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Cite this:Phys.Chem.Chem.Phys.,

2019, 21, 18525

Hybrid patterns from directed self-assembly ofdiblock copolymers by chemical patterns

Wenfeng Zhao and Weihua Li *

The surface affinity is a critical factor for controlling the formation of monolayer nanostructures in block

copolymer thin films. In general, strong surface affinity tends to induce the formation of domains with low

spontaneous curvature. Abiding by this principle, we propose a facile chemoepitaxial scheme for producing

large-scale ordered hybrid patterns by the directed self-assembly of diblock copolymers. The guiding

chemical pattern is designed as periodic stripes with alternately changing surface affinities. As a consequence,

two different geometries of domains are formed on the stripes with different affinities. The self-assembly

process of block copolymers guided by the stripe patterns is investigated using cell dynamics simulations

based on time-dependent Ginzburg–Landau theory, and the kinetic stability diagram is estimated. Hybrid

patterns are successfully achieved with both cylinder-forming and sphere-forming diblock copolymers. In the

cylinder-forming system, the major hybrid pattern exhibiting a considerable stability window is composed of

parallel cylinders and perforated lamellae, while it is composed of monolayer spheres and parallel cylinders in

the other system. Encouragingly, the chemoepitaxial method is valid till the period of the guiding pattern is a

large multiple of the domain spacing. The chemoepitaxial scheme demonstrated in this work serves as a nice

supplement to the graphoepitaxial one proposed in our previous work.

Introduction

The self-assembly of block copolymers provides a powerful plat-form for the fabrication of ordered nanostructures that have widepotential applications.1,2 However, these nanostructures usuallylack long-range order and this restricts their application.2–5 Externalfields are essential to guide the self-assembly of block copolymersfor defect-free nanostructures, i.e. directed self-assembly (DSA).6–8

In the past few decades, many different DSA techniques havebeen developed. Two of the most successful DSA techniquesare referred to as chemoepitaxy and graphoepitaxy, which usechemical and topographical guiding patterns, respectively.3,9,10

Due to the great advances in these two DSA techniques, DSA hasbeen regarded as one of the most promising next-generationlithography techniques in the semiconductor industry.2,7,11–13

For this particular application, one of the most important advan-tages is to extend the conventional lithography to a smaller lengthscale by virtue of the remarkable self-assembly ability of blockcopolymers. To date, both chemoepitaxy and graphoepitaxy havebeen demonstrated to be efficient for the fabrication of large-scaleordered simple-geometry patterns, e.g. dots and lines.3,6,10

To satisfy the common demand of semiconductors forpatterns composed of different geometries, i.e. hybrid patterns,

recently, increasing efforts have been devoted to developingnew DSA techniques for the fabrication of defect-free hybridpatterns.11,14–18 Kim et al. fabricated a hybrid pattern composedof perpendicular cylinders and parallel half-cylinders via the DSAof cylinder-forming PS-b-PMMA diblock copolymer films onchemically stripe-patterned substrates.19,20 A hybrid line-dotnanopattern using mixed chemical patterns composed of ahexagonal array and a line array was obtained by Changet al.21 Instead of designing the guiding pattern, Choi et al.ingeniously created a hybrid pattern composed of standingcylinders and lamellae by tailoring the architecture of a miktoarmblock copolymer.22 Compared with the advances achieved in thoseDSA techniques for neat simple-geometry patterns, there is stillroom for the DSA techniques to be improved, e.g. in the aspects ofcontrolling the defect concentration or improving the directingefficiency.

As a DSA system usually consists of a large number ofvariables including the characteristic parameters of both theblock copolymer and the guiding pattern, it is time-consumingand costly for experiments to develop an efficient DSA scheme.It becomes essential to turn to computer simulations forprescreening some parameters.23–27 Very recently, we proposeda DSA scheme for the formation of line-dot hybrid patternsbased on computer simulations and theoretical calculations,in which the guiding pattern is represented by periodic shallowtrenches.28 In practice, the self-consistent field theory (SCFT)is utilized to predict the thermodynamic stability region of

State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of

Computational Physical Sciences, Department of Macromolecular Science,

Fudan University, Shanghai 200433, China. E-mail: weihuali@fudan.edu.cn

Received 11th May 2019,Accepted 28th July 2019

DOI: 10.1039/c9cp02667c

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the desired line-dot hybrid structures with respect to thecontrol parameters (e.g. trench depth and film thickness),while the cell dynamics simulation (CDS) of time-dependentGinzburg–Landau theory (TDGL) is applied to determine thekinetic stability window. Large-scale ordered line-dot hybridpatterns have been successfully obtained in considerable para-meter windows using both cylinder-forming and sphere-formingdiblock copolymers.

