Self-Assembly of Hierarchical High-χ Fluorinated Block Copolymers with an Orthogonal Smectic-within-Lamellae 3 nm Sublattice and Vertical Surface Orientation.

Hierarchical structure-within-structure assemblies offer a route toward increasingly complex and multifunctional materials while pushing the limits of block copolymer self-assembly. We present a detailed study of the self-assembly of a series of fluorinated high-χ block copolymers (BCPs) prepared via postmodification of a single poly(styrene)-block-poly(glycidyl methacrylate) (S-b-G) parent polymer with the fluorinated alkylthiol pendent groups containing 1, 6, or 8 fluorinated carbons (termed trifluoro-ethanethiol (TFET), perfluoro-octylthiol (PFOT), and perfluoro-decylthiol (PFDT), respectively). Bulk X-ray scattering of thermally annealed samples demonstrates hierarchical molecular assembly with phase separation between the two blocks and within the fluorinated block. The degree of ordering within the fluorinated block is highly sensitive to synthetic variation; a lamellar sublattice was formed for S-b-GPFOT and S-b-GPFDT. Thermal analyses of S-b-GPFOT reveal that the fluorinated block exhibits liquid crystal-like ordering. The complex thin-film self-assembly behavior of an S-b-GPFOT polymer was investigated using real-space (atomic force microscopy and scanning electron microscopy) and reciprocal-space (resonant soft X-ray scattering (RSoXS), grazing incidence small- and wide-angle scattering) measurements. After thermal annealing in nitrogen or vacuum, films thicker than 1.5 times the primary lattice spacing exhibit a 90-degree grain boundary, exposing a thin layer of vertical lamellae at the free interface, while exhibiting horizontal lamellae on the preferential (polystyrene brush) substrate. RSoXS measurements reveal the near-perfect orthogonality between the primary and sublattice orientations, demonstrating hierarchical patterning at the nanoscale.

Composition Dictates Molecular Orientation at the Heterointerfaces of Vapor-Deposited Glasses.

Physical vapor deposition (PVD) can prepare organic glasses with a preferred molecular orientation. The relationships between deposition conditions and orientation have been extensively investigated in the film bulk. The role of interfaces on the structure is less well understood and remains a key knowledge gap, as the interfacial region can govern glass stability and optoelectronic properties. Robust experimental characterization has remained elusive due to complexities in interrogating molecular organization in amorphous, organic materials. Polarized soft X-rays are sensitive to both the composition and the orientation of transition dipole moments in the film, making them uniquely suited to probe molecular orientation in amorphous soft matter. Here, we utilize polarized resonant soft X-ray reflectivity (P-RSoXR) to simultaneously depth profile the composition and molecular orientation of a bilayer prepared through the physical vapor deposition of 1,4-di-[4-(N,N-diphenyl)amino]styryl-benzene (DSA-Ph) on a film of aluminum-tris(8-hydroxyquinoline) (Alq3). The bulk orientation of the DSA-Ph layer is controlled by varying deposition conditions. Utilizing P-RSoXR to depth profile the films enables determination of both the bulk orientation of DSA-Ph and the orientation near the Alq3 interface. At the Alq3 surface, DSA-Ph always lies with its long axis parallel to the interface, before transitioning into the bulk orientation. This is likely due to the lower mobility and higher glass transition of Alq3, as the first several monolayers of DSA-Ph deposited on Alq3 appear to behave as a blend. We further show how orientation at the interface correlates with the bulk behavior of a codeposited glass of similar blend composition, demonstrating a straightforward approach to predicting molecular orientation at heterointerfaces. This work provides key insights into how molecules orient during vapor deposition and offers methods to predict this property, a critical step toward controlling interfacial behavior in soft matter.

CyRSoXS: a GPU-accelerated virtual instrument for polarized resonant soft X-ray scattering.

