Novel Proximal Group ADMM for Placement Considering Fogging and Proximity Effects

Fogging and proximity effects are two major factors that cause inaccurate exposure and thus layout pattern distortions in e-beam lithography. In this paper, we propose the first analytical placement algorithm to consider both the fogging and proximity effects. We first formulate the global placement problem as a separable minimization problem with linear constraints, where different objectives can be tackled one by one in an alternating fashion. Then, we propose a novel proximal group alternating direction method of multipliers (ADMM) to solve the separable minimization problem with two subproblems, where the first subproblem (mainly associated with wirelength and density) is solved by a steepest descent method without line-search, and the second one (mainly associated with the fogging and proximity effects) is handled by an analytical scheme. We prove the property of global convergence of the proximal group ADMM method. Finally, legalization and detailed placement are used to legal and further improve the placement result. Experimental results show that our algorithm is effective and efficient for the addressed problem. Compared with the state-of-the-art work, our algorithm not only can achieve 13.4% smaller fogging variation and 21.4% lower proximity variation, but also has a 1.65× speedup.