• IE interfaces
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• v.16 no.3
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• pp.344-351
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• 2003

Critical dimension is one of the most important characteristics of up-to-date integrated circuit devices. Hence, critical dimension control in a semiconductor wafer fabrication process is inevitable in order to achieve optimum device yield as well as electrically specified functions. Currently, in complex semiconductor wafer fabrication processes, statistical methodologies such as Shewhart-type control charts become crucial tools for practitioners. Meanwhile, given a critical dimension sampling plan, the analysis of variance technique can be more effective to investigating critical dimension variation, especially for on-chip and on-wafer variation. In this paper, relating to a typical sampling plan, linear statistical models are presented for the analysis of critical dimension variation. A case study is illustrated regarding a semiconductor wafer fabrication process.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.2
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• pp.179-189
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• 2003

Gate poly-silicon critical dimension is a prime characteristic of a metal-oxide-semiconductor field effect transistor. It is important to achieve the uniformity of gate poly-silicon critical dimension in order that a semiconductor device has acceptable electrical test characteristics as well as a semiconductor wafer fabrication process has a competitive net-die-per-wafer yield. However, on gate poly-silicon critical dimension, the complexity associated with a semiconductor wafer fabrication process entails hierarchical variance components according to run-to-run, wafer-to-wafer and even die-to-die production unit changes. Specifically, estimates of the hierarchical variance components are required not only for disclosing dominant sources of the variation but also for testing the wafer-level uniformity. In this paper, two experimental designs, a two-stage nested design and a randomized complete block design are considered in order to estimate the hierarchical variance components. Since gate poly-silicon critical dimensions are collected from fixed die positions within wafers, a factor representing die positions can be regarded as fixed in linear statistical models for the designs. In this context, the two-stage nested design also checks the wafer-level uniformity taking all sampled runs into account. In more detail, using variance estimates derived from randomized complete block designs, Duncan's multiple range test examines the wafer-level uniformity for each run. Consequently, a framework presented in this study could provide guidelines to practitioners on estimating the hierarchical variance components and testing the wafer-level uniformity in parallel for any characteristics concerned in semiconductor wafer fabrication processes. Statistical analysis is illustrated for an experimental dataset from a real pilot semiconductor wafer fabrication process.

• Korean Journal of Optics and Photonics
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• v.15 no.1
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• pp.79-85
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• 2004

We report on a transmittance controlled photomask with phase patterns on the back quartz surface. Theoretical analysis for changes in illumination pupil shape with respect to the variation of size and density of backside phase patterns and experimental results for improvement of critical dimension uniformity on a wafer by using the transmittance controlled photomask are presented. As phase patterns for controlling transmittance of the photomask we used etched contact-hole type patterns with 180" rotative phase with respect to the unetched region. It is shown that pattern size on the backside of the photomask must be made as small as possible in order to keep the illumination pupil shape as close as possible to the original pupil shape and to achieve as large an illumination intensity drop as possible at a same pattern density. The distribution of illumination intensity drop suitable for correcting critical dimension error was realized by controlling pattern density of the contact-hole type phase patterns. We applied this transmittance controlled photomask to a critical layer of DRAM (Dynamic Random Access Memory) having a 140nm design rule and could achieve improvement of the critical dimension uniformity value from 24.0 nm to 10.7 nm in 3$\sigma$.TEX>.

• Current Optics and Photonics
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• v.2 no.1
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• pp.69-78
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• 2018

This paper presents a precise edge detection algorithm for the critical dimension (CD) measurement of a Thin-Film Transistor Liquid-Crystal Display (TFT-LCD) pattern. The sigmoid surface function is proposed to model the blurred step edge. This model can simultaneously find the position and geometry of the edge precisely. The nonlinear least squares fitting method (Levenberg-Marquardt method) is used to model the image intensity distribution into the proposed sigmoid blurred edge model. The suggested algorithm is verified by comparing the CD measurement repeatability from high-magnified blurry and noisy TFT-LCD images with those from the previous Laplacian of Gaussian (LoG) based sub-pixel edge detection algorithm and error function fitting method. The proposed fitting-based edge detection algorithm produces more precise results than the previous method. The suggested algorithm can be applied to in-line precision CD measurement for high-resolution display devices.

• Journal of the Optical Society of Korea
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• v.17 no.5
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• pp.392-398
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• 2013

As the essential techniques for the CD (Critical Dimension) measurement of the LCD pattern, there are various modules such as an optics design, auto-focus [1-4], and precise edge detection. Since the operation of image enhancement to improve the CD measurement repeatability, a ring type of the reflected lighting optics is devised. It has a simpler structure than the transmission light optics, but it delivers the same output. The edge detection is the most essential function of the CD measurements. The CD measurement is a vital inspection for LCDs [5-6] and semiconductors [7-8] to improve the production yield rate, there are numbers of techniques to measure the CD. So in this study, a new subpixel algorithm is developed through facet modeling, which complements the previous sub-pixel edge detection algorithm. Currently this CD measurement system is being used in LCD manufacturing systems for repeatability of less than 30 nm.

