Block copolymer self-assembly - a computational approach towards novel morphologies

Block Copolymer Self-Assembly

-

A Computational

Approach Towards Novel Morphologies

by

Karim R. Gadelrab

M.Sc. Materials Science and Engineering

Masdar Institute of Science and Technology (2011)

Submitted to the Department of Materials Science and Engineering in partial

fulfillment of the requirements for the degree of

Doctor of Philosophy in Materials Science and Engineering

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

February 2019

( 2019 Massachusetts Institute of Technology. All rights reserved

Signature redacted

A u th o r

... ...

.

. .

.-.-.

Department of Ma erials Science and Engineering

November 19. 2018

Certified by...

Accepted by ...

FEB 052019

LIBRARIES

Signature redacted

Alfredo Alexander-Katz

Associate ProfPssor ofyterials Science and Engineering

Signature redacted

Thesis Supervisor

6-1

_{Donald R. Sadoway}

Professor of Materials Science and Engineering

Chairman, Departmental Committee on Graduate Studies

Block Copolymer Self-Assembly

-

A Computational

Approach Towards Novel Morphologies

by

Karim R. Gadelrab

Submitted to the Department of Materials Science and Engineering

on November 19, 2018, in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Materials Science and Engineering

Abstract

Spontaneous self-assembly of materials is a phenomenon exhibited by different molecular systems. Among many, Block copolymers (BCPs) proved to be particularly interesting due to their ability to microphase separate into periodic domains. Nonetheless, the rising need for arbitrary, complex, 3D nanoscale morphology shows that what is commonly achievable is quite limited.

Expanding the range of BCPs morphologies could be attained through the implementation of a host of strategies that could be used concurrently. Using directed self-assembly (DSA), a sphere forming BCP was assembled in a randomly displaced post template to study system resilience towards defect creation. Template shear-like distortion seemed to govern local defect generation. Defect clusters with symmetries compatible with that of the BCP showed enhanced stability. Using 44 and 32434 Archimedean tiling templates that are incompatible with BCP six-fold symmetry created low symmetry patterns with an emergent behavior dependent on pattern size and shape.

A variation of DSA is studied using modulated substrates. Layer-by-layer deposition of cylinder forming BCPs was

investigated. Self-consistent field theory (SCFT) and strong segregation theory SST were employed to provide the understanding and the conditions under which particular orientations of consecutive layers were produced. Furthermore, deep functionalized trenches were employed to create vertically standing high-x BCP structures. Changing annealing conditions for a self-assembled lamellar structure evolved the assembled pattern to a tubular morphology that is non-native to diblock copolymers.

A rather fundamental but challenging strategy to go beyond the standard motifs common to BCPs is to synthesize

multiblock molecules with an expanded design space. Triblock copolymers produced bilayer perforated lamellar morphology. SCFT analysis showed a large window of stability of such structures in thin films. In addition, a model for bottlebrush BCPs (BBCPs) was constructed to investigate the characteristics of BBCPs self-assembly. Pre-stacked diblock sidechains showed improved microphase separation while providing domain spacing relevant to lithography applications. A rich phase diagram was constructed at different block concentrations.

The ability to explore new strategies to discover potential equilibrium morphologies in BCPs is supported by strong numerical modeling and simulations efforts. Accelerating SCFT performance would greatly benefit BCP phase discovery. Preliminary work discussed the first attempt to Neural Network (NN) assisted SCFT. The use of NN was able to cut on the required calculations steps to reach equilibrium morphology, demonstrating accelerated calculation, and escaping trapped states, with no effect on final structure.

Acknowledgments

Throughout my journey to get advanced degrees in science, I was fortunate to have the most amazing time, meet people with unique capabilities, and live in countries that I haven't even visited before. With such a rich experience that lasted almost a decade, I will try to recognize those who helped me reach where I am today. Please forgive me if

I fell short naming each and every one, just remember that I am truly grateful to you!

I firstly want to thank my parents (Raafat and Nabila) who taught me the meaning of hard work. Growing up in a

family of academicians, it seemed natural to have insatiable desires to learn. I thank my mom for the support she gave me in my school years. I thank my dad for providing me a library full of references to use in my undergraduate studies. This taught me to never use easy-to-get answers and fully learn about any topic I find. Inevitably, opportunities for growth meant I have to leave home. Going abroad is a selfish decision, but my parents were unconditionally supportive. To that I am very grateful! I am grateful for the sweet laughs I had with my siblings (Ahmed and Ziad). You were there whenever I needed you most.

I would not have made it to MIT without the help of very special people in Masdar Institute, UAE. Prof. Matteo

Chiesa, an advisor and a friend, trusted me to operate expensive tools and do nanoscale research while coming fresh from mechanical engineering undergraduate, where the smallest thing I used was a wrench! I admire Matteo's attitude to relentlessly support every member of his team to the end. I am thankful to him for pushing me, and believing that I can make it to MIT. Dr. Sergio Santos, a mentor and a friend, has shaped my personality and challenged my ideas. His critical mind made me stronger and thorough. Sergio introduced me to the biggest names in his field, and trusted me to present our groundbreaking work. I am very grateful to my mentors in Masdar Institute for preparing me for the MIT life!

I am very grateful to Prof. Alfredo Alexander-Katz. He is the kind of advisor that anyone can hope for. He has the

combination of enthusiasm, energy, and genius mind which is a continuous source of inspiration. My first one-hour meeting with Alfredo lasted more than four hours. I was ecstatic when he was personally telling me about all sorts of research ideas we can work on. Alfredo is very generous with his time and mind. He gave me all the support I needed during my PhD, for that I am very thankful!

I am very grateful to my lab mates. The fun, laughter, and joy I had in the lab was immense. I am thankful to Reid V.

L., Joshua S., Ricardo P. P., Juan A., Yi D., Emiko Z., Shahrzad Y., Shayna H., Pierre C., Zhen C., and Hejin H. I am especially very thankful to Mukarram T. We have gone through this journey together starting with the orientation week to same-month thesis defense. Mukarram helped me in quals preparation, and reminded me with everything that has a deadline (research proposals, assigmnent, conference registration, thesis submission, etc.). Him being a computer genius, he always pushed me to automate and be more efficient in my work. He made me build a GPU setup to run my machine learning code. Without Mukarram's help, I wouldn't have accomplished much.

I am very grateful to the many people I collaborated with. The regular meetings of the block copolymer team taught

me everything I know about experiments. I am fortunate to work with Li-Chen C., Sangho L., Hyung W., Amir T., Sam N., Wubin B., Adam H., and Ken K.

