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Dummy filling is widely applied to significantly improve the planarity of topographic patterns for the chemical mechanical polishing process in VLSI manufactures. The main challenge of dummy filling is balancing multiple objectives, such as fill amounts, planarity, parasitic capacitance, etc. An obvious drawback of traditional rule-based dummy filling methods is pattern densities, instead of post-chemical mechanical polishing (CMP) topographies, being included in optimization objectives. Although the quality of post-CMP topography strongly depends on pattern features of layouts, especially the density uniformity, however, experimental results show that chip surface variations are not exactly the same as density variations. In this article, a unified dummy fill insertion optimization framework is proposed, integrated with the multiple starting points-sequential quadratic programming (MSP-SQP) optimization solver, where all objectives are considered without approximation. Inside this framework, a full-chip CMP simulator is first integrated to evaluate the planarity of the chip surface. By selecting the initial points smartly with heuristic prior knowledge, the proposed method can be effectively accelerated. The effectiveness of the proposed algorithm is verified with the average 25.8% improvement of quality compared with rule-based methods.

This paper describes several interpolation methods for predicting the number of cases of the COVID-19 pandemic. The interpolation methods include some well-known temporal interpolation algorithms including Lagrange interpolation, cubic spline interpolation, and exponential decay interpolation. These temporal interpolation algorithms enable the interpolation of the COVID-19 cases at locations where measures on prior days are available. However, pandemics are not purely temporal but spatio-temporal phenomena. Therefore, the neighboring locations need to be considered too in order to derive accurate interpolation values for future days. This paper introduces a novel spatio-temporal interpolation algorithm that is shown to be better than any purely temporal interpolation algorithm in predicting the COVID-19 cases in the continental United States. In particular, the novel spatio-temporal interpolation method achieves a mean absolute error of 8.44 cases over a million people when predicting two days ahead the number of cases of the COVID-19 pandemic.