Ranking Routes In Semiconductor Wafer Fabs

We develop a method to estimate the quality of processing routes in a wafer fabrication process. Ranking such routes can be useful for identifying the “best” and “worst” routes when making adjustments to recipes. Route categorization is also useful in developing efficient scheduling algorithms. In particular, we propose a method for ranking routes based on count-based metrics such as the number of defects on a wafer. We start with a statistical model to produce a “local” ranking of a tool and then build a “global” ranking via a heuristic procedure. Creating a fully statistical procedure for ranking routes in semiconductor fabrication plants is virtually impossible, given the number of possible routes and the limited data available. Nonetheless, our discussions with working engineers indicate that even approximate rankings are useful for making better operational decisions.

Rigorous numerics for ODEs using Chebyshev series and domain decomposition

<p style='text-indent:20px;'>In this paper we present a rigorous numerical method for validating analytic solutions of nonlinear ODEs by using Chebyshev-series and domain decomposition. The idea is to define a Newton-like operator, whose fixed points correspond to solutions of the ODE, on the space of geometrically decaying Chebyshev coefficients, and to use the so-called radii-polynomial approach to prove that the operator has an isolated fixed point in a small neighborhood of a numerical approximation. The novelty of the proposed method is the use of Chebyshev series in combination with domain decomposition. In particular, a heuristic procedure based on the theory of Chebyshev approximations for analytic functions is presented to construct efficient grids for validating solutions of boundary value problems. The effectiveness of the proposed method is demonstrated by validating long periodic and connecting orbits in the Lorenz system for which validation without domain decomposition is not feasible.</p>

On the Heuristic Procedure to Determine Processing Parameters in Additive Manufacturing Based on Materials Extrusion

We present a heuristic procedure for determining key processing parameters (PPs) in materials-extrusion-based additive manufacturing processes. The concept relies on a design-of-experiment approach and consists of eleven “test objects” to determine the optimal combinations of key PPs values, starting with the PPs for printing the first layer and progressing to more complex geometric features, e.g., “bridges”. In each of the test objects, several combinations of the known PPs’ values are used, and only the values resulting in the best printed-part quality are selected for the following tests. The concept is intrinsically insensitive to different artefacts of the additive manufacturing machine (e.g., discrepancies between the nominal and actual nozzle diameters, and improper calibration of the feeding screws) and the optimal values of key PPs for manufacturing defect-free parts under the actual processing conditions can be determined. We validated the proposed procedure for two common commercial polymer feedstock materials, and we show that, by using the proposed procedure, it is possible to reduce the optimization time down to several hours, as well as to reduce the amount of consumed feedstock material. Tensile tests revealed a strong effect of amorphous and semi-crystalline nature of the polymer on the results of optimization. To the best of our knowledge, this is the first attempt to describe a systematic approach for optimizing PPs for materials extrusion-based additive manufacturing processes without relying on statistical data analysis or virtual simulations. The concept was implemented as a web-tool 3DOptimizer®.

Comparison of Home Advantage in European Football Leagues

Home advantage in sports is important for coaches, players, fans, and commentators and has a key role in sports prediction models. This paper builds on results of recent research that—instead of points gained—used goals scored and goals conceded to describe home advantage. This offers more detailed look at this phenomenon. Presented description understands a home advantage in leagues as a random variable that can be described by a trinomial distribution. The paper uses this description to offer new ways of home advantage comparison—based on the Jeffrey divergence and the test for homogeneity—in different leagues. Next, a heuristic procedure—based on distances between probability descriptions of home advantage in leagues—is developed for identification of leagues with similar home advantage. Publicly available data are used for demonstration of presented procedures in 19 European football leagues between the 2007/2008 and 2016/2017 seasons, and for individual teams of one league in one season. Overall, the highest home advantage rate was identified in the highest Greek football league, and the lowest was identified in the fourth level English football league.