I cannot stress how grateful I am to my kind and supportive wife (Rana). Rana, you have been my companion in this

journey. We both came to the US, pursuing something big and embracing the challenge, but you showed me how to face difficulties with a smile and never forget to have fun. Your perspective of life is always beautiful. I thank you for being with me, listening to the incomprehensible complaints about my work and caring for me when I got overworked.

Love you!

Contents

I

LITERATURE REVIEW ...

15

1.1

Introduction ...

15

1.2

Directed self-assembly of block copolym ers ...

16

1.3

Novel 3D BCP m orphologies...

20

1.4

M ulti-layer stacking of BCP domains...

21

1.5

Unlocking BCP potential through m olecular design...

23

1.6

M odeling and theory ...

25

1.6.1 M ean-field theory... 28

1.6.2 W eak segregation limit ... 30

1.6.3 Strong segregation limit ... 31

1.6.4 Self-consistent field theory (SCFT)... 33

1.7

Conclusion...

35

2

POST TEMPLATED BCPS- TEMPLATE JITTER AND IMPOSED SYMMETRY... 37

2.1

Introduction ...

37

2.2

Lim its of Directed Self-Assem bly in Block Copolym ers ...

38

2.2.1

Experimental details...

38

2.2.2

Results and discussion ...

42

2.2.3

Crystal melting in 2D ...

48

2.2.4

Analysis of local defects ...

52

2.3

Em ergent Sym m etries in Block Copolym er Epitaxy ...

58

2.3.1 Post templating with a square tiling (44)...59

2.3.2

Post template with a

tiling pattern ...

62

2.4

Conclusion...

64

3

STRATEGIES FOR CONTROLLING BCP DOMAIN ORIENTATION- MODULATED

SUBSTRATES AND HIGH ASPECT RATIO TRENCHES ...

66

3.1

Introduction ...

66

3.2

BCP self-assem bly on a m odulated substrate ...

67

3.2.1

Experimental details...

67

3.2.2

SCFT simulations...

69

3.3

Trench wall confinement: out of plane structures and process dependent morphology 83

3.3.1

SCFT simulations...

84

3.3.2

Analytical investigation using Ginzburg Landau model...

89

3.4

Conclusion...

92

4

BEYOND LINEAR DIBLOCK COPOLYMERS ...

94

4.1

Introduction ...

94

4.2

Accessing Novel Morphologies of ABA Triblock Copolymer Thin Films ... 95

4.3

Self-Assem bly of a Diblock Bottlebrush Copolym er ...

100

4.3.1

M odel details...

100

4.3.2

Characteristics of bulk bottlebrush BCP ...

103

4.3.3

Bottlebrush BCPs in ID confinement ...

113

4.4

Conclusion...

118

5

NEURAL-NETWORK ASSISTED SCFT FOR BCP SIMULATIONS ...

120

5.1

Introduction ...

120

5.2

Revisiting diblock block copolym er form alism ...

121

5.3

Rational of using NN for m ean field evolution...

122

5.4

Results and discussion...

124

5.5

Conclusion...

129

6

CON CLU SION AN D FUTURE W ORK ...

131

List of figures

Figure 1. 1. The sequence of observed morphologies in linear diblock copolymer melts. The cartoon structures are depicted by m inority polymer'7 ... . . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . . 15

Figure 1. 2. Phase diagram of AB diblock copolymers for a fixed XN=20 in a thin film with respect to volume fraction and film thickness. A large number of phases (-20) is demonstrated. It is seen that the gyroid phase is missing in the range of thicknesses studied 0... .. . . .. . . .. . . . .. . . .. . . 16

Figure 1. 3. BCP structure control using graphoepitaxy. (A) Scanning electron micrographs showing polycrystalline-like order of sphere forming polystyrene-b-polydimethylsiloxane (PS-b-PDMS) BCP thin film. (B and C) Ordered BCP domains achieved using 2D sparse lattice template of

hydrogen-silsesquioxane (HSQ) posts (bright dots). BCP domains show perfect six-fold symmetric structures. The insets are for the 2D Fourier transforms of the scans indicating the overall state of order in the system"6 .

(D) A scanning electron micrograph of a locally controlled structure of PS-b-PDMS cylinders fabricated

by changing H SQ post periodicity" ... . . . .. . . .. . . . .. . . . .. . . .. . . .. . . .. . . . .. . . . 17

Figure 1. 4. BCP structure control using Chemoepitaxy. (A) SEM images of angled lamellae of a

polystyrene-b-poly(methyl methacrylate) PS-b-PMMA/PS/PMMA blend. The chemical surface pattern is fabricated at different spacing, and the lamellar domains of the block co copolymer blend are

self-assembled and registered at different angles'. (B) SEM images of PS-b-PMMA cylinders (Lo = 27 nm) on

chemical patterns with Ls = 27 and 54 nm". BCP are able to rectify pattern defects and produce density m ultiplication on a sparse chem ical pattern... 18

Figure 1. 5. Aperiodic features generated using graphoepitaxy and chemoepitaxy. (Top) two arbitrary structures created by positioning HSQ posts in a particular fashion predicted by inverse algorithms". (Bottom) SEM images of PS-b-PMMA/PS/PMMA ternary blend directed to assemble into (a) nested array of jogs, (b) isolated PMMA jogs, (c) isolated PS jogs, and (d) arrays of T-junctions. ... . . .. ..... 19

Figure 1. 6. Self-aligned ID customization. (a-h) Schematic and corresponding SEM images of a fabrication process flow. (i) SEM scans of fragmented HSQ pattern and (j) SEM image of the resulting fragmented DSA-generated grating41. Scale bars are 100 nm. ... 19

Figure 1. 7. Cylindrical confinement of PS-b-PB in anodic alumina membranes. Left: TEM scans of lamellar forming BCP in different pore sizes" (scale bar, 50nm). Right: TEM scans of cylinder forming BCP aligned normal to pore axis. Helical structure is produced" (Scale bar, 20nm). ... 20

Figure 1. 8. TEM scans showing morphological transitions of nanoparticles induced by solvent annealing

o f P S -b -P I . . . .... 2 1

Figure 1. 9. Left: Schematic illustration for the fabrication of BCP multilayer. Right: Top-view SEM images for PS-b-PMMA multilayer system after the removal of PMMA, and TEM top-view indicating the registry between the cylinders and lamellar structure7... . . . .. . . .. . . .. . . .. . . .. . . 22 Figure 1. 10. Diverse set of morphology achieved through multi-layer stacking. (Left) SEM images of two-layer nanostructures formed sequential assembly of block copolymer films. The blue boxes highlight structures where both layers belong to the same class of morphology; the red boxes highlight conditions of omparable lattice spacings in the two layers. (Right) Examples of 3D nanostructures fabrictad through m ultilayer stacking. (Scale bar is 100 nm )55 ... . . . .. .. . . . .. . . . .. . . .. . . . .. . . .. . . 22 Figure 1. 11. Arbitrary lattice symmetries by multi-layer stacking, aligned by ss-LZA (Left) Experimental schematic: a focused laser line is absorbed by a layer of germanium underlying a BCP film, inducing local heating. The temperature rise and steep thermal gradients induce accelerated self-assembly of the BCP cylindrical phase. Simultaneously, differential thermal expansion of a transparent PDMS cladding shears the BCP (white arrows), aligning the cylinders along the sweep direction. (Right) (a) Large-area