In our previous graphoepitaxial scheme for hybrid line-dotpatterns, the self-assembly of block copolymers into differentgeometrical domains is mainly controlled by the film thicknessthat is modulated by the topographically patterned substrate.28

For example, the parallel cylinders are formed in the trencheswhile perpendicular cylinders are generated on the steps by thecylinder-forming diblock copolymer melt confined between thetrench-step substrate and a top surface with proper surfaceaffinities. Therefore, it is very critical to precisely control thetrench depth when preparing the guiding pattern in experi-ment. To avoid this issue, we aim to develop an even simplerDSA scheme for the creation of hybrid patterns in the currentwork. Obviously, chemoepitaxy, in which the self-assemblyof block copolymers is guided by a chemically prepatternedsubstrate, is our first choice. Then, we need to induce the self-assembly of a diblock copolymer melt into two differentgeometries of domains by virtue of the alternately varying surfaceaffinity. Similar to that graphoepitaxial scheme, the orientationalorder could result from the unidirectionally oriented boundariesbetween two neighboring arrays of different domains. Whentwo neighboring boundaries are not separated further than thecorrelation length of ordered domains, the ordering processcan propagate from the boundaries into the entire system,finally leading to defect-free hybrid patterns.29

Many experimental and theoretical studies have illustratedthat the surface affinity is a critical factor of controlling the self-assembly of diblock copolymers in thin films.30–37 One generalconclusion is that a strong surface affinity tends to induce theformation of domains with low spontaneous curvature.34–36

Simply speaking, the strong surface affinity induces a high densityof the attracted component on the surface, and thus effectivelyincreases the interfacial segregation of the copolymer. Accordingto the self-assembly behavior of a diblock copolymer, the ordereddomain transforms along the direction of decreasing curvature asthe segregation increases for a fixed composition, e.g. transformingfrom sphere to cylinder, gyroid and lamella. For example, Manskyet al. experimentally confirmed that the interfacial segregation of adiblock copolymer was proportional to the surface potential.30

Similarly, cylinder-/sphere-forming block copolymers were observedto form perforated lamellae/cylinders in thin films with selectivesurfaces.35,36 Therefore, we can tailor the two different surfacepotentials of a chemical pattern to obtain different geometries ofdomains, i.e. producing hybrid patterns.

As the current system has less parameters than our previoustopographical system, we directly use TDGL simulations toexplore the kinetic stability windows of hybrid patterns. Withoutloss of generality, we consider that both the top and substratesurfaces attract the majority B-block, while the substrate is

prepatterned by alternately arranged parallel stripes with weakand strong surface potentials, whose potential strengths areindicated by Lw

b (light) and Lsb (dark), as seen in Fig. 1, respec-

tively. The potential strength of the top surface is indicated by Lt.For the reason of simplicity, we assume that the areas of weakand strong potentials have an equal width, and the period of thechemical pattern is denoted as LP. As the surface affinity tends tolower the curvature of domains, we consider the diblock copo-lymers forming high-curvature domains, i.e. cylinder-formingand sphere-forming. Based on the above argument, a hybridpattern composed of monolayer parallel cylinders in the weak-potential area and perforated lamellae in the strong-potentialarea from the cylinder-forming copolymer, while another hybridpattern composed of monolayer spheres and parallel cylindersfrom the sphere-forming copolymer, could be generated. Notethat the hexagonally arranged holes in the perforated monolayerare a kind of dot array. Therefore, the two kinds of hybridpatterns can be regarded as hybrid line-dot patterns.

