Derivation of Multiple Covarying Material and Process Parameters Using Physics-Based Modeling of X-ray Data

Revealing the 3D Structure of Block Copolymers with Electron Microscopy: Current Status and Future Directions

Block copolymers (BCPs) are considered model systems for understanding and utilizing self-assembly in soft matter. Their tunable nanometric structure and composition enable comprehensive studies of self-assembly processes as well as make them relevant materials in diverse applications. A key step in developing and controlling BCP nanostructures is a full understanding of their three-dimensional (3D) structure and how this structure is affected by the BCP chemistry, confinement, boundary conditions, and the self-assembly evolution and dynamics. Electron microscopy (EM) is a leading method in BCP 3D characterization owing to its high resolution in imaging nanosized structures. Here we discuss the two main 3D EM methods: namely, transmission EM tomography and slice and view scanning EM tomography. We present each method's principles, examine their strengths and weaknesses, and discuss ways researchers have devised to overcome some of the challenges in BCP 3D characterization with EM- from specimen preparation to imaging radiation-sensitive materials. Importantly, we review current and new cutting-edge EM methods such as direct electron detectors, energy dispersive X-ray spectroscopy of soft matter, high temporal rate imaging, and single-particle analysis that have great potential for expanding the BCP understanding through EM in the future.

Determining Structure and Thermodynamics of A-b-(B-r-C) Copolymers

The self-assembly of block copolymers (BCPs) is dictated by their segregation strength, χN, and while there are well-developed methods for determining χ in the weak and strong segregation regimes, it is challenging to accurately measure χ of copolymers with intermediate segregation strengths, especially when copolymers have inaccessible order-disorder transition temperatures. χ_eff is often approximated by using strong segregation theory (SST), but utilizing these values to estimate the interface width (w_m) of BCPs in the intermediate segregation regime often results in predictions that deviate significantly from measured values. Therefore, we propose using the extent of mixing, quantified as the normalized interface width w_m/L₀, where L₀ is the block copolymer pitch, as a thermodynamic parameter. We experimentally measure w_m and L₀ for a series of lamellar A-b-(B-r-C) copolymers via resonant soft X-ray reflectivity and extract values of χ_effN based on previous data collected for A-b-B copolymers. The composition profiles measured via reflectivity match the extracted χ_effN values, while those calculated with SST predict much more mixed composition profiles. The extracted χ_eff values agreed quantitatively between copolymers of different molecular weights. We believe that this methodology will be well-suited for block copolymers used in lithographic applications due to their inaccessible order-disorder transition temperatures, intermediate values of χN, and the importance of w_m for line edge roughness metrics.

Optimized design of block copolymers with covarying properties for nanolithography

The ability to impart multiple covarying properties into a single material represents a grand challenge in manufacturing. In the design of block copolymers (BCPs) for directed self-assembly and nanolithography, materials often balance orthogonal properties to meet constraints related to processing, structure and defectivity. Although iterative synthesis strategies deliver BCPs with attractive properties, identifying materials with all the required attributes has been difficult. Here we report a high-throughput synthesis and characterization platform for the discovery and optimization of BCPs with A-block-(B-random-C) architectures for lithographic patterning in semiconductor manufacturing. Starting from a parent BCP and using thiol-epoxy 'click' chemistry, we synthesize a library of BCPs that cover a large and complex parameter space. This allows us to readily identify feature-size-dependent BCP chemistries for 8-20-nm-pitch patterns. These blocks have similar surface energies for directed self-assembly, and control over the segregation strength to optimize the structure (favoured at higher segregation strengths) and defectivity (favoured at lower segregation strengths).

