Physica B 248 (1998) 1—8
Epitaxial clusters studied by synchrotron X-ray diﬀraction and
scanning tunneling microscopy
M. Nielsen *, R. Feidenhans’l , F. Berg Rasmussen , J. Baker , G. Falkenberg ,
L. Lottermoser , R.L. Johnson , A.J. Steinfort , P.M.L. Scholte
Ris~ National Laboratory, DK-4000 Roskilde, Denmark
II Institut fur Experimentalphysik, University of Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany
Department of Applied Physics, Delft University of Technology, NL-2600 GA Delft, The Netherlands
Nanoscale clusters are often formed during heteroepitaxial crystal growth. Misﬁt between the lattice parameter of the
substrate and the adsorbate stimulates the formation of regular clusters with a characteristic size. The well-known
“hut-clusters” formed during the growth of Ge on Si(0 0 1) are a good example of this type. Adsorbates can also produce
another type of nanocluster; if the surface free energy of a particular crystallographic plane becomes lower than that of
the geometrical surface of the substrate, then the entire surface will break up into regular arrays of small facets which look
similar to the “hut clusters”. We demonstrate that X-ray diﬀraction in combination with scanning tunneling microscopy
can be used to determine the fundamental properties of such clusters. 1998 Elsevier Science B.V. All rights reserved.
Keywords: Nanoclusters; X-ray diﬀraction; STM
1. Introduction interface. In between these regimes a special type of
small clusters are formed at substrate temperatures
The lattice constant of Ge is 4% larger than that below 530 K. They are small regularly shaped dis-
of Si. When Ge is grown on a Si(0 0 1) substrate location-free islands called “hut clusters” which are
then the ﬁrst 2—3 layers will form pseudomorphic depicted in Fig. 1a. All of the facets correspond to
layers which accommodate the lateral compres- +1 0 5, planes and with the proper preparation
sional strain. For thicker ﬁlms nucleation of three conditions the huts are nearly monodisperse in
dimensional islands sets in and the misﬁt is accom- width and height, but they have variable length.
modated by dislocations at the island/substrate Apart from elastic strain relaxation their internal
structure is a continuation of the Si-substrate lat-
tice. For an eﬀective coverage of 8 ML it is found
that the huts almost cover the substrate entirely.
* Corresponding author. Fax: (45) 42 37 01 15; e-mail: The hut clusters were ﬁrst observed by Mo et al.
Mourits.Nielsen@Risoe.dk. , and since then STM measurements have
0921-4526/98/$19.00 1998 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 1 9 3 - 8
2 M. Nielsen et al. / Physica B 248 (1998) 1—8
revealed that similar nanoclusters are common in spected by STM. Best results were obtained with
other systems as well [2—9]. For example, depos- a deposition rate of 0.6 ML/min and a substrate
ition of about a monolayer of In on a Ge(0 0 1) temperature of 430°C (see Fig. 1a).
surface followed by heat treatment at 350°C pro- For the In/Ge(0 0 1) samples, In was evaporated
duces the regular facetted surface shown in Fig. 1b. onto the clean Ge(0 0 1) surface at room temper-
Here all the facets are +1 0 3, planes, the height and ature until at about 1 ML the RHEED spots of the
width of the huts are about 11 and 65 A, respecti- fractional order (4;3) superstructure reached max-
vely. The surface morphology can be varied to imum intensity. On annealing RHEED reﬂections
some extent by altering the substrate temperature characteristic of the +1 0 3, facets appeared. Sys-
and deposition conditions. By optimizing the con- tematic STM investigations revealed that the
ditions, regular arrays of long huts can be produced shape, size, and density of the facets depend criti-
. This is an example of nanofacetting. cally on the temperature. The samples used in these
The last system we will discuss are the internal measurements were annealed at 350°C for 5 min,
facets which form when Cu ﬁlms with thicknesses which produced a surface completely covered with
up to 20 ML grow epitaxially on Ni(0 0 1). The long huts of uniform width as shown in Fig. 1b.
model for the internal facets proposed by Muller ¨ Desorption of In beyond a critical coverage of
et al.  on the basis of STM studies is shown in 0.5 ML at temperatures around 500°C causes the
Fig. 1c. Here the Cu ﬁlm is pseudomorphic with the clusters to decompose and the Ge(0 0 1) surface is
Ni substrate except for the Cu atoms inside the reestablished.