Theory and method

We consider an incompressible melt of asymmetric AB diblockcopolymers confined in thin films with film thickness D. Thevolume fraction of minority A-block is characterized by f. Inthe TDGL model, f(r) = fA(r) � fB(r) is chosen as the orderparameter, where fA(r) and fB(r) are the local volume fractionsof A- and B-blocks, respectively. The free energy functional ofthe diblock copolymer melt in thin film can be written intothree terms as28

F ½f� ¼ FS½f� þ FL½f� þðdrHsurfðrÞfðrÞ: (1)

The short-range term FS is a standard Ginzburg–Landau freeenergy functional38

FS½f� ¼ðdr

C

2ðrfÞ2 þWðfÞ

� �(2)

where C is a positive constant and is fixed as C = 0.5. W(f) isgiven by its derivative form

dW

df¼ �A0tanhfþ f (3)

Fig. 1 (a) Schematic illustration of an AB diblock copolymer film laying ona chemically patterned substrate. (b) Characteristic parameters of thechemical pattern. (c) Schematic illustration of multiple stripes.

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with a positive constant A0. A0 4 1 determines the segregationdegree between immiscible A-/B-blocks.

The long-range term FL was proposed by Ohta and Kawasaki,39

FL½f� ¼a2

ððdrdr0dfðrÞGðr� r0Þdfðr0Þ (4)

where df(r) = f(r) � �f. �f = 2f � 1 is the spatial average value off(r). a is a positive parameter and is chosen as a = 0.02. The Greenfunction G(r � r0) satisfies39

�r2G(r � r0) = d(r � r0) (5)

Impenetrable hard walls are utilized to model the thin film,whose surface affinities are defined by the following potential,28

HsurfðrÞ ¼1

2LX tanh½ðs� dðrÞÞ=e� þ 1f g (6)

for d(r) o 2s and otherwise Hsurf(r) = 0, where d(r) is the shortestdistance from point r to either the top surface or the bottomsubstrate. s and e denote the interaction range and the steepnessof the surface field, respectively. For the top surface, the field

strength is LX = Lt, while it alternately varies between LX = Lwb

and Lsb for the chemically patterned substrate. Note that a

surface with LX 4 0 attracts a B-block, and otherwise it attractsan A-block.

The phase-separating kinetics is described by the conservedCahn–Hilliard equation40

@f@t¼Mr2dF ½f�

dfþ xðr; tÞ (7)

where M = 1 is a phenomenological mobility coefficient. x(r, t)is a random noise term with zero average and satisfies thefluctuation–dissipation theorem, hx(r, t)x(r0, t0)i = �x0Mr2d-(r � r0)d(t � t0). x0 is the noise strength, and here we choosex0 = 0.04. The CDS method is applied to solve the dynamicsequation starting from an initially disordered/structureless state.41

The spacial discretization is chosen as Dx = Dy = Dz = 0.5, and thetime evolution step Dt is fixed as 0.1. Here, the number of timesteps is denoted by Nt. The characteristic parameters s and e of thesurface potential are fixed in the unit of the bulk domain spacingL0 (cylinder-to-cylinder or sphere-to-sphere distance), s = 0.15L0

Fig. 2 Kinetic stability diagram with respect to Lt and D for the directed self-assembly of cylinder-forming diblock copolymers with f = 0.38 and A0 = 1.30on a chemically patterned substrate with Lw

b = 0.005 and LP = 16L0, estimated by TDGL simulations: (a) Lsb = 0.015 and (b) Ls

b = 0.035. (c) Density plots of theordered morphologies observed in the diagram: parallel cylinder (C8), perpendicular cylinder (C>), hybrid perpendicular–parallel cylinders (C>–C8), hybridperpendicular cylinder–perforated lamella (C>–PL), hybrid parallel cylinder–perforated lamella (C8–PL), perforated lamella (PL), hybrid perforated lamella–lamella (PL–L) and lamella (L).

