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We present a collection of simulations of the Edwards–Anderson lattice spin glass at T = 0 to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample the ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a variety of accurate exponents for domain wall stiffness and finite-size corrections, which allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattice Ising spin glasses. [ABSTRACT FROM AUTHOR]

We present a collection of simulations of the Edwards-Anderson lattice spin glass at T = 0 to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample the ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a variety of accurate exponents for domain wall stiffness and finite-size corrections, which allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattice Ising spin glasses. [ABSTRACT FROM AUTHOR]

Different deterministic solution methods are being used to solve the criticality problem of the reflected systems with different anisotropic behaviours for both fission neutrons and neutrons undergoing scattering. In the present study, the criticality problem is simulated using the developed Monte Carlo algorithm. Different angular distributions, such as Inönü, Anlı–Güngör and tetra-anisotropic kernels are taken into account. For each anisotropic kernel, the sampling method of the direction cosine of either newborn fission neutrons or scattered neutrons is presented by extracting the required probability distribution function (PDF). The simulation starts with an initial guess and following the presented procedure, the criticality thickness of the system is estimated with a certain convergence criterion. Different variance reduction methods, such as implicit capture, Russian-roulette and splitting, are also implemented to get more precise results with a reasonable computational time cost. The validity of the presented method is verified by comparing with the results of different deterministic methods. Finally, using an exact scattering function, the three considered kernels are compared with each other. It is seen that the tetra-anisotropic kernel is the best among the considered kernels. [ABSTRACT FROM AUTHOR]

We present a collection of simulations of the Edwards–Anderson lattice spin glass at T=0 to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample the ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a variety of accurate exponents for domain wall stiffness and finite-size corrections, which allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattice Ising spin glasses.

By means of the field-theoretic renormalization group, we study the damping of the viscosity coefficient near the superfluid phase transition. We use the fact that in the infrared region, the complex model used to describe the phase transition belongs to the same universality class as the well-known stochastic model A. This allows us to determine the critical behavior of viscosity using composite operators for model A. Our analysis is based on the -expansion near the upper critical dimension of model A. The critical exponent of viscosity is then calculated from the critical dimensions of composite operators of massless two-component model A. In particular, we present results for critical dimensions of a selected class of composite operators with the canonical dimension to the leading order. [ABSTRACT FROM AUTHOR]

In this paper we consider lower order perturbations of the critical Lane-Emden system posed on a bounded smooth domain Ω ⊂ R N , with N ≥ 3 , inspired by the classical results of Brezis and Nirenberg [4]. We solve the problem of finding a positive solution for all dimensions N ≥ 4. For the critical dimension N = 3 we show a new phenomenon, not observed for scalar problems. Namely, there are parts on the critical hyperbola where solutions exist for all 1-homogeneous or subcritical superlinear perturbations and parts where there are no solutions for some of those perturbations. [ABSTRACT FROM AUTHOR]

Let X= \{X(t), t \in \mathbb {R}^N\} be a centered Gaussian random field with values in \mathbb {R}^d satisfying certain conditions and let F \subset \mathbb {R}^d be a Borel set. In our main theorem, we provide a sufficient condition for F to be polar for X, i.e. \mathbb P\big (X(t) \in F \text { for some } t \in \mathbb {R}^N\big) = 0, which improves significantly the main result in Dalang et al. [Ann. Probab. 45 (2017), pp. 4700–4751], where the case of F being a singleton was considered. We provide a variety of examples of Gaussian random field for which our result is applicable. Moreover, by using our main theorem, we solve a problem on the existence of collisions of the eigenvalues of random matrices with Gaussian random field entries that was left open in Jaramillo and Nualart [Random Matrices Theory Appl. 9 (2020), p. 26] and Song et al. [J. Math. Anal. Appl. 502 (2021), p. 22]. [ABSTRACT FROM AUTHOR]

The expansion of the string coordinates is different curved surfaces and space times. A summation of uniformizing group elements is necessary at genus g = 1. The invariances are listed for the sigma model action in a maximally curved space-time. Thecritical dimension is established through conditions on the quantum commutators. [ABSTRACT FROM AUTHOR]

