Letter Cite This: ACS Macro Lett. 2019, 8, 1122−1127
pubs.acs.org/macroletters
Dynamic Ordering in High‑χ Block Copolymer Lamellae Based on Cross-Sectional Orientational Alignment Ryuichi Nakatani,† Alvin Chandra,† Takumi Uchiyama, Yuta Nabae, and Teruaki Hayakawa* Department of Materials Science and Engineering, School of Materials and Chemical Technology, Tokyo Institute of Technology, 2-12-1-S8-36 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Downloaded via UNIV STRASBOURG on August 21, 2019 at 08:11:05 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
S Supporting Information *
ABSTRACT: Further development of next-generation block copolymer (BCP) lithography processes is contingent on comprehensive studies of the ordering dynamics of high-χ BCPs that can form sub-10 nm features on thin films. However, quantitative analyses of the degree of ordering on the surface and cross sections of thin films have been difficult to execute. To tackle this challenge, we employ a perpendicular lamella-forming high-χ BCP, poly(polyhedral oligomeric silsesquixone-block-2,2,2trifluoroethyl methacrylate) (PMAPOSS-b-PTFEMA), and reveal that the high-χ PMAPOSS-b-PTFEMA requires three times the activation energy (Ea) compared to that of poly(styrene-blockmethyl methacrylate) (PS-b-PMMA) for defect annihilation, at Ea = 2600 ± 420 kJ mol−1, and a transition from a fast ordering regime with a growth exponent of Φ = 0.30 at lower orientational order parameters (ψ2 < 0.36) to a slow ordering regime with Φ < 0.05 at ψ2 > 0.36, where well-aligned lamellae restrict defect annihilations to enthalpically unfavorable glide mechanisms that require BCP intermixing.
T
Conversely, with its well-balanced SFEs, PS-b-PMMA readily self-assembles into perpendicular lamellae. However, the film thicknesses accessible correspond to less than twice the periodic length ( 60 s, attributed to residual solvent effects which accelerated the ordering in the initial stages. Additionally, PS-b-PMMA faces a resolution limit of ∼20 nm (10 nm half pitch) due to its low effective strength of segregation (χeff).19 Furthermore, although the free energy required for defect annihilation in low-χ BCPs has been previously quantified, the free energy required for defect annihilation in high-χ BCPs has only been predicted to be higher due to the increased strength of segregation.20 Therefore, further research
o improve the performance of semiconductor devices, technologies enabling the fabrication of patterns with smaller pitches are required.1 Particularly, block copolymer (BCP) lithography integrated with directed self-assembly (DSA) has attracted significant attention in academia and industry.2−4 Due to the chemical dissimilarities of the constituent polymers connected by a covalent bond, BCPs spontaneously self-assemble into ordered nanostructures such as spheres, cylinders, lamellae, and gyroids with nanometerscale domain spacings.5 Specifically, perpendicularly oriented lamellae are desirable as they offer increased aspect ratios compared to parallel cylindrical structures. Therefore, the integration of BCP lithography with readily available exposure tools can expand current manufacturing nodes to pattern dimensions below 10 nm. However, the presence of entropically and enthalpically driven defects in BCP thin films can cause serious issues in device manufacturing.6−8 To reduce the defect density, a comprehensive understanding of the selfassembly behavior of high-χ BCP thin films is needed. Quantitative analyses using interactive data language are powerful tools to resolve such issues, and to date, poly(styreneblock-methyl methacrylate) (PS-b-PMMA) and poly(styreneblock-2-vinylpyridine) (PS-b-P2VP) have been widely studied using quantitative methods that provide insight into defect annihilation and grain growth mechanisms.9−13 Yet, their intrinsic properties limit their potential applications. The imbalanced surface free energies (SFEs) of the constituents in PS-b-P2VP discourage the lamellar domains from orienting perpendicularly; hence, previous defect analysis studies typically utilized striped patterns of parallel cylinders. © XXXX American Chemical Society
Received: May 10, 2019 Accepted: June 24, 2019
1122
DOI: 10.1021/acsmacrolett.9b00353 ACS Macro Lett. 2019, 8, 1122−1127
Letter
ACS Macro Letters
where θ(r⃗) is defined as the value of θ offset at a distance r away. To calculate θ and ξ against numerous images, the TSUBAME3.0 computing system at the Tokyo Institute of Technology was employed. An example of the calculated results is shown in Figure 1 based on an unprocessed AFM
using combinatorial quantitative analyses of the surface and cross sections of lamellar high-χ BCP thin films is required. Recently, we designed a silicon- (Si) and fluorine-containing BCP, poly(polyhedral oligomeric silsesquioxane methacrylateblock-2,2,2-trifluoroethyl methacrylate) (PMAPOSS-b-PTFEMA) capable of forming sub-10 nm perpendicular lamellae on thin films using simple thermal annealing.21−24 The χeff of PMAPOSS-b-PTFEMA was estimated to be 0.45, one of the largest values reported to date. Additionally, the components exhibited balanced interfacial affinities relative to both the free surface and Si substrates at a wide variety of temperatures of around 100 °C. This strong strength of segregation and balanced affinities enabled the formation of perpendicular domains at thicknesses up to 7L0. Hence, these characteristics enable us to comprehensively address the thus far inaccessible investigation of sub-10 nm surface and cross-sectional lamellar structures in thin films. The time-evolved quantitative characterization of domain sizes and growth was first studied by Harrison and co-workers using parallel cylindrical thin films.25−29 Murphy and coworkers also demonstrated an effective method for the automated quantitative analysis of BCP thin-film structures.9 Based on their procedures, we wrote programming codes using Matlab software (Supporting Information) and quantitatively characterized the self-assembly behavior of perpendicularly oriented lamellae in high-χ PMAPOSS-b-PTFEMA thin films using combinatorial atomic force microscopy (AFM) and cross-sectional scanning electron microscopy (CS-SEM). The thin films were prepared using a lamella-forming PMAPOSS6b-PTFEMA80 (Mn = 18 300 g mol−1, Đ = 1.14, f PMAPOSS = 0.31, dspacing = 16.2 nm), which was synthesized as previously reported and spin-coated from a 3 wt % chloroform solution onto bare Si wafers at 7000 rpm for 30 s.23,24 The film thicknesses were measured to be approximately 110 nm (∼7L0). The order parameter (ψ) for microdomains in two dimensions can be defined as below, where θ is the local orientation of the microdomains. ψ = ψ0 exp(2iθ )
Figure 1. (a) AFM phase image of a PMAPOSS6-b-PTFEMA80 thin film thermally annealed at 170 °C for 1 min, (b) the corresponding orientation color map, and (c) autocorrelation intensity plot.