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and e = 0.5L0. More details about the TDGL model can be found inour previous work.28,29,42,43

Results and discussionHybrid patterns of cylinder-forming diblock copolymers

We first consider a cylinder-forming diblock copolymer,e.g. choosing f = 0.38 and A0 = 1.30 in the TDGL model.The cylinder-to-cylinder distance in the bulk is determined asL0 E 8.9 in the unit of grid spacing. In the DSA system, thereare still five parameters including the pattern period LP, thefilm thickness D, the potential strength Lt of the top surface,and the two potential strengths Lw

b and Lsb of the chemical

pattern. Usually, the pattern period LP has a trivial effect on thegeometry of domains but a significant effect on the domainorder. Moreover, it is necessary to note that the domain spacingof monolayer structures self-assembled by block copolymers inthin films depends on the film thickness.37 Accordingly, it ismore convenient to fix the pattern period, e.g. LP = 16L0. Then,we need to estimate the magnitudes of Lw

b and Lsb for preparing

the chemical pattern. Considering that the phase transition iscontrolled by the synergistic effect of the the top and bottomsurface affinities for a given film thickness, we examine theinfluence of the potential strength on the phase transition in asimple film system with a given D = L0 and two identicalsurfaces, i.e. Lw

b = Lsb = Lt = L 4 0. It is observed that the

phase transition follows a common sequence from perpendi-cular cylinder (C>) to monolayer parallel cylinder (C8), mono-layer perforated lamella (PL) and monolayer lamella (L) asL increases. For nearly neutral surfaces (L o 0.002), C> ispreferred because there is no incommensurability problembetween the domain spacing and the film thickness. As thesurfaces become considerably attractive to the majority B-blocks,the surface energy induces the formation of a wetting B-layeron each surface, leading to the formation of C8 for 0.002 oL o 0.019. When L is increased further, the surface potentialimpacts the packing of not only the adjacent B-blocks but alsothe connected A-blocks, i.e. changing the domain shape. For0.019 o Lo 0.025, PL is formed instead of C8, and it transfers toL when L 4 0.025. This observation leads to a roughly quantita-tive criterion for the potential strength in the phenomenologicalmodel: weak (L o 0.002), moderate (0.002 o L o 0.019), strong(0.019 o L o 0.025) and very strong (L 4 0.025).

According to the above discussion, we can devise a chemicalpattern for the generation of hybrid patterns. For instance, wechoose 0.002 o Lw

b o 0.019 and 0.019 o Lsb o 0.025 to produce

the hybrid pattern composed of parallel cylinders in a weak-potential area and perforated lamellae (denoted as C8–PL).Considering that Lt is usually different from Lw

b or Lsb, the

values of the two strengths can be correspondingly modified tocompensate the effect resulting from the difference of Lt fromthem. It is necessary to note that both the potential strengthof the top surface and the film thickness are relatively easierto control in experiments.7 Therefore, we mainly exploredthe kinetic stability diagram with respect to Lt and D for given

Lwb or Ls

b. In Fig. 2, we show two kinetic stability diagramsfor fixed Lw

b = 0.005 and two different magnitudes of Lsb: (a)

Lsb = 0.015 and (b) Ls

b = 0.035. Surprisingly, a number ofinteresting structures are observed in both the diagrams,including neat patterns (C>, C8, PL and L) and hybrid patterns(C>–C8, C>–PL, C8–PL and PL–L). Obviously, both the twocontrol parameters play significant roles in the kinetic stabilityof these ordered patterns.

In Fig. 2(a), the main phase sequence for 0.75L0 o D o 1.1L0

is C8 - C8–PL - PL - L as Lt increases from 0.005 to 0.035.For Lt B 0.005, the three potential strengths are moderate andthus favor the formation of C8, resulting in a wide stabilitywindow of C8, i.e. 0.78L0 o D o 1.07L0. Outside the window,the film thickness is highly incommensurate with the layeringdistance of monolayer parallel cylinders, thus leading to theformation of perpendicular cylinders in the weak-potential area(C>–C8) or even in the entire area (C>). When Lt is increased tolarger than 0.01, the window of the hybrid pattern C8–PL startsto open, e.g. 0.78L0 o D o 0.91L0 at Lt = 0.01. This impliesthat the domain transforms from cylinder to perforated lamellaand then back to cylinder in the strong-potential area asD increases. In fact, this reentrant transition from a low-curvature phase to a high-curvature phase is commonly seenas Lt increases, which has already been observed in the phasediagram of diblock copolymer films by SCFT.37 The reentranttransition mainly results from the different ability of releasingchain stretching or compression, induced by the incommen-surability between the film thickness and the domain spacingin the normal direction, between different morphologies.For a discrete domain with high curvature, the adjustabledomain spacing in the surface plane provides a freedom to

Fig. 3 Morphological snapshots at Nt = 5000, 10 000, 50 000 and500 000 during the time evolution of (a) C8 for Lw

b = 0.005, Lsb = 0.015,

Lt = 0.015 and D = 1.07L0 and (b) hybrid C8–PL pattern for Lwb = 0.005,

Lsb = 0.035, Lt = 0.01 and D = 0.79L0.

