Spontaneous Assembly of Perfectly Ordered Identical-Size Nanocluster Arrays

Abstract

A method, by which periodic two-dimensional arrays of identical metal clusters of nanometer size and spacing could be spontaneously obtained by taking advantage of surface mediated clustering, is reported. The versatility of the method is demonstrated for a broad range of metals on Si(111)-(7 x 7) substrates. In situ scanning tunneling microscopy analysis of In clusters, combined with first-principles total energy calculations, unveils unique initial-stage atomic structures of the surface-supported clusters and the vital steps that lead to the success of this method. A strong interaction between the clusters and the surface holds the key to the observed cluster sizes.

Full text

VOLUME 88, NUMBER 6 PHYSICAL REVIEW LETTERS 11F
EBRUARY 2002
Spontaneous Assembly of Perfectly Ordered Identical-Size Nanocluster Arrays
Jian-Long Li,1Jin-Feng Jia,1Xue-Jin Liang,1Xi Liu,1Jun-Zhong Wang,1Qi-Kun Xue,1Zhi-Qiang Li,2
John S. Tse,2Zhenyu Zhang,1,3 and S. B. Zhang4
1State Key Laboratory for Surface Physics and International Center for Quantum Structures, Institute of Physics,
Chinese Academy of Sciences, Beijing 100080, China
2Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, K1A 0R6, Canada
3Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6032
4National Renewable Energy Laboratory, Golden, Colorado 80401
(Received 28 September 2001; published 25 January 2002)
A method, by which periodic two-dimensional arrays of identical metal clusters of nanometer size and
spacing could be spontaneously obtained by taking advantage of surface mediated clustering, is reported.
The versatility of the method is demonstrated for a broad range of metals on Si共111兲-共737兲substrates.
In situ scanning tunneling microscopy analysis of In clusters, combined with first-principles total energy
calculations, unveils unique initial-stage atomic structures of the surface-supported clusters and the vital
steps that lead to the success of this method. A strong interaction between the clusters and the surface
holds the key to the observed cluster sizes.
DOI: 10.1103/PhysRevLett.88.066101 PACS numbers: 81.07.–b, 07.79.Cz, 61.46.+w, 68.43.Bc
Ordered arrays of metal nanoclusters are promising
materials for next generation microelectronics [1,2],
ultra-high-density recording [3], and nanocatalysis [4,5].
Self-organization in heterogeneous strained thin-film
growth [6,7] and self-assembly in chemical synthesis [3]
are two of the most commonly used methods to obtain
such nanostructures spontaneously. No method has suc-
ceeded in producing reproducibly identical nanoclusters/
dots with periodic spatial distribution, which is highly
desirable for practical device applications and is an open
question in molecular and solid-state physics of these
“artificial atoms” [8]. Fabrication of uniform-size cluster
arrays at the ultrasmall 1– 2 nm size regime is even more
challenging because fluctuation at a level of only a few
atoms could substantially alter their electronic properties.
On the other hand, ultrasmall cluster arrays of such
dimension have potential for quantum application because
the Fermi wavelength for most metals is around 1 nm. At
such a length scale, one could also maximize quantum
confinement effects and test the fundamental limitations
that such effects could impose on the electronic prop-
erties. Self-assembly of nanoclusters on periodic solid
surface has been shown to be a promising approach to the
problem [9–11], however, growth of ordered arrays of
nanoclusters with identical size and tunable composition
is still a daunting challenge.
Certain clusters with a specific (magic) number of atoms
exhibit electronic and/or atomic closed-shell structures and
hence remarkable stability [12]. For substrate-supported
clusters, while the “closed-shell structure” is still under
debate, several recent studies suggested that supported
clusters of specific or “magic” sizes indeed exist with re-
markable stability against others [13 – 16]. As the substrate
could interact with the clusters, a substrate modification of
the magic sizes may be unavoidable. On the other hand,
such an interaction could play a pivotal role by automati-
cally selecting identically sized clusters that for gas phase
has to be done by mass spectrometry. Here, we explore
this concept and exploit the magic clustering process to
assemble ordered cluster arrays. We show that substrate-
induced spontaneous clustering can be realized by delicate
control of growth kinetics [17], and that periodic identical-
size metal nanocluster arrays can be fabricated on
Si共111兲-共737兲surfaces.
Our experiments were performed with a OMICRON
variable temperature STM operated in ultrahigh vacuum
共⬃5310211 Torr兲. Clean Si(111) substrates were pre-
pared by standard annealing procedures. Boron nitride cru-
cibles were used to produce In (purity 99.999 99%) atomic
beams, while Ag and Mn depositions were performed by
resistant heating in a tungsten bracket filament and a tan-
talum boat, respectively.
