Decoupling capacitor placement in power delivery networks using MFEM

The impedance of the power distribution network (PDN) needs to be minimized in order to prevent unwanted voltage fluctuations at frequencies where current transients occur. To reduce PDN impedance, one can place decoupling capacitors that act as local current sources. However, selecting and placing the right capacitors at the right locations are problematic because of the complexity of modern package and board structures. In addition, decoupling capacitors are not effective at higher frequencies, requiring more complicated techniques such as embedded decoupling. This paper introduces a method of reducing the effort expended by the complex task of decoupling capacitor placement: a genetic algorithm that is customized for the selection and placement of decoupling capacitors. The core engine of this optimizing algorithm is a recently developed technique, the multilayer finite element method (MFEM), which solves for PDN impedances. This paper also highlights a method of incorporating vertical circuit elements into MFEM. Using several test cases, it proves the validity of the inclusion of vertical elements in MFEM and the effectiveness of the optimizer.