Novel Proximal Group ADMM for Placement Considering Fogging and Proximity Effects

Abstract

Fogging and proximity effects (FPEs) are two major factors that cause inaccurate exposure and layout pattern distortions in e-beam lithography. In this article, we propose an analytical placement algorithm that considers both FPEs. We 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 (associated with wirelength and density) is solved by the steepest descent method without line search, and the second one (associated with the FPEs) is handled by an analytical scheme. We prove the property of global convergence of the proximal group ADMM method. Finally, the FPEs-aware legalization and detailed placement are employed to legalize and improve the placement result. The experimental results show that our algorithm is effective and efficient for the addressed problem. Our algorithm achieved 5.7% smaller fogging variation, 6.8% lower proximity variation, and 5.4% lower runtime with a minor wirelength overhead compared with the state-of-the-art work.