Capacitance Calculation for Offset Via Structures Using an Integral Approximation Approach Based on Finite Element Method Open Access

A simple yet efficient approach is presented to extract the via-plane capacitances for an offset via structure. According to the integral approximation approach, the geometry of offset via is first divided into several segments with equally distributed angles from the origin. The two-dimensional FEM method for the concentric case is used for each segment based on its pad-stack parameters. Then, the final offset via-plane capacitance is approximated as the average of these ‘segmental’ capacitance values. Numerical examples demonstrated that the combined method has similar accuracy with a three-dimensional solver but it has much higher efficiency in both CPU time and memory cost.