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release the stretching or compressing energy. Meanwhile, theshape of a discrete domain changes notably in response to thevariation of film thickness, e.g. that cylinders in C8 are con-siderably elongated in the normal direction for D E L0 whilethey are squeezed for D E 0.73L0. As the curvature of thedomain decreases or the domains become more connected inthe surface plane, the adjustability of the domain spacing in

the surface plane tapers and finally vanishes in the monolayerlamella.

When Lt \ 0.015, the effect of the top surface becomesdominant, driving parallel cylinders to the weak-potential areato transform into a perforated lamella and thus leading to theformation of neat PL. Similarly, the neat L morphology appearfor Lt \ 0.03. In contrast to the kinetic stability diagram inFig. 2(a), that in Fig. 2(b) for a larger Ls

b = 0.035 exhibits aremarkably larger window of C8–PL. Moreover, a noticeablewindow of a new hybrid pattern of PL–L is observed. Apparently,the expansion of C8–PL results from the strong potential ofLs

b = 0.035 that induces the formation of PL in a strong-potential area even when Lt is as weak as 0.005. Note that theC8–PL/PL boundary in Fig. 2(b) is similar to that in Fig. 2(a).This is simply because of their same values of Lw

b = 0.005.For 0.025 t Lt t 0.035, PL transforms into L in the strong-potential area under the synergistic effect of strong top andbottom potentials, whereas PL is maintained by the weakbottom potential with Lw

b = 0.005 in the weak-potential area.There is no doubt that the time evolution of morphology is

critical to illustrate its ordering process and thus to reveal thedirecting mechanism of the guiding pattern, which is readilyaccessed by the kinetic TDGL simulation.23 In Fig. 3, somesnapshots within the formation process of two differentmorphologies are shown: (a) C8 with Lw

b = 0.005, Lsb = 0.015,

Lt = 0.015 and D = 1.07L0; and (b) C8–PL with Lwb = 0.005, Ls

b =0.035, Lt = 0.01 and D = 0.79L0. At the initial stage (Nt = 5000) inFig. 3(a), the phase separation is mainly induced by the surface

Fig. 5 Kinetic stability diagram with respect to Lt and D for a sphere-forming diblock copolymer melt with f = 0.36 and A0 = 1.28 on a chemicallypatterned substrate with Lw

b = 0.005 and LP ¼ 8ffiffiffi3p

L0: (a) Lsb = 0.015 and (b) Ls

b = 0.035. (c) Density plots of four ordered morphologies observed in thediagram: monolayer spheres (S), hybrid pattern composed of monolayer spheres and parallel cylinders (S–C8), parallel cylinders (C8) and a hybrid patternof parallel cylinders and perforated lamellae (C8–PL).

Fig. 4 Hybrid C8–PL patterns formed with different periods of guidingpatterns for a typical group of parameters, Lw

b = 0.005, Lsb = 0.035,

Lt = 0.01 and D = 0.79L0: (a) LP E 4L0, (b) LP E 6L0, (c) LP E 8L0 and(d) LP E 16L0.

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potential, and thus it occurs along the normal direction to forma layering structure, especially in the strong-potential area. Asthe weak- and strong-potential areas induce considerably dif-ferent interfacial segregation and thus different geometries ofdomains,30,31 distinct boundaries between the domains in thetwo areas are formed. These unidirectional boundaries guidethe self-assembly of block copolymers into a perfectly orderedstructure. Specifically, well aligned domains are first formed atthe vicinity of the boundaries, and then they propagate theorder into further domains. As the evolution proceeds, perfectlyparallel cylinders are first formed in the weak-potential area. Incontrast, it takes a much longer time to form parallel cylindersin the strong-potential area. This is because the strong surfacepotential reduces the stability of parallel cylinders relative tothat of perforated lamellae. When Ls

b is increased to 0.035 inFig. 3(b), the perforated lamella becomes stable against parallelcylinders, leading to the formation of C8–PL. Surprisingly, theordering process of PL in the strong-potential area is very fast. Itis necessary to mention that the period of the chemical patternexamined above is as large as LP = 16L0. Of course, the currentDSA scheme becomes more safely valid when LP is reduced,e.g. LP = 4L0, 6L0 and 8L0, as shown in Fig. 4.

