Lithographically directed self-assembly of nanostructures

TLDR: In this article, a fluidic assembly method that relies on the local pinning of a moving liquid contact line bylithographically produced topographic features to concentratenanoparticles at those features is presented.

Abstract: The combination of lithography and self-assembly provides apowerful means of organizing solution-synthesized nanostructures for awide variety of applications. We have developed a fluidic assembly methodthat relies on the local pinning of a moving liquid contact line bylithographically produced topographic features to concentratenanoparticles at those features. The final stages of the assembly processare controlled first by long-range immersion capillary forces and then bythe short-range electrostatic and Van der Waal's interactions. We havesuccessfully assembled nanoparticles from 50 nm to 2 nm in size usingthis technique and have also demonstrated the controlled positioning ofmore complex nanotetrapod structures. We have used this process toassemble Au nanoparticles into pre-patterned electrode structures andhave performed preliminary electrical characterization of the devices soformed. The fluidic assembly method is capable of very high yield, interms of positioning nanostructures at each lithographically-definedlocation, and of excellent specificity, with essentially no particledeposition between features.

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Lithographically-Directed Self-Assembly of Nanostructures
J. Alexander Liddle
,† Yi Cui*† and Paul Alivisatos*†
†Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA
*Department of Chemistry, University of California, Berkeley, CA
jaliddle@lbl.gov Room 2-419, Lawrence Berkeley National Laboratory, 1 Cyclotron
Road, Berkeley, CA 94720
ABSTRACT
The combination of lithography and self-assembly provides a powerful means of
organizing solution-synthesized nanostructures for a wide variety of applications. We
have developed a fluidic assembly method that relies on the local pinning of a moving
liquid contact line by lithographically produced topographic features to concentrate
nanoparticles at those features. The final stages of the assembly process are controlled
first by long-range immersion capillary forces and then by the short-range electrostatic
and Van der Waal’s interactions. We have successfully assembled nanoparticles from
50 nm to 2 nm in size using this technique and have also demonstrated the controlled
positioning of more complex nanotetrapod structures. We have used this process to
assemble Au nanoparticles into pre-patterned electrode structures and have performed
preliminary electrical characterization of the devices so formed. The fluidic assembly
method is capable of very high yield, in terms of positioning nanostructures at each

lithographically-defined location, and of excellent specificity, with essentially no particle
deposition between features.
Key words: Lithography, directed self-assembly, nanoparticles, nanostructures
INTRODUCTION
Nanostructures synthesized in solution, such as colloidal metal nanocrystals
1
,
2
and
semiconductor quantum dots,
3
,
4
nanorods
5
and nanotetrapods,
6
can have precisely
controlled sizes in the range of 1 to 100 nm and exhibit behaviors distinct from those of
nanostructures fabricated by vacuum deposition or lithography. They have applications
in electronics,
7
magnetics
8
and photonics.
9
Their high degree of uniformity and relative
ease of production means that they are promising building units for nanotechnology. This
promise will not be fulfilled, however, unless methods of positioning and addressing
these units individually can be developed.
Previous efforts in this area have consisted primarily of lithographic patterning
followed by random deposition,
10
,
11
or electrostatic
12
or magnetic
13
trapping of
nanostructures. These approaches do not provide precise positioning, require specific
susceptibilities, have typically low throughput, and/or are not amenable to scaling. We
have developed a simple fluidic method for reproducibly fabricating large-scale arrays
which incorporate controlled numbers of spherical or complex-shape colloidal
nanocrystals at precise, lithographically-determined locations on a chip and within a
circuit. In contrast to previously described fluidic assembly processes,
14
,
15
our method
yields structures with minimal dependence on the direction of fluid flow, is highly

