Nanopatterns with a Square Symmetry from an Orthogonal Lamellar

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Nanopatterns with Square Symmetry from Orthogonal Lamellar Assembly of Block Copolymers Seung Keun Cha, Daeseong Yong, Geon Gug Yang, Hyeong Min Jin, Jang Hwan Kim, Kyu Hyo Han, Jaeup U. Kim, Seong-Jun Jeong, and Sang Ouk Kim ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b03632 • Publication Date (Web): 13 May 2019 Downloaded from http://pubs.acs.org on May 14, 2019

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ACS Applied Materials & Interfaces

Nanopatterns with Square Symmetry from Orthogonal Lamellar Assembly of Block Copolymers

Seung Keun Cha, † Daeseong Yong, ‡ Geon Gug Yang, † Hyeong Min Jin, † Jang Hwan Kim, † Kyu Hyo Han, † Jaeup U. Kim, ‡* Seong-Jun Jeong, §* Sang Ouk Kim†*

†National Creative Research Initiative Center for Multi-Dimensional Directed Nanoscale Assembly, Department of Materials Science and Engineering, KAIST, Daejeon 34141, Republic of Korea ‡Department of Physics, School of Natural Science, UNIST, Ulsan 44919, Republic of Korea §Department of Organic Materials and Fiber Engineering, Soongsil University, Seoul 06978, Republic of Korea

*Corresponding authors E-mails: [email protected], [email protected], [email protected] Phone numbers to Sang Ouk Kim Office phone: +82-42-350-3339, Fax: +82-42-350-3310

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Abstract

Nanosquare array is an indispensable element for the integrated circuit design of electronic devices. Block copolymer lithography, a promising bottom-up approach for sub-10 nm patterning, has revealed a generic difficulty in the production of square symmetry due to the thermodynamically favored hexagonal packing of self-assembled sphere or cylinder arrays in thin film geometry. Here, we demonstrate a simple route to square arrays via orthogonal selfassembly of two lamellar layers on topographically patterned substrates. While bottom lamellar layers within a topographic trench are aligned parallel to the side walls, top layers above the trench are perpendicularly oriented to relieve the interfacial energy between grain boundaries. The size and period of the square symmetry are readily controllable with the molecular weight of block copolymers. Moreover, such orthogonal self-assembly can be applied to the formation of complex nanopatterns for advanced applications, including metal nanodot square arrays.

Keywords: Block Copolymer, Self-Assembly, Square Array, Nanopatterns, Self-Consistent Field Theory (SCFT)


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Introduction

Square array pattern is an essential component in the integrated circuits, as most of the circuit designs in semiconductor industry have relied upon rectilinear coordinate system.1-5 To date, such nanopatterns in electronic devices have been principally fabricated by photolithographic processes, which are facing an intrinsic challenge in the reduction of critical dimension towards sub-20 nm-level mainly due to the diffraction limit of radiation light sources.

Block copolymer (BCP) lithography is a complementary nanopatterning method to address the limitation of photolithography.6-14 Microseparation of BCPs produces periodic nanostructures assembled from nanoscale spheres, cylinders, and lamellae with a typical feature size of 3-50 nm. BCP lithography enables sub-10 nm scale patterning with a low cost large-area scalable process and, thereby, is potentially useful not only in electronics, but also in plasmonics,15-18 catalysis,19-21 and so on. Unfortunately, spherical or cylindrical nanostructures of BCP thin films generally show hexagonal close packed structures to minimize their internal energy. Square or rectangular packing of the nanostructures causes additional free energy penalty mainly due to the nonuniform polymer chain stretching. To date, several different approaches have been suggested to address the intrinsic thermodynamic limitation and induce square nanoscale patterns from BCP self-assembly. A few research groups have reported the formation of square arrays using chemical or topological prepatterns,22-27 which suffered from low throughput with high cost prepatterning issue. Employment of triblock copolymers or blending diblock BCPs with hydrogen bonding units is another well-recognized strategy to this end,28,29 but requires delicate experimental condition and pattern transfer. Sequential stacking of orthogonal line patterns could yield nanoscale square patterns,30,31 however, two times of nanopatterning process with subtle overlay control remains challenge. A straightforward facile approach based on low cost simple process is still demanded for versatile applications.