(b) SEM of a Pt triangular mesh. (c) Rectangular Pt lattice obtained using two BCPs with distinct

molecular weights. (d) Oblique lattice (450), constructed with the same BCPs as in c. (e) Mixed

composition nanomesh with metallic (Pt) bottom layer and metal oxide (A1203) top layer. (Scale bars in

b-e are 200 nm .). ... 23

Figure 1. 12. Sample morphologies attained by the use of triblock copolymers. (Left) multi-spheres, multi-cylinders, tricontinuous double-diamond, and multi-lamellar phases for three component linear systems". (Right) phase diagram showing the large window of for different morphologies beyond what is achievable with linear diblock copolymers5 9 . . . . .24

Figure 1. 13. (Left) Transmission electron microscope of ISP star block terpolymer /S homopolymer

blend system: polyisoprene (I, black), polystyrene (S, white), and poly(2-vinylpyridine) (P, gray). The

polymer exhibit t (3.3.4.3.4) Archimedean tiling holds for the self-assembled structure2. (Right) Phase diagram of ABC star polymer systems with arm-length ratio 1:1 :x and with symmetric interactions between three components. A (light gray), B (medium gray), and C (dark gray) are displayed. Schematic shows the strong constraint the topology of star polymer puts on the kind of morphologies emerge. The junction point is forced to be a located in 1 D when star arms of comparable length63. . . . .24

Figure 1. 14. Mean-field (a) and experimental PS-b-PI (b) phase diagrams for an AB diblock copolymer m elt in the coordinates of XN and f 8 . ... . . . .. . . .. . . . .. . . .. . . .. . . .. . . .. . . .. .27

Figure 2. 1. Self-assembled monolayer of a sphere-forming BCP: a) fabrication procedure for directed self-assembly of BCP; from step 1 to step 4 are HSQ posts fabrication, PDMS brush layer deposition, spin-coating of BCP and annealing, and plasma etching; respectively. For experimental details, please refer to Methods in the Supplementary Materials; b) large scale SEM image of BCP film without template; c) schematics depicting the <l I> and (20> phases; d) SEM image of a noise free template

without the BCP film; e) BCP film self-assembled on template with no deliberately introduced noise. The posts are apparent as brighter spots in the image; f) BCP film self-assembled on template at noise level CJLo = 0.15; g) Enlarged image (square outline in f) of a template with noise. The absolute value of the

displacement of the posts from their original positions is denoted by r. Notice the appearance of a

dislocation pair highlighted in dashed lines. All scale bars correspond to 100nm. ... 38

Figure 2. 2. 1D probability distribution of a post (black dot) at different levels of noise. The coordinate of th e p o st is (0 ,0)...4 0 Figure 2. 3. Experimental data for BCP self-assembly in close packed templates with different inter-Experimental data for BCP self-assembly in close packed templates with different inter-post distances Lp and levels of noise ( from 0 to 0.15. The inter-post distance Lp that is commensurate with the <l ,> phase is

13Lo,

Phase <1 I>With L/Lo = 1.732. (b) Phase <20>with L,/Lo = 2.0. ... 44

Figure 2. 6. Simulation data for a 2D system with XN = 17, and f= 0:3. The inter-post distances Lp and

noise levels correspond to those shown in Figure 2. 3... 45 Figure 2. 7. Defect free energy calculated for different types of defect clusters. The aggregation of defects reduces the defect free energy with the triangular 5-7 triplet showing the lowest energy penalty.

Delaunay grid where solid small dots represent BCP domains, white big circles are for template posts. Yellow markers are 7 coordinated points, and red markers are for 5 coordinated points...46 Figure 2. 8. Two commensurate patterns for directed self-assembly at low XN=14. The system can sustain high values of noise - 0:15 after which long range order is perturbed. Due to the low interface energy

extended structures similar to lamellae can be generated ... 47 Figure 2. 9. The effect of noise on the directed self-assembly of a high XN = 40 polymer AB. The system is very sensitive to noise where defects started to emerge at noise values as low as 4 = 0:05 for the d l>

phase Lp/Lo = 1:732. The high XN value results in a large energy barrier for defects to annihilate...48

Figure 2. 10. The effect of noise on the directed self-assembly of a high XN = 40 polymer AB after annealing. Numerical annealing is implemented following 49_{. The threshold for defect generation is}

resto red ... 4 8

Figure 2. 11. (Left) Orientation correlation function C6 calculated from the experimental results for both (Left) Orientation correlation function C6 calculated from the experimental results for both the <1 1>, and

<20> phases at different noise levels. The hexatic-liquid transition at a slope of 16 = '/4 is marked by dashed line. (right) The fraction of microdomains with 6-fold coordination as a function of noise level. A strong reduction in 6-fold coordinated domains is observed above a noise level of 0.1...49 Figure 2. 13. Post correlation Orientational correlation function C6 for the experimental results for only

the post pattern of both the <l I>, and <20> phases at different noise levels. The hexatic-liquid transition at a slope of 16 = '/4 is m arked in dash line. ... 50

Figure 2. 14. Orientation correlation function C6 for the experimental results of set 2 of both <l I>, and

<20> phases at different noise levels. The hexatic-liquid transition at a slope of 16 = /4 is marked by a dashed line. The behavior of C6 of this independent dataset matches the results of Figure 2. 11. ... 51