This paper presents a photomask inspection and defect analysis technique to accurately measure the pattern dimensions and to detect the defects of the photomask in a convenient, fast, reliable manner. The beam-shaped knife-edge interferometry (BSKEI) was developed to collect the interferogram created by the superposition of the reference incident wave and the edge-diffracted wave while scanning the photomask. BSKEI consists of a pulsed laser diode, an aperture, an objective lens, and a fiber-coupled photodiode. The objective lens enabled the beam shaping to create a spherical wave as a new source of light, and the beam shaping was effective to enhance the spatial frequency of the interferogram. The interferograms were characterized based on a Fresnel number model, and the corresponding interferogram analysis methods were developed. BSKEI produced different interferograms according to the photomask patterns and defects while scanning the photomask. As a result, BSKEI is capable of the measurement of pattern width, opening width, line-edge quality, and opening area surface quality of the photomask, and is expected to be an alternative tool for critical dimension metrology in many semiconductor applications. • A new photomask inspection technology, the so-called beam-shaped knife-edge interferometry (BSKEI) and advanced fringe analysis methods, were introduced. • This method accurately measures the pattern dimensions and line-edge quality and detects the defects of the photomask in a convenient, fast, reliable manner. • The geometrical optics-based BSKEI model was developed, and simulated the interferogram analysis according to the beam shaping conditions. • As a result, the pattern width, pattern distance, line-edge roughness, and arbitrary defects on the photomask were inspected and characterized by BSKEI. • This method has the potential to be utilized in high-resolution photomask inspection systems. For the future work, the 2 axis precision positioning system will be developed to scan a whole photomask and to reconstruct the pattern shapes and defects. [ABSTRACT FROM AUTHOR]

Atomic force microscope (AFM) is commonly used for three-dimensional characterization of the surface morphology of structures at nanoscale, but the "Inflation effect" of the tip is an important factor affecting the accuracy. A tip characterizer has the advantages of in situ measurement, higher accuracy of probe inversion results, and relatively simple fabrication process. In this paper, we developed a rectangular tip characterizer based on multilayer film deposition technology with protruding critical dimension parts and grooves parts. And the tip characterization is highly consistent across the line widths and grooves, and still performs well even in the sub-5 nm line width tip characterizer. This indicates that tip characterizers produced by this method can synergistically meet the combined requirements of standard rectangular structure, very small line edge roughness, very small geometry dimension, and traceable measurements. [ABSTRACT FROM AUTHOR]

The line width (often synonymously used for critical dimension, CD) is a crucial parameter in integrated circuits. To accurately control CD values in manufacturing, a reasonable CD reference material is required to calibrate the corresponding instruments. We develop a new reference material with nominal CDs of 160 nm, 80 nm, and 40 nm. The line features are investigated based on the metrological scanning electron microscope which is developed by the National Institute of Metrology (NIM) in China. Also, we propose a new characterization method for the precise measurement of CD values. After filtering and leveling the intensity profiles, the line features are characterized by the combination model of the Gaussian and Lorentz functions. The left and right edges of CD are automatically extracted with the profile decomposition and k -means algorithm. Then the width of the two edges at the half intensity position is regarded as the standard CD value. Finally, the measurement results are evaluated in terms of the sample, instrument, algorithm, and repeatability. The experiments indicate efficiency of the proposed method which can be easily applied in practice to accurately characterize CDs. [ABSTRACT FROM AUTHOR]

In this paper, we discuss two general models of random simplicial complexes which we call the lower and the upper models. We show that these models are dual to each other with respect to combinatorial Alexander duality. The behavior of the Betti numbers in the lower model is characterized by the notion of critical dimension, which was introduced by Costa and Farber in [Large random simplicial complexes III: The critical dimension, J. Knot Theory Ramifications26 (2017) 1740010]: random simplicial complexes in the lower model are homologically approximated by a wedge of spheres of dimension equal the critical dimension. In this paper, we study the Betti numbers in the upper model and introduce new notions of critical dimension and spread. We prove that (under certain conditions) an upper random simplicial complex is homologically approximated by a wedge of spheres of the critical dimension. [ABSTRACT FROM AUTHOR]

