Atomic scale analysis of Sn quantum dots (QDs) formed during the molecular beam-epitaxy (MBE) growth of Sn_xSi_(1−x) (0.05 ⩽ x ⩽ 0.1) multilayers in a Si matrix revealed a void-mediated formation mechanism. Voids below the Si surface are induced by the lattice mismatch strain between Sn_xSi_(1−x) layers and Si, taking on their equilibrium tetrakaidecahedron shape. The diffusion of Sn atoms into these voids leads to an initial rapid coarsening of quantum dots during annealing. Since this formation process is not restricted to Sn, a method to grow QDs may be developed by controlling the formation of voids and the diffusion of materials into these voids during MBE growth

H. A. Atwater

K. S. Min

Lin S.

N. D. Browning

P. Möck

R. Ragan

T. Topuria

Y. Lei

English

Lei, Y.

Möck, P.

Topuria, T.

Browning, N. D.

Ragan, R.

Min, K. S.

Atwater, H. A.

Caltech Authors - Main

APPLIED PHYSICS LETTERS VOLUME 82, NUMBER 24 16 JUNE 2003Void-mediated formation of Sn quantum dots in a Si matrix
Y. Lei,a) P. Mo¨ck,b) T. Topuria, and N. D. Browning
Department of Physics, University of Illinois at Chicago, 845 West Taylor Street, Chicago,
Illinois 60607-7059
R. Ragan,c) K. S. Min,d) and H. A. Atwater
Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena,
California 91125
~Received 19 February 2003; accepted 21 April 2003!
Atomic scale analysis of Sn quantum dots ~QDs! formed during the molecular beam-epitaxy ~MBE!
growth of SnxSi12x (0.05<x<0.1) multilayers in a Si matrix revealed a void-mediated formation
mechanism. Voids below the Si surface are induced by the lattice mismatch strain between SnxSi12x
layers and Si, taking on their equilibrium tetrakaidecahedron shape. The diffusion of Sn atoms into
these voids leads to an initial rapid coarsening of quantum dots during annealing. Since this
formation process is not restricted to Sn, a method to grow QDs may be developed by controlling
the formation of voids and the diffusion of materials into these voids during MBE growth. © 2003
American Institute of Physics. @DOI: 10.1063/1.1584073#The interest in Sn quantum dots ~QDs! embedded in a Si
matrix is motivated by their potential applications as band
structure engineered direct-band gap elemental semiconduc-
tors for optoelectronics and thermophotovoltaics.1 As dia-
mond structured a-Sn is a direct zero band gap
semiconductor,2,3 the formation of a substitutional SnxSi12x
alloy is predicted to lead to a direct and tunable energy gap
for x.0.9.1 Quantum confinement is anticipated to increase
and thus further tune the energy gap. The growth of ultrathin
pseudomorphic SnxSi12x multilayers with x50.05 and 0.1
by temperature-modulated molecular beam epitaxy ~MBE!
and ex situ annealing to form Sn-rich QDs has been reported
previously.4,5 However, the coarsening kinetics during post-
growth annealing revealed an unexpected rapid increase of
the average volume of the QDs in the first 2.2 h, though the
subsequent growth slowed down to be linear with time.5
Typically, any deviation from linear behavior is attributed to
diffusion shortcuts related to defects ~dislocations! in the
material,6 but in these samples the QDs nucleated in regions
free from dislocations.7 In this letter, we report an atomic
scale study of a-Sn QDs in these materials4,5 to elucidate the
mechanism behind this initial rapid coarsening, which is of
key importance to the overall properties of prospective de-
vices. The implications for other QD systems will also be
discussed.
The experiments were performed using a combination of
Z-contrast imaging and electron energy-loss spectroscopy
~EELS! in a 200 kV JEOL 2010F Schottky field emission
scanning transmission electron microscope.8 This micro-
scope is capable of obtaining essentially incoherent
a!Electronic mail: ylei1@uic.edu
b!Present address: Department of Physics, Portland State University, P.O.
Box 751, Portland, OR 97207.
c!Present address: Hewlett-Packard Laboratories, 1501 Page Mill Rd., MS
1123, Palo Alto, CA 94304.
d!Present address: Intel Corporation, California Technology and Manufactur-
ing, MS RNB-2-35, 2200 Mission College Blvd., Santa Clara, CA 95052-
8119.4260003-6951/2003/82(24)/4262/3/$20.00
Downloaded 16 Dec 2005 to 131.215.225.9. Redistribution subject toZ-contrast images ~intensity proportional to atomic number!
in the scanning probe mode with a Scherzer resolution of
