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Zusammenfassung Ellipsometrie ist eine der vielseitigsten Methoden zur optischen Nanostrukturcharakterisierung. Insbesondere die Müller-Matrix-Ellipsometrie ermöglicht die Messung von optischen oder geometrischen Parametern mit Genauigkeiten bis in den Sub-Nanometer-Bereich. In der konventionellen Ellipsometrie wird dabei über die komplette Beleuchtungspunktgröße gemittelt. Wenn der strukturierte Bereich auf der Probe kleiner ist als der Beleuchtungspunkt, oder die Struktur keine Periodizität aufweist, kann das Messergebnis durch in den Randbereichen reflektiertes Licht beeinträchtigt werden. Besonders problematisch ist dies bei freistehenden Nanostrukturen mit charakteristischen Größen kleiner als die Beleuchtungspunktgröße. In solchen Fällen kann abbildende Ellipsometrie genutzt werden. Dabei wird eine Müller-Matrix für jedes Pixel in einem Kamerabild gemessen, wodurch der Polarisationseinfluss der Probe lokal bestimmt wird. In diesem Beitrag liefern wir Ansätze, konkrete Zusammenhänge zwischen geometrischen Eigenschaften von Nanostrukturen auf Nebendiagonalelemente der Müller-Matrix zu ermitteln. Dazu haben wir einen Aufbau für die Messung von Müller-Matrix-Bildern bei verschiedenen Einfallswinkeln in Transmission und Reflexion realisiert sowie eine Probe gefertigt, mit der wir geometrische Struktureigenschaften in Müller-Matrix-Bildern systematisch messen. Wir stellen Messungen sowie numerische Simulationen zum Vergleich der Ergebnisse vor. Des Weiteren diskutieren wir thermische Einflüsse auf Messergebnisse und stellen einen Algorithmus zu deren Behandlung vor.

In this contribution, we present a technique for in situ determination of the numerical apertures (NAs) of optical microscopes using calibrated diffraction gratings. Many commonly practiced procedures use an external setup to determine the objective and condenser NAs. However, these values may become modified in the used microscope systems, e.g., by system intrinsic apertures. Therefore, in our improved technique, determination of the imaging NA is conducted in situ within the corresponding microscope at hand. Furthermore, the method has been extended to yield the microscope’s illumination NA as well. In total, we tested this procedure for determination of the imaging NA for four different microscope objectives with nominal values of 0.55 and 0.9, together with the illumination NAs for four different circular aperture diaphragms with diameters between 10 µm and 500 µm using several gratings of different pitches. All determined NA values agree essentially with their nominal values within their experimental uncertainties, but the uncertainties have been reduced by typically an order of magnitude as compared with the manufacturer’s specifications.

Spectroscopic polarization measurement and control using channeled spectrum has several unique features and is useful for various spectroscopic instruments. It utilizes the strong dispersion characteristics in polarization retardation of high-order retarders so that the polarization modulation can be made without using mechanical or active elements for polarization modulation. In this presentation, we describe its principle, basic features, and several applications including a spectroscopic ellipsometer and ultrafast rotations of beam profile and polarization.

A model-based edge detection is always required when quantitatively evaluating the bidirectional measurements of micro- and nanostructures in optical microscopy. For example, the accurate determination of the width of a structure requires the knowledge of the location of the real physical edges in the measured profile. The interpretation of the measured edge profile cannot be performed intuitively due to distortion which is caused by diffraction and refraction. We advise a model-based edge detection algorithm which is based on rigorous simulations of the microscope’s imaging. The intensity level which corresponds to the position of the real physical edge is called the threshold and it is determined in the simulations. For these optical simulations we employ the JCMsuite, which is a software application of the finite-element-method (FEM). Since numerical and semi-analytical methods for the calculation of electromagnetics in optical systems rely to some degree on approximations, their results may vary even when the input parameters are identical. We apply a test suite of input parameters for the purpose of comparing numerical simulation tools regarding the resulting thresholds for measurements on line-shaped nanostructures in a periodic grating. The test suite maintains the illumination and imaging parameters of a transmitted light UV-microscope while the object parameters of a binary line grating are varied. There are 25 grating configurations with different line-to-space ratios, where the line width ranges from the resolution limit up to almost 10 µm. The illumination pupil is discretized in a cartesian grid with 113 grid points in total. We introduce different pupil samplings, after calculating the threshold values of the original test suite. We obtain a high agreement of the thresholds results and the related linewidth values when comparing with already performed results of two additional rigorous applications. Furthermore, we showcase the threshold variation for different samplings of the illumination pupil.

Using conventional Mueller matrix ellipsometry, the geometries of periodic nanostructures can be easily determined if the measurement fields are not smaller than the illumination spot size. Measurements on individual nanostructures smaller than this can be accounted for by imaging ellipsometry, which allows measuring all 16 Mueller matrix elements for each pixel in the camera of the imaging system. These so-called Mueller matrix images contain additional information about the spatial distribution of the sample’s polarizing properties that are useful in the characterization of individual nanostructures. We built an imaging Mueller matrix ellipsometry system for measurements in the visible regime. Our system allows for the analysis arm, which holds the CCD camera and the polarization state analyser, to be rotated freely around the sample. By this, measurements in reflection and in transmission can be performed at arbitrary angles of incidence between 37.5° and 90°. Additionally, we implemented a reflection mode for 0° angle of incidence. Using this setup, our goal is to characterize the shape of individual nanostructures much smaller than the illumination spot using the additional information from the Mueller matrix images. Thus, we designed and fabricated a sample containing various individual nanostructures with different geometrical features. The structures are of square or circular shape, ranging in size from 5 µm to 50 nm. Additionally, the square structures feature corner rounding with different radii for a transition between circle and square. With these structures, we systematically measure the influence of the shape on the Mueller matrix elements. We also investigate in using Mueller matrix images for the characterization of subwavelength sized features significantly smaller than the resolution limit of our microscope system at about 800 nm. First results show clear distinctions between opposing edges of the nanostructures in off-diagonal Mueller matrix images.

In light microscopy, optical aberrations always affect the performance of the employed microscope. They can emerge from imperfect optical components of the microscope, like lenses, or from misalignments of such optical components, which may even change over time. In our contribution, we retrieve the optical aberrations in form of Zernike polynomials from measurements of small point structures by applying the extended Nijboer-Zernike approach. Subsequently, we include the expression for these optical aberrations in rigorous simulations of the microscope’s imaging process. Finally, we will compare the simulations with measurements to demonstrate optical bidirectional measurements on aberrant imaging systems.

To precisely characterize nanostructures while keeping the advantages of optical measurements, modern methods are still being refined. Plasmonic lenses, which are designable with less computational effort than dielectric metalenses, are promising. Simulations showed that sub-wavelength sized focal spots in arbitrary distances are achievable. We describe our simulations of the lens-sample interaction with plasmonic lenses with working distances up to 1 mm combined with single and periodic nanostructures using finite element method. Scanning the focal spot over the sample, we examine transmission and reflection in the far field, the field-structure interaction in the near field, and the applicability in Mueller ellipsometry.

Background: Scatterometry is a fast, indirect and non-destructive optical method for quality control in the production of lithography masks. To solve the inverse problem in compliance with the upcoming need for improved accuracy, a computationally expensive forward model has to be defined which maps geometry parameters to diffracted light intensities. Aim: To quantify the uncertainties in the reconstruction of the geometry parameters, a fast to evaluate surrogate for the forward model has to be introduced. Approach: We use a non-intrusive polynomial chaos based approximation of the forward model which increases speed and thus enables the exploration of the posterior through direct Bayesian inference. Additionally, this surrogate allows for a global sensitivity analysis at no additional computational overhead. Results: This approach yields information about the complete distribution of the geometry parameters of a silicon line grating, which in return allows to quantify the reconstruction uncertainties in the form of means, variances and higher order moments of the parameters. Conclusion: The use of a polynomial chaos surrogate allows to quantify both parameter influences and reconstruction uncertainties. This approach is easy to use since no adaptation of the expensive forward model is required., arXiv admin note: substantial text overlap with arXiv:1910.14435

In this contribution, we emphasize the need for a sophisticated characterization of measurement devices in particular for optical bidirectional measurements. As an example, the ongoing characterization of the UV-microscope at PTB’s linescale comparator is presented. First results of spectroscopic measurements of the employed UV-LED are presented and the impact of deviations in the center wavelength of the LED on the measurements are illustrated by rigorous simulations.

We designed, realized, and characterised an imaging Mueller matrix ellipsometry setup for the pixelwise measurement of the Mueller matrices in microscope images. Our setup is capable of performing measurements in reflection as well as in transmission in a broad range of angles of incidence for wavelengths between 400 nm and 700 nm. We compared measurements of specially designed nanostructured samples with AFM and SEM measurements as well as with numerical simulations using the finite element method.

We realized an imaging Mueller matrix microscope for nanostructure characterization. For investigations on nanoform characterization via Mueller matrix images, we measured and simulated Mueller matrix images of specially designed nanostructures. As an approach towards machine learning evaluation in imaging ellipsometry, we calculated Haar-like features of the images and observed a higher sensitivity to subwavelength features in off-diagonal matrix elements compared to microscopy.

We report a custom microscope setup whose mechanical and optical components are adjusted by the means of an alignment autocollimator (AAC). Residual centring and angular misalignments of the components towards the microscope’s optical axis are below 500 μm and 1 mrad, respectively. We further perform measurements of dot structures with diameters close to the diffraction limit (nominal diameter = 200 nm; chrome on glass mask) as suitable measures for the evaluation of the microscope’s adjustment and to determine/ visualize the optical aberrations, which affect the image formation of microscopes.

Nanowire structures arranged in a hexagonal lattice are to be characterized in terms of their diameter, height and pitch. A scatterometer and an imaging Mueller matrix ellipsometer, which is a combination of a commercial Mueller matrix ellipsometer and a microscope, have been used as measurement tools. These measurements are supported by numerical simulations using the finite element method to characterize the structure parameters.

Dimensional microscopy is an essential tool for non-destructive and fast inspection of manufacturing processes. Standard approaches process only the measured images. By modelling the imaged structure and solving an inverse problem, the uncertainty on dimensional estimates can be reduced by orders of magnitude. At the same time, the inverse problem needs to be solved in a timely manner. Here we present a method of accelerating the inverse problem by reducing images to their elementary features, thereby extracting the relevant information and distinguishing it from noise. The resulting reduction in complexity allows the inverse problem to be solved more efficiently by utilize cutting edge machine learning based optimization techniques. By employing the techniques presented here, we are able to perform for highly accurate and fast dimensional microscopy.

In recent years, DNA origami nanorulers for superresolution (SR) fluorescence microscopy have been developed from fundamental proof-of-principle experiments to commercially available test structures. The self-assembled nanostructures allow placing a defined number of fluorescent dye molecules in defined geometries in the nanometer range. Besides the unprecedented control over matter on the nanoscale, robust DNA origami nanorulers are reproducibly obtained in high yields. The distances between their fluorescent marks can be easily analysed yielding intermark distance histograms from many identical structures. Thus, DNA origami nanorulers have become excellent reference and training structures for superresolution microscopy. In this work, we go one step further and develop a calibration process for the measured distances between the fluorescent marks on DNA origami nanorulers. The superresolution technique DNA-PAINT is used to achieve nanometrological traceability of nanoruler distances following the guide to the expression of uncertainty in measurement (GUM). We further show two examples how these nanorulers are used to evaluate the performance of TIRF microscopes that are capable of single-molecule localization microscopy (SMLM).

Background In this work, a nanostructured guided-mode resonance filter matrix with high transmission efficiency and narrow bandwidth is demonstrated. The developed nano-filter arrays have various usages, e.g., combined with the CMOS image sensors to realize compact spectrometers for biomedical sensing applications. Methods In order to optimize the filter performance, the spectral responses of filters with different structural parameters are carefully studied based on the variable-controlling method. A quality factor is carried out for quantitative characterization. Results In this case, a high fill factor of 0.9 can strongly suppress sidebands, while buffer layer thickness can be adjusted to mainly control the bandwidth. The transmission peaks shift from 386 nm to 1060 nm with good linearity when periods vary from 220 nm to 720 nm. The incident angle dependence is simulated to be ~ 1.1 nm/degree in ±30° range. The filters are then fabricated and characterized. The results obtained from both simulations and experiments agree well, where the filters with the period of 352 nm exhibit simulated and measured transmission peaks of 564 nm and 536 nm, the FWHM of 13 nm and 17 nm, respectively. In terms of metal material, besides aluminum, silver is also investigated towards optimization of the transmission efficiency. Conclusion The transmission spectra of designed filters have high transmission and low sideband; its peaks cover the whole visible and near infrared range. These characteristics allow them to have the possibility to be integrated into image sensors for spectrometer applications.

A non-invasive optical measurement system based on a broadband light source and color filters has been developed for determining pulse rate and arterial blood oxygen saturation (SaO2). In contrast to classical pulse oximetry using red and infrared LEDs to measure the peripheral capillary oxygen saturation (SpO2), we use color filters in our system. Spectral analysis of human tissue can be easily achieved by combining a tiny color filter matrix and a commercial CMOS/CCD image sensor. During system operation, white LED light illuminates our tissue (e.g., a finger), while a CCD sensor covered by filters detects the light transmitted through that tissue. The CCD sensor is controlled by a Field Programmable Gate Array (FPGA) and a microcontroller. The detected photoplethysmographic (PPG) signal is transferred to a host computer and analyzed with MATLAB. After sensor system calibration, pulse rate and SpO2 can be simply extracted from the PPG signal. The heart rate and SpO2 of different volunteers are then measured simultaneously by commercial pulse oximetry and the proposed sensor system, in which results from both devices show good agreement. To integrate more functions into system, nanostructured color filter matrix containing 15 filters for different wavelengths is designed and fabricated. This filter can be designed to provide transmission peaks over the visible and near-infrared range (i.e., the human tissue optical transparent window) and has a high potential to be fabricated directly on top of pixels of an image sensor.

Spectroscopic ellipsometry is a versatile tool to measure dimensional or optical parameters of surface layers or surface structures. The determination of these parameters requires to solve an inverse problem. This is achieved by a fitting procedure, where a merit function is optimized. This merit function compares simulated with measured polarization quantities for each measurement configuration, i. e. for each wavelength and angle of incidence. For the simulation of unstructured samples Fresnel-equations can be used, while for structured surfaces the Maxwells equations must be solved using so-called Maxwell-solvers. For depolarizing samples Mueller ellipsometry must be used, because only the Mueller-stokes formalism is capable to describe depolarization. However, in common approaches to evaluate Mueller matrix measurements depolarization is treated in a nonoptimal way, which leads to inadequate measurement uncertainty estimations and in the worst case may lead to systematic measurement errors. Especially for surfaces with strong depolarization such as rough or textured surfaces this is a problem. To treat these issues, we developed an improved analysis method to attain reliable sample parameters and reliable and mathematically well-founded uncertainty estimations from Mueller ellipsometry measurements. While deterministic non-depolarising samples can be fully described within the well-known Jones formalism and can be simulated by Fresnel- or Maxwell-solvers, a complete simulation of depolarizing samples would require very high computational expenses which are too elaborate or even impossible in practice. Thus the question arises, how to treat depolarization in the optimization process. Commonly used merit functions treat it as a residual error, which is minimized and accept the fit solution with the smallest overall depolarization as the best approximation. However, depolarization is a sample property, which must not be minimized. Therefore, instead we use the depolarization to derive a weight-factor for each residual contribution to the merit-function. We will present the underlying mathematics. The evolved theory is applicated on measurement data obtained with a Sentech SE 850 system. The Mueller-matrices for each measurement configuration are computed from an overdetermined system of raw data achieved with analyzer-scans at discrete polarizer-steps (step-scan-mode). Thus the raw measurement data can additionally be exploited to get statistical information to the measured Mueller matrices and included in the merit function. Embedded into a Bayesian approach the best-fit values and their uncertainties are determined from the posterior distribution in a much more realistic and reliable way. Applied on both virtual and real measurement data, we demonstrate the advantages of this new method and compare the results with different standard analysis methods.

Accurate metrology of nanostructures gains more and more importance and for efficiency reasons optical methods play a significant role here. Unfortunately, conventional optical microscopy is subject to the well-known resolution limit. The necessity to resolve objects smaller than this limit led to the development of superresolution methods which however are barely used in metrology for practical reasons. Non-imaging indirect optical methods like scatterometry and ellipsometry however are not limited by diffraction and are able to determine the critical dimensions of nanostructures. We investigate the application of different approaches for specifically manipulated near-fields in Mueller matrix ellipsometry to achieve an enhanced sensitivity for polarization based sub-wavelength topological information. To this end, we present first numerical simulations of these approaches. To examine the relationship between structural properties and Mueller matrix elements we designed individual structures based on geometrical shapes of varying parameters as well as small arrays. They are realized by lithography as holes in PMMA resist. First, we characterize SEM images of the structures to validate the fabrication process. Numerical simulations of the Mueller matrices of the structures by finite element method are discussed. Results indicate that conventional Mueller matrix ellipsometry alone is unsuitable but the extension to imaging Mueller matrix microscopy is promising for the characterization of sub-wavelength features.

Optical microscopy is widely used for the characterization of micro- and nanostructures in the field of unidirectional and bidirectional dimensional metrology. Despite the general high recognition in the metrological community, the inherent difficulties which are bound to optical bidirectional measurements using commercial vision-based metrology tools are not sufficiently investigated, yet, and require additional insight, which we intend to provide here. We demonstrate the need for sophisticated analysis methods to find a threshold value which locates the correct physical edge position within the microscopical image. The common assumption for the threshold to be at 50% of the intensity level of the edge signal is in essentially any imaging configuration wrong and leads to large systematic measurements errors. For example, the correct threshold values for transmission light microscopy using high NA objectives on chrome on quartz photomasks, are within 15% and 35% of the intensity level in the simulated images. For other measurement configurations the threshold variation can be even much larger. Since the correct threshold values depend on the illumination and imaging parameters of the imaging system as well as on the geometrical and optical parameters of the measurement object, we showcase a selection of them and their respective influence on the determination of the threshold values. Rigorous simulations are the key feature for this analysis since they require all the relevant parameters to be included in the simulation of a microscopical image which enables the correct threshold determination and to extract the correct bidirectional quantities out of the optical images.

Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse problem. To comply with the upcoming need for improved accuracy and precision and thus for the reduction of uncertainties, typically computationally expansive forward models have been used. In this paper we use Bayesian inversion to estimate parameters from scatterometry measurements of a silicon line grating and determine the associated uncertainties. Since the direct application of Bayesian inference using MarkovChain Monte Carlo methods to physics-based partial differential equation (PDE) model is not feasible due to high computational costs, we use an approximation of the PDE forward model based on a polynomial chaos expansion. The expansion provides not only a surrogate for the PDE forward model, but also Sobol indices for a global sensitivity analysis. Finally, we compare our results for the global sensitivity analysis with the uncertainties of estimated parameters.

There are some commonly-used optimization techniques for the analysis of measured data in spectroscopic Mueller matrix ellipsometry (MME) used, for example, to calculate the layer thicknesses of samples under test. Concentrating on the metrological aspects of MME, we identified a non-optimal treatment of depolarization in all these techniques. We therefore recently developed an improved optimization method to adequately take depolarization in MME into account. In a further step, we also included statistical measurement noise and derived a likelihood function, which enabled us to apply both the maximum likelihood method and Bayesian statistics as well as the Bayesian information criterion for data evaluation. In this paper we concentrate on the application of this new method to measurements of SiO2-layer thicknesses on silicon. With a state-of-the-art SENTECH SENresearch 4.0 Mueller ellipsometer, we measured standard samples of different SiO2-layer thicknesses, whose calibrated thicknesses were between about 6 nm and 1000 nm. The MME results were compared to the calibration data. For all samples, an SiO2-SiO double-layer model turned out to be optimal. The measured total oxide layer thicknesses matched excellently with the calibration values, within the estimated range of uncertainties. All the results are presented here. This is the first comparison with traceable reference measurements demonstrating the validity of our novel MME analysis method.

Planar plasmonic lenses have attracted a great deal of interest over the last few years for their super-resolution focusing capabilites. These highly compact structures with dimensions of only a few micrometres allow for the focusing of light to sub-wavelength-sized spots with focal lengths reaching into the far-field. This offers opportunities for new methods in nanometrology; for example, applications in microscopic Mueller matrix ellipsometry setups. However, the conventional plasmonic lens is challenging to fabricate. We present a new design for plasmonic lenses, which is called the inverted plasmonic lens, to accommodate the lithographic fabrication process. In this contribution, we used numerical simulations based on the finite element method in combination with particle swarm optimization to determine ideal parameter ranges and tolerances for the design of inverted plasmonic lenses for different wavelengths in the visible and near-infrared domain and focal lengths between 5 µm and 1 mm.

In this paper, we focus on the metrological aspects of spectroscopic Mueller ellipsometry—i.e. on the uncertainty estimation of the measurement results. With the help of simulated Mueller matrices, we demonstrate that the commonly used merit functions do not return the correct uncertainty for the measurand under consideration (here shown for the relatively simple case of the geometrical parameter layer thickness for the example system of a SiO2 layer on a Si substrate). We identify the non-optimal treatment of measured and sample- induced depolarization as a reason of this discrepancy. Since depolarization results from sample properties in combination with experimental parameters, it must not be minimized during the parameter fit. Therefore, we propose a new merit function treating this issue differently: It implicitly uses the measured depolarization as a weighting parameter. It is very simple and computationally cheap. It compares for each wavelength the measured Jones matrix elements to Cloude’s covariance matrix: ∼ ∑ λ j sim, λ † H meas, λ + j sim, λ . Moreover, an extension will be presented which allows us to include the measurement noise into this merit function. With this, reliable statistical uncertainties can be calculated. Except for some pre-processing of the raw data, there is no additional computational cost.

In this work, a novel multispectral sensing system consisting of nanostructured filter matrix and a charge-coupled device (CCD)-based image sensor has been developed to overcome the limitation of the conventional pigment filtered sensors, which are difficult to be fabricated at a microscale and usually showing a pronounced degradation. By designing the filters in guided-mode resonance (GMR) architecture, light transmission efficiencies of ~90% with low sidebands and sharp peaks can be obtained, which are critical characteristics for realizing precise optical measurement systems. To optimize the transmission functions, various materials and structural parameters have been simulated. Electron beam nanolithography is employed in the device fabrication to fabricate pixel-wise independent filter functions. After being characterized in terms of their wavelength filtering capability, the developed GMR filters are then combined with image sensors, particularly for addressing biological applications.

The optical performance of wire grid polarizers crucially depends on the fabrication accuracy. Reducing the application wavelengths to the ultraviolet spectral range sets the challenge that structural deviations in the range of typically a few nanometers become comparable to the feature sizes of the structure. In this contribution we present a concept to determine structural parameters and structural deviations of DUV wire grid polarizers fabricated with self-aligned double patterning. To this end, we evaluate the properties (i.e the spectral positions, the angular dependence of the spectral positions and widths) of asymmetry induced resonances in the transmittance spectra which occur at wavelengths larger than 380 nm. We derive requirements for measurement setup for nanoscale determination of the structural properties. Our results indicate that the investigation of the angular dependent transmittance at only two different wavelengths and one polarization state is sufficient to determine structural deviations with uncertainties of ±1:7nm for the effective shift of the ridge and ±0:34° for the effective tilt. Thus, the proposed method allows us to retrieve deep subwavelength structural information at the nanoscale with easily accessible transmittance measurements in the visible spectral range.

Recent developments of the PTB in high precision position and size metrology as support for different nanotechnology applications are described. Measurement uncertainties of 1–2 nm for 1D-position of graduation lines on photomasks, or on line scales and incremental encoders of about 300 mm length have been achieved. The measurement of the size of nanoscale features represents additional challenges, because the location of opposite feature edges needs to be precisely determined. Different feature size or CD metrology techniques are applied at PTB, including a recent approach which uses transmission electron microscopy in the traceability chain of AFM CD measurements. The estimated uncertainty for CD measurements on high quality Si line structures is U 95% = 1.6 nm.

The dark-field microscopy method with alternating grazing incidence UV illumination (UV-AGID) developed at the PTB now offers the possibility of measuring lateral structures down to 100 nm. The advantage of this new dark-field method is, in comparison to bright-field microscopy, the better edge localization, since only light that is scattered or diffracted by object details reaches the image plane. Also, in the case of AGID microscopy, the proximity effects are much more reduced. This method can be used for dimensional measurements of micro- and nanostructures, e.g. on wafers, masks or etched Si structures. Determining the linewidth quantitatively from the microscope image is, however, only possible by comparing the measured data with adapted rigorous simulations. To model the intensity distribution in the image, we make use of two different rigorous grating diffraction theories. On the one hand we use the rigorous coupled wave analysis (RCWA) method (for calculations of the diffracted electrical and magnetic fields), on the other hand, the finite elements method (FEM). In particular, it will be discussed what influence the polarization of the illumination and the edge angles of the trapezoidal-shaped lines and spaces have on the microscope image. Also, different quantitative measurements of chromium lines on a COG mask (COG: chromium structures on glass) will be presented. The results will be compared with electron optical measurements.

We report the initial results of a recent bilateral comparison of linewidth or critical dimension (CD) calibrations on photomask line features between two national metrology institutes (NMIs): the National Institute of Standards and Technology (NIST) in the United States and the Physikalisch-Technische Bundesanstalt (PTB) in Germany. For the comparison, a chrome on glass (CoG) photomask was used which has a layout of line features down to 100 nm nominal size. Different measurement methods were used at both institutes. These included: critical dimension atomic force microscopy (CD-AFM), CD scanning electron microscopy (CD-SEM) and ultraviolet (UV) transmission optical microscopy. The measurands are CD at 50 % height of the features as well as sidewall angle and line width roughness (LWR) of the features. On the isolated opaque features, we found agreement of the CD measurements at the 3 nm to 5 nm level on most features – usually within the combined expanded uncertainties of the measurements.

Indirect optical methods like ellipsometry or scatterometry require an optical model to calculate the response of the system, and to fit the parameters in order to minimize the difference between the calculated and measured values. The most common problem of optical modeling is that the measured structures and materials turn out to be more complex in reality than the simplified optical models used as first attempts to fit the measurement. The complexity of the optical models can be increased by introducing additional parameters, if they (1) are physically relevant, (2) improve the fit quality, (3) don't correlate with other parameters. The sensitivity of the parameters can be determined by mathematical analysis, but the accuracy has to be validated by reference methods. In this work some modeling and verification aspects of ellipsometry and optical scatterometry will be discussed and shown for a range of materials (semiconductors, dielectrics, composite materials), structures (damage and porosity profiles, gratings and other photonic structures, surface roughness) and cross-checking methods (atomic force microscopy, electron microscopy, x-ray diffraction, ion beam analysis). The high-sensitivity, high-throughput, in situ or in line capabilities of the optical methods will be demonstrated by different applications.

High quality scatterometry standard samples have been developed to improve the tool matching between different scatterometry methods and tools as well as with high resolution microscopic methods such as scanning electron microscopy or atomic force microscopy and to support traceable and absolute scatterometric critical dimension metrology in lithographic nanomanufacturing. First samples based on one dimensional Si or on Si 3 N 4 grating targets have been manufactured and characterized for this purpose. The etched gratings have periods down to 50 nm and contain areas of reduced density to enable AFM measurements for comparison. Each sample contains additionally at least one large area scatterometry target suitable for grazing incidence small angle X ray scattering. We present the current design and the characterization of structure details and the grating quality based on AFM, optical, EUV and X Ray scatterometry as well as spectroscopic ellipsometry measurements. The final traceable calibration of these standards is currently performed by applying and combining different scatterometric as well as imaging calibration methods. We present first calibration results and discuss the final design and the aimed specifications of the standard samples to face the tough requirements for future technology nodes in lithography.

In this work, we illustrate the benefits and problems of mathematical modelling and effective numerical algorithms to determine the diffraction of light by periodic grating structures. Such models are required for reconstruction of the grating structure from the light diffraction patterns. With decreasing structure dimensions on lithography masks, increasing demands on suitable metrology techniques arise. Methods like scatterometry as a non-imaging indirect optical method offer access to the geometrical parameters of periodic structures including pitch, side-wall angles, line heights, top and bottom widths. The mathematical model for scatterometry is based on the Helmholtz equation derived as a time-harmonic solution of the Maxwell equations. It determines the incident and scattered electric and magnetic fields, which fully specify the light propagation in a periodic two-dimensional grating structure. For numerical simulations of the diffraction patterns, a standard finite element method (FEM) or a generalized finite element method (GFEM) is used for solving the elliptic Helmholtz equation. In a first step, we performed systematic forward calculations for different varying structure parameters to evaluate the applicability and sensitivity of different scatterometric measurement methods. Furthermore our programs include several iterative optimization methods for reconstructing the geometric parameters of the grating structure by the minimization of a functional. First reconstruction results for different test data sets are presented.

In this contribution we demonstrate goniometric scatterometry measurements of gratings with linewidths down to 25 nm on silicon wafers with an inspection wavelength of 266 nm. For each sample, measurements have been performed in four different configurations and the obtained data have been evaluated in parallel. As results we present the reconstruction of the complete cross-section profile. We introduce a novel geometry parameterization which overcomes some limitations of the default parameterization. A co-variance analysis of the parameters is offered to indicate the soundness of the results. A qualitative comparison with cross-section scanning electron microscope (SEM) images shows excellent agreement.

Non-imaging techniques like X-ray scattering are supposed to play an important role in the further development of CD metrology for the semiconductor industry. GISAXS provides directly assessable information on structure roughness and long-range periodic perturbations. The disadvantage of the method is the large footprint of the X-ray beam on the sample due to the extremely shallow angle of incidence. This can be overcome by using wavelengths in the extreme ultraviolet (EUV) spectral range which allow for much steeper angles of incidence but preserve the large range of momentum transfer that can be observed. At the Physikalisch-Technische Bundesanstalt (PTB), the available photon energy range extends from 50 eV up to 10 keV at two adjacent beamlines. PTB commissioned a new versatile Ellipso-Scatterometer which is capable of measuring 6” square substrates in a clean, hydrocarbon-free environment with full flexibility regarding the direction of the incident light polarization. The reconstruction of line profiles using a geometrical model with six free parameters, a finite element method (FEM) Maxwell solver and least-squares optimization yielded consistent results for EUV and deep ultraviolet (DUV) scatterometry. For EUV photomasks, the actinic wavelength EUV scatterometry yields particular advantages. A significant polarization dependence of the diffraction intensities for 0th and +1st orders in the geometry with the grating lines perpendicular to the plane of reflection is observed and the 0th order intensity shows sufficient sensitivity to the line width such that a CD-resolution below 0.1 nm is within reach. In this contribution we present scatterometry data for line gratings using GISAXS, and EUV and DUV scatterometry and consistent reconstruction results of the line geometry for EUV and DUV scatterometry.

