This PDF file contains the front matter associated with SPIE Proceedings Volume 11783 including the Title Page, Copyright information, and Table of Contents.

In this talk, I will discuss several new forms of optical microscopy that my group developed in recent years. Our goal was to recover tiny nanoscale features using a conventional microscope. This problem is challenging because of the low signal to noise ratio for such features. In the first method, we introduced the regularized pseudo-phase and used it to measure nanoscale defects, minute amounts of tilt in patterned samples, and severely noise-polluted nanostructure profiles in optical images. We also extended the method to study the dynamics of droplet condensation using environmental scanning electron microscopy. In the second method, we built upon electrodynamic principles (mechanical work and force) of the light-matter interaction and applied it to sense sub-10 nm wide perturbations. In the third method, we introduced the concepts of electromagnetic canyons and non-resonance amplification using nanowires and applied these concepts to directly view individual perturbations (25-nm radius = λ/31) in a nanoscale volume.

The signal-to-noise ratio and imaging performance of optical instruments is often limited by instrumental straylight. In the case of state-of-the-art spectrometers, scattered light level of the diffraction grating, quantified in terms of its BRDF, remains the main cause. It is therefore essential for the designer to estimate the scattering behavior of diffraction gratings realistically. We thus developed a simple semi-analytical model based on scalar Fourier optics. In this framework, the BRDF is shown to be proportional to the angular spectrum of plane waves emanating from the grating aperture function. The model can easily incorporate different manufacturing errors of real gratings that are specific for the most common mastering methods, i.e. holographic lithography and mechanical ruling. The influence of the most important manufacturing errors is demonstrated and BRDF functions based on the model are compared to measurements from real holographic and mechanically ruled diffraction gratings.

In optics, elements with complex light scattering properties are typically simulated either with the computer models based on the reconstruction of their surface and internal structure or with measured Bi-Directional Scattering Distribution Function (BSDF) which totally describes the dependence of scattering properties on illumination and observation conditions. However, in many cases simulation of precise computer models to specify light scattering properties is impossible because parameters either not available or measured with insufficient accuracy. The approach based on measured BSDF is not applicable in all cases also, for instance, when it is necessary to make a simulation of some light guiding plate (LGP) with rough scattering surfaces. In this case, the properties of light scattering on the rough surfaces should be specified and thus measured separately from the whole LGP. The BSDF for such kinds of surfaces is either impossible to measure at all, or measurements are very expensive due to the need to use additional and very complex equipment. The article considers the third alternative approach to simulate scattering properties based on the reconstruction of the whole BSDF with an optimization process. The objective function is an angular intensity distribution measured with GP-200 goniophotometer. Another problem is the calculation speed of the simulated model. BSDF is a multidimensional function and its calculation with proper resolution can be a difficult task. This work proposes a fast and simple way to simulate the angular intensity distribution of scattering material based on BSDF obtained with a measuring device. The simulation results based on several examples of scattering samples are compared with real measurements.

The method based on the application of integrating spheres and a movable sample for measurements of scattering and absorption coefficients of transparent and turbid media was implemented for the investigation of optical properties of different organosilicone polymers used in fiber optics, including polysiloxanes doped with metal powder. For the determination of the optical absorption and scattering coefficients together with the scattering anisotropy of polymers basing on the experimental data, the inverse problem of the radiation transfer theory was implemented using two approaches: Monte-Carlo simulation and an analytical solution in the single-scattering approximation.

The increasing complexity and decreasing sizes of nanostructures in microelectronic devices challenge the existing metrology methods. Moreover, as the dimensions of nanostructures continue to decrease, the overall effect of imperfections increases. For lithographic lamellar gratings, the most characteristic type of roughness is lineedge roughness, which affects the uniformity of the line edge of the line. Grazing incidence X-Ray fluorescence (GIXRF) is a non-destructive, ensemble and element sensitive method with high sensitivity to the line shapes of lamellar nanostructures. However, the effect of line-edge roughness on the angular distribution of the GIXRF is unknown. Here, the effect of line-edge roughness of lamellar gratings on the GIXRF intensity is investigated using a series of test samples with different artificial line-edge roughness profiles. We observed that the angular distribution of the GIXRF intensity is affected by the roughness.

Multi-wavelength digital holography is a very powerful approach for surface shape measurements. It has the advantage of being contact-less, non-intrusive, and yields full-field surface shape data without any requirement for scanning. When dealing with off-axis digital holography and spatial multiplexing of two-wavelength digital holograms, the method becomes real-time, in the sense that the surface shape can be measured at each time instant at which the holograms are recorded. Thus, phase shifting and sequential recording are suppressed. However, due to the roughness of the inspected surface, speckle decorrelation occurs and noise is included in the final data. The noise amount in the data must be investigated in order to define the best processing approach for holograms. This paper proposes the analysis of the standard deviation of noise in surface-shape data from two-wavelength spatially-multiplexed digital holograms. The influence of noise on the measurements of the surface shape is described by an analytical approach. Relationships to quantify the minimum measurable surface height is given by taking into account the experimental parameters of the set-up. These parameters are related to the spatial bandwidths, modulation of holograms, saturation ratio, number of electrons in pixels, readout noise, quantization noise, photon noise, and speckle decorrelation due to roughness. The theoretical modeling is discussed and analysis when considering practical situation for industrial surface shape measurements.

We present an analytical model for the dynamical self-heating effect in air-cladded optical microring resonators (ORRs). The spatially and time resolved temperature field is calculated by integrating the corresponding boundary value problem of the heat equation. It turns out that the self-heating amplitude is approximately proportional to the total absorbed power and anti-proportional to the thermal conductivity of the cladding material. Further, two-photon absorption plays a major role in the heating process, even for moderate input powers, due to the strong light confinement. Heating times are determined to be in the microsecond range and may limit the response time of ORR devices. The explicit formulas for the temperature fields allow a much faster determination of heating properties compared to elaborate finite element simulations. Thus, our model is predestinated for scanning large parameter spaces. We present such an analytical model for the self-heating effect in ORRs. For this purpose, we solve the heat equation on the ORRs geometrical domain. The heat source is caused by two effects, linear absorption from defect states and quadratic two-photon absorption (TPA). Due to the strong light confinement on resonance, very high light intensities are reachable in the resonator ring and the TPA might become a dominant heat source even for low excitation powers. We utilize insulating Neumann boundary conditions to calculate the temperature increase in the substrate region as a convolution between heat source and the corresponding Greens function. The temperature field in the ring structure is calculated by solving the corresponding eigenvalue problem that arises from a separation ansatz. The result is discussed in terms of maximum self-heating, response time and power dependence for ORRs with very high Q-factors of over 100 000. Finally, we compare the analytical calculations of the self-heating effect with finite element computations.

A conventional Fizeau wedge (FW) is built of two flat reflecting surfaces inclined at a small angle. They form a gap with linearly increasing thickness normally to the wedge ridge. Such FWs with apex angles of 5–100 microradians and 5– 1000 micrometers thickness find application in optical metrology, spectroscopy and laser spectral control. The apex angle, the reflection coefficients and the refractive index in the gap form a unique interference pattern on both FW’s sides. To benefit from a large free spectral range of thin wedges and high spectral resolution of thick wedges, recently we proposed a stack of two FWs with matched parameters. Matching provides the same change of the resonant wavelength at the same lateral displacement of both wedges. The aim of this study is to develop a technique for calculation of the resultant transmission of the stack of two matched wedges at plane wave illumination that is based on determination of the number and optical path differences of the rays leaving the stack at a given point on its rear surface. Only rays with non-negligible contribution as an amplitude are taken into account. Numerical simulation and experimental verification are provided.

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.

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.

Coherence scanning interferometry is one of the most frequently used techniques for optical profiling due to its outstanding axial resolution. However, optical profilers suffer from systematic deviations caused by their transfer characteristics and diffraction effects occurring by means of light-surface interaction with measurement objects. In order to predict these deviations and to get better insight into the physical effects leading to their appearance, analytical and rigorous numerical models are applied. Usually, rigorous models provide higher accuracy whereas analytical models require less computational effort since the light-surface interaction is considered by a phase object approximation. We present a full vectorial three-dimensional modeling of coherence scanning interferometry based on the phase object approximation. Further, we compare three different common approaches using the phase object approximation, usually called Richards Wolf model, Foilmodel and Kirchhoff model. The comparison is validated with respect to rigorously simulated and measured results shown elsewhere.

The strong requirements in particular the fast data acquisition and stability that are imposed on optical in-line inspection systems, have resulted in a rather limited choice of possible optical techniques. Chromatic confocal point sensors fulfill many of the requirement and are therefore often applied. However, when investigating technical surface scattering samples with a small NA a highly disturbed signal is obtained. Moreover, aberrations can lead to a misinterpretation of the confocal signal. It is therefore utmost important to have some guidance in selecting the correct optics and to eliminate for the aberration induced measurment errors. This can be achieved via realistic modelling of the chromatic confocal signal, for which multiple parameters have to be considered such as NA, measurement of off or an-axis object point, wave-aberrations, size of pinhole, spectral bandwidth of light source employed, spectral intensity distribution of light source, chromatic axial spread, spatially coherent or incoherent light, and roughness properties of the object. Summarizing the impact of all these parameters in a single equation is per se an impossible task. Moreover, some artifacts cannot be modelled using a ray tracing approach, such as speckles. We, therefore, developed a chromatic confocal model, which is based on scalar wave-propagation theory. This enables the application of each individual wavelength and in case of a spatially incoherent system multiple source points and their respective coordinates, finally resulting in a realistic signal. With respect to surface roughness, the NA of the wave-optical model can be adjusted until an undisturbed signal is obtained. Moreover, the influence of wave-aberrations on the signal can be simulated, which results in a changed shape and spectral peak position of the chromatic confocal signal, resulting in a false estimate of the z-position. Simulated results and their experimental validation with various parameters, such as numerical aperture, object roughness, object inclination, spatially coherent and spatially incoherent light will be presented.

The semiconductor industry has just recently met the end of “Moore’s Law”, the cyclical reduction in transistor cost observed over several decades. With the smallest dimensions now approaching near-atomic scales, new architectures and materials combinations are anticipated over the next decade to realize smaller, energy-efficient, high-performance, and secure devices. Optics currently is the non-destructive, fast, inexpensive “workhorse” metrology tool in this industry. This present work addresses the potential promise of and possible requirements for wavelength down-scaling for robustly quantifying dimensions at these scales. The requirements for measuring these critical dimensions at the transistor level, also known as the “Front End of the Line” (FEOL) in manufacturing, will be compared against the also-decreasing dimensions at the “back end of the line” (BEOL); the BEOL consists of metals and insulators and facilitates the flow of electrons between the FEOL-patterned transistors and the semiconductor device’s packaging. The main challenges between optics-based metrology at the FEOL and BEOL will be contrasted with solutions suggested, based upon finite-difference time-domain (FDTD) electromagnetic simulation studies of nominal FEOL and BEOL structures.

Parameter reconstruction is a common problem in optical nano metrology. It generally involves a set of measurements, to which one attempts to fit a numerical model of the measurement process. The model evaluation typically involves to solve Maxwell’s equations and is thus time consuming. This makes the reconstruction computationally demanding. Several methods exist for fitting the model to the measurements. On the one hand, Bayesian optimization methods for expensive black-box optimization enable an efficient reconstruction by training a machine learning model of the squared sum of deviations Χ² . On the other hand, curve fitting algorithms, such as the Levenberg-Marquardt method, take the deviations between all model outputs and corresponding measurement values into account which enables a fast local convergence. In this paper we present a Bayesian Target Vector Optimization scheme which combines these two approaches. We compare the performance of the presented method against a standard Levenberg-Marquardt-like algorithm, a conventional Bayesian optimization scheme, and the L-BFGS-B and Nelder-Mead simplex algorithms. As a stand-in for problems from nano metrology, we employ a non-linear least-square problem from the NIST Standard Reference Database. We find that the presented method generally uses fewer calls of the model function than any of the competing schemes to achieve similar reconstruction performance.