Figure 2. 15. A schematic state diagrams for the melting of BCP hexagonal crystals self-assembled on noisy templates. The y axis corresponds to the value of F. The simulation results at different"

temperatures" come from a set of simulations with different XN = 17 and 40. The dotted thin line

interpolates through the results from SCFT simulations with no annealing and the solid line represents the true transition obtained by interpolating the data from simulations with extensive annealing...52 Figure 2. 16. (a,b) Distortion S and dilation D parameters for different template hexagons at different noise levels (shown on each plot) for the <l I> and <20> phases, respectively. The addition of noise results in an increase in the number of distorted hexagons (high S) with no significant effect on D. Unfilled markers represent template hexagons with defects (center post or a BCP microdomain in its vicinity not coordinated by 6 nearest neighbors). (c) SCFT free energy calculations as a function of the distortion parameter S [Lp]. This is achieved by displacing a single post horizontally or vertically in a perfect template (see inset). For a noise free pattern (red markers), the free energy rises with the increase of S (filled markers) until an interstitial is created (unfilled markers) after which the free energy reaches a plateau against further distortion. Moving the corner posts outwards to produce a dilation surrounding the post by -4% (black markers) does not change the trend; however, the free energy exhibits a steeper rise with the onset of defect creation (unfilled markers) taking place at lower S. Running the same analysis in a noisy template (( = 0.08) for five different posts, template distortion shifts the free energy up in

magnitude (filled markers). Every post has its own free energy curve; however, defect creation again stabilizes the free energy at a plateau (unfilled markers). In addition, Density maps of the minority polymer A showing forms of distortions of a hexagonal post pattern in the <Il> phase. Posts are

highlighted as circular white spots for clarity. The displacement of the center post increases the magnitude of S. Large values of S result in the creation of an interstitial opposite to the direction of post

displacement. Triangulation grid shows defects (colors follow figure 2) (d) Change of the total number of domains for different phases. The increase of noise level increases interstitials in the system. Results are from an SCFT simulation of the entire template... 54

Figure 2. 17. Distortion S and dilation D parameters for different template hexagons for the complete noise level range (shown on each plot) for the <1 1> and <20> phase of set-1,2. Unfilled markers represent template hexagons with defects (center post or a polymer domain in its vicinity not coordinated by 6 nearest neighbors)...55

Figure 2. 18. Free energy calculations as a function of the distortion parameter D = \(|AAj/Ao) where the markers are identical to Figure 2. 16c. The free energy calculations do not show a clear correlation with

D ... 5 6

Figure 2. 19. The variation of free energy with D = 4(IAAI/Ao) of an ideal hexagonal post pattern

subjected to pure dilation. The post uniform dilation has a minimal effect on the strain energy below D =

0.2 after which a pronounced change in slope is observed ... 57

Figure 2. 20. Excess free energy by a defect embedded in a lattice as a function of lattice size (examples shown on the right and marked on the plot) for both templated and untemplated BCP domains. The square power decay of FD-Fi shows that these defects have constant energy that gets reduced by increasing system area due to the reduction of defect concentration. ... 57

Figure 2. 21. Density plot of block A guided by a square template. Growing template interpost distance

Lp from left to right allowed more polymer domain to fit inside the square lattice. Cell dimensions are in

un its of R g ... 59

Figure 2. 22. Free energy AF [nkbT] calculations (f=0.7, XN = 15) as a function of interpost spacing in

units of Lo for the alternating rhombuses and the diamond morphologies (obtained by using an odd number of template unit cells). The alternating rhombus structure has a lower AF indicating that it is the

equilibrium m orphology. ... 60

Figure 2. 23. Comparing Voronoi cells in the diamond and rhombus domain configurations. Note that for alterating rhombuses, the common edge between a pentagon and hexagon is not aligned with the lattice side. The Voronoi cells demonstrate the ability of the polymer chains to partition into unequal domain sizes. Diamond domain configuration shows a symmetric pentagonal Vornoi cells. The free energy landscape is calculated as a function of domain separation. The diamond configuration has a higher energy (marked by the plus sign on the symmetry axis) compared to the rhombus configuration (marked

by the off axis plus sign)...6 1

Figure 2. 24. Stretching F,1 and interfacial F, energy components as calculated using SST in units of nkbT

for different domain spacing following Figure 2. 23. The stretching energy mimics shows the lobes of stable phases off the symmetry axis indicating the lower entropic energy penalty achieved by a rhombus. The Interfacial energy shows a continuous decay when reducing domain spacing. Still, lower interfacial energy can be achieved when having a distorted diamond shape...62 Figure 2. 25. Emergent symmetries of BCP (f=0.7, XN = 17) templated by a 32434 post pattern. 'Plain' morphology shows a unique number of domains inside the template rhombus, indicated by a roman number on each density distribution. 'Mixed' phases have alternating rows of different number of domains inside the rhombuses. The stability of all these phases is demonstrated on a free energy plot as a function of interpost spacing (L,) and the acute angle of the template rhombus (0). ... 63

Figure 3. 1. (a) The major steps of the fabrication process. Step 1, spin-coating a BCP film on a Si substrate; step 2, BCP annealing to promote microphase separation forming a monolayer of in-plane PDMS cylinders; step 3, reactive ion etch to remove the polystyrene matrix of the BCP and leave a monolayer of ox-PDMS cylinders on the substrate; step 4, spin-coating a second monolayer of BCP on the ox-PDMS microdomains; step 5, BCP annealing of the second layer; step 6, reactive ion etch to remove the polystyrene matrix of the BCP and leave a mesh-shaped ox-PDMS bilayer pattern on the substrate. (b) SEM image of a complex nanomesh in which the bottom layer, on bare Si, has a short

correlation length. The top inset is a cross-sectional SEM image of the bilayer mesh. The bottom inset is the 2D Fourier transform with distinct circles representing the periodic nature of the mesh without long-range order. (c) SEM image of well-ordered nanoresh patterns in which the bottom layer of cylinders, on PDMS-brushed Si without a template, has a long correlation length. The left inset is a zoomed-in SEM image of two-layer nanomesh pattern. The right inset is the 2D Fourier transform. The twofold, repeating symmetry is represented by the peaks along the x- and y-axes. (d) SEM image of a three-layer nanomesh pattern in which the first and third layers of cylinders (SD45 and SD10) are parallel to each other and orthogonal to the middle layer of cylinders (SD16). Scale bars, 100 nm. ... 68