In this work, we introduce a facile approach to fabricate square nanoarray by self-assembly of lamellae forming BCPs within trench substrate pattern. Orthogonally stacked lamellae layers, where the lower and upper layers align parallel and perpendicular to the trench wall,



respectively, were formed by simple spin-coating and thermal annealing processes. The underlying mechanism of this interesting phenomenon is qualitatively explained by selfconsistent field theory (SCFT), which reveals that the creation of orthogonal lamellar arrays can be enhanced by the reduction of effective surface tension at the grain boundaries. The size and number of square pattern are controllable with the molecular weight of BCPs and the width of trenches. Selective removal of one block and subsequent metal deposition and lift-off process generate metal nanodot arrays with square symmetry.

Results and discussion

Figure 1A illustrates the schematic procedure for metal nanodot array with square pattern. Symmetric polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) thin films with diverse molecular weights and adequate thicknesses were spin-cast on topographically patterned silicon substrates. Thermal annealing of the thin films under a vacuum at 250 C induces orthogonally aligned lamellar nanostructures. The lamellar morphology at the bottom and top layers shows parallel and perpendicular orientation to the trench direction, respectively. Interestingly, highly directional dry etching, such as reactive ion etching (RIE), in the vertical direction rather than conventional wet etching yields the nanomesh template with a square symmetry (Figure S1). Completely etched nanohole array enclosed by orthogonal PS and PMMA vertical walls from the bottom substrate view ensures good processability for the subsequent metal transfer process. Figure 1B shows SEM images of square nanomesh using PS-b-PMMA (Mn: 35 kg/mol for PS, 33.5 kg/mol for PMMA) on the trenches of 190-nm-width and 100-nm-depth after PMMA etching (also see Figure S2 for a large area image). The observed slight deviation of square symmetry is attributed to the line edge roughness of the silicon prepattern.

Figure 1C presents cross-sectional SEM image of the square nanopattern on a silicon substrate. It is clearly observed that PS frames within the silicon trench maintain robust morphology with


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trench parallel alignment whereas the upper lamellar layer was orthogonally oriented over them. It is noteworthy that the lamellar layers right above the silicon mesas show substrate parallel orientation without apparent nanoscale morphologies in the film plane direction. Figures 1D & F show the square nanopatterns with different sizes and periodicities using PS-b-PMMA of different molecular weights (89 and 160 kg/mol for Figures 1D & F, respectively). After metal deposition by evaporation over the entire surface and lift-off of BCP template, metal nanodot array with square symmetry is left over the substrate. Figures 1E & G display the square arrays of Cr nanodots formed within the silicon trenches by employing the BCP templates presented in Figures 1D & F, respectively. Noteworthy that due to the unintended incomplete BCP template removal during RIE, some connected metal dots are observed, which can be further addressed by an optimal etching condition.

Figure 2 shows the variation of lamellar orientation depending on film thickness within the trenches of 190-nm-width. The BCP film thickness on mesas is represented by h in each SEM image. As presented in Figure 2A (h ~ 23 nm), the thin film exhibits trench parallel lamellae driven by well-known graphoepitaxy effect.7 As the film becomes thicker, an intermediate state where the parallel and perpendicular lamellar phases coexist is observed in Figure 2B (h ~ 35 nm). Figure 2C (h ~ 58 nm) shows that the upper lamellar layer aligns perpendicular to the trench when the film is sufficiently thick (also see the cross-sectional SEM images in Figure S3). Notably, a film thickness over 58 nm commonly induces the orthogonal lamellar structure regardless of BCP periods. Thus, we used the same spin-coating condition (2.5 wt%, 2000 rpm) in this work for the formation square array pattern. Such an interesting lamellar orientation dependence on BCP film thickness will be discussed later based on SCFT calculation.

Figure 3A exhibits the morphology change of BCP nanopatterns depending on the relationship between BCP lamellar period and trench width in a substrate. Table 1 provides the periods of lamellar structures (expressed as L1, L2, L3, L4, and L5) assembled from PS-b-PMMA of different molecular weights. We classified the morphologies into four different categories; square pattern without defects (■), square pattern with defects including vacancy or connection (▲), substrate parallel lamellar structure (●), and coexisting morphology of square pattern and substrate parallel lamellae (♦). Each symbol is plotted for the 2D combination of trench width



(190, 220, 270, 290, 360, 400 nm) and BCP period (L1, L2, L3, L4, L5). The number below each symbol is the quotient of trench width normalized by BCP lamellar period. Representative SEM images for each symbol are also shown in Figures 3B-E.

