Self-organized metal nanostructures through laser driven thermocapillary convection
C. Favazza, J. Trice, R. Kalyanaraman
Department of Physics, Washington University in St. Louis, MO 63130 and
Center for Materials Innovation, Washington University in St. Louis, MO 63130
R. Sureshkumar
Department of Energy, Environmental, and Chemical Engineering,
Washington University in St. Louis, MO 63130 and
Center for Materials Innovation, Washington University in St. Louis, MO 63130
When ultrathin metal films are subjected to multiple cycles of rapid melting and resolidification
by a ns pulsed laser, spatially correlated interfacial nanostructures can result from a competition
among several possible thin film self-organizing processes. Here we investigate self-organization
and the ensuing length scales when Co films (1 − 8nm thick) on SiO2 surfaces are repeatedly and
rapidly melted by non-uniform (interference) laser irradiation. Pattern evolution produces nanowires,
which eventually break-up into nanoparticles exhibiting spatial order in the nearest neighbor spac-
ing, λNN2. For films of thickness h0 > 2nm, λNN2 ∝ h
while the particle radius varies as
rp2 ∝ h
. This scaling behavior is consistent with pattern formation by thermocapillary flow and
a Rayleigh-like instability. For h0 ≤ 2nm, a hydrodynamic instability of a spinodally unstable film
leads to the formation of nanoparticles.
Metal nanostructures, possessing spatial order and size uniformity are attractive for a variety of ap-
plications including: optoelectronics, plasmonics, chemical and biomedical sensing, and catalytic devices
[1, 2, 3, 4, 5]. In recent years there has been tremendous research emphasis on finding self-organization
strategies to make strongly correlated metal and semiconductor nanostructures. In the area of thin film
pattern formation, epitaxial strain driven self-organization in crystallographic systems has been somewhat
successful [6, 7, 8, 9]. However, this strategy of exploiting epitaxial strain cannot be applied to materials on
important amorphous surfaces, such as SiO2. One possibility for self-organization on amorphous surfaces
is via dewetting instabilities, such as those observed in liquid polymer films on various inert surfaces, in
which preferred length scales appear when destabilizing long range attractive intermolecular forces over-
come stabilizing surface tension forces [10, 11, 12]. We have previously shown that multiple pulses of
single beam ns laser irradiation of Co films with thickness 1 ≤ h0 ≤ 8nm on SiO2 surfaces demonstrate
self-organization by a thin film hydrodynamic (TFH) instability with length scales characterized by the
metal surface tension (γ), the dispersion force characterized by the Hamaker constant A and film thickness
h0 [13]. The ensuing pattern had short range spatial order (SRO) in the nearest-neighbor (NN ) particle
http://arxiv.org/abs/0704.1179v1
spacing λNN1, which scaled with thickness as h
, while the particle radius varied as rp1 ∼ h
. Recently
we have also provided preliminary evidence that 2-beam laser interference irradiation can give rise to quasi-
2D ordering of the nanoparticles with both long range order (LRO) and SRO [14]. However the evolution
of the 2-beam pattern from the flat film to nanoparticle state was not investigated, and the mechanisms for
spatial ordering were not identified. Here we report detailed experiments of 2-beam interference irradiation
of Co on SiO2 as a function of film thickness for 1 ≤ h0 ≤ 8nm that demonstrate that the pattern evolution
and resulting length scales are consequences of different mechanisms, including the TFH instability, ther-
mocapillary (TC) flow and a Rayleigh-like instability, based on the timescales of these processes. One can
access a particular mechanism via the choice of film thickness and/or thermophysical parameters such as γ,
A and the temperature gradient.