Figure 3. 2. Free energy as a function of wall spacing for a lamellar morphology in ID confinement. Open markers are for domains parallel to walls, while solid markers are for perpendicular orientation. At a non-zero wall attraction (W- = 2), perpendicular orientation is stable even at commensurate wall spacing (left). Increasing wall attraction (W- = 4) stabilizes parallel orientation when wall spacing is an integer multiple

of polym er equilibrium periodicity (right)... 70

Figure 3. 3. Free energy plot for cylindrical BCP morphology as a function of cell width in a monolayer thin film. Equilibrium spacing Lo is smaller than bulk value LB = 3.96 Rg due to the square symmetry

imposed on the monolayer cylinders in thin film confinement...71 Figure 3. 4. Schematic of the computational cell for studying BCP cylindrical self-assembly on a

modulated substrate. BCP cannot access top layer mimicking free surface, and bottom layer resembling a substrate. An inverted parabolic barrier is used that has variable spread (s) and height (h). Top layer has a strong attraction suppressing vertically standing structures (W- = 4). Bottom layer can have a weak preference to either of the blocks (W- = 2). The simulation is run for different cell width (d). Film

thickness is t = 1.5 Lo unless stated otherwise ... 72

Figure 3. 5. 3D Parallel morphology (inset shows 2D slice perpendicular to barrier) for low (h/t = 0.2) and high (h/t = 0.4) modulation for different substrate affinity. Domains adsorb to topography when substrate is attractive to minority polymer, while domains are displaced by the polymer matrix when substrate is attractive to m ajority block...73 Figure 3. 6. 3D perpendicular morphology (inset shows 2D slice) for low (h/t = 0.2) and high (h/t = 0.4) modulation for different substrate affinity. BCP domains tend to curve towards substrate and fuse with

substrate undulation in minority affine case. When substrate is attractive to majority polymer, domains tend to curve aw ay from topography. ... 74

Figure 3. 7. Minority block density sliced at the peak of substrate modulation. Bridging across the substrate barrier persists to large h when substrate is attractive to majority block. For minority affine substrates, domains get disconnected across barriers as they fuse with the wetting layer on the substrate, which minimizes the energy penalty of domain termination...74 Figure 3. 8. Phase diagram of regions of stable parallel orientation calculated by F11-F [103nkbT] for

different cell width and barrier height. The majority attractive substrate shows stable parallel regions near commensurate condition especially for thin barriers. Minority attractive substrate shows large window of stability for perpendicular orientation unless high barriers are present. Still, wide barriers cause the perpendicular orientation to dominate the phase diagram independent of barrier spacing. (t= 1.5Lo)...76 Figure 3. 9. Phase diagram of regions of stable parallel orientation calculated by F 11-F-L [1 3nkbT] for

different cell width and barrier height (W -= 1 and s =0.6)... 77

Figure 3. 10. Phase diagram of regions of stable parallel orientation calculated by F11-F [1 3nkbT] for

different cell width and barrier height (t = 1.7Lo)... 78

Figure 3. 11. Schematic showing parameters employed in calculating free energies of parallel and

perpendicular orientations in the limit of SST... 80

Figure 3. 12. (a) Sample free energy calculations of parallel and perpendicular orientations including interfacial F, and stretching energies FA+FB. Increasing cell width reduces F1, but increases FA+FB for

parallel orientation. The perpendicular orientation shows slight reduction in F with increasing cell width as the BCP domain shape is not altered except near barrier. (b) Phase diagram of stable parallel

orientation calculated by F11-F. [nkbT]. (c) Parallel orientation border at (-10- [nkbT]) for different levels

of substrate repulsion to majority block. The higher the repulsion, the large the stable region of

perpendicular orientation. ... 82

Figure 3. 13. Free energy difference between vertical and horizontal lamellae subjected to trench confinement as a function of top surface attraction field and surrounding trench walls. Free energies are

evaluated at surface attractions marked by circular markers. Black filled markers have negative free energy difference indicating stable vertical lamellar structure, while white markers are for stable horizontal lam ellae...85 Figure 3. 14. SCFT density maps of A for different aspect ratios and surface functionality starting from random initial conditions. These distributions are used to generate figure 5 using a correlation function with a reference horizontal and vertical structure for a particular AR... 87

Figure 3. 15. SCFT results. (a) Summary of the equilibrium morphology for simulations evolving from random fields (XN = 14, f= 0.5). Stripes represent different aspect ratios as explained in the top right corner. The walls are attractive to the red block. At a combination of trench wall and top surface attraction fields, three final structures are obtained: horizontal lamellae, mixed lamellae, vertical lamellae. (b) A representation of the final structures that might emerge from SCFT simulations (AR = 1.4)...88

Figure 3. 16. Concentric structure free energy Fc is compared to a reference FR perfectly vertical (black) and perfectly horizontal (white) lamellae for a given AR and surface conditions. The lowest energy difference is plotted. For AR < 1, horizontal lamellae are favorable, while AR> 1 vertical structure is

stable for such high surrounding fields. For AR of unity, vertical lamellae dominate at higher fields while the energy difference asymptotically approaches zero. It reaches a value of 10'3 nkbT at w,, = 20 an wwall = 19 . ... 8 9

Figure 3. 17. Ginzburg-Landau model. Phase diagram for the stability of vertical (black) and horizontal (white) lamellar structures calculated using GL free energy (XN = 11). (a) All surfaces are subjected to

equal interfacial strength a and block incompatibility at the surface t,= 0.1 hqo3 (inset of free energy of

vertical and horizontal lamellae). Vertical lamellae are stable when AR and a are both either high or low. Horizontal lamellae show periodic stable domains due to the strain imposed by the mismatch between the cell height and polymer equilibrium spacing. (b) Increasing T, = 0.2hqo3

at the surface extends the stability regions of horizontal lamellae to higher a. (c) Top surface has a higher affinity a than the remaining three surfaces causing a significant enhancement of the horizontal lamellae domains even at higher AR. ... 92 Figure 4. 1. Comparison of structures obtained from experiments (left) and SCFT simulations (right): double layer of (a) perforated lamellae and (b) cylinders (top view). The upper cylinders in the simulation image are shown wider than the lower ones. The period of each morphology is indicated...97 Figure 4. 2. Free energy difference (AF) map for the bilayer PL obtained by displacing one layer with respect to the other (right). The value of zero in AF indicates the most stable structure as indicated in the schematic illustration (left). The blue- and yellow-colored circles correspond to the holes in the top and bottom layers...9 8

Figure 4. 3. (top) internal morphology in a PSb-PDMS-b-PS thin film. L, PL, and C represent lamellae, perforated lamellae, and cylinders, respectively. The structures are obtained from SCFT simulations Free energy curves as a function of film thickness for the structures obtained from SCFT simulations when the

volume fraction of the A block (corresponding to the PS block) is (a) 0.60, (b) 0.62, (c) 0.64, (d) 0.66, and

(e) 0.68. Double and triple layers of cylinders are distinguished by 2C (solid line) and 3C (dotted line),

Figure 4. 4. (a) Phase diagram of ABA triblock copolymer thin films as a function of film thickness and volume fraction of the A block (corresponding to the PS block) from SCFT simulations. Bilayer lamellae, perforated lamellae, and cylinders are represented by L (blue), PL (red), and C (yellow), respectively. (b)

Interlayer spacing of bilayer structures as a function of volume fraction of A. Lamellae, perforated lamellae, and cylinders are represented by L (blue circles), PL (red squares), and C (yellow triangles), respectively. The inset of (c) defines the interlayer spacing...100

