Study of Block Copolymer Lithography using SCFT:

New Patterns and Methodology

Su-Mi HurGlenn Fredrickson

Complex Fluids Design Consortium Annual Meeting

Monday, February 2, 2009

Materials Research LaboratoryUniversity of California, Santa Barbara

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Outline

Motivation & Block Copolymer Lithography

Numerical Method

AB + B’C (+ Confinement)

AB+ A + Confinement

Mixed Polymer Brushes + Confinement

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Lithography

Optical printing of complex circuit diagrams into pattern on the wafer (through mask onto photo-resist)

Complicated, expensive, and critical process of modern integrated circuit (IC) manufacturing

Scaling is limited by wavelength of light ( > 22nm)

Equipment cost exponentially increases as reducing the dimension. Aurangzeb Khan , Lecture note of VLSI Desing system

New families of imaging materials

and novel approaches

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Block Copolymer Lithography

Promising high resolution lithographic tool

Microscopic phase separation in the scale of

Various types of geometries in block copolymer thin film

R. Segalman, Matl. Sci. & Eng. 2005, 48, 191-226.

parallel cylinder perpendicular cylinder sphere

parallel lamellar perpendicular lamellar

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Control of Microdomain Ordering

High resolution - demand for smaller device structures

Placement accuracy

Reduction of defects density - yield loss

Throughput - manufacturing cost

Some applications require long-range perfect ordering.

Daniel J.C. Herr, Future Fab. Intl. Sec.5. 2005, Issue 18

Mechanical flow fieldElectrical fieldTemperature gradientChemically patterned substrateTopographically patterned substrate

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“Graphoepitaxy”:Topographically Patterned Substrate

Bottom-up self-assembly of block copolymers on 10 nm scales

Top-down conventional lithography in generating micron-scale wells

Lateral confinement can promote defect-free self-assembled block copolymer features.

J.Y.Cheng et al. Adv. Mater. 2006, 18, 2505-2521 R. A. Segalman and A. Hexemer and E. J. Kramer, Macromolecules. 2003, 36, 6831.

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Outline

Motivation & Block Copolymer Lithography

Numerical Method

AB + B’C (+ Confinement)

AB+ A + Confinement

Mixed Polymer Brushes + Confinement

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SCFT Algorithm

Start: Generate Random Initial

Field Configurations w(x,0)

Solve Modified Diffusion Equationfor chain propagator q (x, s ;[w])

Solve the Single Chain Partition Function Q

Calculate the densities

Update the field w(x,t)

Convergence Criterion is Satisfied?

ENDY

N

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How to Implement Confinement Wall

Predetermined

wall density function

four-fold modulated tanh function

Local incompressibility

Include contact interaction between the wall and A- and B- segments: possible to implement A- or B-wetting wall

Square mask and its cross section

0

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Alternative Approach to Square Confinement

Masking method:Periodic B.C with plane wave basisAdaptable to non-symmetric well geometriesSlow convergenceWasted computation in the masked area

Alternative approach using sine wave basis functionUse the actual cellDirichlet boundary condition at the edges

Sine wave basisSine FFT, rather than the complex FFTNo wasted computations in the masked areasFaster convergence in the field update scheme

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Overview

Block Copolymer Lithography

Numerical Method

AB + B’C (+ Confinement)

AB+ A + Confinement

Mixed polymer brushes + confinement

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AB + B’C

When do we observe square lattice? SCFT simulations of the system varying χBB’N , χACN and

χN( A/B(B’), C/B(B’))

CBA

Y. Mogi et al. Macromolecules, 1992, 25, 5408-5411

ABC triblock copolymer Binary blend of AB and B'C diblockcopolymers in which the B and B' blocks have attractive supramolecularinteractions

C. Tang et al. Science, 2008, 322, 429

CB’’

BA

Square array: canonical structure defined by Semiconductor Industry Association (SIA)

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Effect of repulsive interaction between A and C, χACN

A

HEX A and C are micible.

SQRA and C segregate into the core and shell of the cylinders in order to reduce A/C contacts.

DisorderedFree energy cost of A/C contacts are larger than for the A/B(B’) and C/B(B’).

