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Metrology for Nanolithography
Published in Bruce W. Smith, Kazuaki Suzuki, Microlithography, 2020
Critical dimension and profile information are critical parameters that need to be measured accurately for use in semiconductor manufacturing process control. As device geometry shrinks, traditional metrology methods such as CD-SEM are fast reaching their limits in providing accurate and repeatable CD measurements. While charging due to the electron beam is a major concern for CD-SEMs, profile measurement normally uses destructive methods such as cross-section SEM or TEM, or the very slow atomic force microscopy (AFM). Additionally, these off-line approaches limit the cycle time to results and sampling rate, thereby leading to high wafer cost. As technology nodes move from 90 nm to 65 nm and beyond, lithography process windows continue to shrink, especially so for contact holes for which the process windows are already smaller than those for line-and-space structures of comparable size. This problem is made even more serious by 300 mm wafer production due to the higher wafer cost, increased sampling rate requirements, and the need for integrated metrology on process tools to provide on-tool process control. Scatterometry provides a solution that addresses these issues to meet the challenges of the 90 nm node and beyond.
In-Line Metrology
Published in Robert Doering, Yoshio Nishi, Handbook of Semiconductor Manufacturing Technology, 2017
Critical dimension measurement is done by averaging over a large number of line scans across a length of line deemed representative. (The SEM image is composed of many line scans with the vertical (or horizontal) position of each scan moved by a known increment.) This averages out some of the edge roughness effects and sample variation. At the time of writing this chapter, many different methods of determining edge position exist, and each supplier can chose a method that optimizes the precision of their own instrument. Some of the algorithms are shown in Figure 24.6. It has been shown that the linewidth can vary by 100 nm according to the algorithm selected [12]. Clearly, CD-SEM measurements must be calibrated by a method that is more independent of sample shape and line materials.
SU-8 Photolithography and Its Impact on Microfluidics
Published in Sushanta K. Mitra, Suman Chakraborty, Fabrication, Implementation, and Applications, 2016
Rodrigo Martinez-Duarte, Marc J. Madou
The absolute minimum feature size in a miniature device, whether it involves a channel width, spacing between features, or contact dimension, is called the critical dimension. A critical dimension defines the overall resolution of a process, that is, the consistent ability to print a minimum size image, under conditions of reasonable manufacturing variation (Wolf and Tauber, 2000). Many aspects of the process, including hardware, photoresist, and processing considerations, can limit the resolution of photolithography. Hardware limitations that include diffraction and reflection of light (or scattering of charged particles in the case of charged-particle lithography or hard x-rays), lens aberrations, and mechanical stability of the system (vibrations) must all be minimized. The resist material properties that impact resolution include sensitivity, contrast, and energy absorption at different wavelengths.
Water governance and system coordination across diverse risk-management cultures
Published in Water International, 2022
Brendan Bromwich, Damian Crilly, Jyoti Banerjee
Scale is a critical dimension of the challenge. Business and water resource systems operate at scales larger than the catchment, although the catchment is the key system boundary for flooding and water quality. In France, for example, an ability to combine the regional and catchment perspectives is achieved by water parliaments for each of the six main river basins. They provide a coordinating body at basin level that reflects government, agricultural, municipal and business concerns. Beneath this structure, there is a patchwork of public and private arrangements. A regional perspective – informed by local nuance – will also help integrate other planning frameworks such as transport, energy, food and health. By seeking synergies across these wider systems, the opportunity for creating transformative change is increased.
Concentration phenomenon in the critical exponent problems on hyperbolic space
Published in Applicable Analysis, 2021
The same problem (1) was extended in 2002 by Stapelkamp[10] to domains in the hyperbolic space and obtained very similar results. Later in 2008, Mancini and Sandeep [11] studied the following PDE on n-dimensional hyperbolic space where they completely answer the question of existence and nonexistence of positive entire solutions relative to , and . Moreover, they showed that has at most one entire positive solution(uniqueness), up to hyperbolic isometries when The existence and nonexistence of sign changing solutions to has been proved in [12]. Also refer to [13] in this context. The non-degeneracy properties of positive finite energy solutions to has been studied in [14]. In the case of critical dimension n = 2, the critical exponent problem has been studied by Ganguly and Karmakar in [15] where they established the existence of solution to in Poincaré ball model of hyperbolic space while establishing the Palais-Smale condition for the associated energy functional. They also established the existence of infinitely many signs changing solutions to the problem in the same article.
Discussion of article by Zwetsloot and Woodall: A review of some sampling and aggregation strategies for basic statistical process monitoring
Published in Journal of Quality Technology, 2021
This is a critical dimension in SPM. For example, consider the analysis of a large structured data set or video recordings for online process control. Dimension reduction with principal components analysis (PCA) is usually implemented instead of univariate or bivariate analysis because of performance. Faster, less precise results are considered better. Reis and Delgado (2012) provide such an example where over 15,000 variables are measured with visual technology to monitor the soldering of complex printed circuit boards. In another application domain, Ben Gal et al. (2014) apply a dual information distance (DID) to optimize accuracy and responsiveness of decision trees used in recommender systems. Like in the soldering process-monitoring application, the recommendation you get from Amazon has to be timely so that it is relevant when the decision can be made. Very accurate results, with delays, are generating information of low quality. These considerations are implicitly addressed in the ZW review.