The demand for ever-smaller devices increases with the development of the semiconductor industry. High-resolution patterning based on lithography is significant to fabricate ultra-small nanostructures in various nanodevices. With the minimization of feature size down to nanometric scale, it is challenging to reliably define ultra-small features and structures through lithographic approaches. The ultra-small resist structures defined by lithography approaches usually suffer from mechanical instability behaviors during the development and drying process. The stable mechanical behaviors of lithography-defined resist nanopatterns are the important issue for reliable fabrication. Exploring the mechanical stability of resist patterns is of great importance both scientifically and technologically. Hydrogen silsesquioxane (HSQ) is a high-resolution negative-tone electron-beam resist for sub-10-nm fabrication. But, the ultra-small electron-beam exposed HSQ resist structures usually suffer from collapse and displacement after the development process. Hence, it is essential to understand the stability behavior of HSQ resist nanostructures to reliably fabricate various nanodevices. But, a systematic study of the stability behavior of HSQ is still lacking. To address this issue, we exposed the HSQ nanopillars on different substrates and dried them using different drying methods to probe the factors of critical dimensions, substrate adhesion, and dry methods for reliable HSQ nanopillars fabrication in this work. Through the analysis of experimental data, we found the adhesion dominates the mechanical stability of HSQ nanopillars at the ultra-small scale. By using finite element analysis, we systematically explored the role of the capillary effect in the two main unstable mechanics behaviors (collapse and displacement). To suppress the capillary forces, we optimized the drying process with the use of CO2 supercritical drying. We further provided an effective and facile method through spin-drying in the atmosphere to improve the stability of lithography-defined HSQ pillars. [ABSTRACT FROM AUTHOR]

A complete, self‐sufficient package is prepared to teach the fundamental concepts of lithography. The adapted semianalytical approaches promise to illustratively create an ideal engaging environment for efficiently training next generation lithographers. The presented educational tool, which integrates the well‐known modeling methods from the literature, is shown to capture the photolithography process step by step while offering the students a remote, hands‐on feeling from introductory to graduate‐level work. The importance of optical and chemistry related parameters are discussed with the aim of creating a useful laboratory assessment package for the educators to be easily integrated into their curriculum. [ABSTRACT FROM AUTHOR]

This essay aims to analyse the correspondence between Damaris Masham and G. W. Leibniz (1703-1705) through three discussion dimensions: ontological, epistemological and critical. This analysis could be useful in order to understand the epistemological grounds of the moral and pedagogical rationalism of the English philosopher. In this sense, it offers an integration of elements that make us able to understand the coincidence of apparently antithetical traditions as platonism and empirism in Masham's philosophy, moreover let us appreciate her intellectual independence. [ABSTRACT FROM AUTHOR]

Atomic force microscope (AFM) is commonly used for three-dimensional characterization of the surface morphology of structures at nanoscale, but the “Inflation effect” of the tip is an important factor affecting the accuracy. A tip characterizer has the advantages of in situ measurement, higher accuracy of probe inversion results, and relatively simple fabrication process. In this paper, we developed a rectangular tip characterizer based on multilayer film deposition technology with protruding critical dimension parts and grooves parts. And the tip characterization is highly consistent across the line widths and grooves, and still performs well even in the sub-5 nm line width tip characterizer. This indicates that tip characterizers produced by this method can synergistically meet the combined requirements of standard rectangular structure, very small line edge roughness, very small geometry dimension, and traceable measurements.