Cobalt films ranging in thickness from ∼ 1−8nm were deposited by e-beam evaporation onto optically
smooth SiO2 surfaces in vacuum. Specific details of the experiments are published elsewhere [14, 15]. In
brief, following deposition, the Co films were irradiated in vacuum with a 266nm pulsed laser operating
at a repetition rate of 50Hz with a pulse time τ ∼ 9ns by single beam [13] or 2-beam interference
irradiation. In the single beam case, films were exposed to an unfocused beam at normal incidence. For the
2-beam condition, an interference angle of ∼ 45◦ generated a periodic laser intensity profile whose contrast
was maximized by adjusting the energy density of the off-normal beam with a 750mm lens positioned
300mm away from the sample at angle of ∼ 45◦. In both instances, Co films were irradiated for similar
times as measured by the number of laser pulses, n, for 5 ≤ n ≤ 10, 500. Also, comparable laser energy
densities were used for both types of irradiation, with the energy density, Elaser between EThreshold <
60 ≤ Elaser ≤ 200mJ [16]. The resultant morphological evolution was investigated as a function of n and
was examined and characterized using a Hitachi S-4500 scanning electron microscope (SEM). It was also
verified that all the films studied had minimal evaporation, as confirmed by performing energy dispersive
X-ray spectrometry measurements of the Co concentration after irradiation.
As detailed in prior studies for single beam irradiation [13, 16], the film shows several distinct patterns
enroute to a final robust state of nanoparticles characterized by a spatially correlated nearest neighbor (NN )
spacing. Here we briefly summarize the trends for the purpose of comparison with the pattern evolution
under 2-beam interference irradiation. More detailed analysis the single beam data can be found elsewhere
[13, 16]. At the early stages (n = 10) regular holes with a characteristic diameter form, followed by a
cellular network of polygonal structures. Eventually, the polygonal networks evolve into nanoparticles,
which form predominantly at the vertices of the polygons. An important property of the evolution is that
the patterns possessed a characteristic length scale at every stage. In Fig. 1(a), the scaling behavior of the
spatial correlation in the final stable nanoparticle state is shown for varying initial film thicknesses. The
observed trend with h0 was in agreement with classical linear TFH dewetting theory [10, 11] in which:
ΛTFH =
16π3γ
h2o (1)
where ΛTFH represents the average NN nanoparticle spacing, λNN1, A = 1.4 × 10−18J is the experi-
mentally estimated Hamaker constant for the SiO2/Co/V acuum system , γ = 1.88
is the Co liquid
surface tension and h0 is the film thickness [10, 11]. Furthermore, volume conservation implied that the
nanoparticles will have a radius that will vary with the initial film thickness h0 as:
rp1 =
24π3γ
f(θ)A
o (2)
where f(θ) accounts for the contact angle of the nanoparticles [13]. We experimentally observed a
monomodal particle size distribution with the average radius shown in Fig. 1(b) and a trend consistent
with the above theoretical prediction from linear TFH theory.
The results of 2-beam irradiation were qualitatively different from single beam irradiation. In Fig. 2(a-
c), the typical pattern evolution for films with h0 > 2nm is shown as a function of n. In this case, the
early stages are comprised of spatially periodic film rupture at length scales comparable to the interference
spacing. Longer irradiation yielded the formation of long, cylindrical-like “nanowires” and continued irra-
diation resulted in the break-up of these nanowires into particles. The final particle state is characterized by
a quasi-2D, comprised of the LRO due to periodic laser intensity and SRO resulting from the break-up of
the nanowires. The observed differences from the two processing conditions can be explained on the basis
of the various mechanisms of fluid motion operating under the two irradiation conditions. When irradiating
the metal film with a 2-beam interference pattern, the resulting periodic laser intensity induces a transient
and periodic thermal gradient along the plane of the film which creates a surface tension gradient not present
in the single beam irradiation. Consequently, TC or Marangoni convection of the molten Co can occur. To
contrast the results of single beam and 2-beam irradiation, the time scales for the various mechanisms were
estimated. The timescale for TC flow can be expressed as [17]:
τMa =
Λ2laserη
where Λlaser = 350nm is the laser fringe spacing, η = 4.45 × 10−3 Pas, is the Co metal viscosity,
= −0.34× 10−3Jm−2K−1 is the rate at which the surface tension of the Co changes with temperature
and ∆T is the maximum temperature difference between the peak and valley of the laser fringe. The
timescale for the TFH instability can be expressed as [10, 11]:
96πγη
An important aspect of the above equations is that the time scale of the TC flow decreases with increasing
h0 while the TFH instability increases with increasing h0. We determined that typical liquid lifetimes range
from 1 ≤ τL ≤ 10ns and thermal gradients range from 0.5−0.7 Knm [14, 16]. From Eq. 3 and 4, τs > τMa
for films with ho ≤ 2nm and τs < τMa for films with h0 > 2nm. This implies that pattern formation
is dominated by the TC flow for h0 > 2nm with the TFH flow dominating for h0 < 2nm, as shown in
the comparative timescale plot in Fig. 3. This result was confirmed experimentally as nanowire formation
was observed only above 2nm while it was absent for films < 2nm, as shown in Fig. 3(inset A). For film
thicknesses near the cross-over point of h0 = 2nm, the pattern consisted of particle formation with some
evidence for lateral movement of the metal (Fig. 3(inset B)) indicating that both mechanisms are operative
[18].
