Layout Decomposition for Quadruple Patterning Lithography and Beyond

For next-generation technology nodes, multiple patterning lithography (MPL) has emerged as a key solution, e.g., triple patterning lithography (TPL) for 14/11nm, and quadruple patterning lithography (QPL) for sub-10nm. In this paper, we propose a generic and robust layout decomposition framework for QPL, which can be further extended to handle any general K-patterning lithography (K$>$4). Our framework is based on the semidefinite programming (SDP) formulation with novel coloring encoding. Meanwhile, we propose fast yet effective coloring assignment and achieve significant speedup. To our best knowledge, this is the first work on the general multiple patterning lithography layout decomposition.Comment: DAC'201

L-Shape based Layout Fracturing for E-Beam Lithography

Layout fracturing is a fundamental step in mask data preparation and e-beam lithography (EBL) writing. To increase EBL throughput, recently a new L-shape writing strategy is proposed, which calls for new L-shape fracturing, versus the conventional rectangular fracturing. Meanwhile, during layout fracturing, one must minimize very small/narrow features, also called slivers, due to manufacturability concern. This paper addresses this new research problem of how to perform L-shaped fracturing with sliver minimization. We propose two novel algorithms. The first one, rectangular merging (RM), starts from a set of rectangular fractures and merges them optimally to form L-shape fracturing. The second algorithm, direct L-shape fracturing (DLF), directly and effectively fractures the input layouts into L-shapes with sliver minimization. The experimental results show that our algorithms are very effective

The SIS epidemic model with Markovian switching

Population systems are often subject to environmental noise. Motivated by Takeuchi et al. (2006), we will discuss in this paper the effect of telegraph noise on the well-known SIS epidemic model. We establish the explicit solution of the stochastic SIS epidemic model, which is useful in performing computer simulations. We also establish the conditions for extinction and persistence for the stochastic SIS epidemic model and compare these with the corresponding conditions for the deterministic SIS epidemic model. We first prove these results for a two-state Markov chain and then generalise them to a finite state space Markov chain. Computer simulations based on the explicit solution and the Euler--Maruyama scheme are performed to illustrate our theory. We include a more realistic example using appropriate parameter values for the spread of Streptococcus pneumoniae in children

Parameter estimation for the stochastic SIS epidemic model

In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo-maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and 100(1 − α)% confidence intervals as well as 100(1 − α)% joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic 100(1 − α)% joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory