Determining the shape and periodicity of nanostructures using small-angle X-ray scattering

Talbot effect based sensor measuring grating period change in subwavelength range

Talbot length, the distance between two consecutive self-image planes along the propagation axis for a periodic diffraction object (grating) illuminated by a plane wave, depends on the period of the object and the wavelength of illumination. This property makes the Talbot effect a straightforward technique for measuring the period of a periodic object (grating) by accurately determining the Talbot length for a given illumination wavelength. However, since the Talbot length scale is proportional to the square of the grating period, traditional Talbot techniques face challenges when dealing with smaller grating periods and minor changes in the grating period. Recently, we demonstrated a Fourier transform technique-based Talbot imaging method that allows for controlled Talbot lengths of a periodic object with a constant period and illumination wavelength. Using this method, we successfully measured periods as small as a few micrometers and detected sub-micrometer changes in the periodic object. Furthermore, by measuring the Talbot length of gratings with varying periods imaged through the combination of a thick lens of short focal length and a thin lens of long focal length and large aperture, we determined the effective focal length of the thick lens in close agreement with the theoretical effective focal length of a thick lens in the presence of spherical aberration. These findings establish the Talbot effect as an effective and simple technique for various sensing applications in optics and photonics through the measurement of any physical parameter influencing the Talbot length of a periodic object.

Virtual X-ray critical dimension metrology via Monte Carlo simulation

X-ray critical dimension (XCD) metrology is a highly promising technique for achieving sub-nanometer precision in critical dimension measurements at advanced nodes of integrated circuit manufacturing. Compared to XCD experiments utilizing synchrotron radiation sources, those employing compact X-ray sources encounter challenges like extended testing time and increased uncertainty. To evaluate the influence of experimental conditions on measurement results, we developed an ab initio virtual X-ray critical dimension metrology via a Monte Carlo simulation (MC-VXCD). Through calibrating the system parameters of the MC-VXCD to a home-built compact XCD instrument, we achieved excellent consistency between virtual and actual measurement results. The virtual instrument effectively estimated measurement errors stemming from the reduced exposure time, which significantly influences the measurement accuracy and throughput. Furthermore, through the MC-VXCD, we establish the connection between the application scenarios of the XCD metrology and the geometry of XCD instruments, offering a versatile platform for the system design, experimental configuration optimization, data analysis, etc., in XCD metrology.

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.

Challenges of grazing emission X-ray fluorescence (GEXRF) for the characterization of advanced nanostructured surfaces

The grazing emission X-ray fluorescence (GEXRF) technique offers a promising approach to determining the spatial distribution of various chemical elements in nanostructures. In this paper, we present a comparison with grazing incidence small-angle X-ray scattering (GISAXS), an established method for dimensional nanometrology, on periodic TiO₂ nanostructures fabricated by a self-aligned double patterning (SADP) process. We further test the potential of GEXRF for process control in the presence of residual chromium on the structures. The angle-resolved fluorescence emission as well as the scattered radiation from the surface are collected with photon-counting hybrid pixel area detectors using scanning-free detection schemes. By modelling the X-ray standing wave (XSW) field in the vicinity of and inside the nanostructure, it is possible to obtain both the angle-resolved fluorescence intensities and the far-field scattering intensities from the same model. The comparison also illustrates that for ensemble photon-based measurement methods, accounting for roughness effects and imperfections can be essential when modelling advanced nanostructured surfaces.

Parameter estimation for X-ray scattering analysis with Hamiltonian Markov Chain Monte Carlo

Bayesian-inference-based approaches, in particular the random-walk Markov Chain Monte Carlo (MCMC) method, have received much attention recently for X-ray scattering analysis. Hamiltonian MCMC, a state-of-the-art development in the field of MCMC, has become popular in recent years. It utilizes Hamiltonian dynamics for indirect but much more efficient drawings of the model parameters. We described the principle of the Hamiltonian MCMC for inversion problems in X-ray scattering analysis by estimating high-dimensional models for several motivating scenarios in small-angle X-ray scattering, reflectivity, and X-ray fluorescence holography. Hamiltonian MCMC with appropriate preconditioning can deliver superior performance over the random-walk MCMC, and thus can be used as an efficient tool for the statistical analysis of the parameter distributions, as well as model predictions and confidence analysis.

Developing Anisotropy in Self-Assembled Block Copolymers: Methods, Properties, and Applications

Block copolymers (BCPs) self-assembly has continually attracted interest as a means to provide bottom-up control over nanostructures. While various methods have been demonstrated for efficiently ordering BCP nanodomains, most of them do not generically afford control of nanostructural orientation. For many applications of BCPs, such as energy storage, microelectronics, and separation membranes, alignment of nanodomains is a key requirement for enabling their practical use or enhancing materials performance. This review focuses on summarizing research progress on the development of anisotropy in BCP systems, covering a variety of topics from established aligning techniques, resultant material properties, and the associated applications. Specifically, the significance of aligning nanostructures and the anisotropic properties of BCPs is discussed and highlighted by demonstrating a few promising applications. Finally, the challenges and outlook are presented to further implement aligned BCPs into practical nanotechnological applications, where exciting opportunities exist.

Shape- and Element-Sensitive Reconstruction of Periodic Nanostructures with Grazing Incidence X-ray Fluorescence Analysis and Machine Learning

The characterization of nanostructured surfaces with sensitivity in the sub-nm range is of high importance for the development of current and next-generation integrated electronic circuits. Modern transistor architectures for, e.g., FinFETs are realized by lithographic fabrication of complex, well-ordered nanostructures. Recently, a novel characterization technique based on X-ray fluorescence measurements in grazing incidence geometry was proposed for such applications. This technique uses the X-ray standing wave field, arising from an interference between incident and the reflected radiation, as a nanoscale sensor for the dimensional and compositional parameters of the nanostructure. The element sensitivity of the X-ray fluorescence technique allows for a reconstruction of the spatial element distribution using a finite element method. Due to a high computational time, intelligent optimization methods employing machine learning algorithms are essential for timely provision of results. Here, a sampling of the probability distributions by Bayesian optimization is not only fast, but it also provides an initial estimate of the parameter uncertainties and sensitivities. The high sensitivity of the method requires a precise knowledge of the material parameters in the modeling of the dimensional shape provided that some physical properties of the material are known or determined beforehand. The unknown optical constants were extracted from an unstructured but otherwise identical layer system by means of soft X-ray reflectometry. The spatial distribution profiles of the different elements contained in the grating structure were compared to scanning electron and atomic force microscopy and the influence of carbon surface contamination on the modeling results were discussed. This novel approach enables the element sensitive and destruction-free characterization of nanostructures made of silicon nitride and silicon oxide with sub-nm resolution.

Grazing incidence-x-ray fluorescence for a dimensional and compositional characterization of well-ordered 2D and 3D nanostructures

The increasing importance of well-controlled ordered nanostructures on surfaces represents a challenge for existing metrology techniques. To develop such nanostructures and monitor complex processing constraints fabrication, both a dimensional reconstruction of nanostructures and a characterization (ideally a quantitative characterization) of their composition is required. In this work, we present a soft x-ray fluorescence-based methodology that allows both of these requirements to be addressed at the same time. By applying the grazing-incidence x-ray fluorescence technique and thus utilizing the x-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to their dimensional and compositional characteristics. By varying the incident angles of the exciting radiation, element-sensitive fluorescence radiation is emitted from different regions inside the nanoobjects. By applying an adequate modeling scheme, these datasets can be used to determine the nanostructure characteristics. We demonstrate these capabilities by performing an element-sensitive reconstruction of a lamellar grating made of Si₃N₄, where GIXRF data for the O-Kα and N-Kα fluorescence emission allows a thin oxide layer to be reconstructed on the surface of the grating structure. In addition, we employ the technique also to three dimensional nanostructures and derive both dimensional and compositional parameters in a quantitative manner.

State of the Art and Future Perspectives in Advanced CMOS Technology

The international technology roadmap of semiconductors (ITRS) is approaching the historical end point and we observe that the semiconductor industry is driving complementary metal oxide semiconductor (CMOS) further towards unknown zones. Today's transistors with 3D structure and integrated advanced strain engineering differ radically from the original planar 2D ones due to the scaling down of the gate and source/drain regions according to Moore's law. This article presents a review of new architectures, simulation methods, and process technology for nano-scale transistors on the approach to the end of ITRS technology. The discussions cover innovative methods, challenges and difficulties in device processing, as well as new metrology techniques that may appear in the near future.

Nanoscale Pattern Decay Monitored Line by Line via In Situ Heated Atomic Force Microscopy

We combine in situ heated atomic force microscopy (AFM) with automated line-by-line spectral analysis to quantify the relaxation or decay phenomenon of nanopatterned composite polymer films above the glass-transition temperature of the composite material. This approach enables assessment of pattern fidelity with a temporal resolution of ≈1 s, providing the necessary data density to confidently capture the short-time relaxation processes inaccessible to conventional ex situ measurements. Specifically, we studied the thermal decay of nanopatterned poly(methyl methacrylate) (PMMA) and PMMA nanocomposite films containing unmodified and PMMA-grafted silica nanoparticles (SiO₂ NP) of varying concentrations and film thicknesses using this new approach. Features imprinted on neat PMMA films were seen to relax at least an order of magnitude faster than the NP-filled films at decay temperatures above the glass transition of the PMMA matrix. It was also seen that patterned films with the lowest residual thickness (34 nm) filled with unmodified SiO₂ NP decayed the slowest. The effect of nanoparticle additive was almost negligible in reinforcing the patterned features for films with the highest residual thickness (257 nm). Our in situ pattern decay measurement and the subsequent line-by-line spectral analysis enabled the investigation of various parameters affecting the pattern decay such as the underlying residual thickness, type of additive system, and temperature in a timely and efficient manner.

Depth-correlated backscattered electron signal intensity for 3D-profile measurement of high aspect ratio holes

In-line metrology for measuring 3D features of the high aspect ratio (HAR) holes is becoming more challenging due to the progressing semiconductor technology, particularly in memory devices. Measurements of the bottom critical dimension (CD), taper angles and 3D profiles of the HAR holes require new imaging capabilities. In this work, we explored the characteristics of high-energy backscattered electron (BSE) signals and demonstrated their promising application to 3D metrology. From Monte Carlo simulation results, it is worth noting that BSE signal intensity emitted from an irradiated location in the depth of the hole decreases exponentially with the increase of the depth from the top surface (perpendicular depth) of the hole. Furthermore, the influences of various factors including the electron energy, the depth and the sidewall angle (SWA) of the hole on the attenuation of the BSE signal intensity were investigated. The simulation results show that the attenuation of the BSE signal intensity depends on the electron energy, the depth and the density of the hole but is independent of the SWA and the incident angle of the primary electron beam. Based on the characteristics of the BSE signal intensity, an algorithm was proposed for the 3D metrology of the HAR holes. Finally, the differences in CDs between the measured value and the target value of HAR holes with various geometries were examined. A maximum measurement bias within ±2.0 nm for various holes with different depths, densities and SWA values shows great potential of depth-correlated BSE signals in 3D metrology.

Miniaturization of CMOS

When the international technology roadmap of semiconductors (ITRS) started almost five decades ago, the metal oxide effect transistor (MOSFET) as units in integrated circuits (IC) continuously miniaturized. The transistor structure has radically changed from its original planar 2D architecture to today’s 3D Fin field-effect transistors (FinFETs) along with new designs for gate and source/drain regions and applying strain engineering. This article presents how the MOSFET structure and process have been changed (or modified) to follow the More Moore strategy. A focus has been on methodologies, challenges, and difficulties when ITRS approaches the end. The discussions extend to new channel materials beyond the Moore era.

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.

X-ray Metrology for the Semiconductor Industry Tutorial

The semiconductor industry is in need of new, in-line dimensional metrology methods with higherspatial resolution for characterizing their next generation nanodevices. The purpose of this short course is to train the semiconductor industry on the NIST-developed critical dimension small angle X-ray scattering (CDSAXS) method. The topics will include both data processing and instrumentation. The short course will also provide an opportunity for discussion of the requirements for CDSAXS and the necessary improvements in X-ray source technology. Expected audience include semiconductor manufacturers, equipment manufacturers, and component manufacturers. The presentations were made at “X-ray Metrology for the Semiconductor Industry” short course at the National Institute of Standards and Technology on Aug. 25, 2016.

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.

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.

Metrology for the next generation of semiconductor devices

The semiconductor industry continues to produce ever smaller devices that are ever more complex in shape and contain ever more types of materials. The ultimate sizes and functionality of these new devices will be affected by fundamental and engineering limits such as heat dissipation, carrier mobility and fault tolerance thresholds. At present, it is unclear which are the best measurement methods needed to evaluate the nanometre-scale features of such devices and how the fundamental limits will affect the required metrology. Here, we review state-of-the-art dimensional metrology methods for integrated circuits, considering the advantages, limitations and potential improvements of the various approaches. We describe how integrated circuit device design and industry requirements will affect lithography options and consequently metrology requirements. We also discuss potentially powerful emerging technologies and highlight measurement problems that at present have no obvious solution.

Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

Laterally periodic nanostructures have been investigated with grazing-incidence small-angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerical solution of Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, owing to the discrepancy between the incident wavelength and the finite-element size. This drawback vanishes for GISAXS because of the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art electron-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows the detailed reconstruction of the grating line shape for thick non-homogeneous substrates as well. The reconstructed geometric line-shape models are statistically validated by applying a Markov chain Monte Carlo sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nanometre uncertainty.

Characterizing Patterned Block Copolymer Thin Films with Soft X-rays

The directed self-assembly (DSA) of block copolymers (BCPs) is a potential solution for patterning critical features for integrated circuits at future technology nodes. For this process to be implemented, there needs to be a better understanding of how the template guides the assembly and induces subsurface changes in the lamellar structure. Using a rotational transmission X-ray scattering measurement coupled with soft X-rays to improve contrast between polymer components, the impact of the ratio of the guiding stripe width (W) to the BCP pitch (L₀) was investigated. For W/L₀ < 1, continuous vertical lamella were observed, with some fluctuations in the interface profile near the template that smoothed out further up the structure. Near W/L₀ ≈ 1.5, the arrangement of the lamella shifted, moving from polystyrene centered on the guiding stripe to poly(methyl methacrylate) centered on the guiding stripe.

Grazing-incidence small-angle X-ray scattering (GISAXS) on small periodic targets using large beams

Grazing-incidence small-angle X-ray scattering (GISAXS) is often used as a versatile tool for the contactless and destruction-free investigation of nano-structured surfaces. However, due to the shallow incidence angles, the footprint of the X-ray beam is significantly elongated, limiting GISAXS to samples with typical target lengths of several millimetres. For many potential applications, the production of large target areas is impractical, and the targets are surrounded by structured areas. Because the beam footprint is larger than the targets, the surrounding structures contribute parasitic scattering, burying the target signal. In this paper, GISAXS measurements of isolated as well as surrounded grating targets in Si substrates with line lengths from 50 µm down to 4 µm are presented. For the isolated grating targets, the changes in the scattering patterns due to the reduced target length are explained. For the surrounded grating targets, the scattering signal of a 15 µm × 15 µm target grating structure is separated from the scattering signal of 100 µm × 100 µm nanostructured surroundings by producing the target with a different orientation with respect to the predominant direction of the surrounding structures. As virtually all litho-graphically produced nanostructures have a predominant direction, the described technique allows GISAXS to be applied in a range of applications, e.g. for characterization of metrology fields in the semiconductor industry, where up to now it has been considered impossible to use this method due to the large beam footprint.