Commensurability between the trench width and the BCP period has been found as a critical parameter determining the final morphology. If BCP lamellar period is commensurable with the trench width, the bottom lamellae would be highly aligned along trench parallel direction due to the symmetric wetting condition of PS-b-PMMA confined within two sidewalls.32,33 The commensurate numbers close to integers (e.g. 2.9, 3.9, 5.1) tend to generate the square patterns with a high degree of ordering (■), as presented in Figure 3C. By contrast, incommensurate numbers (e.g. 3.3, 3.4) produce defective morphologies (▲). As shown in Figure 3B, vacancies or broken lamellae are observed as typical defects.

Interestingly, substrate parallel lamellar morphology is more preferred, as the commensurate number increases even while satisfying an integer. In the case of a sample with 107 kg/mol molecular weight and 56 nm period (L4), square arrays are dominant at the small commensurate number (3.9). However, the morphology is transformed into the coexistent state of square arrays and substrate parallel lamellae (♦) at a larger commensurate number (5.2), as shown in Figure 3D. Within the widest trench width of 400 nm (commensurate number: 7.1), surface parallel lamellar structure without any noticeable in plane nanoscale pattern is dominant over the entire substrate (●), as displayed in Figure 3E. As the trench becomes wider, the influence from the bottom surface within trench becomes more dominant for the self-assembly of BCPs compared to that from side walls, which results in the preferential wetting of lamellar layers parallel to the bottom surface.

We have conducted theoretical investigation on the stability of orthogonally packed lamellar structure using integral SCFT with finite range interaction. Since typical Si substrates with native oxide layer prefer PMMA nanodomains to PS domains, we consider that the lamellae on the substrate mesa are parallel to the substrate and those inside the trench are aligned along the side wall of trench, as shown in Figures 4A-C. Even under this well-defined initial boundary


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condition, we can still consider three different candidates for the lamellar alignment above the trench. The first candidate (Figure 4A) has three twist grain boundaries (TGB), and exhibits square pattern when observed from above through film thickness direction. The TGB model images from various viewing angles are illustrated in Figures 4E-G for a better understanding. The second candidate maintains the vertical lamellar structure above the trench region, and it has two T-junction boundaries at the side surfaces as shown in Figure 4B (TJB||). The third one (Figure 4C) has only one T-junction boundary at the mesa level and surface parallel lamellar layers cover the entire area above mesa level (TJB=).

The comparison of free energy among the three phases suggests that the stability of morphology formation strongly depends on the film thickness h and trench width w. It is possible to explain this observation using the concept of effective surface tension associated with the grain boundaries and the polymer-air surface.7,34 Calculation of the effective surface tension is performed by artificially creating a target surface. After the calculation of free energy per chain of a given system and of a bulk, f and fbulk, respectively, the effective surface tension is calculated by (Lz/aN1/2) (f−fbulk) aρ0/N1/2, where Lz is the thickness of system.35,36

Using this method, we calculate the effective surface tensions of twist grain boundary and Tjunction boundary, which turn out to be γTGB = 0.101 aρ0kBT/N1/2 and γTJB = 0.219 aρ0kBT/N1/2, respectively, for the parameters we chose. Unlike the standard SCFT tool, the integral SCFT with finite range interaction has the ability to distinguish the surface tensions of surface-parallel lamellae, γ=, and the surface-perpendicular lamellae, γ||. In our current calculation, γ= = 2.861 aρ0kBT/N1/2 and γ|| = 2.823 aρ0kBT/N1/2. Using these parameters, we can estimate the free energy per unit length of the three candidate morphologies as follows. 𝐹TGB = (2ℎ + 𝑤)𝛾TGB +𝑤𝛾||

(1)

𝐹TJB|| = 2ℎ𝛾TJB +𝑤𝛾||

(2)

𝐹TJB = = 𝑤𝛾TJB +𝑤𝛾 =

(3)

For the stabilization of TGB phase, both FTGB − FTJB|| and FTGB − FTJB= must be negative, otherwise one of the TJB phases will be formed instead. Figure 4D shows that when the film



is too thin, h < 0.43w, TJB|| is the preferable morphology, and in the other extreme case, h > 0.77w, TJB= is likely to be chosen. At a proper film thickness, 0.43w < h < 0.77w, the TGB phase is the most preferred one, and the energy gap is maximized around h/w = 0.59. Thus, our theoretical analysis using effective surface tensions suggests that the square array nanopatterns can be stabilized by tuning the film thickness and trench width.