• Proceedings of the Korean Vacuum Society Conference
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• 2016.02a
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• pp.213-213
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• 2016

현재 반도체 산업에서는 디바이스의 고 집적화, 고 수율을 목적으로 패턴의 미세화 및 웨이퍼의 대면적화와 같은 이슈가 크게 부각되고 있다. 다중 패터닝(multiple patterning) 기술을 통하여 고 집적 패턴을 구현이 가능해졌으며, 이와 같은 상황에서 각 패턴의 임계치수(critical dimension) 변화는 패턴의 위치 및 품질에 큰 영향을 끼치기 때문에 포토마스크의 임계치수 균일도(critical dimension uniformity, CDU)가 제작 공정에서 주요 파라미터로 인식되고 있다. 반도체 광 리소그래피 공정에서 크롬(Cr) 박막은 사용되는 포토 마스크의 재료로 널리 사용되고 있으며, 이러한 포토마스크는 fused silica, chrome, PR의 박막 층으로 이루어져 있다. 포토마스크의 패턴은 플라즈마 식각 장비를 이용하여 형성하게 되므로, 식각 공정의 플라즈마 균일도를 계측하고 관리 하는 것은 공정 결과물 관리에 필수적이며 전체 반도체 공정 수율에도 큰 영향을 미친다. 흔히, 포토마스크 임계치수는 플라즈마 공정에서의 라디칼 농도 및 식각 선택비에 의해 크게 영향을 받는 것으로 알려져 왔다. 본 연구에서는 Cr 포토마스크 에칭 공정에서의 Cl2/O2 공정 플라즈마에 대해 O2 가스 주입량에 따른 식각 선택비(etch selectivity) 변화를 계측하여 선택비 제어를 통한 Cr 포토마스크 임계치수 균일도 향상을 실험적으로 입증하였다. 연구에서 사용한 플라즈마 계측 방법인 발광분광법(OES)과 optical actinometry의 적합성을 확인하기 위해서 Cl2 가스 주입량에 따른 actinometer 기체(Ar)에 대한 atomic Cl 농도비를 계측하였고, actinometry 이론에 근거하여 linear regression error 1.9%을 보였다. 다음으로, O2 가스 주입비에 따른 Cr 및 PR의 식각률(etch rate)을 계측함으로써 식각 선택비(etch selectivity)의 변화율이 적은 O2 가스 농도 범위(8-14%)를 확인하였고, 이 구간에서 임계치수 균일도가 가장 좋을 것으로 예상할 수 있었다. (그림 1) 또한, spatially resolvable optical emission spectrometer(SROES)를 사용하여 플라즈마 챔버 내부의 O atom 및 Cl radical의 공간 농도 분포를 확인하였다. 포토마스크의 임계치수 균일도(CDU)는 챔버 내부의 식각 선택비의 변화율에 강하게 영향을 받을 것으로 예상하였고, 이를 입증하기 위해 각각 다른 O2 농도 환경에서 포토마스크 임계치수 값을 확인하였다. (표1) O2 11%에서 측정된 임계치수 균일도는 1.3nm, 그 외의 O2 가스 주입량에 대해서는 임계치수 균일도 ~1.7nm의 범위를 보이며, 이는 25% 임계치수 균일도 향상을 의미함을 보인다.

• ETRI Journal
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• v.27 no.2
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• pp.188-194
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• 2005

We report on the improvement of critical dimension (CD) linearity on a photomask by applying the concept of process proximity correction to a laser lithographic process used for the fabrication of photomasks. Rule-based laser process proximity correction (LPC) was performed using an automated optical proximity correction tool and we obtained dramatic improvement of CD linearity on a photomask. A study on model-based LPC was executed using a two-Gaussian kernel function and we extracted model parameters for the laser lithographic process by fitting the model-predicted CD linearity data with measured ones. Model-predicted bias values of isolated space (I/S), arrayed contact (A/C) and isolated contact (I/C) were in good agreement with those obtained by the nonlinear curve-fitting method used for the rule-based LPC.

• Journal of the Korean Chemical Society
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• v.40 no.6
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• pp.401-408
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• 1996

In general, the high temperature superconductors have two-dimensional anisotropic structures. It is important to investigate the dependence of the critical temperature on the dimensions of the electron's motion. The equation of state for electron gas is deduced which describes the electron's motion in superconductors using the kinetic theory of gas. And the critical temperatures of three, two, and one dimensional gases were calculated. According to these equations, restricting the dimension of the electron's motion induces the increase of the critical temperatures. This implies the possibility that the multi-critical temperature of some superconductors is caused by the change of the dimension related to the pathways of the electron.

• The Journal of Korean Academy of Prosthodontics
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• v.60 no.4
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• pp.301-312
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• 2022

In an extensive oral rehabilitation, determining a proper occlusal vertical dimension is a critical step and the starting point for successful treatment. Since changing the occlusal vertical dimension could be time-consuming, financially challenging, and physically demanding for both clinicians and patients, multi-faceted analysis and careful consideration are essential in the diagnosis and further treatment process. The purpose of this narrative review is to discuss the occlusal vertical dimension and its current issues, and to summarize previous methods of evaluating occlusal vertical dimension to propose clinical guidance for determining a viable occlusal vertical dimension for full-mouth rehabilitation.

• Journal of Ocean Engineering and Technology
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• v.10 no.4
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• pp.84-91
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• 1996

A fractal analysis on fracture surface of aluminium-particulate SiC composites was attempted. As the volume fraction of SiC in composites increases, the fractal dimension tends to increase. However, no correlation between the fractal dimension and the fracture toughness in terms of critical energy release rate was observed. Since the fractal dimension represents the roughness of fracture surface, the fracture toughness would be a function of not only fracture surface roughness but also additional parameters. Thus the applicability of fractal analysis to the estimation of fracture toughness must depend on the proper choice and interpretation of additioal paramerters. In this paper, the size of characteristic strctural unit for fracture was considered as an additional parameter. As a result, the size appeared to be a function of only volume fraction of SiC. Finally, a master curve for fracture toughness of aluminium-particulate SiC composites was proposed as a function of fractal dimension and volume fraction of SiC.