This article looks at one of the most popular recent installation works, Eliasson's The Weather Project, which still is probably the Danish-Icelandic artist's most famous work. To explain both the iconicity within Eliasson's oeuvre and the enormous popularity of the work, we argue that it essentially addresses an aesthetic conflict between a critical and a populist potential; or, more specifically--reformulates this conflict. For what seems to be clear is that although the critical dimension is explicitly present in the work, it is largely insignificant in terms of the overall aesthetic experience. What we find, then, is a work whose aesthetics in many ways attempts to distance itself from late 20th century predecessors by blatantly surrendering to a seductive spectacle that suspends the critical. In doing so, The Weather Project points towards a new political paradigm emerging around the beginning of the 21st century, which in more recent years seems to have found a temporary culmination through events such as Brexit and the election of Donald Trump as the US president. The post-9/11 political paradigm moved away from an idea prevalent during the late 20th century, embodied in Fukuyama's thesis of the end of history and the concomitant idea of the absolutely secure world (and, by implication, the erasure of the outside/inside distinction). After an ill-defined war on terror that undoubtedly has made the world less secure, financial crises that have made the gap between rich and poor wider, the rise of populism amidst even the most solid and oldest democratic institutions, and more generally a widening gap between 'the people' and 'the elite'--it is as if we have returned to political antagonisms that many thought were no longer relevant. We argue that it is within this context that one may appreciate The Weather Project's intervention as an art work recreating an atmosphere, a mood, that reminds us of a collective body the binding of which is essentially a pre-political moment--a moment at which we may, yet again, ask the forgotten question: why we need the political at all. [ABSTRACT FROM AUTHOR]

In recent DRAM processes, obtaining the maximum capacitor presents a difficult challenge. Also, the aspect ratio continually increases during the process. To address these issues, the thickness of the top and bottom layers must be constant. However, the thickness is not constant due to the time difference between the bottom and top processes, and because the source changes in each step. To solve this problem, the same reaction should occur at all times while the density of the gas at the bottom and top is gradually changed. In this study, a new vaporizer is developed and evaluated to ensure a constant rate of density change and a rapid vaporization response of the liquid source. To develop a vaporizer that responds quickly, we experimentally evaluated the structures of the vaporizer's showerhead and vaporizing part. To keesp the density of the liquid source for evaporation constant, several holes were made in the showerhead from which the evaporation source is discharged. Also, to ensure a constant flow of liquid to the chamber where the source droplet meets the carrier gas, a helical structure was proposed and evaluated. In addition, using an orifice, the pressure was decreased to increase the vaporization efficiency. As a result, the settling time decreased from 10 to 3 s, overshooting decreased from 25 to 1%, and flow fluctuation decreased from 2.6 to 1.8%. Therefore, this new vaporizer is well-adapted to the process of new devices and provides greater capacitance design margins. [ABSTRACT FROM AUTHOR]

As the development of display technologies, much smaller critical dimension design is an inevitable trend and much tighter statistical process control is needed and necessary. Electron Beam Review System can provide much more precise critical dimension measurement without glass to be broken compared with traditional optical metrology tools. Besides, taper CD or taper angle is a critical parameter for display product quality control and Electron Beam Review System is the only tool in display Fabs that can provide such information. [ABSTRACT FROM AUTHOR]

A novel application-oriented sub-pixel measurement method utilizing an active contour model with image resampling is presented for a critical dimension (CD) measurement of pixel patterns of a flat-panel thin film transistor crystal display (TFT-LCD) and organic light-emitting diode display. In modern manufacturing of flat panel display, optical measurement of each dimension of pixel patterns has a critical role in the process control, and the resolution of a measurement system becomes a limitation of the manufacturing process. Several methods have been developed to overcome this limit at the image post processing stage, but as the level of pixel integration and manufacturing throughput are increasing rapidly, more robust and effective inspection approach is required. In this paper, a novel sub-pixel level edge detection algorithm with active contour method and fast pixel resampling is proposed for micron scale CD measurement, and its advantages on measurement repeatability and noise handling are presented, along with the results of various industrial sample measurements and comparison with conventional critical dimension measurement algorithms. [ABSTRACT FROM AUTHOR]

BACKGROUND: Our previous study confirmed that BTO/P(VDF-TrFE) piezoelectric nanocomposita membrane containing 5%BTO (BaTO3, BTO) nanoparticles could significantly promote bone marrow mesenchymal stem cells (BMSCs) adhesion, growth, osteogenic differentiation and repair of bone defects due to its bionic potential. However, for clinical applications, it is not clear whether there is any difference between the bone repair effect of this material as a guide for tissue regeneration and that of the existing clinically non-degradable membrane products. OBJECTIVE: To compare the effects of BTO/P(VDF-TrFE) piezoelectric nano-composne membrane materials with commercial PTFE membrane in repairing critical-sized defects of SD rat skull. METHODS: BTO/P(VDF-TrFE) piezoelectric nanocomposne membrane containing 5% BTO nanoparticles was prepared by solution casting method. Scanning electron microscope, atomic force microscope and water contact angle measuring instrument were used to observe the surface morphology, measure the surface roughness and surface hydrophilicity and hydrophobicity of the material. In SD rats (purchased from the Laboratory Animal Center, Beijing University Hospital of Stomatology, China), a 5-mm sized full-thick bone defect was made on both sides of the sagittal suture of the skull. The left bone defect was covered with PTFE membrane (control group). The right bone defect was covered with BTO/P(VDF-TrFE) piezoelectric nano-composita membrane (experimental group). At postoperative 4 and 12 weeks, micro-CT and histological methods were used to evaluate the repair of the skull defect in rats. This study was approved by Animal Ethics Committee, Beijing University Hospital of Stomatology. RESULTS AND CONCLUSION: The piezoelectric nanocomposite membrane had smooth and dense surface and BTO nanoparticles were evenly distributed. PTFE membrane was composed of loose coarse fibers. The piezoelectric nanocomposite membrane had lower surface roughness (P< 0.001) and higher hydrophilicity (P< 0.001) than PTFE membrane. Micro-CT and histological results showed that at 4 weeks after surgery, new bone formation was found in both groups, but new bone formation was more obvious in the center of the defect in the experimental group than in the control group. At 12 weeks after surgery, bone defects healed in both groups, but the maturity of newly formed bone in the experimental group was greater than that in the control group. These results suggest that BTO/P(VDF-TrFE) piezoelectric nanocomposite membrane containing 5%BTO (BaTO3, BTO) nanoparticles can be used as a membrane guiding tissue regeneration. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the microelectronics industry, most of the dimensional metrology relies on critical dimension (CD) estimation. These measurements are mainly performed by critical dimension scanning electron microscopy, because it is a very fast, mainly nondestructive method and enables direct measurements on wafers. To mea- sure CDs, the distance is estimated between the edges of the observed pattern on an SEM image. As the CD becomes smaller and smaller, the needs for more reliable metrology techniques emerge. In order to obtain more meaningful and reproducible CD measurements regardless of the pattern type (line, space, contact, hole, etc.), one needs to perform a CD measurement at a known and constant height due to a methodology that determines the topographic shape of the pattern from SEM images. An SEM capable of bending the electron beam (up to 12 deg in our case) allows images to be caught at different angles, giving access to more information. From the analysis of such images, pattern height and sidewall angles can be determined using geometric considerations. Understanding interaction between three-dimensional (3-D) shapes, pattern materials, and the electron beam becomes essential to correlate topography information. A preliminary work based on Monte-Carlo simulations was conducted using JMONSEL, a software developed by the National Institute of Standards and Technology. With this analysis, it is possible to determine theoretical trends for different topographies and beamtilt conditions. Due to the effects highlighted by simulations, the processing of the tilted beam SEM images will be presented, as well as the method used to create a mathematical model allowing topographic reconstruction from these images. Finally some reconstruction using this model will be shown and compared to reference measurements. The overall flow used to process images is presented. First, images are transformed into grayscale profiles. After a smoothing procedure, positional descriptors are computed for specific profile derivatives values. Then, from these descriptors coming from two images of the same pattern taken at different tilt angles, we use a low-complexity linear model in order to obtain the geometrical parameters of the structure. This model is created and initially calibrated using JMONSEL simulations and then recalibrated on real silicon patterns. We demon- strate that the use of real SEM images coming from real silicon patterns with our model leads to results that are coherent with conventional 3-D measurements techniques taken as reference. Moreover, we are able to make reliable reconstructions on patterns of various heights with a single calibrated model. Our batch of experiment shows a three-sigma standard deviation of 10 nm on the estimated height for heights ranging from 50 nm to more than 200 nm. Based on simulations, we are able to reconstruct the corner rounding (CR) from SEM images. However, because our wafer has no CR variability, measurements still need to be assessed on real wafer. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract Three-dimensional (3D) imaging of nanostructures with high aspect ratio features is a challenging problem of broad relevance to nanoscience and nanotechnology. Though a wide variety of experimental strategies to improve 3D imaging capabilities have been proposed, current measurement capabilities are mainly limited to imaging deep trenches, in large part due to the lack of truly 3D scanning algorithms and limited dynamic control of the tilt angle. Herein, we report a non-contact atomic force microscope (AFM) strategy that overcomes these challenges by employing an intelligent 3D scanning algorithm that combines sidewall detection and real-time adjustment of the probe's direction. To test this approach, we measured the depth and sidewall topography of porous anodic aluminum oxide (trench), via holes and silicon nanopillar (protrusion) with precision tracing. Using a carbon nanotube-based AFM probe, it was possible to measure the depth of holes with an aspect ratio of 5.9. In addition to this, we have successfully achieved the 3D image of via holes with an aspect ratio of 4.3 and a resolution of 2 nm, which enables realistic profiling of the sidewall and bottom edge of holes. Taken together, our findings demonstrate how the intelligent scanning algorithm based on detection-and-decision with a high-aspect-ratio probe can be utilized as a broadly applicable nanoscience measurement tool to characterize 3D topographical features of nanostructures. [ABSTRACT FROM AUTHOR]

