# title
A Preconditioned Hierarchical Algorithm for Impedance Extraction of Three-Dimensional Structures With Multiple Dielectrics

# abstract
This paper presents the first boundary element method (BEM) impedance extraction algorithm for interconnects with multiple dielectrics. Multiple dielectrics are common in integrated circuits and packages. However, previous BEM algorithms, including FastImp and FastPep, assume uniform dielectric due to their limitation, thus causing considerable errors. Our algorithm introduces a circuit formulation which makes it possible to utilize 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 unknowns and the application of 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, our algorithm is more accurate than FastImp while its number of unknowns is ten times less than that of FastImp. For multiple dielectric problems, its relative error with respect to HFSS is below 3%.  2008, IEEE. All rights reserved.

# publicationVenue.label
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

# publicationOutlet
IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS

# publisher.label
Institute of Electrical and Electronics Engineers (IEEE)

# keywords[]
Partial Element Equivalent Circuit (peec) Modeling