Combining model-based measurement results of critical dimensions from multiple tools

Model-based measurement techniques use experimental data and simulations of the underlying physics to extract quantitative estimates of the measurands of a specimen based upon a parametric model of that specimen. The uncertainties of these estimates are based upon not only the uncertainties in the experimental data, but also the sensitivity of that data to the model parameters, and parametric correlations among those parameters. The combination of two or more model-based techniques as well as the Bayesian approach are shown to be optimal for obtaining the lowest possible uncertainties. As an example, using this form of hybrid metrology, state-of-the-art sub-14 nm-wide lines from semiconductor manufacturing are measured using a combined regression from critical-dimension small-angle x-ray scattering and scanning electron microscopy that leads to lower uncertainties.

Modeling the polarized X-ray scattering from periodic nanostructures with molecular anisotropy

There is a need to characterize nanoscale molecular orientation in soft materials, and polarized scattering is a powerful means to measure this property. However, few approaches have been demonstrated that quantitatively relate orientation to scattering. Here, a modeling framework to relate the molecular orientation of nanostructures to polarized resonant soft X-ray scattering measurements is developed. A variable-angle transmission measurement called critical-dimension X-ray scattering enables the characterization of the three-dimensional shape of periodic nanostructures. When this measurement is conducted at resonant soft X-ray energies with different polarizations to measure soft material nanostructures, the scattering contains convolved information about the nanostructure shape and the preferred molecular orientation as a function of position, which is extracted by fitting using inverse iterative algorithms. A computationally efficient Born approximation simulation of the scattering has been developed, with a full tensor treatment of the electric field that takes into account biaxial molecular orientation, and this approach is validated by comparing it with a rigorous coupled wave simulation. The ability of various sample models to generate unique best fit solutions is then analyzed by generating simulated scattering pattern sets and fitting them with an inverse iterative algorithm. The interaction of the measurement geometry and the change in orientation across a periodic repeat unit leads to distinct asymmetry in the scattering pattern which must be considered for an accurate fit of the scattering.

Rapid ordering of block copolymer thin films

Block-copolymers self-assemble into diverse morphologies, where nanoscale order can be finely tuned via block architecture and processing conditions. However, the ultimate usage of these materials in real-world applications may be hampered by the extremely long thermal annealing times-hours or days-required to achieve good order. Here, we provide an overview of the fundamentals of block-copolymer self-assembly kinetics, and review the techniques that have been demonstrated to influence, and enhance, these ordering kinetics. We discuss the inherent tradeoffs between oven annealing, solvent annealing, microwave annealing, zone annealing, and other directed self-assembly methods; including an assessment of spatial and temporal characteristics. We also review both real-space and reciprocal-space analysis techniques for quantifying order in these systems.

Characterization of the shape and line-edge roughness of polymer gratings with grazing incidence small-angle X-ray scattering and atomic force microscopy

Grazing-incidence small-angle X-ray scattering (GISAXS) is increasingly used for the metrology of substrate-supported nanoscale features and nanostructured films. In the case of line gratings, where long objects are arranged with a nanoscale periodicity perpendicular to the beam, a series of characteristic spots of high-intensity (grating truncation rods, GTRs) are recorded on a two-dimensional detector. The intensity of the GTRs is modulated by the three-dimensional shape and arrangement of the lines. Previous studies aimed to extract an average cross-sectional profile of the gratings, attributing intensity loss at GTRs to sample imperfections. Such imperfections are just as important as the average shape when employing soft polymer gratings which display significant line-edge roughness. Herein are reported a series of GISAXS measurements of polymer line gratings over a range of incident angles. Both an average shape and fluctuations contributing to the intensity in between the GTRs are extracted. The results are critically compared with atomic force microscopy (AFM) measurements, and it is found that the two methods are in good agreement if appropriate corrections for scattering from the substrate (GISAXS) and contributions from the probe shape (AFM) are accounted for.