Complex nanopatterns can be produced in conjunction with various substrate prepattern structures based on the orthogonal self-assembly of lamellar layers. Figure 5A shows unconventional nanostructures where bottom lamellar layers within trenches consist of circles or ellipses directed by the topographical patterns, whereas the linear lamellar layers are stacked over them. Figure 5B presents the alternate nanopatterns composed of square and line arrays in the alternate trenches of two different widths. Since the thickness of BCP film within each trench is dependent on the trench width after the BCP spin coating over the entire area, two different arrays can be easily generated by one-step BCP assembly. In addition, orthogonal lamellar layers are assembled not only on silicon trenches, but on photoresist trenches (Figure S4). It is expected that more diverse and tailored nanopatterns can be generated by the orthogonal lamellar assembly combined with many different types of substrate prepatterns.

Conclusions

We have successfully demonstrated an efficient method to generate nanoscale square array patterns by means of orthogonally directed self-assembly of BCP thin films. BCP thin films spontaneously phase separate into two perpendicularly stacked lamellar layers over topographically patterned trench substrates to minimize effective interfacial energy. Moreover, complicated nanopatterns as well as size controllable square arrays can be created by changing the trench shape and the molecular weight of BCPs. Our straightforward approach for square nanopatterns can offer a new possibility for lithographic platform for 2D and 3D circuit design including memory devices and bit-patterned media.


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Methods Assembly of Orthogonally Aligned Lamellar Layers: PS-b-PMMA (Mn: 25-b-26, 35-b-33.5, 45-b-44, 53-b-54, 80-b-80 kg/mol, purchased from Polymer Source, Inc.) were dissolved in toluene (purchased from Sigma-Aldrich) with suitable concentration (2~3 wt %). Silicon substrates were topographically patterned by a KrF scanner and subsequent etching process with various widths (190, 220, 270, 290, 360, and 400 nm), shapes (circle, ellipse) and 100 nm depth. The widths of alternating linear pattern used in Figure 5 are 190 and 220 nm, respectively. The prepatterned substrates were cleaned in a piranha solution (volume ratio of H2SO4 and H2O2: 7/3) for 1h at 110 C and rinsed with deionized water for several times. The prepared BCP solutions were spin-cast onto the trench patterned substrates with adequate thickness. For a sufficiently thick BCP film formation for orthogonal lamellae, 2.5 wt%-BCP solution with 2000 rpm-spin-coating was typically used regardless of BCP molecular weights. The BCP thin films were thermally annealed in a vacuum oven for 6h at 250 C. For a clear SEM observation of the surface morphology, PMMA block was selectively removed by RIE (50 W, O2 10 sccm, Ar 40 sccm, 40 sec).

Pattern Transfer to Metallic Nanodots with Square Symmetry: For a desired pattern transfer, the PMMA block of the orthogonally assembled lamellar structure should be completely removed. The O2/Ar plasma by RIE was treated to take away the PMMA block with appropriate conditions (50 W, O2 10 sccm, Ar 40 sccm, 120~180 sec). Cr (~5 nm) was deposited onto the square mesh by e-beam evaporator (made by SNTEK). After the metal deposition, the BCP template and excessive metal layers were lifted-off in a piranha solution to leave over a Cr dot array with square symmetry.

Preparation of Photoresist (PR) Patterns: Before PR patterning, neutral layer was required to induce a surface perpendicular lamellar structure within wide PR trenches. The neutral film (hydroxyl group functionalized PS-r-PMMA) was spin-cast on a piranha treated silicon



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substrate and thermally annealed in a vacuum oven at 160 C for 1 day. After annealing, unreacted excessive polymers were removed by toluene rinsing. A negative tone photoresist (SU-8, purchased from MicroChem Corp.) was spin-cast on the neutral surface with an appropriate thickness and soft-baked at 100 C for 1 minute. The PR film was exposed to UV light (365 nm) through a pattern mask structure in an I-line photolithography equipment (Midas/MDA-6000 DUV). Subsequent post baking (100 C, 2 min) and development process (SU-8 developer & isopropyl alcohol) generate well-defined PR pattern.

Self-Consistent Field Theory (SCFT) Calculation: For the modeling of the PS-b-PMMA BCPs, we adopt integral SCFT37-42 with finite range interaction.37,40 We expect that the introduction of finite range interaction helps us to correctly represent the effective surface tension at the neutral boundaries as well as at the grain boundaries.37 In our simulation, we use symmetric AB BCPs with A (PS) and B (PMMA) segment numbers, NA and NB, are set to 50. The bond connecting the segments is represented by a Gaussian distribution function with standard deviation a, 𝑔(𝐫) =

3 2

( ) exp( ― ). 3

2π𝑎

3𝐫2

The system consists of np incompressible chains

2𝑎2

2

occupying volume 𝑉 = 𝑛𝑝𝑁𝜌0―1, where the segment volume is 𝜌0―1, and N = NA + NB is the total segment number. Gaussian shaped finite range function u(r) represents the interaction between two segments at distance r 3

𝑢(𝐫) ≡

( ) ( 3

2π𝑎2

2

3𝐫2

)

(4)

exp ― 2𝑎2 .