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Abstract Stray light exists in optical lithography, and causes the CD (Critical Dimension) Variation. Therefore, it is important to obtain an appropriate description model of imaging with stray light. An improved optical lithography imaging model considering medium-range and long-range flare is proposed by using the PSF F (Point Spread Function of Flare) model and the Kirk flare model. The proposed simulation model is confirmed to have much better precision when compared to the experiment data. The effect of flare on CD is studied, in which the total flare is the same but the ratio of medium-range and long-rang flares are varied. The simulation results show that long-range flare has a bigger impact on CD than medium-range flare. The greater the proportion of long-rang flare, the smaller line-width of CD will be. Thus, long-range flare should be taken fully into account in optical lithography. [ABSTRACT FROM AUTHOR]

With reduction in the die sizes it is very critical to control the Critical Dimension (CD) within a very precise window. In this work we present a root cause analysis and solution to a bimodal CD distribution seen from the center of the wafer. The CD bimodality displays a sharp cliff at the center of the wafer, wherein one side of the wafer has the higher CD and the other side has lower CD with respect to the target value. The bimodality was also seen in the center column of the wafer. [ABSTRACT FROM AUTHOR]

Shrinkage in semiconductor devices affects the process window of all wafer fabrication steps including plasma etching. Drifts or shifts are most significant effects on the etching process due to shrinkage in semiconductor devices. Any drift or shift affects on critical dimensions (CD) of the wafer and changes the thickness and the width over time. Therefore, there would be an essential need for estimation and minimization of CD variation on a wafer-to-wafer basis by optimization techniques. This study aims to design a learning-based control system for monitoring the CD in Dry-Etching process. Feedforwardfeedback control technique is used to reduce CD variation. Among all learning-based control systems, the Iterative Learning Control (ILC) integrated with Virtual Meteorology (VM) data, as a well-known system which can involve both feedforward signal from the past events, and feedback signals from the output of the current event is used to learn the behavior of the system and enhance the performance of the controller run-by-run. The proposed control model is optimized by gradient learning approach. The result is validated through the simulated study manipulated from empirical data and shows the advantage of the proposed feedforward-feedback learning controller than the common run-to-run exponentially weighted moving average (EWMA) control design. [ABSTRACT FROM AUTHOR]

Highlights • An independent automation stage has been developed for low-noise AFM. • The travel length of the external stage is 10 mm. • Initial position errors (< 6 µm) of the AFM tip stage were examined by the indentation method. • The 30-times-repeated measurements and 10-times-reproduced CD values using an IVPS100 sample were 141.9 ± 0.6 nm and 142 ± 0.8 nm, respectively. • The results of the measured undercut patterns using TGX1 reveals that tip wear was minimized even after the CD measurements. Abstract An independent external stage for low noise atomic force microscope has been developed for mid-range movements so that it aids in measurements of critical dimensions through the low-noise atomic force microscope. The maximum travel length of the external four-axes stage is 10 mm. For image scanning of the specific target region, the sample needs to be moved through two steps: coarse positioning with the external stage and fine positioning with PI XY piezo scanner. Prior to the CD measurements, we confirmed that the position errors caused by the external stage and tip stage were negligible through the reproducibility experiments. In this study, custom-designed software stored the initial position of the probe and then moved it precisely to the sample location to be measured. Subsequently, the sidewalls of an improved vertical parallel structure were measured and the repeatability and reproducibility of the CD measurements were estimated using a CDR30-EBD tip. Finally, we confirmed that tip wear could be minimized by measuring TGX1 samples with undercut structures. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

We mainly investigate the global boundedness of the solution to the following system, ut=u-·(uv)in O×R+, vt=v-v+w, in O×R+, wt=w-w+u, in O×R+, under homogeneous Neumann boundary conditions with nonnegative smooth initial data in a smooth bounded domain ORn with critical space dimension n=4. This problem has been considered by K. Fujie and T. Senba in [5]. They proved that for the symmetric case the condition Ou0<(8p)²/yields global boundedness, where u0 is the instal data for u. In this paper, inspired by some new techniques established in [3], we give a new criterion for global boundedness of the solution. As a byproduct, we obtain a simplified proof for one of the main results in [5]. [ABSTRACT FROM AUTHOR]

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

We consider the semilinear elliptic equation Δu+K(|x|)eu=0 in RN for N>2, and investigate separation phenomena of radial solutions. In terms of intersection and separation, we classify the solution structures and establish characterizations of the structures. These observations lead to sufficient conditions for partial separation. For N=10+4ℓ with ℓ>-2, the equation changes its nature drastically according to the sign of the derivative of r-ℓK(r) when r-ℓK(r) is monotonic in r and r-ℓK(r)→1 as r→∞. [ABSTRACT FROM AUTHOR]

Model-based library (MBL) method, based on the fundamental physics of electron-solid interaction and Monte Carlo simulation of electron transport and secondary electron (SE) cascades, is an ideal algorithm in critical dimension (CD) metrology by CD-SEM, which exceeds the experiential structure characterization with SE profile curve. Particularly, comparing to the threshold method, the MBL method can extends to 3D metrology of CD by including many more geometrical structural parameters, such as, top CD, bottom CD, height and sidewall angles. In this work, we study the SE signal profile shape in CD metrology for the MBL method. The gate lines in trapezoidal cross section shape with arc corners are modeled for the simulation of SE linescans. The sensitivity of the SE intensity profiles to the different topographic parameters are investigated. In addition, the practical aspects of CD evaluation including pre-processing of experimental SE image and profile matching procedure are discussed. The work will be beneficial to the related standardization of CD measurement. [ABSTRACT FROM AUTHOR]

In modern integrated circuit (IC) fabrication processes, the photoresist receives considerable illumination energy that is reflected by underlying topography during optical lithography of implantation layers. Bottom antireflective coating (BARC) is helpful to mitigate the reflection. Often, however, BARC is not used, because its removal is technically challenging, in addition to its relatively high economic cost. Furthermore, the advanced technology nodes, such as 14/10-nm nodes, have introduced fin field effect transistor (FinFET), which makes reflection from nonuniform silicon substrates exceptionally complicated. Therefore, modeling reflection from topography becomes obligatory to accurately predict printing of implantation shapes. Typically, FinFET is always fixed in one direction in realistic designs. However, the same implantation rectangle may be oriented in either horizontal or vertical direction. Then, there are two types of relations between the critical dimension (CD) and FinFET, namely a parallel-to and a perpendicular-to relation. We examine the fin directionality impact on CD. We found that this impact may be considerable in some cases. We use our in-house rigorous optical topography simulator to reveal underlining physical reasons. One of the major causes of the CD differences is that in the parallel orientation, the solid sidewalls of the fins conduct considerable light reflections unlike for the perpendicular orientation. This finding can aid the compact modeling in optical proximity correction of implantation masks. [ABSTRACT FROM AUTHOR]