For films with h0 > 2nm nanowire formation under the 2-beam irradiation also permitted access to a
Rayleigh-like instability in which cylinders are unstable to wavelengths ≥ 2πrcyl, with the fastest growing
wavelength scaling as ΛR ∝ rcyl , where rcyl is the radius of the cylinder. The characteristic time scale for
this process can be expressed as [12, 19]:
ρr3cyl
where ρ = 7.8 g
is the liquid density of Co [20]. Assuming these are partial cylinders with contact angles
> 90◦and using the projected width of these regions from SEM images, we estimated rcyl, preceding
the break-up into nanoparticles, to be in the range of 35 − 55nm. Based on these values of rcyl, the
typical magnitude for the cylinder break-up time was estimated as τRay ∼ 1 − 2ns. Since this time scale
is comparable to or smaller than the typical liquid lifetimes, the Rayleigh process is clearly accessible
whenever a cylinder is formed. Also, according to the Rayleigh formulation, the particle radius scales
linearly with both the spacing between particles and the radius of the original cylinder [19, 21, 22]. Through
volume conservation, the cylinder radius varies as rcyl ∝ h
o , resulting in a similar scaling relation for
the size of the particle as rp2 ∝ h
o . As shown in Fig. 1(a-b), the particle spacing and the size both
scale as h
o and the ratio of particle spacing to radius is independent of film thickness. While, the ratio
in the classical Rayleigh break-up of a perfect cylinder is expected to be λNN2
∼ 4.7 [19, 21, 22] our
measured ratio was ≃ 5.6. We have ruled out previously existing explanations for how this ratio can be
modified [23, 24, 25, 26, 27, 28]. Nichols et al. [23] have shown that if the break-up is dominated by solid-
state surface diffusion, then the ratio is maintained, however, if the flow is generated by external volume
diffusion, then the ratio grows to ∼ 6.1. However, the timescale over which external volume diffusion
can cause break-up has been estimated as ∼ 0.3 s (τvol ∼
13DV γΩ
, where Dv is the volume self-diffusion
coefficient, Ω is the atomic volume and f is the correlation factor [23]) for cylinder with rcyl = 40nm.
This timescale is well outside the realm of the laser processing time (for t = 0.3 s, n ∼ O(106)), and
as such can be disregarded as a possible break-up mechanism. We have also estimated the correction to
the ratio for situations in which truncated cylinders break-up based on the work by McCallum et al. [24]
and determined that only a small change to the ratio will be introduced. While there have also been papers
examining the effect of having a non-uniform contact line or an anisotropic surface, these models also do
not yield the observed 5.6 ratio [27, 28]. It is possible that the thermocapillary flow and a Rayleigh-like
instability can drive self-organization of the film such that the liquid profiles are stationary solutions to the
non-linear equations describing the pattern evolution [29, 30]. However, a nonlinear analysis along with
further experiments are required to verify such a hypothesis.
In conclusion, self-organization leading to spatially correlated nanostructures under ns laser irradiation
of ultrathin Co films on SiO2 has been investigated. For films with thickness 2 − 8nm, non-uniform laser
irradiation by 2-beam interference leads to pattern formation characterized by the formation of nanowires
via thermocapillary flow and eventually to nanoparticles via a Rayleigh-like break-up of the nanowires.
The nanowire break-up results in an average nearest-neighbor particle spacing of λNN2 ∝ h
with radius
rp2 ∝ h
in contrast to the TFH instability in which λNN1 ∝ h20 and rp1 ∝ h
. For films with
h0 ≤ 2nm nanowire formation was absent because the TFH time scales were much shorter than the TC
timescale. These results show that self-organization through laser-induced hydrodynamic flow can be used
to make a variety of strongly correlated surface nanostructures on amorphous substrates by selecting the
appropriate film thickness based upon thermophysical parameters.