Scatterometry is a common technique for dimensional characterisation of nanostructures in the semiconductor industry. Currently this technique is limited to relative measurements for process development and process control. Although the high sensitivity of scatterometry is well known, it is not yet applied for absolute measurements of critical dimensions (CD) and quality control due to the lack of traceability. Thus we aim to establish scatterometry as traceable and absolute metrological method for dimensional measurements. Suitable high quality calibrated scatterometry reference standard samples are currently developed as one important step to enable traceable absolute measurements in industrial applications. The reference standard materials will base either on Si or on Si3N4. A traceable calibration of these standards will be provided by applying and combining different scatterometric as well as imaging calibration methods. First Silicon test samples have been manufactured and characterised for this purpose. The etched Si gratings have periods down to 50 nm and contain areas of reduced density to enable AFM measurements for comparison. We present the current design and first characterisations of structure details and the grating quality based on AFM measurements, optical, EUV and X-Ray scatterometry as well as spectroscopic ellipsometry. Finally we discuss possible final designs and the aimed specifications of the standard samples to face the tough requirements for future technology nodes in lithography.

Scatterometry is a common tool for the dimensional characterization of periodic nanostructures. In this paper we compare measurement results of two different scatterometric methods: a goniometric DUV scatterometer and a coherent scanning Fourier scatterometer. We present a comparison between these two methods by analyzing the measurement results on a silicon wafer with 1D gratings having periods between 300 nm and 600 nm. The measurements have been performed with PTB’s goniometric DUV scatterometer and the coherent scanning Fourier scatterometer at TU Delft. Moreover for the parameter reconstruction of the goniometric measurement data, we apply a maximum likelihood estimation, which provides the statistical error model parameters directly from measurement data.

Dimensional metrology based on optical vision systems is commonly used at the industrial level, for example in optical coordinate measurement machines (CMMs). Measurement uncertainties of well below 1 μm are more and more required. Thus for calibration samples a measurement uncertainty of the order of 100 nm is required. To enable accurate and traceable measurements both unidirectional (e. g. distance) measurements and bidirectional measurements (e. g. width or diameter) have to be performed for system calibrations and the reverification of the performance [1]. However, up to now the national metrology institutes (NMIs) are not able to offer internationally recognized bidirectional calibrations, which are covered by the Mutual Recognition agreement (MRA [2]) and documented in the key comparison database [3]. Currently only one NMI offers optical widths calibrations on suitable user-supplied samples, including line scales, as well.

According to the International Technology Roadmap for Semiconductors (ITRS) the semiconductor industry will start to apply Extreme Ultraviolet (EUV) Lithography for printing high-end electronic circuits within the next few years. For the critical dimensional structure parameters like CD, sidewall angle and line edge roughness (LER) besides SEM also atomic force microscopy (AFM) and scatterometry will be important metrology methods.

The impact of line-edge (LER) and line-width roughness (LWR) on the measured diffraction patters in extreme ultraviolet (EUV) scatterometry has been investigated in recent publications. Two-dimensional rigorous numerical simulations were carried out to model roughness. Simple analytical expressions for the bias in the mean efficiencies stemming from LER and LWR were obtained. Applying a similar approach for DUV scatterometry to investigate the impact of line roughness we obtain comparable results.

The precise and accurate determination of critical dimensions of photo masks and their uncertainties is important in the lithographic process to ensure operational reliability of electronic compounds. Scatterometry is known as a fast, non-destructive optical method for the indirect determination of geometry parameters. In recent years novel methods for solving the inverse problem of scatterometry have enabled a more reliable determination of grating parameters. In this article we present results from maximum likelihood parameter estimations based on numerically simulated EUV scatterometry data. We approximately determine uncertainties of these parameters by a Monte Carlo method with a limited amount of samplings and by employing the Fisher information matrix. Furthermore, we demonstrate that the use of incomplete mathematical models may lead to severe distortions in the calculations of the uncertainties by the approximate Fisher matrix approach as well as to substantially larger uncertainties for the Monte Carlo method.

At PTB we investigate the prospects of scatterometric methods for quantitative dimensional metrology of periodic micro- and nanostructures. Commonly applied approximations and simplifications may lead to contributions to the measurement uncertainty or even to systematic measurement errors. Here we present a short overview about the main effects connected with these simplifications. In particular we present numerical investigations of the influence of a finite beam size on the scatterometry results. The results indicate, that an impact of the finite beam size becomes significant only for tightly focused beams with a beam waist radius wo smaller than 10 μm.