Trapezoidal Line Research Articles

Transfer of micron pattern with reactive atmospheric plasma jets into fused silica

Pattern transfer by plasma etching is a traditional standard technology in microelectronics and other micron technologies. These technologies require vacuum conditions, which limit throughput, size, and low-cost fabrication. Recent developments in low cost atmospheric plasma technologies may be suitable to realize pattern transfer without vacuum conditions. Reactive atmospheric plasma jet etching has been used to transfer aluminum mask patterns to fused silica. Aluminum line patterns of 2.5 to 50 µm width on fused silica wafer are exposed to a static as well as a scanning CF4/O2 reactive atmospheric plasma jet with a footprint diameter of 0.85 mm (full width at half maximum), resulting in etching only the SiO2 and causing a nearly isotropic etch with an etch rate of about 200 nm/s. As a result, line narrowing, trapezoidal line cross-sections, and under-etching were observed. The successfully transferred line patterns with the demonstrated widths and depths are of technological interest in various fields of application. Therefore, this approach enables low-cost patterning of fused silica through the use of reactive atmospheric plasma jet etching for micron-scale pattern transfer. This advancement addresses the limitations of both traditional vacuum-based and wet etching methods.

Application of a machine learning method to model-based library approach for critical dimension measurements using CD-SEM

A model-based library (MBL) method has already been established for the accurate measurement of the critical dimension (CD) of semiconductor linewidth using critical dimension scanning electron microscope (CD-SEM) images. In this work, the MBL method is further investigated by combining CD-SEM image simulation and a neural network algorithm. The secondary electron linescan profiles were first calculated using a Monte Carlo simulation method, enabling us to obtain the dependence of linescan profiles on the selected values of various geometrical parameters (e.g. top CD, sidewall angle and height) for Si and Au trapezoidal line structures. Machine learning methods have then been applied to predict the linescan profiles from a randomly selected training set of the calculated profiles. The predicted results agree very well with the calculated profiles with the standard deviations of 0.1% and 6% for the relative error distributions of Si and Au line structures, respectively. The findings show that the machine learning methods can be practically applied to the MBL method for reducing the library size, accelerating the construction of the MBL database and enriching the content of the available MBL database.

STensile behaviour of T-stub to hollow section column using elliptical-head one-side bolts

The Elliptical-head one-side bolt (EOB) is a typical representative of the third generation for one-side bolts, relying on its elliptical head and bolt hole to achieve orthogonal anchorage, and the application scenario is mainly the bolted connection of closed-section members. Studies have been reported for the shear performance of EOBs bolted lap connections and the tensile behaviour of concrete-filled steel tubes, but there is still a lack of the tensile performance of EOBs connecting Hollow section columns (HSCs), which is necessary for the application of the component method for the beam-column joints design. Therefore, numerical simulation and theoretical analysis methods were employed in this paper to demonstrate the feasibility of adopting EOBs for this type of connection, including typical failure modes, novel yield line pattern in the HSC wall, comparison with the Conventional high-strength bolt (CHB) connections, analysis of the parameters related to the elliptical bolt head and hole, and the establishment and validation of the methodology for calculating the HSC bearing capacity. The results show that: The novel trapezoidal yield line pattern tended to show in the HSC wall with the smaller bolt pitch distance and larger gauge distance; The yield strength of the EOBs bolted T-stub to HSC connections was reduced by about 15% compared to the CHBs bolted ones; Vertical layout of bolt holes, accuracy of rough assembly, rotation deviation of bolt shank within 20° and avoidance of bolt offsets in bolt hole were recommended for EOB connections; The novel yield line pattern established in this paper predicted the yield strength of the connections, and the accuracy and stability were verified by comparing with finite element modelling (FEM) results.

Transmission shaft and its parameters for feed choppers in agriculture

The article presents the results of research on the selection of a transmission shaft of an optimal design for a small-sized, simple-constructed crushing device and theoretical determination of its parameters. According to the analysis of rectangular, trapezoidal, oval, tubular and conical transmission rods, trapezoidal rods have an optimal construction. Such rods ensure the convenient transmission of the stalks to be crushed, as well as compression of the material from both sides, accumulation and transmission. For this reason, we adopt a trapezoidal transmission line to the blue stem feed shredder. Based on the results of the theoretical research of transmission rods, it was determined that the stalks transmitted from the rod to the crusher depend on the shape of the rod and some parameters. According to theoretical studies, in order to transfer the crushed feed to the device and its supply channels with a comfortable and low resistance, the length of its transfer chute should be 65 cm, the width of the front part of the chute should be 40 cm, the width of the part connected to the supply chute should be 20 cm, and the slope of the chute should be 27°.

Spoof Surface Plasmon Polaritons Developed from SIW Using Ring Slots and Vias

A new type of spoof surface plasmon polaritons (SSPPs) developed from conventional substrate integrated waveguide (SIW) using ring slots and vias is proposed in this paper. The asymptotic frequency and lower cutoff frequency of the SSPP structure can be easily tuned by changing the width of SIW walls and radius of the ring slot, respectively. A trapezoidal microstrip line and a small ring slot are used for the efficient mode conversion to smoothly transit from microstrip line to the proposed SSPP structure. The presented SSPPs have a flat bandpass filtering response with adjustable center frequency and bandwidth. In order to better verify the transmission and cutoff characteristics, two bandpass filters using the proposed SSPPs with relative bandwidths of 61.7% and 76.4%, respectively, are fabricated and measured. Good agreement between the simulations and measurements verifies the proposed design idea.

Scattering Parameters Characterization of Periodically Nonuniform Transmission Lines With a Perturbative Technique

In this article, a novel procedure for the frequency-domain solution of nonuniform transmission lines (NUTLs) is presented. The procedure is based on a recently proposed perturbative technique, which is proven to be computationally more efficient than standard solution approaches, which are based on line subdivision into uniform cascaded sections. With respect to the original perturbation technique, the procedure proposed here offers more flexibility, as it provides a representation of the NUTL under analysis in terms of $S$ and/or $T$ parameters at its ports. Moreover, it retains the same prediction accuracy at the price of a slight increase in computational burden, which can be mitigated anyway through parallel computing. Furthermore, even without ad hoc (parallel) implementations, the proposed procedure outperforms other approaches to solve differential lines with partially or fully repetitive geometries. Namely, it assures accurate prediction of output quantities with reduced simulation time. This is proven by three application examples, namely, two differential trapezoidal tabbed lines (one with interdigital tabs and one with facing tabs), and a differential microstrip line with a varying common-mode (CM) impedance (as such reducing CM noise). Comparison with full-wave simulations allows assessing the prediction accuracy of the proposed procedure. Comparison with the aforementioned transmission-line-based solutions allows appreciating the enhanced computational efficiency.

Study on EEBS for linewidth imaging by a Monte Carlo method

A systematic analysis about the influences of electron beam focusing on scanning electron microscope (SEM) imaging for silicon (Si) trapezoidal lines was performed based on a sophisticated Monte Carlo (MC) simulation program. It was found that the focus position and the aperture angle highly affect the final quality of SEM imaging. The effective electron beam shape (EEBS) is hence suggested as the broadening function to overcome this issue for theoretical analysis, rather than the widely-used Gaussian profile. However, EEBS is hardly acquired due to it strongly depends on both the sample topography and the electron beam focusing condition, which make it is impossible to be applied in practical analysis. An approach is proposed to find a best-fit traditional Gaussian profile, which can optimally replace the EEBS in the case of the same sample structure and experimental condition for establishing a database of the parameter in traditional Gaussian profile. Experimenters will benefit from this database to obtain true line-scan profiles for accurate gate linewidth measurement. This investigated result could greatly improve the accuracy of linewidth measurement.