wedge-shaped clusters. These are bounded by The Cu/Ni(0 0 1) samples were prepared follow-
+1 1 1, planes towards the surrounding Cu ﬁlm and ing the prescription given by Muller et al. . For
by a +0 0 1, plane upwards. The atoms inside the Cu coverages from 1 to 20 ML the clusters appear
wedges are translated half a nearest neighbour dis- with the same density, the clusters simply grow in
tance along the axis of the wedges and about 0.5 A maximum width because the number of rows of
upwards, thereby opening some space for strain atoms in the top layer of the wedge equals the
relaxation. For the three systems illustrated in number of atomic layers in the Cu ﬁlm. The wedge
Fig. 1 we will show how synchrotron X-ray diﬀrac- shaped clusters have their long axis parallel to the
tion can be used to measure the fundamental struc- 11 1 02 direction of the Ni crystal. At monolayer
tural properties. coverage the “clusters” are single rows of atoms
and at 20 ML the clusters start to merge. We have
done diﬀraction measurements in the regime from
2. Measurements 5 to 20 ML .
All measurements were performed with the verti-
cal scattering diﬀractometer on the BW2 wiggler 3. Analysis
beam line at HASYLAB (DESY, Hamburg). The
samples were prepared in the STM Laboratory at We will now discuss the results of the X-ray
the nearby II. Institute fur Experimentalphysik,
¨ diﬀraction measurements. For the three systems
University of Hamburg. After preparation and Ge/Si(0 0 1), In/Ge(0 0 1), and Cu/Ni(0 0 1) we have
characterization with RHEED and LEED the sam- clusters bounded by +5 0 1,, +3 0 1,, and +1 1 1,
ples were studied by STM. Subsequently the facets respectively. This provides us with a conve-
sample was transferred into a portable small UHV nient method to selectively observe the diﬀraction
chamber with a hemispherical Be window which signal from the clusters, namely by measuring the
was mounted on the diﬀractometer for the X-ray crystal truncation rods (CTR) from these facets. As
measurements. a ﬁrst model we ignore scattering from the “end
For preparing the Ge/Si(0 0 1) samples Ge was gables” of the huts (since the length is much larger
deposited from a Knudsen cell onto a clean Si(0 0 1) than the width of the huts), and we assume the
surface. After deposition the hut clusters were in- internal structure to be a simple continuation of the
M. Nielsen et al. / Physica B 248 (1998) 1—8 3
Fig. 1. (a) STM image of Ge hut-clusters on Si(0 0 1), the area shown is 1000;900 A. The samples were prepared by depositing 6 ML
Ge on Si(0 0 1) at 430°C. (b) STM image of the In/Ge(0 0 1) sample after the formation of the +1 0 3,-facets. About 1 ML of In was
deposited on Ge(0 0 1) at room temperature followed by 5 min annealing at 350°C. (c) A model of the buried Cu clusters in Cu/Ni(0 0 1)
ﬁlms. The large gray circles represent 5 layers of pseudomorphic Cu atoms on the Ni substrate which is indicated by small black circles.
The large black circles represent the Cu atoms inside the wedge-shaped cluster, all displaced half a neighbour distance in the long cluster
direction and a little upwards.
substrate, except for Cu/Ni(0 0 1) which include gives a convenient reference frame and Figs. 2—4
also a uniform translation. As indicated in Figs. 2 show examples of measured diﬀraction results from
and 3 the CTRs from the facets are straight lines scans in symmetry directions across CTRs, and as
perpendicular to the facet planes extending from expected we get scattering peaks at the CTR posi-
each Bragg point of the internal structure. In this tions. The important point now is that the relative
picture we also ignore that the facets are not large intensities of the scattering groups from diﬀerent
compared to the wavelength. This simple model CTRs depend sensitively on the non-uniform strain
4 M. Nielsen et al. / Physica B 248 (1998) 1—8
Fig. 2. Measured and ﬁtted X-ray diﬀraction proﬁles for the Ge/Si(0 0 1) system around the (1 1 l), (2 0 l), and (4 0 l) reciprocal lattice
points of Si. The panel on the right illustrates how the scans cut through the CTRs. The strong asymmetry of the intensity in the (4 0 l)
scans is an eﬀect of non-uniform strain relaxation.
inside the huts, and this give us a ﬁrst order duce a lattice parameter a (z) allowing a homogene-
measure of the strain relaxation [12,13]. ous expansion in each atomic layer z described by
To analyze the data we assume a realistic model
for the cluster including the inhomogeneous strain z
a (z)a #(a !a ) ,
relaxation and calculate the diﬀraction response by W
summing the phase factor over all atomic positions.
