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Laterally Confined Diblock Copolymer Thin
Films August W. Bosse, Tanya L.
Chantawansri, Glenn H. Fredrickson, and Carlos
García-Cervera Departments of Chemical
Engineering and Mathematics, UCSB FENA Theme 3
Modeling, Simulations and Computations
Objective The problem of controlling and
understanding microdomain ordering in block
copolymer thin films has attracted much attention
from polymer technologists. In the context of
block copolymer lithography, a challenge is to
improve long-range in-plane order of
microdomains. Here we present a computational
study of micron-scale, lateral confinement as a
means of achieving defect-free configurations in
thin block copolymer films. Specifically, we will
focus on thin films of cylinder-forming AB
diblock copolymers confined laterally by a
hexagonal well. Since the size of the hexagonal
well can be made commensurate with the optimal
hexagonal lattice formed by block copolymer
cylinders in the bulk and planar steps are known
to improve order in adjacent microdomains, it is
reasonable to hope that confinement to hexagonal
wells can reproducibly yield defect-free
configurations. In order to numerically
simulate such a system, we apply a
self-consistent field theory (SCFT) model for an
AB diblock copolymer melt combined with a masking
technique to define the well geometry1-3. We
have chosen the size of the hexagonal confining
well such that nine cylinder rows fit across the
hexagon, which corresponds to proposed
experimental confinement sizes (Kramer group
UCSB).
A Wetting Majority Component
Figure 1 Representative density
composition profiles, FA in yellow and
corresponding Voronoi diagrams (hexagon in white,
pentagon in gray, and heptagon in black) for an
A-attractive wall. (a) and (b) are density
profiles and Voronoi diagrams, respectively, for
l 15.00 Rg, (c) and (d) are for l 16.25 Rg,
and (e) and (f) are for l 17.75 Rg.
Numerical SCFT Modified Diffusion
Equation Single Chain Partition
Function Density Equations Saddle Point
Equations
B Wetting Minority Component Figure
2 Representative density composition profiles,
FA in yellow and corresponding Voronoi diagrams
(hexagon in white, pentagon in gray, and heptagon
in black) for a B-attractive wall. (a) and (b)
are density profiles and Voronoi diagrams,
respectively, for l 18.00 Rg, (c) and (d) are
for l 19.00 Rg, and (e) and (f) are for l
20.00 Rg.
The Model AB diblock copolymer s contour
variable in units of N (index of
polymerization) f fraction of A monomers in an
AB diblock copolymer Hexagonal well ?
strength of the A and B segment repulsive
interactions l hexagonal side length We use a
hexagonal wall field, fW(r), to laterally confine
the polymer melt. This field is specified as a
six-fold modulated tanh function. Local
incompressibility is enforced by the following
constraint fA(r) fB(r) fW(r) 1.
Introduction Block copolymer thin films
represent a promising sub-optical lithographic
tool. In particular, there is considerable
technological interest in using self-assembled
block copolymer microdomains to define 10 nm
scale features. Thin films consisting of a large
array of microphase-separated block copolymer
spheres, cylinders, or lamellae can be used to
pattern a substrate with a corresponding array of
10 nn scale dots or lines. Such arrays are
potentially useful in next generation
high-density magnetic media and semiconductor
devices. However, if such devices are to be
realized, the feature arrays must exhibit high
uniformity and order. Although it is
considerably difficult to generate large, 2D
arrays of uniform, well-ordered microdomains,
there has been substantial work on enhancing
order in block copolymer thin films. Possible
techniques of inducing order include applying
external fields, shearing the film, and
graphoepitaxy (lateral confinement), among
others. Segalman et al.4 have examined the
effects of a planar wall on the ordering of
microdomains, where they observed increased
lateral microdomain order within a region
extending approximately 4.75 µm from the wall.
Here we study the role of confinement geometry by
investigating microdomain ordering of block
copolymer thin films laterally confined in a
hexagonally-shaped well.
