A Linear-Time Complex-Valued Eigenvalue Solver for Large-Scale FullWave Extraction of On-Chip Interconnect Structures
Jongwon Lee*, Venkataramannan Balakrishnan, Cheng-Kok Koh, and Dan Jiao School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA
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Abstract: This paper proposes a linear-time complex-valued eigenvalue solver for large-scale on-chip interconnect structure problems. The fast eigenvalue solution is achieved by eigenvalue clustering, system reduction with negligible cost, and fast linear-time solution of the reduced system. The accuracy and efficiency of the proposed method are demonstrated by numerical and experimental results. Keywords: Eigenvalue solver, on-chip interconnects, full-wave analysis, frequency domain.
1. Introduction With continued breakthrough in processing technology, interconnect design has become one of the biggest challenges in the design of today’s and next generation integrated circuits. In particular, fullwave-based analysis can be used to characterize global electromagnetic coupling through the common substrate and power delivery network. However, on-chip interconnect structures present many modeling challenges to electromagnetic analysis [1]. In recent years, both partial differential equation (PDE) based solutions and integral equation (IE) based solutions have been developed to address these challenges. Among these techniques, the frequency-domain eigenvalue-based method in [2] is particularly geared towards full-wave modeling of large-scale on-chip interconnect structures. The original wave propagation problem of large-scale on-chip interconnect structures involves a very large number of unknowns, N, in a 3D computational domain. Formulated as a generalized eigenvalue problem, the technique in [2] partially addressed the complexity issue by seeking the solutions of only a few 2D interconnect structures, each involving only M (
