Closed-form formula for frequency dependent bonding pad characterization

It is well known that on-die bonding pad capacitance and conductance is quite frequency-dependent due to the existence of lossy substrate. This paper describes a very simple yet accurate method to determine them. The pad capacitance is divided into two parts, the parallel plate capacitance and the fringing capacitance. By taking the bonding pad as a transmission line four times, we can determine the fringing capacitances along the four edges. Closed-form formulas for all the capacitances are available. The conductance can then be determined from the capacitance. The results show good agreement with the full wave simulation results, which justifies the validity of our modeling.