Self-Organized Hexagonal Patterns of Independent Magnetic
Nanodots**
By Thomas Bobek,* Nikolai Mikuszeit, Julio Camarero, Stepan Kyrsta, Lin Yang, Miguel Angel Niño,
Christian Hofer, Lidia Gridneva, Dimitri Arvanitis, Rodolfo Miranda, Juan Jose de Miguel, Christian
Teichert, and Heinrich Kurz
Self-organized hexagonal nanodot patterns can be formed
by ion bombardment on semiconductor surfaces. Here it is
shown how this method can be applied to the production of
ordered nanostructures of almost any type of material by
transferring the pattern originally developed on an appropriate formation layer to an intercalated thin film. Our experiments using Co as the buried material have resulted in the appearance of large-area, isotropic arrays of magnetic
nanoparticles. The same procedure could be used with other
nonmagnetic buried layers, whether metallic, semiconducting,
or heterostructure.
Self-organization, or the spontaneous appearance of longrange order in either arrays of objects or morphological features, is a common phenomenon in nature, spanning all length
–
[*]
Dr. T. Bobek, Dr. L. Yang, Dr. H. Kurz
Institute of Semiconductor Electronics, RWTH Aachen
Sommerfeldstrasse 24, 52074 Aachen (Germany)
E-mail: [email protected]
Dr. N. Mikuszeit, Dr. J. Camarero, Dr. M. A. Niño, Dr. R. Miranda,
Dr. J. J. de Miguel
Departamento Física de la Materia Condensada and Instituto de
Física de Materiales “Nicolás Cabrera”
Universidad Autónoma de Madrid
Cantoblanco, 28049 Madrid (Spain)
Dr. S. Kyrsta
Materials Chemistry, RWTH Aachen
Kopernikusstrasse 16, 52074 Aachen (Germany)
Dr. C. Hofer, Dr. C. Teichert
Institut für Physik, Montanuniversität Leoben
Franz-Josef-Strasse 18, 8700 Leoben (Austria)
Dr. L. Gridneva, Dr. D. Arvanitis
Department of Physics, Uppsala University
Box 530, 75121 Uppsala (Sweden)
Dr. R. Mirando
Dpto. Física de la Materia Condensada
Univ. Autónoma de Madrid
Cantoblanco, 28049 Madrid (Spain)
Dr. R. Mirando
IMDEA, Madrid Institute for Advanced Studies
Madrid (Spain)
[**] We thank Professor Antonio Hernando and Professor Dominique
Givord for fruitful discussions on the interpretation of the magnetic
properties of the nanoparticles. This work has been financed by the
European Union through the “NAMASOS” project, no. NMP2-CT2003-505854. Work by the Spanish group has also been partially
supported by Project FIS2004-01026. J.C. acknowledges support
through a “Ramón y Cajal” contract from the Spanish Ministry of
Science and Technology.
Adv. Mater. 2007, 19, 4375–4380
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DOI: 10.1002/adma.200701163
scales from clusters of galaxies through sand dunes and molecular arrangements down to the crystalline state of matter.
It arises from the competition between different interactions,
as a result of which some preferential lengths are defined that
become continuously amplified while the rest are progressively annihilated.[1] As the process of device miniaturization
truly reaches the nanometer range, the complexity and cost of
top-down lithographic methods rises exponentially, and the
use of nanostructural self-organization as an alternative patterning technology is becoming particularly appealing thanks
to its low cost and high production efficiency. Particularly intense attention is being devoted nowadays to these alternative
fabrication schemes from the field of magnetism, driven
mainly by the quest for ever higher density storage media,[2]
but also for various applications such as nanosensors or nanoparticulate catalysts.
For many of these applications it is important not only to
produce the nanometer-scale objects, but also to have them
suitably distributed on an appropriate substrate. Reasonably
monodisperse nanoparticles can be synthesized by chemical
processes[3,4] and functionalized for different purposes, but
arranging them in an orderly fashion on a surface seems impracticable. For this reason, many other fabrication methods
currently being investigated rely on first creating and then utilizing some sort of template that guides and dictates the spatial distribution of the material of interest upon its deposition.
Some examples are filling of nanopores in anodized alumina[5,6] or phase-separated block copolymers,[7,8] patterning
through assemblies of spherical particles,[9–12] or controlling
epitaxial growth processes to induce nucleation of nanometric
islands at specific surface positions.[13,14] While all these methods have demonstrated their viability for some specific purposes, the main weakness of these bottom-up approaches is
the highly specific combination of factors or components
required for their occurrence, as they involve very special substrates or processing techniques that can be difficult to integrate with the technologies currently used in industry.