Exploring the accurate size measurement method for two typical nanostructures basing on SEM imaging

The accurate size measurement has been necessary in modern nanotechnology /semiconductor industry. Based on a sophisticated Monte Carlo scanning electron microscope simulation tool, gold nanorods and the silicon trapezoidal line, two commonly used nanostructures, were studied for aspect ratio and linewidth measurements, respectively. Accurate measurement for aspect ratio is significant for the optical property of gold nanorods. This work adopted an image-based method with a Monte Carlo simulation to obtain an accurate value of the aspect ratio. In the case of 10% division interval, it was found that if the distances at 40% and 50% of the height of the two peaks in a line-scan profile are respectively taken as the lengths of long axis and short axis of nanorod, the aspect ratio can be obtained with minimum error. Besides, a systematic calculation of bias for top-CD and bottom-CD was performed for a silicon trapezoidal line under various parameters. Calculation results show that the bias for bottom-CD is less than that for top-CD due to side wall angle. The bias increases with side wall angle and primary electron energy, but decreases with width of trapezoid top surface.

Monte Carlo Simulation on the CD-SEM Images of SiO2/Si Systems.

Silicon dioxide (SiO2) has been the most important insulator in the highly-developed field of silicon (Si) technology. Accurate pitch and gate linewidth measurements for SiO2/Si systems (systems with a SiO2 insulating layer and Si substrate) have become necessary. Studying one such system obviously presents different results from that of the widely researched Si/Si structure, because the edge profile of the secondary electron (SE) signal contains contributions from two materials. In this work, several scanning electron microscope (SEM) images and SE profiles of SiO2/Si pitch and trapezoidal line structures, using various geometric and experimental parameters, were simulated through the use of Monte Carlo (MC) methods. It was found that, in contrast to Si/Si systems, the height of the insulating layer cannot be ignored during the evaluation of pitch and linewidth. The thickness (i.e., height) factor does play an important role in the contrast of SEM imaging and the shape of the SE profile in these two-material systems. The mechanism of the influence of insulating layer thickness for imaging was studied in detail. In addition, the SiO2/Si pitch structure with a real rough surface was also studied. This work has significant implications for the study of various kinds of two-material systems and could help to optimize the pitch and gate linewidth measurements.

Research on Electron Emission from Dielectric Materials by a Monte Carlo Method

The charge accumulation in an insulating material under an electron beam bombardment exerts a significant influence to scanning electron microscopic imaging. This work investigates the charging formation process by a self-consistent Monte Carlo simulation of charge production and transportation based on a charge dynamics model. The charging effect in a semi-infinite SiO2 bulk and SiO2 trapezoidal lines on a SiO2 or Si substrate has been studied. We used two methods to calculate the spatial distributions of electric potential and electric field for two different systems respectively: the image charge method was used to deal with a semi-infinite bulk, and, random walk method to solve the Poisson equation for a complex geometric structure. The dynamic charging behavior depending on irradiation time has been investigated for SiO2. The simulated CD-SEM images of SiO2 trapezoidal lines with charging effect included were compared well with experimental results, showing the contrast change of SEM image along with scanning frames due to charging.

Monte Carlo Study on Electron Emission from Dielectric Materials

ABSTRACTThe charge accumulation in an insulating material under an electron beam bombardment exerts a significant influence on scanning electron microscopic imaging. This work investigates the charging formation process by a self-consistent Monte Carlo simulation of charge production and transportation based on a charge dynamics model. The charging effect in a semi-infinite SiO2 bulk and SiO2 trapezoidal lines on a SiO2 or Si substrate has been studied. We calculated the spatial distributions of electric potential and electric field for two different systems by two methods respectively: the image charge method was used to deal with a semi-infinite bulk, and random walk method to solve the Poisson equation for a complex geometric structure. The dynamic charging behavior depending on irradiation time has been investigated for SiO2. The simulated CD-SEM images of SiO2 trapezoidal lines with charging effect included showing the contrast change of SEM image along with scanning frames due to charging.