Figure 4. 5. Schematic showing BBCPs consisting of series of m AB sidechains grafted on a C backbone divided into m + I segm ents...10 1

Figure 4. 6. (Left) Variation of critical X'AB parameter as a function of number of sidechains m, for different linker length Nc. Adding more chains to the backbone enhances phase separation. Scaled x X'ABm/ax recovers the XN = 10.5 for m=1 similar to AB linear diblock. A small but systematic reduction in

XN that is pure structural is observed. (right) Recording maximum density of block A for a lamellar

structure in the vicinity of phase separation. For a short linker Nc /N = 2% and large m, a strong order-disorder transition is observed resembling a I" order phase transition in the limit of large m. This

behavior is very different from the gradual density increase at Nc/N = 20% which resembles the expected

2"nd order phase transition in the m ean field limit. ... 104

Figure 4. 7. (left) Percent increase in lamellar domain spacing as a function m for different linker length Nc and degree of segregation XN. Parameters that increase side chain crowding (large m and small Nc) result in a significant increase in domain spacing due to sidechain stretching. (right) Change of domain

spacing for a single AB chain (m =1) as a function of fc compared to the linear diblock (fc = 0). The

segregation of C to the AB interface improves the overall mixing between AB chains and reduces the overall dom ain spacing. ... 106

Figure 4. 8. Concentric ellipses are the probability distribution of finding the end of the last segment of the backbone chain C mapped for m = 4 (left) and m = 29 (right). The chains extend along the interface

while maintaining the confinement normal to the interface. The spread of probability distribution is estim ated to a fitted G aussian (see inset)... 106

Figure 4. 9. q <R2_{>. DP (m) for BBCP normal and parallel to the interface. Root mean square end-to-end}

distance of the backbone chain C as a function of the number of backbone segments m. The chain size normal to the interface rapidly reaches a plateau determining the interface width. However, parallel to the

interface, the chain size continuously increases as m grows. The curve accurately follows \<R2> -N0 54. This result shows that the backbone chain is slightly stretched due the dense packing of the AB side chain s. ... 10 7

Figure 4. 10. Block density profile of lamellar morphology for XN = 12 and 50, and Nc/N = 2% and 20% for a single AB system (m = 1). Block C is localized at the AB interface due to the incompressibility

constraint. Such localization tends to minimize the effective degree of segregation creating diffuse AB

interfaces... 10 7

Figure 4. 11. (left) Variation of interface width w for a lamellar system as a function in for different linker length Nc and degree of segregation XN. Interfaces are sharper when increasing sidechain grafting. Small linker length Nc and strong segregation (large XN) result in smallest magnitude of w. (right) Density profile of block A at a low degree of segregation (QN = 12) for short (Nc/N = 2%) and long (Nc/N = 20%) linker lengths. The substantial increase in block C creates a very diffuse interface where adding more chains (arrow of increasing m) does not significantly change... 108

Figure 4. 12. Ternary phase diagram for XN = 30, m= 4 (XAcN = yjcN = 0). The phase diagram is dominated by lamellar morphology with a small region of core-shell cylindrical ones at low fc and fA.

The chemical neutrality of block C and the incompressibility constraint makes block C to act as a filler that effectively increase fA producing flat interfaces. ... 109

Figure 4. 13. Phase plots as a function of the total volume fraction fA and m = 4, at X'ABN = 12 and X'ABN

= 17. The low X'ABN show defective bicontinuous morphologies for fA < 0.44. Gyroid structure is observed fA = 0.44-0.46 after which lamellar structure is formed. The bicontinuous structures are

suppressed at high X'ABN where the structure goes from cylinders to lamellae at fA 0.36....--...1 10

Figure 4. 14. The probability distribution (blue) of end of the backbone chain C when the starting point lies on the tripe junction of a gyroid. The gyroid junction is represented using OA . At low m, the

probability grows symmetrically to remain confined in the triple junction volume. Only at large m >19, where it extends to reach the gyroid arm ... I I

Figure 4. 15. The probability distribution (blue) of end of the backbone chain C when the starting point lies on the gyroid arm. The gyroid strcuture is represented using 4A .It is seen that the probability grows unsymmetrically aiming at reaching the nearest triple junction. ... Ill

Figure 4. 16. Ternary phase diagram for m = 4 and equal block interaction (XAcN =XBcN = XABN = 30).

The phase diagram is dominated shows rich morphologies: Hexagonal lattice circular domains (C), Lamellar phase (L), lamellar phase with alternating beads (D), lamellar phase with alternating squares (S), lamellar phase with alternating pentagons (P), Octagonal phase (0). block densities of each phase are show n w ith corresponding labels... 113

Figure 4. 17. Stability of polymer domain orientation under confinement. (left) free energy plots of polymer domains aligned parallel (open marker), and perpendicular (solid markers) to trench walls as a function of trench width D[Rg]. At XN = 12, single AB chain polymer (m =1) shows the free energy of the perpendicular structure consistently lower than the parallel orientation resembling the behavior obtained for simple diblock copolymers. On the other hand, the bottlebrush polymer with m = 29 is showing a

lower free energy for the parallel orientation near the commensurability condition compared to the perpendicular orientation. Dashed lines are fit using equation

(4. 13). (right) A summary of the free energy difference between the perpendicular F1 and parallel F11

orientation at the commensuration condition for different values of XN. Every marker point represents a F- F11 at the minimum of a semi-parabolic curve of F11. The arrows point to the direction of increasing D.

115

Figure 4. 18. Density profiles for polymer domains lying parallel to the confining walls. Density vanishes at extremities due to the applied external fields. Increasing XN results in a stronger AB segregation with sharper interface. The incompressibility constraint localizes the neutral block C at the AB interface... 116 Figure 4. 19. Equilibrium domain spacing Lo for different simulation conditions extracted from confined simulations (circular markers) compared to the corresponding bulk values (square markers). Bottlebrush polymers with m = 29 have consistently larger Lo indicating extended AB sidechains. ... 116

Figure 4. 20. Free energy AF plots as function of trench width D for varying segregation strength XN and num ber of A B sidechains m ... 116

Figure 4. 21. Master free energy plots for parallel structures showing the change AF when the polymer domains are strained. The plot is generated (o) by collapsing the AF calculations shown in Figure 4. 20. Free energy AF plots as function of trench width D for varying segregation strength XN and number of AB sidechains m.by dividing D by the corresponding commensurate number of parallel domains. Dashed lines are fit using equation

(4. 13).

