Proceedings of the 40th annual Design Automation Conference
Proceedings of the 42nd annual Design Automation Conference
A fast hierarchical algorithm for three-dimensional capacitance extraction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Sparse transformations and preconditioners for 3-D capacitance extraction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A parallel and incremental extraction of variational capacitance with stochastic geometric moments
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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In this paper, we present the first BEM impedance extraction algorithm for multiple dielectrics. The effect of multiple dielectrics is significant and efficient modeling is challenging. However, previous BEM algorithms, including FastImp and FastPep, assume uniform dielectric, thus causing considerable errors. The new algorithm introduces a circuit formulation which makes it possible to utilizes either multilayer Green's function or equivalent charge method to extract impedance in multiple dielectrics. The novelty of the formulation is the reduction of the number of unknowns and the application of the hierarchical data structure. The hierarchical data structure permits efficient sparsification transformation and preconditioners to accelerate the linear equation solver. Experimental results demonstrate that the new algorithm is accurate and efficient. For uniform dielectric problems, the new algorithm is one magnitude faster than FastImp, while its results differ from FastImp within 2%. For multiple dielectrics problems, its relative error with respect to HFSS is below 3%.