RK and RS acknowledge support by the NSF through a CAREER grant DMI-0449258 and grant CTS
0335348 respectively.
*Electronic address: ramkik@wuphys.wustl.edu, †Electronic address: suresh@wustl.edu
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http://arxiv.org/
http://arxiv.org/abs/cond-mat/0609182
Figure captions
• Figure 1: Self-organized length scales versus initial film thickness: (a)
h0 dependency for the parti-
cle radius from 2-beam interference irradiation (open squares); and h
dependency from single beam
irradiation (closed triangles). (b)
h0 dependency for the particle spacing from 2-beam irradiation
(open squares) and h2
dependency from single beam irradiation (closed triangles).
• Figure 2: SEM images depicting the stages of pattern formation for 2-beam interference irradiation
of a ∼ 6 nm film as a function of increasing number of laser pulses n: (a) periodic rupture (b)
nanowires and (c) the final nanoparticle state which exhibits both LRO and SRO. (Co rich and SiO2
rich regions correspond to bright and dark contrast respectively).
• Figure 3: Comparison of the time scales for TFH dewetting and thermocapillary (TC) flow as a
function of initial film thickness with the morphology for various film thickness following irradiation
(insets). (A) h ≤ 1nm film showing that the entire film dewets; (B) h ∼ 2nm film showing that
while TC flow causes the film to split there is still evidence for TFH dewetting and (C) h ∼ 4.5nm
film showing that TC forces completely dominate morphology change. (Co rich and SiO2 rich
regions correspond to bright and dark contrast respectively).
(a) (b)
Figure 1:
(a) (b) (c)
Figure 2:
Figure 3:
	References
	Figure captions

  When ultrathin metal films are subjected to multiple cycles of rapid melting
and resolidification by a ns pulsed laser, spatially correlated interfacial
nanostructures can result from a competition among several possible thin film
self-organizing processes. Here we investigate self-organization and the
ensuing length scales when Co films (1-8 nm thick) on SiO_{\text{2}} surfaces
are repeatedly and rapidly melted by non-uniform (interference) laser
irradiation. Pattern evolution produces nanowires, which eventually break-up
into nanoparticles exhibiting spatial order in the nearest neighbor spacing,
\lambda_{NN2}.The scaling behavior is consistent with pattern formation by
thermocapillary flow and a Rayleigh-like instability. For h_{0}\leq2 nm, a
hydrodynamic instability of a spinodally unstable film leads to the formation
of nanoparticles.

Self-organized metal nanostructures through laser driven thermocapillary convection
C. Favazza, J. Trice, R. Kalyanaraman
Department of Physics, Washington University in St. Louis, MO 63130 and
Center for Materials Innovation, Washington University in St. Louis, MO 63130
R. Sureshkumar
Department of Energy, Environmental, and Chemical Engineering,
Washington University in St. Louis, MO 63130 and
Center for Materials Innovation, Washington University in St. Louis, MO 63130
When ultrathin metal films are subjected to multiple cycles of rapid melting and resolidification
by a ns pulsed laser, spatially correlated interfacial nanostructures can result from a competition
among several possible thin film self-organizing processes. Here we investigate self-organization
and the ensuing length scales when Co films (1 − 8nm thick) on SiO2 surfaces are repeatedly and
rapidly melted by non-uniform (interference) laser irradiation. Pattern evolution produces nanowires,
which eventually break-up into nanoparticles exhibiting spatial order in the nearest neighbor spac-
ing, λNN2. For films of thickness h0 > 2nm, λNN2 ∝ h
while the particle radius varies as
rp2 ∝ h
. This scaling behavior is consistent with pattern formation by thermocapillary flow and
a Rayleigh-like instability. For h0 ≤ 2nm, a hydrodynamic instability of a spinodally unstable film
leads to the formation of nanoparticles.