Quasicontinuum simulations of geometric effect on onset plasticity of nano-scale patterned lines

Onset plasticity of metallic nano-lines or nano-beams is of considerable scientific and technological interest in micro-/nano- mechanics and interconnects of patterned lines in electronic devices, where capability of resistance to deformation is important. In this study, a multiscale quasicontinuum (QC) method was used to explore such an issue in a nano-scale copper (Cu) line protruding from a relatively large single crystal Cu substrate during compression. The results show that the yield stress of a rectangular beam on the substrate can be greatly reduced compared with that of a flat surface of the same area. For the rectangular line, the aspect ratio (width/height) affects dislocation morphology at the onset plasticity without much change of yield stress. However, for the trapezoidal line, the yield stress decreases with the base angle (α), especially when the α is over 54.7°. As the sidewall orientation changes from 〈100〉 at α = 0°, then to 〈111〉 at α = 54.7° and finally to 〈110〉 at α = 90°, a higher surface energy could enable easier dislocation formation and lower yield stress. Meanwhile, it is found that the interaction between the line and the support substrate also shows a great effect on yield stress. Moreover, although it is possible to open two extra dislocation slip planes inside from the two bottom corners of the Cu line with the α over 54.7°, dislocation nucleation derived from them is only observed at α = 90°.

Monte Carlo Simulation of CD‐SEM Images for Linewidth and Critical Dimension Metrology

In semiconductor industry, strict critical dimension control by using a critical dimension scanning electron microscope (CD-SEM) is an extremely urgent task in near-term years. A Monte Carlo simulation model for study of CD-SEM image has been established, which is based on using Mott's cross section for electron elastic scattering and the full Penn dielectric function formalism for electron inelastic scattering and the associated secondary electron (SE) production. In this work, a systematic calculation of CD-SEM line-scan profiles and 2D images of trapezoidal Si lines has been performed by taking into account different experimental factors including electron beam condition (primary energy, probe size), line geometry (width, height, foot/corner rounding, sidewall angle, and roughness), material properties, and SE signal detection. The influences of these factors to the critical dimension metrology are investigated, leading to build a future comprehensive model-based library.

Research on cutoff wavelength of dominant mode and field patterns in trapezoidal microshield lines

The influence of the position of the metallic signal strip on the cutoff characteristic of the dominant mode and the field patterns in 3 types of trapezoidal microshield lines are calculated by the edge-based finite element method. These trapezoidal microshield lines include trapezoidal microshield lines with a single signal line, dual signal lines, and 3 signal lines. The cutoff wavelength of the dominant mode can be adjusted by changing the dimensions of metallic signal strips as well as by adjusting their positions. Field patterns of the dominant mode and the first-higher-order mode for different dimensions and the dielectric constant of the dielectric substrate are also illustrated. The numerical results in this article provide an extension of the existing design data of trapezoidal microshield lines and are useful in practical applications.

A novel closed-form resistance model for trapezoidal interconnects

A closed-form model for the frequency-dependent per-unit-length resistance of trapezoidal cross-sectional interconnects is presented. The frequency-dependent per-unit-length resistance R(f) of a trapezoidal interconnect line is first obtained by a numerical method. Using the method we quantify the trapezoid edge effect on the resistance of the interconnect and the current density distribution in the cross section. Based on this strict numerical result, a novel closed-form model R(f) for a single trapezoidal interconnect is fitted out using the Levenberg–Marquardt method. This R(f) can be widely used for analyzing on-chip interconnects when the frequency is changing. The model is computationally very efficient with respect to the numerical method, and the results are found to be accurate.