Discussion and Future Plans In order to examine
how hexagonal, lateral confinement influences
long-range order in block copolymer thin films,
we conducted 2D SCFT simulations. For all
simulations we set f 0.7, thus the majority
block component is A. For the quenched
simulations, ?N is held fixed at ?N 17. These
values of f and ?N yield SCFT solutions
corresponding to hexagonally ordered cylindrical
microdomains. For the annealing simulations ?N is
ramped from ?N 12 to the final value of ?N
17. The value of ?wN was selected to be ?wN 17
or ?wN -17 for an A attractive or B-attractive
wall respectively. To identify the width of the
commensurability window in hexagon size l that
yields a perfect array of microdomains, we report
both the average total number of microdomains
inside the confining hexagon ltNgt and the standard
deviation (SD) of nearest neighbors (NN)
microdomain separations inside the confining
hexagon ltsgt. For the quenched simulations, we
observe a commensurability window of l 15.75 to
l 17.00 for the case of an A-attractive wall.
For the B-attractive wall, the ordered window
extends from l 18.75 to l 19.25. For the
annealed simulations, the ordered window extends
from l 15.75 to l 17.75 for the A-attractive
wall. For the B-attractive wall, we see an
ordered window that extends from l 17.75 to l
19.75. Thus the ?N annealing has effectively
equalized the ordering effects of the A- and
B-attractive walls. This can be explained by the
formation of a wetting layer of microdomains
below (?N)ODT. Future work includes studying
defect formation in smaller and larger
hexagonally confined systems and studying other
copolymer architectures and the role of
additives. In addition, we will explore other
confinement geometries such as triangular wells.
Annealed Simuations Figure 4 Graphs of
(a) ltNgt vs. l and (c) ltsgt vs. l after a ?N
anneal from random initial conditions at ?N 12
to ?N 17 for an A attractive wall (?wN 17).
There is a region from l 15.75 to l 17.75
over which there is a perfect array of 61
hexagonally ordered microdomains. Graphs of (b)
ltNgt vs. l and (d) ltsgt vs. l after a ?N anneal
from random initial conditions at ?N
12 to ?N 17 for a B attractive wall
(?wN -17). There is a region from l 17.75 to
l 19.75 over which there is a perfect array of
61 hexagonally ordered microdomains.

• Quenched Simulations
• Figure 3 Graphs of (a) ltNgt vs. l and (c) ltsgt
  vs. l after a quench from random initial
  conditions
• to ?N 17 for an A attractive wall (?wN 17).
  There is a region form l 15.75 to l 17.00
  over
• which there is a perfect array of 61 hexagonally
  ordered microdomains.
• Graphs of (b) ltNgt vs. l and (d) ltsgt vs. l
  after a quench from random initial conditions to
  ?N
• 17 for a B attractive wall (?wN -17). There
  is a region from l 18.75 to l 19.25 over
  which
• there is a perfect array of 61 hexagonally
  ordered microdomains.

References 1 Fredrickson, GH. The Equilibrium
Theory of Inhomogeneous Polymers. Clarendon
Press, Oxford, 2006. 2 Matsen, MW. Thin films
block copolymer. Journal of Chemical Physics 106
(1997), 7781. 3Wu, Y, Cheng, G, Katsov, K,
Sides SW, Wang J, Tang, J, Fredrickson GH,
Moskovits, M, and Stucky, GD. Chiral
mesostructures by nano-confinement. Nature
Materials 3 (2004), 816. 4 Segalman, RA,
Hexemer, A, and Kramer EJ, Edge effects on the
order and freezing of a 2D array of block
copolymer spheres. Physical Review Letters 91
(2003), 196101
Acknowledgements We are grateful to Gila Stein,
Edward Kramer, and Kirill Katsov for useful
discussions. Funding for this project was
provided by the MARCO Center on Functional
Engineered Nano Architectonics (FENA). This work
made use of MRL Central Facilities supported by
the MRSEC Program of the National Science
Foundation under award No. DMR05-20415.