Metal nanostructures, possessing spatial order and size uniformity are attractive for a variety of ap-
plications including: optoelectronics, plasmonics, chemical and biomedical sensing, and catalytic devices
[1, 2, 3, 4, 5]. In recent years there has been tremendous research emphasis on finding self-organization
strategies to make strongly correlated metal and semiconductor nanostructures. In the area of thin film
pattern formation, epitaxial strain driven self-organization in crystallographic systems has been somewhat
successful [6, 7, 8, 9]. However, this strategy of exploiting epitaxial strain cannot be applied to materials on
important amorphous surfaces, such as SiO2. One possibility for self-organization on amorphous surfaces
is via dewetting instabilities, such as those observed in liquid polymer films on various inert surfaces, in
which preferred length scales appear when destabilizing long range attractive intermolecular forces over-
come stabilizing surface tension forces [10, 11, 12]. We have previously shown that multiple pulses of
single beam ns laser irradiation of Co films with thickness 1 ≤ h0 ≤ 8nm on SiO2 surfaces demonstrate
self-organization by a thin film hydrodynamic (TFH) instability with length scales characterized by the
metal surface tension (γ), the dispersion force characterized by the Hamaker constant A and film thickness
h0 [13]. The ensuing pattern had short range spatial order (SRO) in the nearest-neighbor (NN ) particle
http://arxiv.org/abs/0704.1179v1
spacing λNN1, which scaled with thickness as h
, while the particle radius varied as rp1 ∼ h
. Recently
we have also provided preliminary evidence that 2-beam laser interference irradiation can give rise to quasi-
2D ordering of the nanoparticles with both long range order (LRO) and SRO [14]. However the evolution
of the 2-beam pattern from the flat film to nanoparticle state was not investigated, and the mechanisms for
spatial ordering were not identified. Here we report detailed experiments of 2-beam interference irradiation
of Co on SiO2 as a function of film thickness for 1 ≤ h0 ≤ 8nm that demonstrate that the pattern evolution
and resulting length scales are consequences of different mechanisms, including the TFH instability, ther-
mocapillary (TC) flow and a Rayleigh-like instability, based on the timescales of these processes. One can
access a particular mechanism via the choice of film thickness and/or thermophysical parameters such as γ,
A and the temperature gradient.
Cobalt films ranging in thickness from ∼ 1−8nm were deposited by e-beam evaporation onto optically
smooth SiO2 surfaces in vacuum. Specific details of the experiments are published elsewhere [14, 15]. In
brief, following deposition, the Co films were irradiated in vacuum with a 266nm pulsed laser operating
at a repetition rate of 50Hz with a pulse time τ ∼ 9ns by single beam [13] or 2-beam interference
irradiation. In the single beam case, films were exposed to an unfocused beam at normal incidence. For the
2-beam condition, an interference angle of ∼ 45◦ generated a periodic laser intensity profile whose contrast
was maximized by adjusting the energy density of the off-normal beam with a 750mm lens positioned
300mm away from the sample at angle of ∼ 45◦. In both instances, Co films were irradiated for similar
times as measured by the number of laser pulses, n, for 5 ≤ n ≤ 10, 500. Also, comparable laser energy
densities were used for both types of irradiation, with the energy density, Elaser between EThreshold <
60 ≤ Elaser ≤ 200mJ [16]. The resultant morphological evolution was investigated as a function of n and
was examined and characterized using a Hitachi S-4500 scanning electron microscope (SEM). It was also
verified that all the films studied had minimal evaporation, as confirmed by performing energy dispersive
X-ray spectrometry measurements of the Co concentration after irradiation.
As detailed in prior studies for single beam irradiation [13, 16], the film shows several distinct patterns
enroute to a final robust state of nanoparticles characterized by a spatially correlated nearest neighbor (NN )
spacing. Here we briefly summarize the trends for the purpose of comparison with the pattern evolution
under 2-beam interference irradiation. More detailed analysis the single beam data can be found elsewhere
[13, 16]. At the early stages (n = 10) regular holes with a characteristic diameter form, followed by a
cellular network of polygonal structures. Eventually, the polygonal networks evolve into nanoparticles,
which form predominantly at the vertices of the polygons. An important property of the evolution is that
the patterns possessed a characteristic length scale at every stage. In Fig. 1(a), the scaling behavior of the
spatial correlation in the final stable nanoparticle state is shown for varying initial film thicknesses. The
observed trend with h0 was in agreement with classical linear TFH dewetting theory [10, 11] in which:
ΛTFH =
16π3γ
h2o (1)
where ΛTFH represents the average NN nanoparticle spacing, λNN1, A = 1.4 × 10−18J is the experi-
mentally estimated Hamaker constant for the SiO2/Co/V acuum system , γ = 1.88
is the Co liquid
surface tension and h0 is the film thickness [10, 11]. Furthermore, volume conservation implied that the
nanoparticles will have a radius that will vary with the initial film thickness h0 as:
rp1 =
24π3γ
f(θ)A
o (2)
where f(θ) accounts for the contact angle of the nanoparticles [13]. We experimentally observed a
monomodal particle size distribution with the average radius shown in Fig. 1(b) and a trend consistent
with the above theoretical prediction from linear TFH theory.