Delicate regulation of the growth parameters allows for
the growth of periodically ordered nanocluster arrays on
the Si(111) substrate. Taking the In clusters in Fig. 1(a)
as an example, even at 0.05 ML coverage a local ordering
is already evidenced and all of them occupy the faulted
half unit-cells (FHUCs) of Si共111兲-共737兲[18,19]. Also,
the nanoclusters show high uniformity: every cluster in
Fig. 1(a) is exclusively imaged as a hollow-centered, six-
spot equilateral triangle. At a coverage of 0.12 ML, a
perfectly ordered nanocluster array forms with a nearest
neighbor distance of 2.7 nm [Fig. 1(b)]. With increasing
In coverage, the clusters begin to occupy the unfaulted half
unit cells (UFHUCs) of the surface without damaging the
existing clusters on the FHUCs, which is different from the
Tl case [9]. These clusters exhibit the same appearance as
those in the FHUCs [Fig. 1(a)]. At ⬃0.24 ML, a charac-
teristic ordered honeycomb structure develops (not shown),
due to full occupation of both halves of the unit cell.
The general applicability of the method has been
demonstrated by growing more than 12 ordered arrays of
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FIG. 1 (color). (a) STM image of In nanoclusters on Si(111)
at an In coverage of ⬃0.05 ML (1ML 苷one adsorbed atom
per substrate atom). (b) Perfectly ordered In nanocluster arrays
at ⬃0.12 ML In coverage. (c) I-Vcurves measured on bare Si
surface (red) and on top of In clusters (green).
identical-size nanoclusters with different metals. An in-
teresting example is the ordered arrays of even complex
nanostructures. Here, the chemical identity of the STM
image features can be determined by tracing deposition
history. The complex array in Fig. 2(a) consists of two
equivalent In and Mn cluster triangular lattices occupying,
respectively, the FHUCs and UFHUCs, formed by de-
positing ⬃0.1 ML Mn on the In covered surface shown in
Fig. 1(b). If ⬃0.06 ML Ag rather than Mn is deposited, an
array of identical-size In兾Ag alloy clusters forms. In this
case [Fig. 2(b)], the subsequently deposited Ag atoms sit
on top of the predeposited, ordered In clusters, rather than
on the UFHUCs. The In cluster array therefore dictates
the growth of the Ag cluster array. This salient feature is
best illustrated at lower In兾Ag coverage where the magic
In clusters appear as a three-spot triangle indicated by the
yellow triangle in Fig. 2(c). In contrast, the In兾Ag binary
clusters show four-spot triangles (with one spot at the
center) as typified by the dark-blue triangle in Fig. 2(c).
In situ Auger electron spectroscopy measurement shows
the presence of Ag on the surface. Hence the center
spots can be assigned to the tunneling current from the
later-deposited Ag atoms.
Because the physical properties of the nanostructures
are both size and material specific, and the cluster size and
their array periodicity are comparable to the Fermi wave-
lengths of electrons in most metals, this method renders
the potential to fabricate “customized”quantum devices.
We note that (i) all the ordered cluster arrays shown here
are stable with temperatures up to 200 ±C. This feature
is to be contrasted with metal clusters on metal surfaces,
which are typically stable only at low temperatures [e.g.,
up to 150 K for Ag clusters on Pt(111) [7]. (ii) There
is no fundamental limitation on fabricating identical-size
clusters, as identical size has been demonstrated for In兾Ag
in Fig. 2(b). Thus, upon further improvement the present
approach can be made precise and practical in fabricat-
ing various identical-size cluster arrays. We emphasize
that our approach is not limited to Si. It applies as long
as the substrate template used to accumulate and separate
these building blocks exists or can at least be prepared.
The Si3N4共0001兲-共838兲surface is among the candidate
templates [20].
To understand the basic principles governing the array
formation process, we have studied in some detail the
atomic structures of the In clusters. The In clusters
are an important component in Fig. 2 and in many
aspects the most interesting. This is evidenced by the
high-resolution STM images in Figs. 1(a) or 3(b) in which
the In clusters appear as hollow-centered six-spot equilat-
eral triangles. The triangular pattern is quite unusual in
terms of normal close-packed structures [13,14,21]. An
intuitive interpretation of the images could be that each
bright spot of the triangle represents an In atom, which
agrees with In coverage calibration in our experiment.