The appearance of densely packed arrays of nanodots upon
normal-incidence ion sputtering was first demonstrated for
GaSb surfaces by Facsko et al.,[15] and it has since been observed for other semiconductor surfaces, such as InP[16], Si,[17]
and Ge;[18] for metallic surfaces ripple formation has been
reported upon glancing-incidence ion bombardment.[19] Ordered patterns of metallic dots have only been found with a
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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larger lateral periodicity and a lower dot amplitude compared
to the dots presented here.[20] The explanation of this effect is
based on the dependence of the sputtering yield on the surface curvature,[21] combined in a subtle way with surface diffusion and the different mechanisms of mass transport and redeposition;[22–24] for this reason, the application of this
nanostructuring method to metallic substrates is difficult, producing structures with a rather low aspect ratio that are stable
only below room temperature.[19]
In this Communication we describe a successful method of
transferring the dot pattern created on a semiconducting
(GaSb) formation layer to a buried metallic film. In this way,
discs or columns of almost any type of material can be obtained. We demonstrate the capability of our method with a
specially challenging system, namely producing hexagonal
arrays of magnetically independent Co nanoparticles. The
procedure is schematically depicted in Figure 1. First of all a
metallic layer or heterostructure with the desired thickness
and composition (polycrystalline, 5 nm thick, Co film with
pattern before the pattern intersects the intercalated metallic
film. The nanodot size and separation can be controlled by
tuning the ion energy, in the range between approximately
15 and 80 nm.[25] A systematic study showed that, in our system, the best results could be obtained using 400 eV ions.
In order to determine the time evolution of the surface morphology, a time series of sputter experiments with 400 eV Ar+
ions on amorphous (a-)GaSb was recorded. The surfaces were
then characterized by means of atomic force microscopy
(AFM). The root mean square (rms) roughness values determined from those measurements are presented in Figure 2.
An initial exponential increase of the surface roughness can
be observed, similar to what has been found for crystalline
Figure 2. Time dependence of the surface roughness (filled circles) of
amorphous GaSb during erosion with 400 eV Ar+ ions, growing simultaneously with the emergence of the dot pattern. The initial roughness data
can be fitted with an exponential function (solid line) with a time constant s = 672 s, before stabilization occurs. The open squares display the
evolution of the roughness wavelength: no well-defined surface periodicity could be observed below 1000 s sputter time.
Figure 1. Schematic representation of the nanofabrication method employed. The self-organized nanodot pattern that develops during the Ar+
ion bombardment at normal incidence on the capping GaSb layer (top
panel) advances towards the buried metallic film (middle) until it intersects it (bottom), thus creating an array of disc- or pillar-shaped metallic
dots.
(111) texture in this case) is grown on a GaSb substrate by a
standard technique, for instance magnetron sputtering, and
then covered in a similar way with another GaSb film. Upon
ion bombardment under normal incidence and with the appropriate parameters, a self-organized arrangement of nanodots gradually appears in the GaSb formation layer, which
must be thick enough to allow full development of the surface
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material[26] but with a much longer time constant. After
approximately 1500 s of erosion a stable, uniform surface pattern is established, with a stationary roughness level and a
characteristic wavelength that remains constant for the rest of
the sputtering process, consistent with the theoretical models
of the dot formation mechanism.[21,27] The sputter velocity was
determined to be approximately 0.5 nm s–1, which combined
with the time evolution described above requires a minimal
thickness of at least 750 nm for the a-GaSb formation layer.
In our experiments we used 1000 nm thickness to ensure that
the dot pattern was fully developed and time independent
before it intersected the buried Co film.
The progress of the erosion process was monitored in real
time by mass spectrometric depth profiling. In Figure 3, both
the Ga and Co signals are shown as a function of sputter time.
The increase of the Ga signal is due to the preferential sputtering of this element in comparison to Sb. The Sb signal
decreases by the same amount during the sputtering process.
From the appearance of the Co signal at point A after
ca. 1800 s, an erosion velocity of 0.53 nm s–1 can be determined for the a-GaSb formation film. Within the Co layer, in
contrast, the material removal is much slower; a velocity of
approximately 0.1 nm s–1 has been determined from different
experiments using Co layers of thickness between 5 and
36 nm. After reaching a maximum at point B, corresponding
© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2007, 19, 4375–4380
to the center of the metallic layer, the Co signal nearly disappears at point C, indicating that this material has been completely removed from the exposed areas within the surface
troughs, turning the original continuous film into an array
of separated nanometer-sized discs. This detection method
thus provides accurate endpoint control for the patterning
process.