The trend to produce semiconductor devices having more complex nanostructures results in the increasing importance of exquisite systems measuring multiple Critical Dimensions (CDs) of nanostructures. However, from a practical point of view, it is difficult to apply conventional methodologies to mass production because of cost and complexity issues. In this study, we propose an application of machine learning techniques utilizing optical information to measure nanoscale profiles of channel holes in High-Aspect-Ratio (HAR) structure of vertical NAND flash, which is applicable to mass production. By combining the conventional methodologies, the proposed method yields data pairs for supervised learning which include optical spectra obtained with Rotating Polarizer Ellipsometer (RPE) and images obtained with Scanning Electron Microscopy (SEM). Several preprocessing steps and machine learning techniques are introduced to train a model with sufficient performance to be applicable to mass production. In experiments, we obtained a model with coefficient of determination (R²) of 0.8 and Root Mean Square Error (RMSE) of 1.3 nm when predicting hundreds of nanoscale profiles of the channel holes which are measured with SEM. Furthermore, we confirmed that only 500 samples of data are sufficient to achieve the model performance with R² greater than 0.7 and RMSE less than 1.5 nm. The proposed method is capable of replacing the conventional methods of profile measurement in the mass production stage by reducing the cost of destructive methods and accurately measuring the profiles of complex nanostructures without theoretical modeling.

Development of efficient absorber masks and highly reflective mirrors in the EUV spectral range is a key challenge for upcoming lithography techniques in semiconductor technology. There is an improved need to precisely know the optical constants of the materials at hand for specialized applications such as phase shifting absorber masks. A further field of application is the interpretation and accompanied modeling of scattering data of complex nanostructures. At PTB, we measured the spectral reflectance of thin film samples in the angular range from normal incidence to grazing incidence in the range of 10nm to 20nm using PTB’s lubrication-free Ellipso-Scatterometer at the soft x-ray beamline at the electron storage ring BESSY II. This allowed us to determine the optical constants of a variety of metals, semimetals and their alloys from model fits based on Fresnel’s equations for layered material stacks.

We describe a dynamic spectral ellipsometric Direct filtering phase extraction method based on a monolithic polarizing Michelson interferometry scheme. The proposed dynamic phase extraction method is three times faster and it can evaluate a spectrally resolved ellipsometric phase Δ(k) with utmost the same level of precision and accuracy compared to Fourier Transform method. The performance of the proposed dynamic spectral ellipsometric phase extraction method is demonstrated by using a SiO₂ thin film with a nominal thickness of 500 nm deposited on Si bare wafer.

In this work, the task was to investigate the properties of niobium oxide layers (geometric thickness, their optical constants n and k) in the design of a multilayer interference filter, in the manufacture of which a system for indirect control of the thickness of the deposited films is used. As an indirect control system, we used both quartz control and optical broadband control. The experiment was based on using a 6-position changer, which makes it possible to change the substrate on which the coating is deposited during the process of making a light filter by the electron beam evaporation. Thanks to this, we obtained substrates with a niobium oxide film, which corresponded to 1, 9, 17, 25 and 31 layers of an interference filter. Analysis of the obtained samples allows us to determine the geometric layer thickness, refractive index and absorption and to evaluate the effect of a change in the solid angle of the flow of the evaporated substance due to a change in the amount of substance in the crucible on the thickness of the sprayed film on the substrate, when we use indirect methods of thickness control. We used Ferrotec EV M-10 electron beam guns to evaporate the construction materials of the interference filter. For the evaporation of SiO₂, a stock stream crucible was used; for the evaporation of Nb²O₅, we ourselves made a special crucible in order to optimize the evaporation mode of this material. We managed to optimize the power of the electron beam and at the same time to obtain the desired form of the flow of the evaporated substance. Analysis of the obtained samples made it possible to answer the question of whether physicochemical changes in niobium oxide in the crucible occur when exposed to an electron beam for a sufficiently long time. In the course of the research, an X-ray phase analysis of the Nb2O5 film-forming material from various manufacturers was carried out.