Analysis of Transient Behavior of Vertical Interconnects in Stacked Circuit Board Layers Using Quasi-Static Techniques

Fuzz-buttons can interconnect up to fifty circuit board substrate layers in conjunction with metallic vias. As a result, the use of three-dimensional multichip modules (MCM‘s) with fuzz-buttons may be able to achieve very high packaging densities. On the other hand, the vertical interconnects, surrounded by different dielectric materials and passing through many ground mesh holes, are three-dimensional nonuniform transmission lines. Therefore, the electromagnetic analysis of fuzz-button interconnects is not straightforward. In this paper, we propose a method to analyze fuzz-buttons under quasistatic assumptions. We apply the electrostatic method to find the charge distribution and the distributed capacitance of the fuzz-buttons, and a quasimagnetostatic approach to calculate the inductance. By using image theory, a free space Green's function is formulated. The effect of the via holes is taken into account by utilizing the equivalence principle. A set of integral equations is established and solved by a combination of the point-matching method and Galerkin's method. An iterative algorithm is imposed to solve the matrix equations. After the equivalent nonuniform transmission line model is established, we then apply the transmission (ABCD) matrix method, allowing the propagation parameters to be obtained easily. Finally, we employ the fast fourier transform (FFT) to convert the frequency results into the time domain. Waveform distortion, time delay, and crosstalk values for a 60 ps risetime input signal are evaluated. The quasistatic approach is compared against the finite difference time domain (FDTD) algorithms and good agreement is observed.