In this way we can take into account ﬁnite size where h is the height of the hut. The vertical lattice
eﬀects, surface structures, and interference scatter- parameter is determined using the Poisson ratio
ing between diﬀerent huts. In the following we 0.28. Fair agreement with the complete set of
discuss the three systems in more detail. measured data is obtained with an onset relaxation
Fig. 2 show examples of measured data for the at the bottom of the hut of 0.5% and full relaxation
Ge/Si(0 0 1) system. The proﬁles have three (or ﬁve) (4% expansion) at the apex of the hut. This simpli-
peaks corresponding to three (or ﬁve) CTRs cross- ﬁed model does not include inhomogeneity within
ed in the scans. The central peak is the CTR from each layer or bowing distortions of the lattice
the (0 0 1) surface. This has contributions from the planes, but it has been suﬃcient for determining the
hut/substrate interface and from the pseudomor- dominant parameters of the non-uniform strain.
phic Ge layers between the huts, and interference The In/Ge(0 0 1) system was studied and ana-
between these. We do not include the central peak lyzed in much the same way. The samples used in
in the data analysis. In axial scans at high mo- the diﬀraction measurements were completely
mentum transfer q the asymmetry of the intensity covered with clusters of nearly uniform width and
is very pronounced (see the right-hand panel of with a high ratio of length to width. In Fig. 1b each
Fig. 2 with scans through the CTR from the (4 0 0)
stripe is a single hut cluster 65 A wide and 11 A
Bragg point). This asymmetry is an eﬀect of in- high. The volume of all clusters corresponds to
homogeneous strain relaxation and the full curves a coverage of 4 ML and thus they cannot be built
in the ﬁgure are the result of a ﬁtted model consist- up of In atoms. The STM measurement showed
ing of huts 300 A long and 130 A wide (9 atomic that the side of the clusters are +1 0 3, facets which
layers high). Along the long axis we use no strain consist of narrow +0 0 1, terraces separated by
relaxation but along the short (130 A) side we intro- single atomic steps. Fig. 3a show examples of the
M. Nielsen et al. / Physica B 248 (1998) 1—8 5
Fig. 3. Diﬀraction results from the In/Ge(0 0 1) system. (a) Measured proﬁles in scans through the CTRs from the (2 0 2) Bragg point of
Ge. Notice the absence of the central peak and the relative symmetry of the intensities. (b Measured proﬁles near the Ge(4 0 0) reﬂection
which illustrate the strong interference scattering. (c) sketch of the scans through the CTRs in panel (a). (d) model of the In covered
11 0 32 facets. The large open circles are In atoms, and the smaller grey shaded circles are Ge atoms at diﬀerent heights. Each In atom
saturates three dangling Ge bonds.
6 M. Nielsen et al. / Physica B 248 (1998) 1—8
Fig. 4. Measured and ﬁtted X-ray proﬁles for the Cu/Ni(0 0 1) system. Here LEED notation is used for (h k l) so that [1 0 0] is parallel to
the long cluster axis. The left hand panel show transverse scans through (1 0 l) points, and the insert shows the small intensity in
transverse scans through (h 0 l) when h is even. The right hand panel presents longitudinal (axial) scans through (1 0 l), and illustrates the
strong asymmetry of the scattering intensity.
diﬀraction results. The ﬁrst point to observe here is An interesting aspect of the In/Ge(0 0 1) system is
that there is no central peak corresponding to the the ordering of the huts. We observe, most dramati-
CTR from a substrate/adsorbate interface and thus cally in the nearly in-plane scans, the interference
the huts are simply a continuation of the Ge sub- scattering in the diﬀraction measurements. This is
strate crystal. The role of the In atoms is to ener- shown in Fig. 3b. The single hut scattering provides
getically stabilize the +1 0 3, surfaces. So, where a form factor for the scattering and this completely
strain relaxation was the important mechanism for dominates the picture for Ge/Si(0 0 1). For
understanding the growth of the Ge/Si(0 0 1) hut In/Ge(0 0 1) this form factor is multiplied with
clusters, the surface energy is here the important a line spectrum given by the superlattice of the huts
factor. Complete sets of diﬀraction scans were mea- and the width of each line is given by the range of
sured through the CTRs within the instrumental ordering in the superlattice, which is around
range and the measured proﬁles compared to
1000 A. For increasing vertical momentum transfer
model calculations as above. Now, to a ﬁrst ap- the eﬀect become less important but it is noticeable
proximation, the scattering intensity is symmetrical throughout the zone and is included in the model
around the central position (the non-existing cen- calculations.
tral rod) signaling little or no strain in the huts. The last system, Cu/Ni(0 0 1) is quite diﬀerent
However, the relative intensity of the two side again. Now we have huts of Cu buried in Cu
peaks on each side is very sensitive to the occu- and they are upside down with the apex to-
pancy of the In atoms. Combining the STM and wards the substrate. However, for the diﬀraction
diﬀraction results we arrive at the model shown in measurements we have a quite analogous situation.