Hybrid patterns of sphere-forming diblock copolymers

According to the general mechanism of surface-induced phaseseparation, a hybrid pattern consisting of monolayer spheresand parallel cylinders (S–C8) can be created with a sphere-forming diblock copolymer. In the TDGL model, we choosef = 0.36 and A0 = 1.28 to generate a spherical phase in the bulk.The sphere-to-sphere distance is estimated as L0,s E 8.5 in theunit of grid spacing. Similar to our previous work, we fix the

period of chemical pattern as LP � 8ffiffiffi3p

L0;s. In Fig. 5, two kineticstability diagrams in the Lt–D plane are presented for two typicalchemical patterns with Lw

b = 0.005 and (a) Lsb = 0.015 and

(b) Lsb = 0.035. The diagram in Fig. 5(a) consists of three ordered

nanostructures including neat monolayer spheres (S), hybridmonolayer spheres and parallel cylinders (S–C8) and neat parallelcylinders (C8). All nanostructures exhibit a considerable stabilitywindow. Similar to the diagrams in Fig. 2, the stability windowof S–C8 is significantly expanded by increasing Ls

b from 0.015to 0.035. Furthermore, there is a notable window of anotherhybrid pattern (C8–PL). As the two systems of cylinder-formingand sphere-forming copolymers resemble similar mechanisms,herein, we do not repeatedly explain them.

Conclusions

In this work, we propose a chemoepitaxial scheme for directingthe self-assembly of diblock copolymers into large-scale orderedhybrid patterns. According to the mechanism that surfacepotential strengthens the interfacial segregation of block copo-lymers and thus reduces the curvature of self-assembled domains,the chemical pattern of the substrate is devised to be composed ofstripes with alternately varying surface potential. In other words,domains of high curvature are formed on the stripe of weak

potential, while those of low curvature are formed on the stripeof strong potential. As a result, the alternately arranged areas oftwo kinds of different domains constitute a hybrid pattern. Wedemonstrate the validity of the DSA method for both cylinder-forming and sphere-forming diblock copolymers by constructingthe kinetic stability diagrams using the high-efficient TDGLsimulations. In the diagrams of cylinder-forming copolymers, ahybrid pattern composed of parallel cylinders and perforatedlamellae exhibits considerable windows. Moreover, the stabilitywindow can be significantly expanded by increasing the contrastof surface potentials of the chemical pattern. While in the otherdiagrams of sphere-forming copolymers, another hybrid patterncomposed of monolayer spheres and parallel cylinders isachieved in large windows. In addition to the hybrid patterns,neat line (monolayer parallel cylinders) and dot (monolayerspheres or perforated lamellae) patterns are also successfullyobtained in respective considerable windows.

Besides the usual film thickness, the formation of hybridpatterns is controlled by the top and bottom surface potentialsin the proposed chemoepitaxial scheme. The top surfacepotential can be tailored by changing the vapor componentand pressure, while the surface potentials of the chemicalpattern can be tuned by controlling the exposure time in theirradiating modification of X-ray or plasma. Note that the topsurface is usually ‘‘soft’’, and it is ideally hard in our model. Thehard surface may generate a stronger confining effect than thesoft one, and should favor the formation of hybrid patterns. Asthe hybrid patterns exhibit large processing windows, theyshould be feasible in a ‘‘soft’’ confined case, especially, theS–C8 morphology with the largest stability window and fastestformation process. In addition, it is important to note that thechemoepitaxial scheme is still valid for the generation of large-scale ordered hybrid patterns when the period of chemicalpattern is as large as 16 times the domain spacing. This impliesthat even for a rather small domain spacing, L0 B 20 nm, thepattern period is larger than 300 nm and thus can be preparedby advanced lithography techniques at a reasonably low cost.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural ScienceFoundation of China (Grant No. 21774025).

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