Field-based Simulations for Block Copolymer Lithography (Self-Assembly of Diblock Copolymer Thin Films in Square Confinement)

Transcription

1 Field-based Simulations for Block Copolymer Lithography (Self-Assembly of Diblock Copolymer Thin Films in Square Confinement) Su-Mi Hur Glenn H. Fredrickson Complex Fluids Design Consortium Annual Meeting Monday, February 4, 2008 Materials Research Laboratory University of California, Santa Barbara

2 Introduction Block Copolymer Lithography - promising high resolution lithographic tool Epitaxy :chemically patterned substrate Graphoepitaxy :topographically patterned substrate S.O. Kim et al. Nature, 2003, 424, J.Y.Cheng at al. Adv. Mater. 2006, 18,

3 Graphoepitaxy Bottom-up self-assembly of block copolymers on 10 nm scales Top-down conventional lithography in generating micron-scale wells Lateral confinement B block wetting f = 0.7 χn = 17, χ w N= -17 l = R g l = R g l = R g R. Segalman, Matl. Sci. & Eng. 2005, 48, A. W. Bosse, C. Garcia-Cervera, G. H. Fredrickson Macromolecules 40, 9570 (2007) 3

4 Objective Role of lateral confinement ( graphoepitaxy ) as a means of inducing long-range, in-plane order in thin film block copolymer systems Self-consistent field theory (SCFT) simulations of various block copolymer thin films confined in square well to force tetragonal order Exploring the effect of the well size, wetting conditions, additive, segregation strength χn and thermal annealing conditions etc. 4

5 Numerical Method self-consistent field theory (SCFT) Implementing square well confinement Predetermined density mask (square well field, φ W (r) ) Four-fold modulated tanh function. Local incompressibility : φ A (r) +φ B (r) + φ W (r) =1. 5

6 System I: AB Diblock Copolymer side length, l s = contour variable in units of N (index of polymerization) f = 0.7, fraction of A monomers in an AB diblock copolymer l = 20Rg A attractive wall Annealed simulation: χ AB N:12 17 A plot of the error vs the number of field iteration with representative density composition profiles of A segments 6

7 System II: AB Diblock Copolymer + A Homopolymer Interstitial sites filled by highly stretched copolymers Adding A homopolymers Depends on the length (α) and volume (V Ah ) fraction of the A homopolymer additive f = 0.7 α = N Ah /(N f) = ratio of lengths of A homopolymer and the A block of the copolymer V Ah = volume fraction of A homopolymer Annealed simulation: χ AB N :12 17 S=0 S= N Ah /N 7

8 Sys II: Hexagonal Ordering Low molecular weight additive at low concentration Walls promote tetragonal ordering upon annealing. A homopolymer is highly miscible with the A block micelle coronas and is unwilling to pay the translational entropy cost of partitioning into the interstitial sites. l = 21 Rg B wetting wall α =2.5 V ah = 0.17 Total A segment concentration A homopolymer segment concentration 8

9 Sys II: Macroscopic Phase Separation Excess of long A homopolymer l = 26 Rg B wetting wall α =2.5 V Ah = 0.3 Total A segment concentration A homopolymer segment concentration Excess of long A homopolymer & A wetting wall l = 19 Rg A wetting wall α =4.3 V Ah = 0.28 Total A segment concentration A homopolymer segment concentration 9

10 Sys II: Tetragonal Ordering Intermediate amounts and lengths of A homopolymer : decreases the free energy of the square configuration such that it is energetically more favorable than the hexagonal configuration. l = 23 Rg B wetting wall α =2.5 V Ah = 0.23 Total A segment concentration Line edge roughness A homopolymer segment concentration Total A segment concentration l = 16 Rg A wetting wall α =2.0 V ah =

11 Sys II: Phase Diagram for B-Wetting Wall 11

12 Sys II: Phase Diagram for A-Wetting Wall Volume fraction of A homopoymer Hexagonal Ordering Tetragonal Ordering Macroscopic Phase Separation II Macroscopic Phase Separation I Ratio of length fractio of A homopolymer 12

13 System III: AB + A C Blend Tetragonal ordering in bulk films of triblock copolymer (difficulty of synthesis ) Symmetric diblock copolymer mixture f A = f A =0.7 N 2 /N 1 =1, V 2 /V 1 =1, ratio of lengths and volume of two block copolymers Weak attraction between major blocks A and A Strong repulsion between the minor blocks B and C Experimentally utilizing supramolecular interactions between A and A blocks C. Tang, C. J. Hawker, E. J. Kramer (2008) S=0 A C S= 1 13

14 System III: AB + A C Blend Preliminary simulations show good potential. Large defect-free tetragonal lattices l = 84Rg χ AA N = , χ BC N = 55.5 χ ij N(except χ AA Nand χ BC N) = C attractive and B repulsive wall S=0 A C S= 1 Evolution of B segment concentration 14

15 Conclusions 2D SCFT simulations of various copolymer thin films confined in square wells In the AB diblock copolymer thin film, even though A- attractive and B-attractive walls assist in generating tetragonal ordering, the lattice subsequently twists into hexagonal ordering. By adding a suitable A homopolymer additive to the system, we were able to stabilize square lattices composed of B cylinders. Large-area, defect-free square lattices is obtained by blending chemically different diblock copolymers with suitable attractive interactions between blocks. 15

16 Acknowledgments Prof. Glenn H. Fredrickson Prof. E. J. Kramer Prof. Carlos J. García-Cervera August W. Bosse, Tanya L. Chantawansri, Won Bo Lee, Jong-hoon Lee NSF Grant No. DMR and the MARCO Center on Functional Engineered Nano Architectonics (FENA) 16