Fig. 3d. Each In atom bonds to three Ge atoms and We use the CTRs from the clusters and analyze the
saturates all of the Ge dangling bonds, [14—16]. By strain by ﬁtting the measured scan proﬁles with
ﬁtting the diﬀraction results we determined the In model calculations. The clusters are conveniently
coordinates. made visible in diﬀraction by the homogeneous
M. Nielsen et al. / Physica B 248 (1998) 1—8 7
translation of the whole wedge by half a neighbour b 1.0, 0.07, and n 7 in Ni lattice units.
distance in the direction of the long axis 11 1 02 (see The vertical lattice spacing inside the huts follow
Fig. 1c). If the translation is r we have for the layer by layer that of the ﬁlm outside the huts and it
scattering function of the homogeneous ﬁlm plus is 4% expanded relative to the Ni spacing. The
wedges: homogeneous vertical translation of the wedges is
determined to be 0.5 A and it is the same for all
F(q)f (q)#f (q)(e q r!1) thicknesses. At ﬁlm thicknesses around 20 ML the
lateral lattice spacing in the huts approaches that of
where q is the momentum transfer, f the scatter-
the Ni lattice and this type of cluster formation
ing function of a complete pseudomorphic ﬁlm, and
becomes ineﬀective in relaxing the strain energy. At
f that of the wedges. This is like an antifer-
the same time the wedges begin to merge and the
romagnet and considering q components along r
growth pattern changes.
we have constructive (destructive) interference for
It was observed in the data analysis that the
odd (even) reciprocal lattice numbers. For this
positions of the side peaks from the +1 1 1, facets
argument we have neglected the small component
do not follow closely the straight lines given by the
of r in the vertical direction.
CTRs of +1 1 1, surfaces, but instead the ﬁtted
Fig. 4 show examples of measured diﬀraction
midpoints follow lines not going through the Bragg
proﬁles for the Cu/Ni(0 0 1) system. They conﬁrm
points. This behaviour was duplicated nicely in the
the essential points of the model proposed by
calculation for the model cluster and is due to the
Muller et al. . The side peaks and their shift in
ﬁnite size of the clusters .
position with the vertical momentum transfer
l show the existence of the +1 1 1, facets and as
illustrated by the insert the transverse scans with
even indices have insigniﬁcant intensity conﬁrming
the half neighbour distance translation. The asym-
We have proved that surface X-ray diﬀraction in
metry of the scattering intensity around the central
combination with STM is an eﬀective technique for
position is dramatic in the longitudinal (axial)
measuring the internal structure of hut clusters.
scans. Again this is an eﬀect of the non-uniform
The regular shape of these clusters allows the scat-
strain inside the clusters. A good global ﬁt to all
tering from the huts to be distinguished from that of
measured data is obtained with a model having
the substrate and coexisting adsorbed ﬁlms by fo-
lateral strain relaxation of the atomic layers inside
cussing on the scattering from the CTR from the
the clusters only. The ﬁrst few layers near the apex
sloping facets. The intensity of this scattering is
of the huts are fully laterally relaxed to the natural
sensitively dependent on small deviations in the
Cu spacing and the strain increases with height
positions of the atoms in the clusters from the
above the substrate. We have used
extrapolated substrate lattice and is therefore
n a good measure of non-uniform strains. The small
b(n)b # ) exp! ! , size of the clusters makes it simple to compare the
scattering with that from model clusters. A natural
where b(n) is the lateral lattice parameter of layer n, extension of the present analysis would be to calcu-
the extra relaxation at bottom (n0) and late the shape of the clusters by applying elasticity
theory or for the semiconductors the Keating
n a ﬁtted decay length. For a 9 ML ﬁlm we ﬁnd
model , and comparing the calculated diﬀrac-
tion signal with the measured X-ray data. Such
an analysis would allow a more detailed descrip-
tion of the huts including parameters not discussed
Because the Cu clusters are aligned parallel to the axes of the
(1;1) Ni surface structure we apply here LEED notation for the
in this paper such as substrate deformation, be-
in-plane q-component, which means that the (h, 0, l,) coordi- nding of the atomic layers, or nonuniformity within
nates equals the (h, h, l,) of the 3D reciprocal lattice of Ni. individual layers, and altogether further improve
8 M. Nielsen et al. / Physica B 248 (1998) 1—8
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