Algebraic multigrid Laplace solver for the extraction of capacitances of conductors in multi-layer dielectrics

This paper describes the development of a robust multigrid, finite element-based, Laplace solver for accurate capacitance extraction of conductors embedded in multi-layer dielectric domains. An algebraic multigrid based on element interpolation is adopted and streamlined for the development of the proposed solver. In particular, a new, node-based agglomeration scheme is proposed to speed up the process of agglomeration. Several attributes of this new method are investigated through the application of the Laplace solver to the calculation of the per-unit-length capacitance of configurations of parallel, uniform conductors embedded in multi-layer dielectric substrates. These two-dimensional configurations are commonly encountered as high-speed interconnect structures for integrated electronic circuits. The proposed method is shown to be particularly robust and accurate for structures with very thin dielectric layers characterized by large variation in their electric permittivities. More specifically, it is demonstrated that for such geometries the proposed node-based agglomeration systematically reduces the problem size and speeds up the iterative solution of the finite element matrix.