phase image obtained from a thin film annealed at 170 °C for 1 min. The blue dots and red line indicate the experimental data and fitting plot, respectively. As expected, g(r⃗) decays exponentially with distance and ξ was calculated to be 89.8 nm. The investigation of the temperature and time dependence of the self-assembly behaviors of PMAPOSS6-b-PTFEMA80 was then conducted using a series of thin films thermally annealed under different conditions (90 to 190 °C, at 1 min to 24 h). At each thermal annealing condition, four AFM images were taken to calculate an average ξ, and the corresponding standard deviations were used to represent experimental uncertainty. The striped pattern coarsening processes were generically formulated according to a power law30,31
(1)
The AFM phase images were converted into false-color maps after calculating the orientation angles θ at all points of the image, enabling the clear visualization of the grain sizes and boundaries. From the data sets of orientation angles, correlation lengths as defined by the distance between how each domain is related can be extracted using the autocorrelation function g(r⃗), shorthand for the crosscorrelation of two identical functions at the positional vector r⃗. By performing an autocorrelation on the order parameter ψ expressed in eq 1, we obtain g ( r ⃗) =
∫ ψ (x ⃗)ψ *(x ⃗ + r ⃗)∂x ⃗ ∫ ψ (x ⃗)ψ *(x ⃗)∂x ⃗
ξ(t ) = ξ0, T t ϕ
where ξ(t) is the correlation length associated with a grain size at an annealing time t; ξ0,T is the temperature (T)-dependent coefficient at t = 0 s; and Φ is the growth exponent. Therefore, from the plots of the calculated ξ against t, Φ was approximated at each T. The data are summarized in Figure 2 where ξ increases steeply with Φ > 0.30 (fast ordering) at all times for 90 °C and at t < 1 h for 110 °C. Conversely, at t ≥ 1 h for 110 °C or at all times for higher temperatures, ξ increases slowly with Φ < 0.05 (slow ordering). The presence of a fast and slow ordering regime is in line with the earlier study by Perego and co-workers.16 While a similar abrupt change in Φ was detected after annealing the high-χ BCP thin films at 110 °C for 1 h, the cause cannot be determined from just the topdown view AFM phase images.
(2)
For systems with only local alignment, g(r⃗) will gradually decay as the distance between evaluated points increases. For a wide variety of systems, g(r⃗) decays exponentially with a correlation length (ξ) defined as i −r y Real(g ( r ⃗)) = ⟨cos 2(θ − θ( r ⃗))⟩ ∼ expjjjj zzzz k ξ {
(4)
(3) 1123
DOI: 10.1021/acsmacrolett.9b00353 ACS Macro Lett. 2019, 8, 1122−1127
Letter
ACS Macro Letters
Figure 2. Correlation length ξ versus annealing time t for lamella-forming PMAPOSS6-b-PTFEMA80 striped patterns in thin films. The error bars indicate the standard deviation of the four images used to calculate the correlation length at each annealing condition.
To determine the origin of the fast and slow ordering regimes, the cross-sectional structures of the thin films annealed at 110 °C were quantitatively evaluated. However, the calculation of ξ as shown above is not applicable for perpendicularly oriented patterns as ξ would become infinity. Therefore, a different image analytical technique was employed to determine the quality of alignment, namely, the orientational order parameter ψ2 defined as follows32−35 ψ2 = ⟨cos[2(θi − θ0)]⟩
(5)
where θi is the local angle of orientation of the microdomains and θ0 is the angle at perpendicular orientation (90°). When the microdomains are oriented perpendicularly, randomly, or parallel relative to the substrate, ψ2 = 0, 1, or −1, respectively. Before calculating ψ2, the CS-SEM images were cropped at the free surface and substrate. The cropped images were then Fourier-filtered and smoothed out to produce a two-dimensional gradient, and the local orientation θi was calculated at every pixel using the same method as the correlation length calculations (Supporting Information). Moreover, ϕ cross defined as the growth exponent of ψ2 was also calculated from the plots, and the results are shown in Figures 3 and 4. Interestingly, the plot of ψ2 against t showed similar trends to that of the calculated ξ against t at the same temperature (110 °C). Cross-referring to the CS-SEM images, it was discovered that in the fast ordering regime at t < 1 h growth of the cross-sectional microdomains occurred rapidly with ϕcross = 0.70. However, the microdomains were oriented randomly and had yet to form direct connections from the substrate to the free surface, leading to lower ψ2 (