Buried Structure in Block Copolymer Films Revealed by Soft X-ray Reflectivity

Interactions between polymers and surfaces can be used to influence properties including mechanical performance in nanocomposites, the glass transition temperature, and the orientation of thin film block copolymers (BCPs). In this work we investigate how specific interactions between the substrate and BCPs with varying substrate affinity impact the interfacial width between polymer components. The interface width is generally assumed to be a function of the BCP properties and independent of the surface affinity or substrate proximity. Using resonant soft X-ray reflectivity the optical constants of the film can be controlled by changing the incident energy, thereby varying the depth sensitivity of the measurement. Resonant soft X-ray reflectivity measurements were conducted on films of polystyrene-b-poly(2-vinylpyridine) (PS-b-P2VP) and PS-b-poly(methyl methacrylate) (PS-b-PMMA), where the thickness of the film was varied from half the periodicity (L₀) of the BCP to 5.5 L₀. The results of this measurement on the PS-b-P2VP films show a significant expansion of the interface width immediately adjacent to the surface. This is likely caused by the strong adsorption of P2VP to the substrate, which constrains the mobility of the junction points, preventing them from reaching their equilibrium distribution and expanding the observed interface width. The interface width decays toward equilibrium moving away from the substrate, with the decay rate being a function of film thickness below a critical limit. The PMMA block appears to be more mobile, and the BCP interfaces near the substrate match their equilibrium value.

Confinement and Processing Can Alter the Morphology and Periodicity of Bottlebrush Block Copolymers in Thin Films

Bottlebrush block copolymers (BBCPs) are intriguing architectural variations on linear BCPs with highly tunable structure. Confinement can have a significant impact on polymer assembly, giving rise to changes in morphology, assembly kinetics, and properties like the glass transition. Given that confinement leads to significant changes in the persistence length of bottlebrush homopolymers, it is reasonable to expect that BBCPs will see significant changes in their structure and periodicity relative to the bulk morphology. Understanding how confinement influences assembly will be important for designing BBCPs for thin film applications including membranes, integrated photonic structures, and potentially BCP lithography. In order to study the effects of confinement on BBCP conformation and morphology, a blade coating was used to prepare films with continuous variation in film thickness. Unlike thin films of linear BCPs, islands/holes were not observed, and instead mixtures of parallel and perpendicular morphologies emerge after annealing. The lamellar periodicity (L₀) of the morphologies is found to be thickness dependent, increasing L₀ with decreasing film thickness for blade coated films. Films coated out of tetrahydrofuran (THF) resulted in a single well-defined lamellar periodicity, verified through atomic force microscopy (AFM) and grazing incidence small-angle X-ray scattering (GISAXS), which increases dramatically from the bulk value (30.6 nm) and continues to increase as the film thickness decreases. The largest observed L₀ was 65.5 nm, and this closely approaches the estimated upper limit of 67 nm corresponding to a fully extended backbone in a bilayer arrangement. Films coated out of propylene glycol methyl ether acetate (PGMEA) resulted in a mixture of perpendicular lamellae and a smaller, likely cylindrical morphology. The lamellar portion of the film shows the same thickness dependence as the lamellae observed in the THF coated films. The scaling of the lamellar L₀ with respect to film thickness follows predictions for confined semiflexible polymers with weak excluded volume interactions and can be related to models for confinement of DNA. Spin coated films shows the same reduction in periodicity, although at very different film thicknesses. This result suggests that the material has shallow free-energy barriers to transitioning between different L₀ and morphologies, a property that could be taken advantage of for patterning diverse structures with a single material.

Soft crystal martensites: An in situ resonant soft x-ray scattering study of a liquid crystal martensitic transformation

Liquid crystal blue phases (BPs) are three-dimensional soft crystals with unit cell sizes orders of magnitude larger than those of classic, atomic crystals. The directed self-assembly of BPs on chemically patterned surfaces uniquely enables detailed in situ resonant soft x-ray scattering measurements of martensitic phase transformations in these systems. The formation of twin lamellae is explicitly identified during the BPII-to-BPI transformation, further corroborating the martensitic nature of this transformation and broadening the analogy between soft and atomic crystal diffusionless phase transformations to include their strain-release mechanisms.

