K
nature as for basic Ge/Si. This is illustrated in Fig. 4
which shows a layer with x = 0.3 at mean deposit
thicknesses of 2.5 and 10 nm. It is clear that, at 2.5 nm
thickness, the overall layer is very flat but exhibits an
array of shallow flat-bottomed pits (the dark features).
However, at this thickness, island formation has
already taken place such that all the islands (the bright
features) lie along pit edges. Indeed, the general
growth behaviour seems to be of the type which
yielded ‘quantum fortress’ structures seen for lower
temperature growth [46]. When the mean deposit
thickness is increased to 10 nm, the islands have
grown substantially larger and have increased in
number density. Most importantly, there is no
evidence for an ATG instability (see Fig. 4a), which
would induce rippling of the whole surface. Therefore,
we may say that, for MBE growth and over at least the
range x = 0.3–1, the morphological characteristics of
islanding in the Si1�xGex/Si system are as expected for
a standard S–K transition. In possible contradistinc-
tion, for growth of Si1�xGex/Si by chemical vapour
A.G. Cullis et al. / Applied Surface Science 244 (2005) 65–70 69
Fig. 4. AFM images of Si0.7Ge0.3 alloy layers grown on (0 0 1) Si at 700 8C by MBE at layer thicknesses of (a) 2.5 nm and (b) 10 nm.
deposition (CVD), it has been reported [19] that an
S–K transition to island formation occurs for x > 0.6,
while for 0.2 < x < 0.6 an ATG (nucleationless)
instability leads to island growth. The latter may
occur due to the presence of hydrogen surfactant
which would be expected [47] to partially suppress Ge
segregation processes. More studies are required in
this area.
The experimental work described here relates
primarily to MBE growth of strained layers showing
the S–K islanding transition in the InxGa1�xAs/GaAs
and Si1�xGex/Si systems. However, many other MBE-
and CVD-grown epitaxial systems of similar materials
with high misfit exhibit the S–K transition. It is
conjectured that, in most if not all cases, the WCNH
mechanism involving elemental segregation is likely
to underpin the initial island formation process.
4. Conclusions
The manner in which the WCNH segregation
mechanism is expected to drive the S–K islanding
transition is considered in detail. Across the complete
range of deposition fluxes for MBE growth of the
(0 0 1) InxGa1�xAs/GaAs epitaxial system, there is
excellent agreement between theory (involving in
segregation) and experiment regarding derivation of
critical ‘wetting’ layer thickness. This gives strong
support for the segregation-based mechanism. Further-
more, the morphological characteristics of the initial
growth of Si1�xGex/Si for both MBE and ranges of
CVD deposition show the same features of S–K
islanding and are expected to be similarly driven by Ge
segregation. It is considered that, for all other epitaxial
systems exhibiting the S–K transition, when elemental
segregation within the ‘wetting’ layer is not suppressed,
such segregation will be a key factor determining the
critical point at which islanding occurs.
Acknowledgements
Dr T. Grasby is thanked for Si1�xGex/Si growth and
EPSRC is thanked for financial support. Extremely
helpful discussions with Profs. B.A. Joyce, A.
Madhukar, I. Goldfarb and J. Tersoff are gratefully
acknowledged.
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