Growth shapes of Ag crystallites on the Si„111… surface
W. X. Tang
Department of Physics, The Hong Kong University of Science and Technology, Hong Kong and Department
of Physics, Fudan University, Shanghai, China
K. L. Man
Department of Physics and Institute of Nanoscience and Technology, The Hong Kong University of Science
and Technology, Hong Kong
Hanchen Huang and C. H. Woo
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong
M. S. Altmana)
Department of Physics and Institute of Nanoscience and Technology, The Hong Kong University of Science
and Technology, Hong Kong
共Received 14 May 2002; accepted 30 September 2002兲
Kinetically limited growth shapes of Ag crystallites on the Si共111兲 surface have been studied by low
energy electron microscopy and diffraction. Triangular hexagons are predominant with the 共111兲
plane parallel to the substrate. The major side facets are determined by facet diffraction spot analysis
to be 兵100其. Absence of facet diffraction spots from the minor side facets suggests that they may be
the more steeply inclined 兵 11̄1 其 or 兵 12̄1 其 orientations. Preliminary evidence is also obtained that
codeposition of In causes the steeper side facets to dominate the growth shape. © 2002 American
Vacuum Society. 关DOI: 10.1116/1.1523372兴
I. INTRODUCTION
Advances in the fabrication of nanostructures and devices
depend largely upon the degree to which one can understand
and control the growth process. Growth shape and morphology will be affected, or even dictated, by kinetic limitations
that may be present during growth. One such limitation,
which has received a great deal of attention, occurs in growth
at surfaces when there is a Schwoebel–Ehrlich 共SE兲 diffusion energy barrier to atomic motion descending a monolayer
height step.1,2 It has recently been proposed that an analogous energy barrier is associated with atomic diffusive motion across the ridge that separates two facets on a threedimensional crystal.3,4 Conceptually, this so-called threedimensional 共3D兲 SE barrier stems from the reduced
coordination at the ridge. The relationship between this barrier, the SE barrier in two dimensions and a kink or cornercrossing barrier in quasi-one dimension has been pointed
out.5 Differences of the adatom formation energies on adjacent facets, which are linked to the coordination, cause the
3D SE barrier to be asymmetric. This asymmetry is expected
have an impact on growth shapes of 3D crystals beyond the
earlier concept that the growth rates of crystal faces is simply
proportional to their surface energies.6
In the present work, we have examined the growth shapes
of 3D Ag crystallites on the Si共111兲 surface using low energy
electron microscopy 共LEEM兲 and low energy electron diffraction 共LEED兲. Ag/Si共111兲 has been one of the most widely
studied metal–semiconductor systems.7–10 It is well known
that stable 3D Ag crystallites form on top of a twodimensional )⫻)R30° Ag wetting layer, i.e., following
the Stranski–Krastanov mode, above T⬃470 K. Orientation
of the crystallite 共111兲 facet parallel to the substrate results
a兲
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J. Vac. Sci. Technol. B 20„6…, NovÕDec 2002
from excellent epitaxy in this relationship. However, a kinetic growth shape is not well documented. Measurement
and careful characterization of the growth shape is crucial for
comparison to predictions that take the 3D SE barrier into
account. One of these predictions is that surfactants can alter
the growth shape through modification of the 3D SE barrier.
Therefore, we have also performed preliminary investigations of Ag crystallite growth with In codeposition.
II. EXPERIMENTAL DETAILS
The in situ experiments were carried out in a low energy
electron microscope with base pressure of 1⫻10⫺10 Torr.
The imaging principle and real-time capability of LEEM
have been described previously.11,12 The sample had a nominal miscut of 0.1° from the 共111兲 direction. Doping was n
type 共phosphorous兲 with resistivity 10 ⍀ cm. The sample was
heated by electron bombardment from the rear. Deposition
was made from electron beam heated sources with integral
shutter and flux measurement by proportional ion current.
The absolute flux calibration was made by direct observation
of the formation of characteristic Ag and In-induced structures using LEEM. A deposition temperature of T⬃500 K
and Ag deposition rate of 0.35 ML/min were used in our
work. These conditions resulted in lateral crystallite size and
separation that were convenient for LEEM observations. The
In deposition rate during codeposition experiments was 0.05
ML/min.
III. EXPERIMENTAL RESULTS AND DISCUSSION
The 共111兲 epitaxial relationship of Ag crystallites on the
Si共111兲 surface was confirmed in our work by the LEED
spots that derived from the crystallites relative to the substrate spots 关Fig. 1共a兲兴. Most crystallites were observed with
1071-1023Õ2002Õ20„6…Õ2492Õ4Õ$19.00
©2002 American Vacuum Society
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Tang et al.: Growth shapes of Ag crystallites on the Si„111… surface
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FIG. 2. LEEM images of Ag crystallite growing on the Si共111兲 surface 共a兲 in
a clean state immediately prior to In codeposition, and 共b兲 after codeposition
of In. The imaging energy was E⫽15.0 eV.