SQRCylinders composedsolely of either the Aor C component.

Increasing repulsive interaction between the minor blocks A and C, χACN

5 10 15 20 25 30 35 40

A+C

Fixing χBB’N = -7.468 , χN = 18.875, fB/B’ = 0.7 CB’’

BA

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Phase Diagram of AB+B’CIncreasing repulsive interaction between the minor blocks A and C, χACN

Increasing repulsive

interaction between other

blocks,χN

5 10 15 20 25 30 35 40

12

16

18.875

20

25

30

40

50

Representative density profiles of A and C

Fixing χBB’N = -7.468

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AB+B’C in a square well

Square lateral confinement controls and improves defect-free tetragonal orderingχBB’N = -3.468, χACN = 55.5 χN = 13.875 (A/B(B’) and C/B(B’))C attractive and A repulsive square wall Side length, L = 84Rg ~ 1 μm

Evolution of A segment concentration

CB’’

BAL

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Overview

Block Copolymer Lithography

Numerical Method

AB + B’C (+ Confinement)

AB+ A + Confinement

Mixed Polymer Brushes + Confinement

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AB + Square well

fA = 0.7A-attractive square wellL = 14 Rg

χN = 13.75 15.75 17 17Tetragonal ordering is induced by the square lateral confinement during annealing stage.

Lattice subsequently twists into hexagonal ordering in order to reduce the stress in the interstitial sites.

Representative density profiles of A segment

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AB + A + Square well

Total A-segment density profiles

A homopolymersegment concentration

fA = 0.7L = 23 RgB wetting wallα =1.75 (NAh/N)VAh = 0.23

Lα = NAh/NNAh/

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Phase Diagrams

fA = 0.7, A attractive wall conditionfixed α = 2.1 (NAh/N)

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Robustness on Line Edge Roughness

Perturbation on the wall

Tetragonal OrderingDefective

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Present system Reference system(Tetragonal Ordering)

A. Onikoyi , E. J. Kramer (2008)

Order parameter

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Robustness on Line Edge Roughness

∆ = 0 0.5 1 (Rg)

Perturbation on the wall Tetragonal OrderingDefective

L =16 (Rg)

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AB + A + 60° Bends

AB + neutral wall

fA = 0.5, L = 18 Rg

AB + A-attractive wall

+ A (α = 0.5 (NAh/N), V_Ah=0.2)

M. P.Stoykovich et al. Materials today. 2006, 9(9), 20

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Overview

Block Copolymer Lithography

Numerical Method

AB + B’C (+ Confinement)

AB+ A + Confinement

Mixed Polymer Brushes + Confinement

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Mixed Polymer Brushes

Collaboration with Sandia National Lab.Predict phase-separated morphologies and mechanisms Understand how the system parameters affect the feasibility of targeted pattern.

Project Proposal of Sandia National Lab.

~ μm ~ nm

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Laterally Confined Polymer Brush

Simulation domain: mixed polymer brushes region only

Prefixed narrow pure polymer brush wall in lateral direction

Virtual wall in z-direction, including substrate and surface interaction

Sine basis simulation

Delta function initial condition of propagator at the grafting point at z= dz one step analytic extension

Non-uniform grafting density over the substrate due to lateral wall

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Surface Interaction

Increasing surface attraction, χw(top)N

Doubling grafting density

fA = 0.5χABN = 12 0

12

16

20

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Lateral Confinement

fA = 0.5χABN = 12

Turn on the B-attractive wall on the side, χWN = -12

Turn on the B-attractive wall on the side

Increase NB(=1.5 NA)

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Ripple Phase in 3D

Usov et al, Macromolecules, 2007

Laterally confined by pure brush region

30 Rg

3Rg

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Evolution of Long-ranged Defect-free Structure

Pattern size

~ 56 Rg3Rg

Evolution and self-healing of long-ranged ordering

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Conclusions

Phase diagram of AB+B’C helps us understand to important parameters in designing systems which will produce a square lattice.

Confinement helps AB+B’C in generating and controlling square ordering.

AB + A + confinement can generate square lattice and non-regular structures.

Mixed brushes phase separation can be controlled using a new graphoepitaxy-type technique.