Its partition function is calculated by the following integral equation

(

𝑞(𝐫,s + ∆s) ≡ exp ―

𝑤(𝐫) 2𝑁

)∫𝑑𝐑𝑔(𝐑)exp( ―

𝑤(𝐫 ― 𝐑) 2𝑁

)𝑞(𝐫 ― 𝐑,s),

(5)

where w(r) is the mean field potential acting on the segment located at r, and the calculation of the segment density and free energy follows the formalism introduced in Ref. 9. We set the Flory-Huggins interaction parameter χ = 0.02, so that χN = 20 and the lamellar period becomes 1.69 aN1/2 with the 𝑢(𝐫) which we have chosen. When calculating the equilibrium morphology, we use neutral boundary condition in the film thickness direction, and Neumann boundary condition is used in other directions. The side wall of trench is filled with B


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43 homopolymers fixed by external field 𝑤ext B = ―10.

Characterization: All the morphologies including BCP nanopatterns and square arrays were imaged using a Hitachi S-4800 FE-SEM. Film thickness was also measured by cross-sectional SEM image.

Acknowledgements This research was supported by the National Creative Research Initiative (CRI) Center for Multi-Dimensional Directed Nanoscale Assembly (2015R1A3A2033061), and the Hybrid Interface Materials Research Group (Global Frontier Project 2013M3A6B1078874) through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (MSIP). D. Yong and J. U. Kim acknowledge the support by the Basic Science Research Program through the NRF funded by the MSIP (2017R1A2B4012377).

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Schematic illustration of orthogonal lamellar morphology changes during RIE process and square nanopattern morphologies at various angles, additional planar and cross-sectional SEM images of orthogonally stacked lamellar layers, scheme and SEM images for square array using photoresist (PDF).

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Figure Legends Figure 1. (A) Schematic illustration for metal nanodot array with square array. (B) Planar and (C) cross-sectional SEM images of orthogonally assembled PS-b-PMMA (35-b-33.5) lamellar structure. SEM images of (D & F) orthogonally aligned lamellar structures with different molecular weights (45-b-44 for (D), 80-b-80 for (F)) and the corresponding Cr nanodot arrays after pattern transfer process (E & G).

Figure 2. PS-b-PMMA (35-b-33.5) lamellar orientation change with the film thickness within the trench of 190-nm-width. The thickness of BCP films on the mesas (h) are (A) ~23, (B) ~35, and (C) ~58 nm, respectively.

Figure 3. (A) Morphology change depending on the BCP period and the trench width. Each symbol represents different self-assembled nanostructures. SEM images of corresponding morphologies – (B) square pattern with defects, (C) highly ordered square pattern, (D) square pattern mixed with substrate parallel lamellae, and (E) substrate parallel lamellae.

Figure 4. PS density plot of AB diblock copolymers after erasing PMMA block near the trench with width of w, calculated by integral SCFT method. The thickness of BCP film outside of trench (on mesa) is h. Each morphology has (A) three twist grain boundaries (TGB), (B) two T-junction boundaries perpendicular to the substrate (TJB||), and (C) one T-junction boundary parallel to the substrate (TJB=). (D) Comparison of surface energy difference among the competing phases. The TGB phase is preferred at 0.43 < h/w < 0.77. The free energy per length is divided by waρ0kBT/N1/2 to make it dimensionless. (E) Top, and (F) side view of the TGB phase. (G) Cross-sectional view near the grain boundary of the TGB phase.

Figure 5. (A) Complex nanopatterns composed of curved and linear lamellar layers in circleand ellipse-shaped trenches. (B) Alternate square and line arrays self-assembled in the alternate trenches with two different widths.


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Table 1. Periods of lamellar nanopatterns with the molecular weight of PS-b-PMMA.



Figure 1.


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Figure 2.



Figure 3.


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Figure 4.



Figure 5.


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Table 1. Molecular weight (kg/mol)

25-26

35-33.5

45-44

53-54

80-80

Period (nm)

26.8 [L1]

37.6 [L2]

48.5 [L3]

56.0 [L4]

66.4 [L5]



Table of Contents


Page 24 of 24

Nanopatterns with a Square Symmetry from an Orthogonal Lamellar

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