Polarized resonant soft X-ray scattering (P-RSoXS) has emerged as a powerful synchrotron-based tool that combines the principles of X-ray scattering and X-ray spectroscopy. P-RSoXS provides unique sensitivity to molecular orientation and chemical heterogeneity in soft materials such as polymers and biomaterials. Quantitative extraction of orientation information from P-RSoXS pattern data is challenging, however, because the scattering processes originate from sample properties that must be represented as energy-dependent three-dimensional tensors with heterogeneities at nanometre to sub-nanometre length scales. This challenge is overcome here by developing an open-source virtual instrument that uses graphical processing units (GPUs) to simulate P-RSoXS patterns from real-space material representations with nanoscale resolution. This computational framework - called CyRSoXS (https://github.com/usnistgov/cyrsoxs) - is designed to maximize GPU performance, including algorithms that minimize both communication and memory footprints. The accuracy and robustness of the approach are demonstrated by validating against an extensive set of test cases, which include both analytical solutions and numerical comparisons, demonstrating an acceleration of over three orders of magnitude relative to the current state-of-the-art P-RSoXS simulation software. Such fast simulations open up a variety of applications that were previously computationally unfeasible, including pattern fitting, co-simulation with the physical instrument for operando analytics, data exploration and decision support, data creation and integration into machine learning workflows, and utilization in multi-modal data assimilation approaches. Finally, the complexity of the computational framework is abstracted away from the end user by exposing CyRSoXS to Python using Pybind. This eliminates input/output requirements for large-scale parameter exploration and inverse design, and democratizes usage by enabling seamless integration with a Python ecosystem (https://github.com/usnistgov/nrss) that can include parametric morphology generation, simulation result reduction, comparison with experiment and data fitting approaches.

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. χeff is often approximated by using strong segregation theory (SST), but utilizing these values to estimate the interface width (wm) 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 wm/L0, where L0 is the block copolymer pitch, as a thermodynamic parameter. We experimentally measure wm and L0 for a series of lamellar A-b-(B-r-C) copolymers via resonant soft X-ray reflectivity and extract values of χeffN based on previous data collected for A-b-B copolymers. The composition profiles measured via reflectivity match the extracted χeffN values, while those calculated with SST predict much more mixed composition profiles. The extracted χeff 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 wm for line edge roughness metrics.

Characterization of the Interfacial Orientation and Molecular Conformation in a Glass-Forming Organic Semiconductor.

The ability to control structure in molecular glasses has enabled them to play a key role in modern technology; in particular, they are ubiquitous in organic light-emitting diodes. While the interplay between bulk structure and optoelectronic properties has been extensively investigated, few studies have examined molecular orientation near buried interfaces despite its critical role in emergent functionality. Direct, quantitative measurements of buried molecular orientation are inherently challenging, and many methods are insensitive to orientation in amorphous soft matter or lack the necessary spatial resolution. To overcome these challenges, we use polarized resonant soft X-ray reflectivity (p-RSoXR) to measure nanometer-resolved, molecular orientation depth profiles of vapor-deposited thin films of an organic semiconductor Tris(4-carbazoyl-9-ylphenyl)amine (TCTA). Our depth profiling approach characterizes the vertical distribution of molecular orientation and reveals that molecules near the inorganic substrate and free surface have a different, nearly isotropic orientation compared to those of the anisotropic bulk. Comparison of p-RSoXR results with near-edge X-ray absorption fine structure spectroscopy and optical spectroscopies reveals that TCTA molecules away from the interfaces are predominantly planar, which may contribute to their attractive charge transport qualities. Buried interfaces are further investigated in a TCTA bilayer (each layer deposited under separate conditions resulting in different orientations) in which we find a narrow interface between orientationally distinct layers extending across ≈1 nm. Coupling this result with molecular dynamics simulations provides additional insight into the formation of interfacial structure. This study characterizes the local molecular orientation at various types of buried interfaces in vapor-deposited glasses and provides a foundation for future studies to develop critical structure-function relationships.

Polarized X-ray scattering measures molecular orientation in polymer-grafted nanoparticles.

Polymer chains are attached to nanoparticle surfaces for many purposes, including altering solubility, influencing aggregation, dispersion, and even tailoring immune responses in drug delivery. The most unique structural motif of polymer-grafted nanoparticles (PGNs) is the high-density region in the corona where polymer chains are stretched under significant confinement, but orientation of these chains has never been measured because conventional nanoscale-resolved measurements lack sensitivity to polymer orientation in amorphous regions. Here, we directly measure local chain orientation in polystyrene grafted gold nanoparticles using polarized resonant soft X-ray scattering (P-RSoXS). Using a computational scattering pattern simulation approach, we measure the thickness of the anisotropic region of the corona and extent of chain orientation within it. These results demonstrate the power of P-RSoXS to discover and quantify orientational aspects of structure in amorphous soft materials and provide a framework for applying this emerging technique to more complex, chemically heterogeneous systems in the future.

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.

Addressing the challenges of modeling the scattering from bottlebrush polymers in solution.

Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.

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.

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.

Spatial Control of the Self-assembled Block Copolymer Domain Orientation and Alignment on Photopatterned Surfaces.