The surface morphology of the eroded samples was characterized in detail by AFM at different stages during sputtering.
Figure 4 shows images acquired at the three characteristic positions marked in Figure 3. At the beginning of the Co layer
(point A) a fully developed dot pattern consisting of uniformly shaped dome structures with short-range hexagonal
order can be observed. An average dot height of 15 nm was
determined, corresponding to a surface roughness of 4 nm.
The central image of Figure 4, taken at point B in the center
of the Co layer, reveals that the self-organized pattern has
been successfully transferred to it. Finally, the image taken at
point C, with its great similarity to both A and B, proves that
the dot pattern has been preserved during the passage
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Figure 3. Real-time depth profiling of the heterostructure during sputtering. The Co layer can be clearly detected in secondary neutrals mass
spectrometry (SNMS) measurements, providing endpoint control of the
process. The arrows mark the time positions where the erosion was interrupted to record the AFM images displayed in Figure 4.
through the metallic layer. The average dot height has increased to 25 nm, i.e., 8 nm rms roughness, thanks to the mask
effect provided by the Co film: since the erosion velocity is
slower within it, the minima in the surface profile deepen
much faster, compared to the hillsides, once they reach the
underlying GaSb base layer.
The degree of ordering of the nanodot array can best be
assessed from the fast Fourier transforms (FFTs) of the AFM
images. The inset in Figure 4C depicts the two-dimensional
(2D) power spectrum of the topographic image. Several concentric intensity rings can be identified. The radial distribution of intensity, obtained by angular integration of the FFT
pattern, is presented in Figure 4D; it shows the existence of at
least four well-defined peaks, indicating a remarkable longrange positional order, i.e., comparable interdot distances.
The separation between the peaks translates into a characteristic distance between dots of 44 nm, corresponding to a dot
density of 6 × 1010 cm–2. The average diameter of the dots, as
determined also from the AFM images, is ca. 25 nm. The outer rim of the Co discs is likely to have become amorphized
during the sputter process within the penetration depth of the
impinging ions, that is approximately 3 nm at a kinetic ion
energy of 400 eV. Additionally, we have routinely performed
Co L-edge X-ray absorption spectroscopy (XAS) experiments, to be reported elsewhere, using both the X-ray fluorescence and total electron yield secondary channels. From the
spectral shape of the Co L-edge white lines in the sputtered
area, we can conclude that the Co atoms in the dots are in the
metallic state. Oxygen-induced multiplet features at the Co
white lines are absent from almost the whole area of the
eroded region. They are only weakly visible at the outer rim
of this region. Furthermore, extended X-ray absorption fine
structure (EXAFS) data measured at the Co K-edge also reveal that the Co within the dots is in a structural state quite
similar to that of the original film, with only a minor increase
in disorder, which is probably related to the amorphous rim.
The magnetic behavior of both the resulting dot array after
patterning and the continuous Co thin film reference (mea-
Figure 4. Three AFM snapshots of the surface of a GaSb/Co/GaSb heterostructure during sputtering with 400 eV Ar+ ions. A) Some tens of nanometers above the Co layer. B) In the middle of the 5 nm thick Co film. C) At the bottom edge of the Co layer. These snapshots correspond to the positions
labeled A, B, and C in Figure 3. The z-scale (brightness) |OK?| spans 40 nm in all three images. The corresponding rms roughness values are
4.0 nm (A), 4.4 nm (B), and 7.9 nm (C). The inset in (C) displays the 2D power spectrum obtained by FFT of the topographic AFM image. D) Radial
profile of intensity versus wavevector qr as calculated by integration of the 2D power spectrum in circles as a function of qr. The characteristic distance
between the dots (ddot = 44 nm) is determined from the peak positions.
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sured on an equivalent sample with a thinner capping, before
sputtering) was characterized by means of vectorial Kerr magnetometry (see Experimental). The angular dependence of
the magnetization reversal was studied by measuring simultaneously the two components of the in-plane magnetization,
parallel (M||) and perpendicular (M?) to the field direction
(angle h).[28] Figure 5a shows selected in-plane resolved hysteresis loops measured on the continuous film and on the
dotted area. The saturation of the parallel component of the
former is taken as 1; all other loops are normalized to this value. A uniaxial magnetic anisotropy is found in the continuous
film, probably originating from a remanence stray magnetic
field of the magnetron source during deposition. Parallel to
the easy axis (h = 0°), a negligible M? and a sharp irreversible
transition in M||, with a remanence close to saturation and a
coercive field of just 1.8 mT, are found. Irreversible and reversible transitions in both M|| and M? components are seen
when the field is applied out of the easy axis. Larger M? values are found close to a hard axis, i.e., h = 90°. Around the
easy-axis and hard-axis directions, M||(H) and M?(H) curves
show identical and symmetric (different sign) behaviors,
respectively.