However, the open triangular geometry seems to be un-
stable in view of the loose packing, the low coordination
number, and in particular the strong steric strain with
registry to atoms on the Si substrate. Alternatively, one
might attribute the six spots seen to a dynamical time
averaging of more than six atoms [9]. It was recently
FIG. 2 (color). (a) Mixed array of equal-size In and Mn clusters formed by depositing ⬃0.1 ML Mn on preexisting array of In
clusters shown in Fig. 1(b). The blue half circle highlights the In cluster, while the light green half circle highlights the Mn cluster.
(b) Identical In兾Ag alloy cluster array prepared by depositing ⬃0.06 ML Ag atoms (⬃three Ag atoms per unit cell) on the In cluster
array shown in Fig. 1(b). (c) STM image for the surface with low In兾Ag coverage, demonstrating that the nanoclusters in (b) are
In兾Ag alloy. The FHUC of the Si共111兲-共737兲is highlighted by a white triangle, whereas these occupied by pure In cluster and by
mixed In兾Ag cluster are highlighted by a yellow and a dark-blue triangle, respectively.
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FIG. 3 (color). (a) The dimer-adatom-stacking-fault model of Si共111兲-共737兲surface (Ref. [18]). The FHUC is to the upper-right
corner. The sites relevant to the discussion are indicated as R1-R3for Si rest atoms and A1-A6for Si adatoms. The yellow balls
are Si atoms in the substrate, the blue balls are Si adatoms, and the red balls are Si rest atoms. (b) and (c) The STM images of the
In clusters recorded at sample bias voltages of 10.6 and 20.3 V, respectively. (d) Top view of the calculated atomic structure of
the six-In cluster on Si共111兲-共737兲. The dark-blue balls are In atoms. The calculated STM images are shown in (e) (for positive
bias 10.6 V) and (f) (for negative bias at 20.3 V with respect to the Fermi energy) for the atomic structure in (d). The colors
indicate the height of the images: dark blue being low and red being high. At typical experimental tip height of about 1 nm above
the surface, only the most protruding features can be seen.
shown that the potential energy surface of a Si adatom
on Si共111兲-共737兲is quite shallow [22]. Therefore,
it is possible that at room temperature In atoms may
hop quickly along the local energy minimum sites [9]
within the basin formed by one Si rest-atom and three Si
adatoms [Fig. 3(a)], and the six bright spots reflect these
energy minimum sites with higher occupation proba-
bility. This possibility, however, can be ruled out because
our STM experiment at ⬃30 K shows exactly the same
six-spot pattern. Furthermore, this model fails to account
for the observed orientation of the triangles.
To address these puzzling issues, we carried out first-
principles total energy calculations. A Vanderbilt ultrasoft
pseudopotential [23] was used with a 100 eV cutoff energy
and 1 special kpoint in the Brillouin zone sum. The bare
737unit cell (without counting the Si adatoms) contains
six Si layers and a vacuum layer equivalent to six Si layers.
We calculated the STM images following the Tersoff and
Hamann formula [24] as detailed in Refs. [25,26].
Two possible In-cluster structures are considered:
(i) six-In-atom cluster forming a hexagonal ring;
(ii) six-In-atom cluster forming a hollow-center triangle.
In case (i), each of the six In atoms is bonded to either
one of the three Si adatoms 共A1-A3兲or one of the three
Si rest atoms 共R1-R3兲[Fig. 3(a)]. The In atoms are also
bonded among themselves forming a distorted hexago-
nal ring. This model cannot explain the STM images,
in particular the image for the filled states [Fig. 3(c)].
Its energy is also 1.2 eV兾cluster higher than case (ii).
In case (ii), six threefold-coordinated In form a triangle
[Fig. 3(d)]. For In atoms at the corners of the triangle,
the bond lengths are 2.57, 2.64, and 2.64 Å, whereas the
bond angles are 113±,113±, and 88±, respectively. For In
atoms on the edges, the bond lengths are 2.67, 2.60, and
2.60 Å, whereas the bond angles are 113±,116±, and 116±,
respectively. Angles larger than the 109.5±-tetrahedral
angle are preferential as threefold In prefers planar 120±
bond angles. Both the three Si adatoms 共A1-A3兲and the
three Si rest atoms 共R1-R3兲become fourfold coordinated.
Noticeably, Si adatoms A1-A3are displaced towards
the triangle center considerably, which strengthens their
bonds with the substrate atoms by resuming the 109.5±-
tetrahedral angles. Each Si adatom has two 80±, one 83±,
and three close-to-tetrahedral angles. Similar geometries
have been suggested for low energy defects in hydro-
genated Si [27] and for the DX center in III-V alloys [28].