Polarity-switching photopatternable guidelines can be directly used to both orient and direct the self-assembly of block copolymers. We report the orientation and alignment of poly(styrene-block-4-trimethylsilylstyrene) (PS-b-PTMSS) with a domain periodicity, L0, of 44 nm on thin photopatternable grafting surface treatments (pGSTs) and cross-linkable surface treatments (pXSTs), containing acid-labile 4-tert-butoxystyrene monomer units. The surface treatment was exposed using electron beam lithography to create well-defined linear arrays of neutral and preferential regions. Directed self-assembly (DSA) of PS-b-PTMSS with much lower defectivity was observed on pXST than on pGST guidelines. The study of the effect of film thickness on photoacid diffusion by Fourier transform infrared spectroscopy and near-edge X-ray absorption fine structure spectroscopy suggested slower diffusion in thinner films, potentially enabling production of guidelines with sharper interfaces between the unexposed and exposed lines, and thus, the DSA of PS-b-PTMSS on thinner pXST guidelines resulted in better alignment control.

The Concentration Dependence of the Size and Symmetry of a Bottlebrush Polymer in a Good Solvent.

Bottlebrush polymers consist of a linear backbone with densely grafted side chains which impact the rigidity of the molecule. The persistence length of the bottlebrush backbone in solution is influenced by both the intrinsic structure of the polymer and by the local environment, such as the solvent quality and concentration. Increasing the concentration reduces the overall size of the molecule due to the reduction in backbone stiffness. In this study we map out the size of a bottlebrush polymer as a function of concentration for a single backbone length. Small-angle neutron scattering (SANS) measurements are conducted on a polynorbornene-based bottlebrush with polystyrene side chains in a good solvent. The data are fit using a model which provides both the long and short axis radius of gyration (R g,2 and R g,1, respectively), providing a measure for how the conformation changes as a function of concentration. At low concentrations a highly anisotropic structure is observed (R g,2/R g,1 ≈ 4), becoming more isotropic at higher concentrations (R g,2/R g,1 ≈ 1.5). The concentration scaling for both R g,2 and the overall R g are evaluated and compared with predictions in the literature. Coarse-grained molecular dynamics simulations were also conducted to probe the impact of concentration on bottlebrush conformation showing qualitative agreement with the experimental results.

X-ray characterization of contact holes for block copolymer lithography.

The directed self-assembly (DSA) of block copolymers (BCPs) is a promising low-cost approach to patterning structures with critical dimensions (CDs) which are smaller than can be achieved by traditional photolithography. The CD of contact holes can be reduced by assembling a cylindrical BCP inside a patterned template and utilizing the native size of the cylinder to dictate the reduced dimensions of the hole. This is a particularly promising application of the DSA technique, but in order for this technology to be realized there is a need for three-dimensional metrology of the internal structure of the patterned BCP in order to understand how template properties and processing conditions impact BCP assembly. This is a particularly challenging problem for traditional metrologies owing to the three-dimensional nature of the structure and the buried features. By utilizing small-angle X-ray scattering and changing the angle between the incident beam and sample we can reconstruct the three-dimensional shape profile of the empty template and the residual polymer after self-assembly and removal of one of the phases. A two-dimensional square grid pattern of the holes results in scattering in both in-plane directions, which is simplified by converting to a radial geometry. The shape is then determined by simulating the scattering from a model and iterating that model until the simulated and experimental scattering profiles show a satisfactory match. Samples with two different processing conditions are characterized in order to demonstrate the ability of the technique to evaluate critical features such as residual layer thickness and sidewall height. It was found that the samples had residual layer thicknesses of 15.9 ± 3.2 nm and 4.5 ± 2.2 nm, which were clearly distinguished between the two different DSA processes and in good agreement with focused ion beam scanning transmission electron microscopy (FIBSTEM) observations. The advantage of the X-ray measurements is that FIBSTEM characterizes around ten holes, while there are of the order of 800 000 holes illuminated by the X-ray beam.

Xi-cam: a versatile interface for data visualization and analysis.

Xi-cam is an extensible platform for data management, analysis and visualization. Xi-cam aims to provide a flexible and extensible approach to synchrotron data treatment as a solution to rising demands for high-volume/high-throughput processing pipelines. The core of Xi-cam is an extensible plugin-based graphical user interface platform which provides users with an interactive interface to processing algorithms. Plugins are available for SAXS/WAXS/GISAXS/GIWAXS, tomography and NEXAFS data. With Xi-cam's `advanced' mode, data processing steps are designed as a graph-based workflow, which can be executed live, locally or remotely. Remote execution utilizes high-performance computing or de-localized resources, allowing for the effective reduction of high-throughput data. Xi-cam's plugin-based architecture targets cross-facility and cross-technique collaborative development, in support of multi-modal analysis. Xi-cam is open-source and cross-platform, and available for download on GitHub.

Functional group quantification of polymer nanomembranes with soft x-rays.