The results of 2-beam irradiation were qualitatively different from single beam irradiation. In Fig. 2(a-
c), the typical pattern evolution for films with h0 > 2nm is shown as a function of n. In this case, the
early stages are comprised of spatially periodic film rupture at length scales comparable to the interference
spacing. Longer irradiation yielded the formation of long, cylindrical-like “nanowires” and continued irra-
diation resulted in the break-up of these nanowires into particles. The final particle state is characterized by
a quasi-2D, comprised of the LRO due to periodic laser intensity and SRO resulting from the break-up of
the nanowires. The observed differences from the two processing conditions can be explained on the basis
of the various mechanisms of fluid motion operating under the two irradiation conditions. When irradiating
the metal film with a 2-beam interference pattern, the resulting periodic laser intensity induces a transient
and periodic thermal gradient along the plane of the film which creates a surface tension gradient not present
in the single beam irradiation. Consequently, TC or Marangoni convection of the molten Co can occur. To
contrast the results of single beam and 2-beam irradiation, the time scales for the various mechanisms were
estimated. The timescale for TC flow can be expressed as [17]:
τMa =
Λ2laserη
where Λlaser = 350nm is the laser fringe spacing, η = 4.45 × 10−3 Pas, is the Co metal viscosity,
= −0.34× 10−3Jm−2K−1 is the rate at which the surface tension of the Co changes with temperature
and ∆T is the maximum temperature difference between the peak and valley of the laser fringe. The
timescale for the TFH instability can be expressed as [10, 11]:
96πγη
An important aspect of the above equations is that the time scale of the TC flow decreases with increasing
h0 while the TFH instability increases with increasing h0. We determined that typical liquid lifetimes range
from 1 ≤ τL ≤ 10ns and thermal gradients range from 0.5−0.7 Knm [14, 16]. From Eq. 3 and 4, τs > τMa
for films with ho ≤ 2nm and τs < τMa for films with h0 > 2nm. This implies that pattern formation
is dominated by the TC flow for h0 > 2nm with the TFH flow dominating for h0 < 2nm, as shown in
the comparative timescale plot in Fig. 3. This result was confirmed experimentally as nanowire formation
was observed only above 2nm while it was absent for films < 2nm, as shown in Fig. 3(inset A). For film
thicknesses near the cross-over point of h0 = 2nm, the pattern consisted of particle formation with some
evidence for lateral movement of the metal (Fig. 3(inset B)) indicating that both mechanisms are operative
[18].
For films with h0 > 2nm nanowire formation under the 2-beam irradiation also permitted access to a
Rayleigh-like instability in which cylinders are unstable to wavelengths ≥ 2πrcyl, with the fastest growing
wavelength scaling as ΛR ∝ rcyl , where rcyl is the radius of the cylinder. The characteristic time scale for
this process can be expressed as [12, 19]:
ρr3cyl
where ρ = 7.8 g
is the liquid density of Co [20]. Assuming these are partial cylinders with contact angles
> 90◦and using the projected width of these regions from SEM images, we estimated rcyl, preceding
the break-up into nanoparticles, to be in the range of 35 − 55nm. Based on these values of rcyl, the
typical magnitude for the cylinder break-up time was estimated as τRay ∼ 1 − 2ns. Since this time scale
is comparable to or smaller than the typical liquid lifetimes, the Rayleigh process is clearly accessible
whenever a cylinder is formed. Also, according to the Rayleigh formulation, the particle radius scales
linearly with both the spacing between particles and the radius of the original cylinder [19, 21, 22]. Through
volume conservation, the cylinder radius varies as rcyl ∝ h
o , resulting in a similar scaling relation for
the size of the particle as rp2 ∝ h
o . As shown in Fig. 1(a-b), the particle spacing and the size both
scale as h
o and the ratio of particle spacing to radius is independent of film thickness. While, the ratio
in the classical Rayleigh break-up of a perfect cylinder is expected to be λNN2
∼ 4.7 [19, 21, 22] our
measured ratio was ≃ 5.6. We have ruled out previously existing explanations for how this ratio can be
modified [23, 24, 25, 26, 27, 28]. Nichols et al. [23] have shown that if the break-up is dominated by solid-
state surface diffusion, then the ratio is maintained, however, if the flow is generated by external volume
diffusion, then the ratio grows to ∼ 6.1. However, the timescale over which external volume diffusion
can cause break-up has been estimated as ∼ 0.3 s (τvol ∼
13DV γΩ
, where Dv is the volume self-diffusion
coefficient, Ω is the atomic volume and f is the correlation factor [23]) for cylinder with rcyl = 40nm.