;0.13 nm. The EELS technique is exploited to quantify fluc-
tuations in chemical composition, as changes in the intensity
of core-loss signals give a direct measure of the quantity of
specific elements.9 Using the Z-contrast image as a map to
position the probe for spectroscopy allows a direct correla-
tion between the two techniques with atomic spatial resolu-
tion. The specimens for the microscopy study were prepared
by standard thinning procedures.
Figure 1~a! shows a @110# cross-sectional Z-contrast im-
age of the Sn0.1Si0.9 /Si sample, indicating QDs with a diam-
eter in the range of 7–10 nm were formed. Although the
majority of the Sn-rich QDs are at the SnxSi12x layers, there
are also QDs within the Si spacer layers, which typically
appear to possess a tetrakaidecahedron shape bounded by
$111% and $100% facets @Fig. 1~b!#. The formation of these
QDs cannot be explained by the phase separation
mechanism5 that was proposed to operate within the
SnxSi12x layers. Figure 2~a! shows another QD that has a
particularly low intensity, i.e., low Sn content, instead of the
essentially uniform brightness presented in Fig. 1~b!. This
QD also shows higher brightness at the edges, indicating that
a-Sn lines its interface with the Si matrix. Since it is not
FIG. 1. @110# Cross-sectional Z-contrast images of: ~a! the Sn0.1Si0.9 /Si
multilayer structure and ~b! one QD within the Si spacer layers pointed by
one of the arrows plotted in ~a!.2 © 2003 American Institute of Physics
 AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
4263Appl. Phys. Lett., Vol. 82, No. 24, 16 June 2003 Lei et al.viable to determine the Si content inside the dot from the
image intensity alone ~as the size of the embedded QD is
much smaller than the thickness of the matrix!, in order to
obtain the compositional information, a series of EELS spec-
tra were acquired along a line across the center of this dot
and perpendicular to the @001# growth direction. The
Si L-edge intensity is plotted as solid circles in Fig. 2~b!. The
zero point on the spatial position axis corresponds to the
position of the center, while the two edge points corresponds
to the Si matrix around this QD. The plot indicates a sharp
decrease of Si content within the QD relative to the Si ma-
trix, as expected from a QD that contains Sn. However, fur-
ther EELS analysis of the Sn content reveals that the drop in
the Si concentration is much greater than the increase in the
Sn content @the Sn M -edge intensity is plotted as triangles in
Fig. 2~b!#. In this calculation, Sn atoms were assumed to
occupy positions of Si atoms without lattice expansion, as no
obvious lattice expansion was observed from the images.
This implies that these QDs are voids in the Si matrix that
are only partially filled. This is consistent with the equilib-
rium shape of a void in Si, which has been shown to be the
same tetrakaidecahedron10 shape shown in Figs. 1~b! and
2~a!.
Two theoretical calculations on an ideal void and a QD
fully filled by Sn were further performed and compared with
the experimental results. Both this ideal void and QD were
assumed to have the same size and shape as the original QD,
and to be in a Si matrix of the same thickness in the experi-
ment ~this thickness has been calculated from the EELS
spectrum!.11 After the shape parameters of this tetrakaideca-
hedron were determined based on the image, the effective
thickness of Si along the @110# direction in the region con-
taining this ideal void was calculated. The expected changes
in the Si L-edge intensity are then plotted in Fig. 2~b!, which
shows the consistency with the experimental results. Simi-
larly, the expected changes in Sn M -edge intensity in the
case of a full Sn QD are also plotted @Fig. 2~b!#, and the large
discrepancy from the experiment verifies the assertion of a
partially occupied Sn structure.
It has been observed that voids of ;10 nm in diameter
and a number density of ;1010 cm22 can form ;10 nm
below a fresh Si surface when it is exposed to air, due to the
FIG. 2. ~a! @110# Cross-sectional Z-contrast image of a QD within the Si
spacer in the Sn0.1Si0.9 /Si sample containing a very small amount of Sn. ~b!
Experimental results of Si L-edge counts ~solid circles! and Sn M -edge
counts ~triangles! at the spatial positions along a line across the center of this