Polyamide nanomembranes are at the heart of water desalination, a process which plays a critical role in clean water production. Improving their efficiency requires a better understanding of the relationship between chemistry, network structure, and performance but few techniques afford compositional information in ultrathin films (<100 nm). Here, we leverage resonant soft x-ray reflectivity, a measurement that is sensitive to the specific chemical bonds in organic materials, to quantify the functional group concentration in these polyamides. We first employ reference materials to establish quantitative relationships between changes in the optical constants and functional group density, and then use the results to evaluate the functional group concentrations of polyamide nanomembranes. We demonstrate that the difference in the amide carbonyl and carboxylic acid group concentrations can be used to calculate the crosslink density, which is shown to vary significantly across three different polyamide chemistries. A clear relationship is established between the functional group density and the permselectivity (α), indicating that more densely crosslinked materials result in a higher α of the nanomembranes. Finally, measurements on a polyamide/poly(acrylic acid) bilayer demonstrate the ability of this approach to quantify depth-dependent functional group concentrations in thin films.

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 (χe). 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 (wM) to be determined simultaneously, through a direct characterization of the composition profile of BCP lamellae oriented parallel to a substrate. A series of high χe BCPs with χe ranging from ≈0.04 to 0.25 and χeN from 19 to 70 have been investigated. The L0/wm 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 χe and L0/wm. 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 χe needed to achieve small interface width for samples with sub-10 nm L0.

Self-Assembly of ABC Bottlebrush Triblock Terpolymers with Evidence for Looped Backbone Conformations.

Bottlebrush block copolymers offer rich opportunities for the design of complex hierarchical materials. As consequences of the densely grafted molecular architecture, bottlebrush polymers can adopt highly extended backbone conformations and exhibit unique physical properties. A recent report has described the unusual phase behavior of ABC bottlebrush triblock terpolymers bearing grafted poly(D,L-lactide) (PLA), polystyrene (PS), and poly(ethylene oxide) (PEO) blocks (LSO). In this work, a combination of resonant soft X-ray reflectivity (RSoXR), near edge X-ray absorption fine structure spectroscopy (NEXAFS), and self-consistent field theory (SCFT) was used to provide insight into the phase behavior of LSO and underlying backbone chain conformations. Consistent with SCFT calculations, RSoXR measurements confirm a unique mesoscopic ACBC domain connectivity and decreasing lamellar periods (d 0) with increasing backbone length of the PEO block. RSoXR and NEXAFS demonstrate an additional unusual feature of brush LSO thin films: when the overall film thickness is ~3.25d 0, the film-air interface is majority PS (>80%). Since PS is the midblock, the triblocks must adopt looping configurations at the surface, despite the preference for the backbone to be extended. This result is supported by backbone concentrations calculated through SCFT, which suggest that looping midblocks are present throughout the film. Collectively, this work provides evidence for the flexibility of the bottlebrush backbone and the consequences of low-χ block copolymer design. We propose that PEO blocks localize at the PS/PLA domain interfaces in order to screen the highest-χ contacts in the system, driving the formation of loops. These insights introduce a potential route to overcome the intrinsic penalties to interfacial curvature imposed by the bottlebrush architecture, enabling the design of unique self-assembled materials.

Methodology for evaluating the information distribution in small angle scattering from periodic nanostructures.

Optimizing the extraction of information from x-ray measurements while minimizing exposure time is an important area of research in a variety of fields. The semiconductor industry is reaching a point where the traditional optical metrologies need to be augmented in order to better resolve the critical dimensions of structures with feature sizes below 10 nm. Critical dimension small angle x-ray scattering (CDSAXS) is one measurement technique that is capable of characterizing detailed features of periodic nanostructures. As currently implemented, the measurement utilizes the combined scattering from up to 60 different angles. Reducing the number of angles would dramatically improve the feasibility of CDSAXS for implementation in a fabrication setting, but currently there are no clear guidelines as to which angles provide the most information to minimize the uncertainty in the shape of the target structure while maximizing the throughput. In order to develop guidelines for optimizing the angle selection, simulation studies were conducted on a wide variety of structures with subsets of the full angular range to identify which angles minimized the overall shape uncertainty. Analyzing sets of two angle pairs (including all combinations between 0 deg and 60 deg) provides guidance on which angles best constrain the samples. For select samples, higher numbers of angles were included to explore the impact of additional information on the model uncertainty. In general, low angles (<3 deg) best contributed to minimizing the line-width uncertainty, while higher angles near high curvature regions of the scattering profile best constrained the height of the structure. The minimum uncertainty was generally achieved with combinations of the two. This simulation approach can be used to minimize the number of angles measured on real samples and significantly reduce the measurement time.