117

Figure 4. 22. Master free energy showing the effect of trench spacing in real units [Rg] on polymer strain en erg y ... 1 18

Figure 5. 1. Evolution of BCP morphology during SCFT calculations. The magnitude of F [nkbT]

gradually decays as the BCP undergoes microphase separation. Snapshots of the WA show the correlated structural evolution where domain position and shape evolve with iteration. Nonetheless, after just ~ 100 iterations clear domains can be clearly distinguished. (f, XN)= (0.22,39)... 123

Figure 5. 2. The mapping of 8"A/B at different stages (marked on Figure 5. _{1) during the evolution of F for} WA/B. It is seen that the distribution of 8"A/B is relatively flat especially beyond p2. Significant undulations

are localized near domain boundaries. These undulations cause domain shape change during fields

evo lu tio n ... 124 Figure 5. 3. Schematic of ResCNN. Each input is processed through a series of convolution/activation

steps in three parallel branches. The results of all branches is added to the input to synthesize the network output. In this architecture, 8"A/B and 'A/B are used as input and are compared to reference S A/B = 8" A/B.

The sizes of the convolution filters are listed for every branch. ... 125

Figure 5. 4 ResCNN training. (a) Training schedule showing variable batch size (B) and number of epochs. (b) The loss function change with the cumulative number of epochs during network training. The training schedule of (a) shows a lower loss function compared with a fixed B = 32 for the same number of

epochs. Smaller gap between training and validation curves is observed. ... 126

Figure 5. 5. ResCNN predictions on validation data compared to true reference from SCFT calculations. Good agreement is observed where undulations are localized near domain boundaries. No spurious features are introduced by the network. The approximate behavior of the network is evident the exact numbers and the poor description of the low frequency undulations. Te network performance is general for different cell sizes and m olecular characteristics... 127

Figure 5. 6. Sample free energy plots demonstrating the power of hybrid ResCNN-SCFT algorithm.

Significant reduction in the required SCFT iteration is observed in all cases. An approximate 3X gain in calculation speed in achieved. No artifacts are introduced by the network and all structure are converged to the final morphologies evident by the matching of F curves with vanilla SCFT within the simulation iteratio n s... 12 8

Figure 5. 7. Employing the 2D ResCNN in evolving a 3D structure. This is achieved by slicing the computational cell into a series of 2D images to be processed by the network. Free energy calculations show comparable reduction in the number of SCFT iterations. Simulations show the ability to produce

1

LITERATURE REVIEW

1.1 Introduction

The modem advancement in the field of nanotechnology relies on our ability to fabricate intricate structures

at very small length scales. Using "top-down" lithography techniques, complex fabrication processes are

used to add and remove materials, creating arbitrary geometry with extreme precision, accuracy, and

registration'. Nevertheless, the current fabrication capabilities are challenged by the need to pattern at the

10nm length scale

_{for high performance semiconductor, photovoltaics, and next generation storage}

devices". 'Bottom-up' approaches through self-organizing materials have the potential to meet both

resolution and throughput requirements

The inherent capability of materials to self-assemble provides

low-cost, relatively simple, large-area periodic nanostructured domains'. Block copolymers (BCPs) stand

out as a powerful self-assembling system that is able to generate nanoscale periodic domains at the range

of tens of nanometers with varying shapes, periodicities, and morphologies

. Due to their simplicity, linear

diblock copolymers are the most extensively studied system of BCP, both experimentally and

theoretically'

. In the bulk, diblock copolymers undergo microphase separation into spherical, cylindrical,

gyroid, and lamellar microdomains (see Figure 1. 1), depending on the volume fraction of constituents and

the degree of incompatibility between them' ,12. The integration of BCP in advanced industries requires the

generation of ultra-dense patterns of addressable nanoscopic elements with perfect order on a macroscopic

length scale"

However, the low energy cost of creating varying types of defects disrupting the perfect

periodicity of BCP, causes the system to deviate from perfect organization and to exhibit grain-like domains

with different orientations and extent'

.

A in B matrix

B in A matrix

I

res

Figure 1. 1. The sequence of observed morphologies in linear diblock copolymer melts. The cartoon structures are depicted by minority polymer".

Externally applied fields provide the means to guide the self-assembly process of BCP, and to control the

global orientation of their microdomains

. Applied fields examined are surface fields

,

_{ENREF 14,}

electric fields

or shear flow

Surface fields in particular are applied through confinement. In fact,

ID confinement is a natural result in thin films, where the polymer is confined in the vertical direction

between the free surface and the substrate, while the two other directions are unconstrained". Under

confinement, the parameter space controlling the self-assembly of BCP expands significantly, where the

final structure is a balance between interfacial effects

_'

_{breaking of translational symmetry, and structural}

frustration due the incommensurability between the natural periodicity of the polymer and film thickness

28,29

Simulating the effect of only the volume fraction and film thickness in thin film diblock copolymers

resulted in about 20 morphologies including centrosymmetric and non-centrosymmetric ones

, as shown

in Figure 1. 2.

XN = 20

urfaces attract B block

S

*-i

0

Figure 1. 2. Phase diagram of AB diblock copolymers for afixedXN=20 in a thin film with respect to volume fraction and film

thickness. A large number ofphases (-20) is demonstrated. It is seen that the gyroid phase is missing in the range of thicknesses studied3 0

1.2

Directed self-assembly of block copolymers

Surface fields are extensively utilized in what is known as Directed self-assembly (DSA)

. In this process,

the spontaneous organization of BCP is guided through chemical or topographical templates to achieve

lower defect density and controlled orientation. Topographical templates (known as graphoepitaxy"') such

as trenches'

and posts1

' 314

are fabricated using conventional lithography techniques. With the proper

choice of size and spacing of fabricated structures, long range periodic, defect free domains of spheres,

cylinders, and lamellae can be achieved

see Figure 1. 3.

PL"

PC,

S1

Figure 1. 3. BCP structure control using graphoepitaxy. (A) Scanning electron micrographs showing polyciystalline-like order of

sphereftrming polystyrene-b-polydimethylsiloxane (PS-b-PDMS) BCP thin film. (B and C) Ordered BCP domains achieved using 2D sparse lattice template of hydrogen-silsesquioxane (HSQ) posts (bright dots). BCP domains show perfect six- bid symmetric structures. The insets are for the 2D Fourier transf/rms of the scans indicating the overall state of order in the

system 16. (D) A scanning electron micrograph of a locally controlled structure of PS-b-PDMS cylinders fabricated by changing

HSQ post periodiciV

Alternatively, control over BCP domains can be achieved through chemical treatment (known as

chemoepitaxy) of the substrate. An interfacial layer at the substrate is chemically patterned to preferentially

interact with a particular component of the BCP, promoting BCP domain alignment. Careful control over

chemical pattern composition, spacing, and thickness promoted long range order and vertical orientation of

PS-b-PMMA domains

In general, either of the external patterns are in fact sparse, where a few

number of structures or treatments are fabricated on the surface. The polymer aligns with the structures

causing density multiplication, see Figure 1. 3B and Figure 1. 4B.