specific and is compatible with relatively sparse lithographic features and with low-
concentration nanoparticle suspensions.
In this paper we will discuss the mechanism of the self-assembly process and
describe our recent results.
FORCES ON NANOPARTICLES
At this point it is worth reviewing the forces that act on a nanoparticle in solution
in order to determine which might prove suitable for assembling the nanoparticles at
lithographically-defined features. We require a force that: can overcome the Brownian
motion or thermal energy of the particles, is long range, is localized at the lithographic
feature, and is capable of retaining the particle at the feature once the fluid has
evaporated. For particles smaller than about 1 m in diameter, gravitational/buoyancy
forces may be neglected, having a magnitude (for a 1 m Au particle in water) of 10
–3
nN. These may be compared to the thermal energy, kT, by calculating the work done on
a particle in moving it, for example, a distance equal to its diameter. For a nominal
10 nm Au particle the gravitational/buoyancy work becomes equivalent to a negligible
10
–11
kT.
Electrostatic forces can be quite substantial and, in the absence of screening
effects, are certainly long-range. The actual magnitudes are highly dependent on
experimental conditions such as pH and ionic concentration. At the lower end, a SiO
2
surface in pH 7 water might have a surface charge of 10
-4
to 10
-3
e
-
/nm
2
,
16
exerting an
unscreened force of order 100 fN on a point charge, while for a highly charged material,
the surface charge might be 0.8 e
-
/nm
2
, with a corresponding force of order 100 pN. The
potential energy of two 10 nm Au particles with a typical surface potential of

20 to125 mV,
17
and including the relevant screening effects,
18
is a few kT. The screening
length is typically of order 10 to 100 nm.
17
The Van der Waal’s interaction energy between two particles of diameter D,
separated by distance d, is given approximately by:
W
Van der Waals
 AD/24d
[1]
where A is the Hamaker constant (2.5 x 10
-19
J for Au in water).
17
For two 10 nm Au
particles in water at a separation of 2 nm this energy is again equivalent to a few kT. We
note that the electrostatic and Van der Waal’s energies must be comparable at small inter-
particle separations for the colloid to be stable.
Finally, we may also calculate the energies,

W, of the flotation and immersion
capillary forces acting on particles.
19
The first of these arises from the deformation of the
meniscus by the weight of the particles, and, for two identical particles, is given
approximately by:
20
W
Flotation


q
4
r
6
Ln[qL]
[2]
where

is the liquid/vapor surface energy, r is the particle radius, L is their separation,
and q
-1
= [

/g

]
1/2
is the capillary length, with

the fluid density and g the acceleration
due to gravity. For

= 50 mN/m,

W
Flotation
is of order kT for r = 10 m, and, given the
r
6
dependence, rapidly becomes insignificant for smaller particles. The second is also a
result of meniscus deformation, and occurs as a result of the fluid wetting behavior in thin

films, when, for example, the particles are confined by a surface (Fig. 1). It is given
approximately by:
W
Immersion


r
2
Ln[qL]
[3]
This remains large with respect to kT, even for particles as small as 1 nm, and,
because of the r
2
dependence, is long range, with a characteristic capillary length of q
-1
.
In the bulk, the capillary length for water is approximately 2.7 mm, and remains
relatively large (i.e. > 1 m), even in very thin (i.e. 25 nm) films.
21
From this brief survey, we may thus conclude that the immersion forces acting
between nanoparticles, or between nanoparticles and lithographically-defined nanoscale
surface topographies, meet our requirements and are capable of bringing nanoparticles
together over relatively long distances and of confining them effectively.
MECHANISM OF LITHOGRAPHICALLY-DIRECTED FLUIDIC ASSEMBLY
The notion that the immersion capillary force can cause nanoparticles to assemble
at a topographic feature relies on there being a thin liquid film containing a suitable
concentration of nanoparticles very close by. Figure 2 is an SEM micrograph of holes,
approximately 100 nm in diameter on a 1 m pitch, in resist, each of which contains
approximately 7 nanoparticles. There are no nanoparticles between the lithographically-
defined features. The nanoparticles were assembled from solutions with nanoparticle
volume fractions of 0.0125% or 0.0006%, corresponding to interparticle spacings of
1 m to 2.8 m respectively. The assemblages represent an increase in concentration of

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Lithographically-directed self-assembly of nanostructures" ?

