Understanding and closed-form-formula determination of frequency-dependent bonding-pad characterization

A newly developed method is introduced in this paper to efficiently model frequency-dependent on-die pad capacitance and conductance, which can be easily integrated in computer-aided-design tools. An equivalent lumped circuit is used to model the pad parasitic effect. Three critical frequencies are defined to characterize the pad-frequency characteristics based on this model. A relationship between normalized pad capacitance and normalized frequency is then established to guide practical pad designs. Three different methods are compared to determine the parameters in the equivalent lumped circuit. Our newly developed quasi-static method gives the best agreement with full-wave simulation. In this method, each capacitance in the model is divided into the parallel-plate part and the fringing part. The pad is innovatively treated as transmission lines several times, and a closed-form formula is used to extract the per-unit-length (p.u.l.) capacitance for these transmission lines. The fringing capacitances are then calculated from these p.u.l. capacitances. The substrate conductance can be determined from the substrate capacitance. Simulation results based on our model show good agreement with full-wave simulation results, which justify the validity of our modeling. Such a method with fast computation and good accuracy is very helpful in the early integrated circuit design stage