In addition to achieving improved order, the ability to generate aperiodic structures was demonstrated

through the implementation of graphoepitaxy

_{and chemoepitaxy}

_{, where carefully designed guiding}

templates (employing inverse design optimization algorithms) were employed to create arbitrary shapes

_,

or exploiting defects such as dislocations and jogs as tools to create isolated features that are relevant to the

microelectronic industry' as shown in Figure 1.

5.

A

B

w

o:

Figure 1. 4. BCP structure control using Chemoepitaxy. (A) SE M images of angled lamellae of a polystyrene-b-poly(methyl methacrylate) PS-b-PMMA/PS/PMMA blend. The chemical surface pattern isffabricated at different spacing, and the lamellar

domains of the block co copolymer blend are self -assembled and registered at different angles9. (B) SEM images of PS-b-PMMA

cylinders (Lo = 27 nm) on chemical patterns with Ls = 27 and 54 nm3". BCP are able to rectify pattern defects and produce

density multiplication on a sparse chemical pattern.

-(I

'I

Figure 1. 5. Aperiodic features generated using graphoepitaxy and chemoepitaxy. (Top) two arbitrary structures created by

positioning HSQ posts in a particular fashion predicted by inverse algorithms3 2. (Bottom) SEM images of

PS-h-PMAIA/PS/PMMA ternary blend directed to assemble into (a) nested array ofjogs, (b) isolated PMMA jogs, (c) isolated PS jogs,

and (d) arravs of T-junctions,.

Another strategy to produce customizable BCP patterns employed simple alignment strategies that aligned BCP domains in a particular direction, accompanied by 'line cuts' to create line terminations' ". The

resulting patterns follow the state-of-the-art gridded circuit design, Figure 1. 6. Terminations could be

registered to layout either by the extent of template walls, or by using non-guiding rectangular elements that finally be transferred to the substrate to create elaborate customizable features.

HSO

f rlnmtaton contronmatenal Hard mask

fOranic transfer layer

*Ps SSpn-on ctrn b

a

1111

1W

Figure 1. 6. Self-aligned JD customization. (a-h) Schematic and corresponding SEM images f afaibrication processflow. (i)

SEM scans of fragmented HSQ pattern and (j) SEM image of the resulting fragmented DSA -generated grating41. Scale bars are

100 nm. *0.9 0,8

r0.7

a

I

I

3

4

1.3 Novel 3D BCP morphologies

Despite efforts put in understanding and controlling BCP systems, the focus is mainly directed towards 2D

structure generation and control. Nevertheless, few key achievements are noted towards creating complex

3D patterns. Daoulas et al.

have assembled a tri-blend of PS-b-PMMA and the respective homopolymers

on a functionalized surface with a chemically patterned square array. The complex 3D structure was

generated through the frustration of the natural six-fold symmetry of BCP structure with the enforced

four-fold symmetric pattern. The structure demonstrated perforated lamella morphology with necks and

protrusions in the vertical direction. Russell and coworkers

, ' investigated the 2D confinement of

symmetric diblock copolymer of styrene and butadiene PS-b-PB, using nanoscopic cylindrical pores in

alumina membranes. Different geometries arose depending on the pore size. Concentric cylinders were

generated for large pore sizes, but the structure turned into stacked disks when the pore size became

comparable to the natural periodicity of the polymer

_{.When the experiment was run on a cylinder forming}

PS-b-PB polymer, helical structure was attained ", as shown in Figure 1. 7. The potential of cylindrical

confinement of BCP was investigated through simulation by Pinna et al.

who demonstrated a complex

spectrum of structures (helical, concentric cylinders, interwoven helices, helix surrounded cylinders, etc.)

by just varying the pore size.

A

C D

b

Figure 1. 7. Cylindrical confinement of PS-b-PB in anodic alumina membranes. Left: TEM scans of lamellarforming BCP in

different pore sizes"3 (scale bar, 50nm). Right: TEM scans of cylinder forming BCP aligned normal to pore axis. Helical

structure is produced'4 (Scale bar. 20nm).

BCP suspended droplets represent 3D confinement. This was initially investigated by an aerosol approach,

where small droplets of a polymer solution are sprayed and as the solvent evaporates, BCP microphase

separates inside such drops in a 3D confinement

. Several other approaches have been devised including

emulsions

'

reprecipitation

' 49,

and colloid crystal templating

. Transmission electron microscopy

(TEM) of the 3D confined structure revealed intricate patterns (concentric alternating layers, extended

tubes, nanospheres, core-shell spherical structures) that vary according to annealing time", see Figure 1. 8.

(a) M ( (d ()

(") (h- (i) (k!

Figure 1. 8. TEM scans showing morphological transitions of nanoparticles induced by solvent annealing of PS-b-PP". 1.4 Multi-layer stacking of BCP domains

3D structures can be attained through layer-by-layer stacking"1, 52. This approach is able to significantly expand the palette of accessible BCP morphologies using existing chemistries and molecular architectures. Layer-stacking can combinatorically create multi-scale hierarchical nanostructures beyond the native-morphologies of BCPs. The final structure is mainly governed by the processing conditions and the geometric and interfacial interactions across layers. Typically, the integrity of the base layers can be preserved through crosslinking, or by depositing hard materials between every stack. Ruiz and coworkers

" fabricated a horizontally oriented PS-b-PMMA cylinders. The structure was exposed to UV light causing

the crosslinking of PS. This was followed by depositing a lamellar forming PS-b-PMMA BCP. The top lamellar microdomains followed the underlying cylindrical topography similar to chemical templating.

Rose et al.1 decoupled the orientation of the stacked layers by sputtering porous, permeable silicon membrane that preserves the pattern of BCP during wet etching of PMMA. A second layer of dense silicon layer in deposited to seal the porous membrane and act as a substrate to support the subsequent BCP film. Despite layer-stacking potential, limited number of attempts were undertaken to particularly evaluate this

approach. Jung et al.7 _{studied the multilayer stacking in PS-b-PMMA by depositing lamellar forming phase} on a vertically aligned cylindrical phase in the bottom layer. The bottom structure had PS initially

crosslinked with UV exposure before depositing the second layer to preserve the lower topography during subsequent film processing steps. It is seen that there is a registry between the lamellar forming structure and the vertical cylindrical one, where SEM scans show cylindrical holes between the lamellar lines. The registry is further confirmed with top view TEM showing white dots of PS with perfect alignment with the