A well-conditioned integral-equation formulation for transient analysis of low-frequency microelectronic devices

A hierarchically-regularized coupled set of time-domain surface and volume electric field integral-equations (TD-SEFIE and TD-VEFIE) for analyzing low-frequency electromagnetic phenomena in microelectronic devices comprising conducting surfaces and (finite) dielectric volumes, is presented. The TD-SEFIE and TD-VEFIE, which enforce fundamental boundary and field consistency conditions on conducting surfaces and dielectric volumes, are solved by marching-on-in-time (MOT) [1]. Hierarchical regularization [2–3] is applied to the TD-SEFIE to render it immune to low-frequency breakdown; no regularization is applied to the TD-VEFIE as it is protected from low-frequency breakdown by an identity term [1]. At low-frequencies (i.e., when the time-step size is large), the MOT matrices constructed using hierarchical bases are far better-conditioned than those constructed using standard RWG [4] and loop-star bases [5]; hence the iterative solution of hierarchically-regularized MOT systems is considerably faster than that of its unregularized counterpart. The proposed technique is used to analyze low-frequency electromagnetic transients on realistically modeled computer boards.