Thus, by displacing Si adatoms not only can the perceived
steric strain be avoided, but also the displaced Si adatoms
serve as the “missing”links between the otherwise loosely
packed In atoms. An In cluster on the UFHUC is found to
be 0.1 eV兾cluster higher in energy than that on the FHUC.
The atomic registry of the In cluster in Fig. 3(d) further
explains why the number six is so special or magic, as
either addition or removal of one In atom will destabilize
the cluster. The same argument applies to larger clusters,
but will not be discussed here. Our results suggest that
local optimization of the chemical bonds is essential for
the exceptional stability of the magic clusters. The energy
barrier for the In atoms to reach their optimal positions
is expected to be only moderate as the cluster formation
involves only the insertion of In into the existing 737
surface network that is quite flexible compared to bulk.
Massive rearrangement of the surface should be avoided,
as it will lead to p33p3or other structures [29].
The calculated STM images in Figs. 3(e) and 3(f)
are in remarkable qualitative agreement with experiment
[Figs. 3(b) and 3(c)]. Interestingly, in the empty state
image [Fig. 3(e)], the three brightest spots are from the
lowest In atoms, which are 0.6 Ålower than Si A1A3
with an average bond angle of 105±(thus sp3-like). The
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three second-brightest spots are from the other In atoms,
which are 0.3 Ålower than Si A1-A3with an average
bond angle of 115±(thus sp2-like). Si adatoms A1-A3
are almost invisible, as they do not involve any dangling
bond. A large disparity between an STM image and actual
height of group III atoms has been demonstrated for an
As vacancy on GaAs(110) surface [25]. Another striking
feature in Fig. 3(c) is the disappearance of the six-In
triangle spots under small reverse bias, whereas the three
Si corner adatom spots 共A4A6兲become significantly
brighter. Our calculation reveals that this change is not due
to In diffusion but has an electronic origin. The calculated
density of states reveals a 0.33 eV band gap 0.2 eV below
the Fermi energy 共EF兲. States below the gap have mainly
the Si兾In bonding character. States above the gap but
below EFhave mainly the dangling-bond character and
are predominantly on Si A4A6. The In dangling bond
states are found to be above EFthus can only be seen
in the empty state image. A micro C-Vprofile above In
clusters should unveil this semiconducting characteristics.
Indeed, this is confirmed in our experiment [Fig. 1(c)]
and by others [30].
Our discussion hereto suggests that while the clusters
are locally stable, globally they are metastable. Then, what
has led to the success of the current approach while it has
not been possible in the past? Our experiment demon-
strates that it needs delicate control of the growth kinetics
[17]. (i) One must suppress the formation of any unde-
sirable clusters of inhomogeneous sizes. If the substrate
temperature during deposition is too low (room tempera-
ture or lower) and the deposition rate is too high, the In
atoms do not have enough time to arrive at the expected
destination as required for the formation of stable clus-
ters. Instead, they combine to form immobile nuclei of
smaller sizes. “Hot-landing”at high temperatures would
allow energetic In atoms to agglomerate into larger clus-
ters which then coalesce into islands via Ostwald ripening,
or phase transition into the p33p3structure. (ii) The
calculated energy difference between In clusters on the
FHUC and UFHUC is only 0.1 eV兾cluster. Given such
a modest energy difference, the kinetics have to be manip-
ulated in such a way that the atom hopping rate between
the two halves must exceed the atom arrival rate enough to
complete the ordering. To achieve such balance, we find
that the substrate temperature during deposition should be
higher than 100 ±C but lower than 200 ±C while the de-
position rate should be around 0.01 ML兾min for In, Ag,
and Mn.
In summary, we have demonstrated an efficient method
for fabricating “customized”highly uniform nanocluster
arrays on Si(111) with atomic precision. The physical
origin of the stable or magic sizes that makes the method
possible is established and the atomic structures for the
In clusters are determined by first-principles calculations.
The ability to assemble nanoclusters and the thermal sta-
bility up to 200 ±C for the nanocluster arrays on Si allow
for integration with existing microelectronic architectures.
Finally, the ability to form magnetic and/or alloyed
nanocluster arrays may lead to breakthroughs in other
important areas such as surface nanocatalysis [4] and
nanomagnetism [5].
S. B. Z. thanks W.E. McMahon for a critical reading of
the manuscript. Work at IOP was supported by the NSF of
China (69625608), at NREL by the U.S. DOE /SC/BES un-
der Contract No. DE-AC36-99GO10337 and by the U.S.
DOE/NERSC for supercomputer time, and by Oak Ridge
National Laboratory, managed by UT-Battell, LLC for the
U.S. DOE under Contract No. DE-AC05-00OR22725, and
by the U.S. NSF (DMR-0071893), respectively.
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