FIG. 1. LEED patterns of Ag(111)⫹Si(111)⫺Ag )⫻)R30°. In 共a兲 at
E⫽28.0 eV, the Ag共111兲, Si共111兲 and )⫻)R30° diffraction spots are
indicated. In 共b兲 at E⫽12.4 eV, facet diffraction spots from the major side
facets 关labeled B in Fig. 2共a兲兴 are indicated. 共c兲 Schematic drawing of the
LEED pattern at several energies. The )⫻)R30° diffraction spots are
depicted as large black circles. The small shaded circles indicate the positions of the facet diffraction spots from the major side facets at different
energies ranging from 7 eV 共black兲 to 14 eV 共white兲.
LEEM to have six side facets, similar to earlier observations
of Ag crystallites on Si共111兲,8,9 although irregular crystallite
shapes were also occasionally seen, especially near defects.
The most common crystallite shape on flat terraces or spanning one to a few atomic steps was the ‘‘triangular hexagon’’
关Fig. 2共a兲兴. This shape is characterized by two types of
edges, A and B, having unequal lengths l A and l B , respectively. A regular hexagon is recovered when l A ⫽l B . The
faint bright/dark lines that run diagonally through the Ag
crystallite in Fig. 2 are due to the strain field associated with
atomic steps at the Ag/Si interface.9 For clarity, the crystallite
in Fig. 2 is shown with the same orientation as the diffraction
pattern in Fig. 1. The image in Fig. 2共a兲 was formed using
JVST B - Microelectronics and Nanometer Structures
the specularly reflected 共0,0兲 diffraction beam at normal incidence. Therefore, only the facet parallel to the substrate,
which lies on the top of the Ag crystallite, is observed.
The side facets of the Ag crystallite that are not parallel to
the substrate can be identified with LEED, in principle, by
the facet diffraction spot motion that occurs when the incident electron energy is changed. Facet spots derived from the
long edge labeled B in Fig. 2共a兲 were clearly seen 关Fig. 1共b兲兴.
The positions of these facet diffraction spots are shown schematically in Fig. 1共c兲 for a number of incident energies.
However, the side facets at the short edges labeled A in Fig.
1共a兲 did not give rise to facet diffractions spots.
Analysis of facet diffraction spots in a low energy electron microscope must take into account acceleration of the
electron beam in the objective lens. An electron which
emerges at an angle of ␪ 0 from the surface normal direction
will assume an angle of ␪ after acceleration. The emission
and post-acceleration, angles, ␪ 0 and ␪, respectively, are related according to
sin ␪ ⫽sin ␪ 0 冑V 0 /V,
共1兲
where V 0 is the incident energy and V is the microscope
potential (V⫽20 kV here兲.13 For a beam normally incident to
a surface, the Ewald construction gives sin ␪0⫽a*/k, where
a * is the reciprocal lattice spacing between diffraction rods
and k is the incident wave vector. Since sin ␪0 is proportional
, the observed angle and therefore the diffraction
to V ⫺1/2
0
spot position in LEEM depends only upon the V and a * and
does not change when the incident energy is changed. Accordingly, the post-acceleration angle for the )⫻)R30°
diffraction spots closest to the 共00兲 beam in the present work
is ␪ ())⫽0.726°. Conversely, the position of a diffraction
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Tang et al.: Growth shapes of Ag crystallites on the Si„111… surface
FIG. 3. 共a兲 Ewald construction for a facet plane inclined from the surface
normal. 共b兲 Plot of the x and z components of the momentum transfer ⌬k for
all of the facet diffraction spots shown in Fig. 1共c兲. The solid line in 共b兲
represents the 共22兲 diffraction rod from the 兵100其 planes from which the
facet diffraction spots are derived.
spot relative to the 共00兲 spot is a representation of the the
post-acceleration angle. This can be used to determine the
facet spot angle ␪ ( f ) after acceleration
d共 f 兲
␪共 f 兲⫽
␪共 ) 兲,
共2兲
d共 ) 兲
where d( f ) and d()) are the distances of the facet and
)⫻)R30° diffraction spots from the 共00兲, respectively, in
the diffraction pattern. The emission angle from the facet,
␪ 0 ( f ) is determined by inversion of Eq. 共1兲.
The relation between the momentum transfer ⌬k, the
wave vector, and emission angle is known from the Ewald
construction 关Fig. 3共a兲兴. By plotting ⌬k z ⫽k 关 1⫹cos ␪0(f )兴
against ⌬k x ⫽k sin ␪0(f ), we obtain a representation of the
diffraction rod from the tilted plane that gives rise to the
facet diffraction spots 关Fig. 3共b兲兴. The slope and intercept of
this rod are simply related to its reciprocal lattice distance
from the specular rod of the facet b * and the facet angle
from horizontal ␾. From the data presented in Fig. 3共b兲 for
the diffraction spots from the major side facets 共labeled B in
Fig. 2兲, the facet angle ␾ ⫽54.5°⫾0.4°, and reciprocal lattice distance b * ⫽3.55⫾0.14 Å ⫺1 are determined. This corresponds to the 共22兲 diffraction rod from the 兵100其 surfaces,
which have ␾ ⫽54.3° and b * ⫽3.51 Å ⫺1 .