For the Co dots, several differences are observed with
respect to the continuous film. First, the saturation intensity is
approximately one-third that measured on the continuous
film, corresponding to the partial removal of the material during the patterning process. Second, the coercive field increases
by almost one order of magnitude, up to 15.3 mT. This effect
can be explained by a change in the mechanism of magnetization reversal. In the continuous layer the latter is mostly
achieved by the propagation of domain walls after the nucleation barriers are overcome at low coordination sites, such as
defects or grain boundaries. In contrast, this mechanism can
be neglected for the dots because they have sizes of the order
of the domain wall width, and therefore can be expected to be
single-domain. Their magnetization reversal must hence be
governed by coherent rotation, for which a large coercive field
is expected.[29] These observations thus already reveal that
independent, self-organized, magnetic nanoparticles with a
lateral periodicity of 44 nm have been successfully produced
by our pattern transfer method.
An additional indication of nanomagnet formation comes
from the remarkable observation that no in-plane anisotropy
exists within the dotted area. Negligible M? and similar reversal with nearly 100 % remanence in M|| are found at all angles.
This means not only that the original uniaxial anisotropy of
the buried Co film has disappeared, but also that no preferential direction exists within the dot ensemble. In general, an array of uncoupled and magnetically isotropic particles would
also present isotropic reversal behavior, but this would yield
hysteresis curves with both zero coercive field and zero remanence, which is in contradiction to the experiment. The absence of anisotropy could also be understood in a hexagonal
array of particles with some amount of disorder without anisotropy but strongly coupled; however, the remanence in
those systems decreases with increasing system size, and in
the limit of an infinite array it approaches zero.[30] We consider then a third alternative, by assuming that the system consists of an array of particles with negligible coupling but randomly distributed n-fold anisotropy. For instance, elliptic
particles would induce a uniaxial shape anisotropy of magnetostatic origin, with n = 1. Crystal lattices with square and
hexagonal symmetries such as face-centered cubic (fcc) [100]
and [111] orientations would yield magnetocrystalline anisotropies with n = 2 and n = 3, respectively.
In order to test the third alternative, we have performed numerical simulations based on the Stoner–Wohlfarth model.[31]
In the presence of an applied magnetic field, in the general
case, the total energy density is
Etot ˆ Kn sin 2 n…j
h†
l0 MS H cos …j†
(1)
where Kn is the anisotropy constant, MS the saturation magnetization, and j the angle between magnetization and field,
while h is the angle between applied field H and the easy anisotropy axis. Hysteresis loops are determined numerically via
energy minimization of Equation 1. Based on our structural
characterization of the Co film by X-ray diffraction (XRD),
Figure 5. a) Selected in-plane resolved magnetization curves acquired by vectorial Kerr magnetometry in the continuous 5 nm thick Co film (left
graphs) and in the Co dot array after patterning (right graphs). The vertical axes have been normalized to the saturation value of the parallel component of the continuous film. b) Comparison of the hysteresis curves measured in the Co dot array (symbols) and those derived from the model (continuous lines) described in the text. The inset shows schematically a dot array with randomly oriented threefold anisotropy (denoted by three white lines
corresponding to the three easy axes of magnetization). The randomness over the array results in zero effective anisotropy.
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© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2007, 19, 4375–4380
Experimental
All the samples used in the sputtering experiments reported here
were grown upon commercially available 2 in (ca. 5 cm) intrinsic Si
wafers with (100) orientation. Three layers were deposited by magnetron sputtering: a 100 nm bottom GaSb buffer, followed by a thin Co
Adv. Mater. 2007, 19, 4375–4380
layer (5 nm), and a top GaSb film with a thickness of 1 lm. The sputter deposition parameters were optimized to yield a surface roughness
of less than 0.2 nm and thickness inhomogeneities of less than ±5 %;
the pressure and power density used were 0.43 Pa and 1.5 W cm–2, respectively, for the GaSb layers, and 0.26 Pa and 2.0 W cm–2 for the Co
layer. This results in deposition rates of 19 and 13 nm min–1 for GaSb
and Co, respectively. The films’ crystallinity was characterized by
means of XRD: according to these measurements, the GaSb films
were amorphous while the Co layers had a polycrystalline nature with
(111) texture. The surface roughness was determined by means of
AFM images acquired after the deposition of each layer. The rms
roughness of the Co film was found to be about 0.2 nm, whereas the
GaSb layers displayed a surface roughness of approximately 0.4 nm.