This timescale is well outside the realm of the laser processing time (for t = 0.3 s, n ∼ O(106)), and
as such can be disregarded as a possible break-up mechanism. We have also estimated the correction to
the ratio for situations in which truncated cylinders break-up based on the work by McCallum et al. [24]
and determined that only a small change to the ratio will be introduced. While there have also been papers
examining the effect of having a non-uniform contact line or an anisotropic surface, these models also do
not yield the observed 5.6 ratio [27, 28]. It is possible that the thermocapillary flow and a Rayleigh-like
instability can drive self-organization of the film such that the liquid profiles are stationary solutions to the
non-linear equations describing the pattern evolution [29, 30]. However, a nonlinear analysis along with
further experiments are required to verify such a hypothesis.
In conclusion, self-organization leading to spatially correlated nanostructures under ns laser irradiation
of ultrathin Co films on SiO2 has been investigated. For films with thickness 2 − 8nm, non-uniform laser
irradiation by 2-beam interference leads to pattern formation characterized by the formation of nanowires
via thermocapillary flow and eventually to nanoparticles via a Rayleigh-like break-up of the nanowires.
The nanowire break-up results in an average nearest-neighbor particle spacing of λNN2 ∝ h
with radius
rp2 ∝ h
in contrast to the TFH instability in which λNN1 ∝ h20 and rp1 ∝ h
. For films with
h0 ≤ 2nm nanowire formation was absent because the TFH time scales were much shorter than the TC
timescale. These results show that self-organization through laser-induced hydrodynamic flow can be used
to make a variety of strongly correlated surface nanostructures on amorphous substrates by selecting the
appropriate film thickness based upon thermophysical parameters.
RK and RS acknowledge support by the NSF through a CAREER grant DMI-0449258 and grant CTS
0335348 respectively.
*Electronic address: ramkik@wuphys.wustl.edu, †Electronic address: suresh@wustl.edu
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http://arxiv.org/
http://arxiv.org/abs/cond-mat/0609182
Figure captions
• Figure 1: Self-organized length scales versus initial film thickness: (a)
h0 dependency for the parti-
cle radius from 2-beam interference irradiation (open squares); and h
dependency from single beam
irradiation (closed triangles). (b)
h0 dependency for the particle spacing from 2-beam irradiation
(open squares) and h2
dependency from single beam irradiation (closed triangles).
• Figure 2: SEM images depicting the stages of pattern formation for 2-beam interference irradiation
of a ∼ 6 nm film as a function of increasing number of laser pulses n: (a) periodic rupture (b)
nanowires and (c) the final nanoparticle state which exhibits both LRO and SRO. (Co rich and SiO2
rich regions correspond to bright and dark contrast respectively).
• Figure 3: Comparison of the time scales for TFH dewetting and thermocapillary (TC) flow as a
function of initial film thickness with the morphology for various film thickness following irradiation
(insets). (A) h ≤ 1nm film showing that the entire film dewets; (B) h ∼ 2nm film showing that
while TC flow causes the film to split there is still evidence for TFH dewetting and (C) h ∼ 4.5nm
film showing that TC forces completely dominate morphology change. (Co rich and SiO2 rich
regions correspond to bright and dark contrast respectively).
(a) (b)
Figure 1:
(a) (b) (c)
Figure 2:
Figure 3:
	References
	Figure captions