According to the Wulff construction for an fcc metal,4 the
兵111其 planes that dominate the equilibrium shape are six
J. Vac. Sci. Technol. B, Vol. 20, No. 6, NovÕDec 2002
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sided and bounded at the sides by 兵100其 and 兵110其 planes.
Therefore, the existence of 兵100其 side facets on the kinetic
growth shape is also expected on thermodynamic grounds.
However, the absence facet diffraction spots from the minor
side facets 共labeled A in Fig. 2兲 indicate that the less inclined
( ␾ ⫽35.7°) 兵110其 facets are absent, or are so roughened that
the scattered intensity is smeared out in k space as to make it
undetectable. The absence of facet spots may also be explained if the minor side facets are the 兵 11̄1 其 which are
inclined by ␾ ⫽70.5° from the top 共111兲 plane, provided the
scattering factor for facet diffraction spots is very small for
such a steep inclination. Alternatively, the minor facets may
be the 兵 12̄1 其 , which are perpendicular to the top 共111兲 plane.
The presence of 兵 12̄1 其 facets on the growth shape, which are
not present in the Wulff construction, would have to be the
result of purely kinetic effects during growth.
Finally, experiments were performed to test the
suggestion3,4 that surfactants can modify the 3D SE barrier.
Given the potential impact of the 3D SE barrier on growth,
modification of the barrier is expected to be manifested in
the growth shape. It was found that codeposition of In causes
a dramatic change of the growth shape from triangular hexagons with 兵100其 major side facets and 兵 11̄1 其 or 兵 12̄1 其 minor
side facets to triangular shapes 关Fig. 2共b兲兴. The triangular
crystallites are inverted with respect to the major side facets
in clean growth. Inversion and the absence of facet diffraction spots from side facets on the triangular crystallites suggest that the 兵 11̄1 其 or 兵 12̄1 其 side facets have grown at the
expense of the 兵100其 side facets.
IV. CONCLUSION
In conclusion, triangular hexagonal Ag crystallites on the
Si共111兲 surface have been observed, which are believed to be
representative of the kinetically limited growth shape. Facet
diffraction spot analysis identifies the major side facets to be
兵100其 orientation. Absence of facet diffraction spots from the
minor side facets suggests that they could be highly roughened 兵110其, or either of the more steeply inclined 兵 11̄1 其 or
兵 12̄1 其 orientations. The former could be expected on the
basis of the Wulff construction, but the presence of 兵 12̄1 其
facets may be due in part to kinetic effects, such as the recently proposed ‘‘three-dimensional’’ Schwoebel–Ehrlich
barrier. Further work is required to clarify the identity of the
minor side facets. Codeposition of In surfactant has also
been found to cause a dramatic change of the growth shape
to inverted triangle. This observation has been presented here
for one deposition condition. A more detailed study is underway to rule out other possibilities and will be reported later.
ACKNOWLEDGMENTS
The authors acknowledge helpful discussions Dr. T. Yasue. This work was supported by a grant from the Institute of
Nanoscience and Technology of the Hong Kong University
of Science and Technology. H.H. and C.H.W. acknowledge
support from PolyU 1/99C.
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R. L. Schwoebel and E. J. Shipsey, J. Appl. Phys. 37, 3682 共1966兲.
G. Ehrlich and F. G. Hudda, J. Chem. Phys. 44, 1039 共1966兲.
3
S. J. Liu, E. G. Wang, C. H. Woo, and H. Huang, J. Comput.-Aided
Mater. Des. 7, 195 共2001兲.
4
S. J. Liu, H. Huang, and C. H. Woo, Appl. Phys. Lett. 80, 3295 共2002兲.
5
M. G. Lagally and Z. Zhang, Nature 共London兲 417, 907 共2002兲.
6
See the pioneering works of Kossel and Stranski which are reviewed in
H. E. Buckley, Crystal Growth 共Wiley, New York, 1951兲 and B. Honigmann, Gleichgewichts- und Wachtumsformen von Kristallen 共Steinkopf
Verlag, Darmstadt, 1958兲.
7
M. Hanbücken, M. Futamoto, and J. A. Venables, Surf. Sci. 147, 433
1
2
JVST B - Microelectronics and Nanometer Structures
2495
共1984兲.
J. Tersoff, A. W. Dernier van der Gon, and R. M. Tromp, Phys. Rev. Lett.
70, 1143 共1993兲.
9
R. M. Tromp, A. W. Dernier van der Gon, F. K. LeGoues, and M. C.
Reuter, Phys. Rev. Lett. 71, 3299 共1993兲.
10
J. K. Zuo and J. F. Wendelken, Phys. Rev. B 56, 3897 共1997兲, and references therein.
11
E. Bauer, Rep. Prog. Phys. 57, 895 共1994兲.
12
W. F. Chung and M. S. Altman, Ultramicroscopy 74, 237 共1998兲.
13
T. Yasue, T. Koshikawa, M. Jalochowski, and E. Bauer, Surf. Sci. 493,
381 共2001兲.
8