QD and perpendicular to the growth direction, compared with two theoret-
ical calculations when assuming this QD is an ideal void with no Si inside,
and fully filled by Sn, respectively.Downloaded 16 Dec 2005 to 131.215.225.9. Redistribution subject tocompressive strain induced by the growth of SiO2 on the
surface.12 Thus, the appearance of voids in these multilayer
materials is probably induced by the growth of SnxSi12x
layers imposing a similar strain on the Si surface, and the
thermal cycling during the growth4,5 finally ensures pre-
formed voids of any shape to grow and reach their equilib-
rium shape. Therefore, the initial rapid coarsening observed
in Ref. 5 may be explained by diffusion shortcuts to these
voids.
To confirm this hypothesis, a QD in the Si spacer layer
of the Sn0.05Si0.95 /Si sample was investigated during an in
situ heating process performed at 300 °C for 3 h. The
Z-contrast images taken before and after the heating indicate
that the intensity within this QD increased ~after being nor-
malized according to Si matrix intensity! and became uni-
form, while it remained the same tetrakaidecahedron shape
~Fig. 3!. Although the lattice resolution was lowered a little
due to the residual shaking of the heating stage, the fast
Fourier transform of the image confirmed the Sn structure as
diamond. Since this heating process is exactly analogous to
the annealing used in the sample growth, the result is con-
sistent with the QD initially being a void, to which the Sn
diffuses during annealing. As the diffusion of Sn atoms into
the voids in the Si matrix can further minimize the elastic
strain energy between the SnxSi12x layers and Si matrix dur-
ing the phase separation of the SnxSi12x layers, these voids
are the preferential sinks for diffusing Sn atoms. Therefore,
this void mediated mechanism dominates at the beginning of
QD formation, and results in the initial rapid coarsening.
In conclusion, the analysis of Sn QDs in a SnxSi12x /Si
multilayer system revealed a void mediated formation
mechanism. The voids, created by the deposition of lattice
mismatched SnxSi12x layers on the Si, are filled with endot-
axially grown Sn to form pure a-Sn QDs. This mechanism
explains the initial rapid increase of the size of QDs during
postgrowth annealing, and is not restricted to Sn, as any
material producing strain on the substrate may induce voids.
It is noted that the results here are similar to previous studies
that report the formation of hollow and partially filled pre-
cipitates in Si by ion implantation coupled with thermal
treatments.13–16 However, the size distribution of the precipi-
tates is too wide to be suitable for device quality QD fabri-
cation. By using MBE, the resultant voids have a well-
defined shape and narrow size distribution. A method to
grow uniform QDs may be developed by controlling the for-
FIG. 3. @110# Cross-sectional Z-contrast images of a QD within the Si
spacer layer in the Sn0.05Si0.95 /Si sample ~a! before and ~b! after in situ
heating at 300 °C for 3 h. Fast Fourier transform of the images at the corners
indicate the Sn diamond structure remained same. AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
4264 Appl. Phys. Lett., Vol. 82, No. 24, 16 June 2003 Lei et al.mation of voids and the diffusion of materials into these
voids during MBE growth.
This work was supported by NSF under Grant No.
DMR-9733895 to N.D.B. and a grant to P.M. by CRB of
UIC. The JEOL 2010F was purchased in part with support
from NSF under Grant No. DMR-9601792. Nanocrystal syn-
thesis and characterization at Caltech ~H.A.A., R.R., and
K.S.M.! was supported by NSF under Grant No. ECS-
0103543.
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Void-mediated formation of Sn quantum dots in a Si matrix

The void mediated formation mechanism of Sn quantum dots in an Si matrix was analyzed. It was found that the diffusion of Sn atoms into these voids leads to an initial rapid coarsening of the quantum dots during annealing. However, as this process is not restricted to Sn, the quantum dots could be grown by controlling the formation of voids and the diffusion of materials in these voids during molecular beam epitaxy

Void-mediated formation of Sn quantum dots in a Si matrix

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