The combination of lithography and self-assembly provides a powerful means of organizing solution-synthesized nanostructures for a wide variety of applications. The authors have developed a fluidic assembly method that relies on the local pinning of a moving liquid contact line by lithographically produced topographic features to concentrate nanoparticles at those features. The authors have successfully assembled nanoparticles from 50 nm to 2 nm in size using this technique and have also demonstrated the controlled positioning of more complex nanotetrapod structures. The authors have used this process to assemble Au nanoparticles into pre-patterned electrode structures and have performed preliminary electrical characterization of the devices so formed. The fluidic assembly method is capable of very high yield, in terms of positioning nanostructures at each lithographically-defined location, and of excellent specificity, with essentially no particle deposition between features. 

Q2. What is the effect of the relative surface energies of the liquid, particle and substrate?

Adjustment of the relative surface energies of the liquid, particle and substrate provides additional degrees of freedom for controlling the ordering of the nanostructures. 

Q3. How was the velocity of the contact line controlled?

The velocity of the contact line was typically on the order of 10 m/min and was controlled through natural or forced evaporation. 

Q4. What is the key effect leading to high yield and high specificity?

The key effect leading to high yield and high specificity is the concentration of the nanostructures at the lithographically-defined location through pinning of the moving liquid contact line. 

Q5. What is the kT of the r 6 dependence?

For = 50 mN/m, WFlotation is of order kT for r = 10 m, and, given the r 6 dependence, rapidly becomes insignificant for smaller particles. 

Q6. What is the mechanism that causes the formation of particles at the contact line?

In the case that the accumulated particles exert a sufficient pinning force on the contact line, then the phenomenon of selfpinning occurs, leading to an even greater build-up of particles. 

Q7. What is the energy of the vapor and liquid particles?

The first of these arises from the deformation of the meniscus by the weight of the particles, and, for two identical particles, is given approximately by:20WFlotation q 4r6Ln[qL] [2]where is the liquid/vapor surface energy, r is the particle radius, L is their separation, and q -1 = [ /g ] 1/2 is the capillary length, with the fluid density and g the accelerationdue to gravity. 

Q8. How do the authors control the position of nanostructures?

The authors have demonstrated controlled positioning of particles as small as 2 nm indiameter – the same scale as individual protein molecules – with this technique, as well as that of complex nanostructures such as nanotetrapods, and nanoparticles of a wide variety of materials. 

Q9. What is the effect of the immersion force on the nanoparticles?

The nanoparticles will be further concentrated and assembled into the features asa result of the immersion capillary force described earlier and secured by Van der Waal's and electrostatic forces to one another and the sides/base of the defined features. 

Q10. What is the equilibrium of the three-phase contact line of a liquid?

In brief, the equilibrium of the three-phase contact line of a liquid is normally determined by the Young condition26 and, when liquid evaporates from a drop, the drop will maintain a constant shape, by shrinking, as a consequence of that equilibrium (Fig. 3b). 

Q11. What is the effect of the flow direction on the yield of Au electrodes?

Inthis instance, because the Au electrodes are above rather than below the surface, the flow direction has an influence on the yield, as shown in Figure 11b. 

Q12. What is the common method used for assembling nanostructures?

Previous efforts in this area have consisted primarily of lithographic patterningfollowed by random deposition, 10,11 or electrostatic12 or magnetic13 trapping of nanostructures. 

Q13. What is the effect of the immersion forces on nanoparticles?

21From this brief survey, the authors may thus conclude that the immersion forces actingbetween nanoparticles, or between nanoparticles and lithographically-defined nanoscale surface topographies, meet their requirements and are capable of bringing nanoparticles together over relatively long distances and of confining them effectively. 

Q14. How do the authors calculate the energy of the electrostatic forces of a SiO2 surface?

At the lower end, a SiO2 surface in pH 7 water might have a surface charge of 10 -4 to 10 -3 e - /nm 2 ,16 exerting an unscreened force of order 100 fN on a point charge, while for a highly charged material, the surface charge might be 0.8 e - /nm 2 , with a corresponding force of order 100 pN. 

Q15. What is the main difference between the two approaches?

This approach offers a straightforward and generally applicable method for integrating bottom-up solution-processed nanostructures with top-down lithographically prepared devices, and it has the potential to be scaled up to wafer-size for many functional nanoelectronics and nanophotonics applications.