The Influence of Additives on the Interfacial Width and Line Edge Roughness in Block Copolymer Lithography

The challenges of patterning next generation integrated circuits have driven the semiconductor industry to look outside of traditional lithographic methods in order to continue cost effective size scaling. The directed self-assembly (DSA) of block copolymers (BCPs) is a nanofabrication technique used to reduce the periodicity of patterns prepared with traditional optical methods. BCPs with large interaction parameters (χ eff), provide access to smaller pitches and reduced interface widths. Larger χ eff is also expected to be correlated with reduced line edge roughness (LER), a critical performance parameter in integrated circuits. One approach to increasing χ eff is blending the BCP with a phase selective additive, such as an Ionic liquid (IL). The IL does not impact the etching rates of either phase, and this enables a direct interrogation of whether the change in interface width driven by higher χ eff translates into lower LER. The effect of the IL on the layer thickness and interface width of a BCP are examined, along with the corresponding changes in LER in a DSA patterned sample. The results demonstrate that increased χ eff through additive blending will not necessarily translate to a lower LER, clarifying an important design criterion for future material systems.

Unwarping GISAXS data

Grazing-incidence small-angle X-ray scattering (GISAXS) is a powerful technique for measuring the nanostructure of coatings and thin films. However, GISAXS data are plagued by distortions that complicate data analysis. The detector image is a warped representation of reciprocal space because of refraction, and overlapping scattering patterns appear because of reflection. A method is presented to unwarp GISAXS data, recovering an estimate of the true undistorted scattering pattern. The method consists of first generating a guess for the structure of the reciprocal-space scattering by solving for a mutually consistent prediction from the transmission and reflection sub-components. This initial guess is then iteratively refined by fitting experimental GISAXS images at multiple incident angles, using the distorted-wave Born approximation (DWBA) to convert between reciprocal space and detector space. This method converges to a high-quality reconstruction for the undistorted scattering, as validated by comparing with grazing-transmission scattering data. This new method for unwarping GISAXS images will broaden the applicability of grazing-incidence techniques, allowing experimenters to inspect undistorted visualizations of their data and allowing a broader range of analysis methods to be applied to GI data.

Optimizing self-consistent field theory block copolymer models with X-ray metrology

A block copolymer self-consistent field theory (SCFT) model is used for direct analysis of experimental X-ray scattering data obtained from thin films of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) made from directed self-assembly. In a departure from traditional approaches, which reconstruct the real space structure using simple geometric shapes, we build on recent work that has relied on physics-based models to determine shape profiles and extract thermodynamic processing information from the scattering data. More specifically, an SCFT model, coupled to a covariance matrix adaptation evolutionary strategy (CMAES), is used to find the set of simulation parameters for the model that best reproduces the scattering data. The SCFT model is detailed enough to capture the essential physics of the copolymer self-assembly, but sufficiently simple to rapidly produce structure profiles needed for interpreting the scattering data. The ability of the model to produce a matching scattering profile is assessed, and several improvements are proposed in order to more accurately recreate the experimental observations. The predicted parameters are compared to those extracted from model fits via additional experimental methods and with predicted parameters from direct particle-based simulations of the same model, which incorporate the effects of fluctuations. The Flory-Huggins interaction parameter for PS-b-PMMA is found to be in agreement with reported ranges for this material. These results serve to strengthen the case for relying on physics-based models for direct analysis of scattering and light signal based experiments.

Characterizing the Interface Scaling of High χ Block Copolymers near the Order-Disorder Transition

Advancements in the directed self-assembly of block copolymers (BCPs) have prompted the development of new materials with larger effective interaction parameters (χ_e). This enables BCP systems with phase separation at increasingly small degrees of polymerization (N). Very often these systems reside near the order-disorder transition and fit between the weak and strong segregation limits where the behavior of BCP systems is not as thoroughly understood. Utilizing resonant soft X-ray reflectivity (RSoXR) enables both the BCP pitch (L₀) and interface width (w_M) to be determined simultaneously, through a direct characterization of the composition profile of BCP lamellae oriented parallel to a substrate. A series of high χ_e BCPs with χ_e ranging from ≈0.04 to 0.25 and χ_eN from 19 to 70 have been investigated. The L₀/w_m ratio serves as an important metric for the feasibility of a material for nanopatterning applications; the results of the RSoXR measurement are used to establish a relationship between χ_e and L₀/w_m. The results of this analysis are correlated with experimentally established limits for the functionality of BCPs in nanopatterning applications. These results also provide guidance for the magnitude of χ_e needed to achieve small interface width for samples with sub-10 nm L₀.