Adaptive‐network‐based fuzzy inference system models for computing the characteristic impedances of air‐suspended trapezoidal and rectangular‐shaped microshield lines

AbstractIn this article, adaptive‐network‐based fuzzy inference system (ANFIS) models are proposed to compute the characteristic impedances of air‐suspended trapezoidal‐shaped microshield lines (AS‐TSMLs) and air‐suspended rectangular‐shaped microshield lines (AS‐RSMLs). The ANFIS is a fuzzy inference system implemented within the architecture and optimization procedure of adaptive networks. Four optimization algorithms, hybrid learning, simulated annealing, genetic, and least‐squares, are used to determine optimally the design parameters of ANFIS. The characteristic impedance results of ANFIS models are in very good agreement with the results available in the literature. When the performances of ANFIS models are compared with each other, the best results are obtained from the ANFIS model trained by the hybrid learning algorithm. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 20–24, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24829

Artificial Neural Networks for Calculating the Characteristic Impedance of Air-Suspended Trapezoidal and Rectangular-Shaped Microshield Lines

Neural models for calculating the characteristic impedance of air-suspended trapezoidal and rectangular-shaped microshield lines, based on the multilayered perceptrons (MLPs), are presented. Six learning algorithms, bayesian regulation (BR), Levenberg-Marquardt (LM), quasi-Newton (QN), scaled conjugate gradient (SCG), resilient propagation (RP), and conjugate gradient of Fletcher-Powell (CGF), are used to train the MLPs. The characteristic impedance results obtained by using neural models are in very good agreement with the results available in the literature. When the performances of neural models are compared with each other, the best test result is obtained from the MLPs trained by the BR algorithm.

Unilateral Visual Cueing and Asymmetric Line Geometry Share a Common Attentional Origin in the Modulation of Pseudoneglect

Numerous factors influence the leftward bias (pseudoneglect) in perceived line midpoint of normal subjects in line bisection tasks. Cues are a potent factor; left and right cues promote shifts in perceived midpoint to the left and right, respectively. Trapezoidal lines have recently been shown to influence perceived line midpoint, displacing it toward the larger side. The present experiments test the hypothesis that the effect of line geometry, like that of unilateral cues, results from an exogenous recruitment of spatial attention. Normal right-handed subjects (N = 60) participated in two experiments employing a tachistoscopic forced-choice line bisection task. Experiment 1 crossed the effect of cue position and cue contrast, and confirmed that a significant interaction could be obtained. Experiment 2 crossed the effect of line geometry and cue position, revealing that line geometry and cue location both significantly influence perceived line midpoint, and produce a significant interaction. According to Additive Factors Logic the finding that spatial cueing interacts with line geometry suggests that both types of stimuli modulate spatial attention at a common site of processing, supporting the conclusion that the effect of line geometry itself derives from asymmetric cueing. An explanation for the interaction is offered that is based on the existence of a hypothesized compressive nonlinearity that maps attentional bias to perceptual error.

Stimulus modulation of pseudoneglect: influence of line geometry

A variety of stimulus factors have recently been shown to influence the performance of normal subjects on line bisection tasks (i.e., pseudoneglect), independent of motoric factors such as scanning or hand use [ McCourt & Jewell (1999) Neuropsychologia 35, 843–55]. An experiment is described which further examined the modulating influence of line geometry in determining the magnitude of pseudoneglect. Subjects bisected horizontally oriented trapezoidal lines presented in central vision whose narrow end pointed either left or right. A highly significant influence of line geometry was found which modulated a tonic leftward error (i.e., pseudoneglect). The results are interpreted in the context of a “center-of-mass” effect [ Shuren, Jacobs & Heilman (1997) Brain and Cognition, 34, 293–300]. Further studies designed to tease apart the potentially independent effects of perceptual and attentional asymmetry on bisection performance are suggested.

Boundary element analysis of a trapezoidal transmission line

A full-wave analysis is a transmission line with a trapezoidal cross-section is described. The boundary element method (BEM) is used, and by making a convenient choice for the dyadic Green's function, it is shown to be very efficient in comparison to alternative methods of analysis. It is shown that for electrically small dimensions, spurious solutions are suppressed by the selection of integral equations. The analysis is verified by comparisons to calculated results from a vector finite element computer program, and some dispersion data are presented. >