The samples were rinsed in ethanol before the erosion process. The
ion sputtering apparatus is a commercial depth profiling system Leybold INA 3, operating in secondary neutrals mass spectrometry
(SNMS) mode. The temperature of the sample holder was kept at
about 80 °C during sputtering with the help of a water cooling circuit.
The Ar+ ions used in all the experiments reported here are generated
in a plasma chamber and extracted with the aid of a voltage applied
between the chamber aperture and the sample, which is located at
8 mm distance. This extraction method produces a very monoenergetic, collimated ion beam that impinges on the surface perpendicularly. The ion flux is about 6 × 1015 cm–2 s–1.
In the Kerr magnetometer p-polarized incident light is combined
with the simultaneous detection of the two orthogonal components of
the reflected light to allow the simultaneous measurement of the two
components of the in-plane magnetization, parallel (M||) and perpendicular (M?) to the field direction.[28] M|| originates from the difference of the two components of the reflected light, i.e., Kerr rotation,
whereas M? originates from the small variation of their sum, i.e., reflectivity changes. The sample is mounted in a stepper-motorized eucentric goniometer head that keeps the reflection plane fixed for the
whole set of experiments, so that the absolute values of the magnetization determined in different measurements can be compared. Inplane resolved hysteresis loops were obtained at room temperature
by averaging many successive iterations, with an acquisition time of
ca. 1 s per sweep. The whole angular range was probed every 4.5°,
with 0.5° angular resolution.
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which revealed a polycrystalline nature with (111) texture, we
chose n = 3. The overall zero anisotropy is accounted for by
averaging over all field directions h, which is equivalent to a
random distribution of the easy axis directions among the particles (see the inset in Fig. 5b).
The average of M?(H) is zero, resulting from the symmetric
behavior of the independent curves with respect to the
easy and hard axis directions. The averaged M||(H) hysteresis
curve presents 0.95 remanence value,[32] in agreement with
the experimental one. Using saturation magnetization
MS = 1.40 × 106 A m–1 for Co,[33] the experimental hysteresis
curves could be fitted with an anisotropy of
K3 = (3.3 ± 0.1) × 103 J m–3 (see Fig. 5b). This is within 10 % of
the literature value for the threefold anisotropy of bulk cobalt;[34] no other free parameters were used in the calculation.
The agreement between the experimental data and the calculation is striking, given the simplicity of the model. Only small
deviations are observed near the onset of the magnetization
reversal: the experimental transition is less sharp than predicted, which can easily be explained by assuming some inevitable dispersion in the sizes and shapes of the Co nanoparticles, as well as in the orientation of their crystallographic axes
with respect to the surface normal. Lastly, a finite, albeit
weak, interparticle coupling, not considered in the model, will
change the local switching fields of the particles.
In summary, we have demonstrated how the self-organized
pattern created by ion erosion on a GaSb film can be successfully transferred to an intercalated metallic layer (Co in this
case), resulting in the formation of an array of nanoparticles
that displays short-range hexagonal order, with a density of
ca. 0.38 Tb/in2; (terabits per square inch) the nanomagnets’
size and separation can be tuned by adjusting the ion energy.
Their magnetic behavior has been explained with the aid of a
model calculation and corresponds to an array of particles
with bulk-like, in-plane, threefold anisotropy, with the (111)
axis perpendicular to the surface and randomly oriented in
the surface plane. While these characteristics do not make this
material competitive as a candidate for magnetic data storage,
several improvements appear possible: work is already in
progress to replace the Co used in these experiments as the
magnetic material by (Co/Pt) multilayer stacks with higher
coercivity and a well-defined perpendicular anisotropy. The
degree of long-range order might also be improved by combining the sputtering technique with some sort of imprinting
or lithography.[8] And, most importantly, this method should
be readily applicable, with little adjustment, to the fabrication
of large-area arrays of nanometer-sized particles of many
other materials, whether semiconductors, metals, or heterostructures.
Received: May 13, 2007
Revised: July 11, 2007
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